ABSTRACT
Title of dissertation: ELECTRONIC TRANSPORT MEASUREMENTS
IN THE ELECTRON-DOPED HIGH-TEMPERATURE
SUPERCONDUCTOR Pr2?xCexCuO4??
Paul Leonard Bach, Doctor of Philosophy, 2011
Dissertation directed by: Professor Richard L. Greene
Department of Physics
This thesis is composed of four major parts centered around the electron-doped
superconductor Pr2?xCexCuO4??: angular magnetoresistance studies of antiferromag-
netism, doping effects of oxygenation, Tc enhancement by the creation of superlattices,
and comparison of high-temperature resistivity with the pnictides.
ThefirstpartfocusesontransportmeasurementsofthemagnetisminPr2?xCexCuO4??
and La2?xCexCuO4??. It was found that the thermal evolution of the angular depen-
dence of magnetoresistance in Pr2?xCexCuO4?? can be used to determine the N?eel tem-
perature in that material. This angular magnetoresistance technique was also applied to
La2?xCexCuO4??; evidence for antiferromagnetism in this system was observed as well.
This section additionally develops angular magnetoresistance as a useful probe in other
cuprate projects here described.
The second part investigates over-oxygenated and irradiated Pr2?xCexCuO4??, in
under- and optimal dopings. Resistivity, Hall effect, and angular magnetoresistance mea-
surements show oxygen both doping and disordering the system, in agreement with over-
doped films. The evolution of both the Hall effect and angular magnetoresistance shows
that over-oxygenation results in significant changes in the number of charge carriers, re-
gardless of the increase in scattering incurred. Additionally, this study indicates that
annealing primarily removes apical oxygen, rather than other proposed behaviors.
The third part studies multi-layer films of Pr2?xCexCuO4?? and La2?xCexCuO4??.
These superlattices exhibit a significant Tc enhancement over component layers? Tcs. In-
terface effects are excluded as a source of this Tc increase based upon critical current
measurments. The Tc enhancement is found to be due to charge redistribution. Based
on Hall and angular magnetoresistance measurements, the result of this redistribution is
slightly net-under-doped films.
The fourth part uses Pr2?xCexCuO4?? and Nd2?xCexCuO4?? as comparisons to in-
vestigatethehigh-temperatureresistivitybehaviorintheSrFe2As2 system. Pr2?xCexCuO4??
and Nd2?xCexCuO4?? are shown to be similar to other cuprate systems in that they
strongly violate the Mott-Ioffe-Regel limit, an indication of strong correlations. The
SrFe2As2 system was found to saturate near the Mott-Ioffe-Regel resistivity, ruling out
strong, cuprate-like correlations in the pnictide superconductors.
Finally,someabortedattemptsatsynthesisofthinfilmsofsuperconductingPr2CuO4
and iron-based superconductors are discussed. Pr2CuO4 is suggested to be an important
system for understanding oxygenation in Pr2?xCexCuO4??.
ELECTRONIC TRANSPORT MEASUREMENTS IN THE
ELECTRON-DOPED HIGH-TEMPERATURE SUPERCONDUCTOR
Pr2?xCexCuO4??
by
Paul Leonard Bach
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2011
Advisory Committee:
Professor Richard L. Greene, Chair/Advisor
Professor Ichiro Takeuchi
Professor Johnpierre Paglione
Professor J. Robert Anderson
Professor H. Dennis Drew
c?Copyright by
Paul Leonard Bach
2011
Table of Contents
List of Tables iv
List of Figures v
List of Abbreviations xiii
1 Introduction 1
1.1 Introduction to Superconductivity . . . . . . . . . . . . . . . . . . . . . 1
1.2 Introduction to this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Cuprate Background 8
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Spin Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Preparation of Pr2?xCexCuO4?? Thin Films and Electronic Transport Measure-
ments 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Pulsed Laser Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Target Making . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 Film Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.3 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Film Patterning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 Electronic Transport Measurements Introduction . . . . . . . . . . . . . 43
3.5 Resistance Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6 Measurement Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.7 Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 Angular Magnetoresistance (AMR) 54
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3 Pr2?xCexCuO4?? Results . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4 Pr2?xCexCuO4?? Discussion . . . . . . . . . . . . . . . . . . . . . . . . 69
4.5 La2?xCexCuO4?? Results . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5 Disorder and Oxygenation in Pr2?xCexCuO4?? 80
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
ii
6 Tc Enhancement in Electron-Doped Cuprate Heterostructures 115
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2 Superlattice Film Preparation . . . . . . . . . . . . . . . . . . . . . . . . 116
6.2.1 Superlattice Film Growth . . . . . . . . . . . . . . . . . . . . . . 118
6.2.2 Superlattice Film Characterization . . . . . . . . . . . . . . . . . 121
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7 High Temperature Resistivity Measurements 145
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.2 Mott-Ioffe-Regel Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.3 SrFe2As2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
7.4 Experimental Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.4.1 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . 156
7.4.2 Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.5 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
7.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
8 Other Projects 175
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.2 Superconductivity in Pr2CuO4? . . . . . . . . . . . . . . . . . . . . . . . 175
8.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.2.2 Film Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
8.2.2.1 Metal Organic Deposition . . . . . . . . . . . . . . . . 177
8.2.2.2 Amorphous PLD . . . . . . . . . . . . . . . . . . . . . 183
8.2.2.3 Pulsed Laser Deposition . . . . . . . . . . . . . . . . . 185
8.2.3 Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
8.3 Thin Films of Iron-Based Superconductors . . . . . . . . . . . . . . . . . 191
8.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
8.3.2 SrFe2?xCoxAs2 Films . . . . . . . . . . . . . . . . . . . . . . . 192
8.3.3 FeSe1?xTex Films . . . . . . . . . . . . . . . . . . . . . . . . . 194
9 Summary and Future Directions 199
9.1 Angular Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . 199
9.2 Oxygen and Disorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
9.3 Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
9.4 High Temperature Resistance . . . . . . . . . . . . . . . . . . . . . . . . 203
9.5 Superconducting Pr2CuO4 and Pnictide/Chalcogenide Thin Films . . . . 204
Bibliography 205
iii
List of Tables
5.1 Pr2?xCexCuO4?? film samples used for transport measurements. . . . . . 85
8.1 A sample of heating schedules used for Pr2CuO4 films grown by metal
organicdeposition. Roomtemperatureresistancewasusedtocharacterize
the Pr2CuO4 fims grown by metal organic deposition. . . . . . . . . . . 181
8.2 A sample of growth parameters for Pr2CuO4 films grown by amorphous
pulsed laser deposition. For insulating films without a Tonsetc , the temper-
ature where the resistivity surpassed 1 M? characterized films. . . . . . . 184
iv
List of Figures
2.1 The Tprime (left) and T (right) crystal structures [21]. The major difference
between the two structures is the placement of the oxygen atoms. The T
structure surrounds the copper atoms with oxygens, forming CuO6 octa-
hedra, while the Tprime structure forms CuO2 planes. . . . . . . . . . . . . . 11
2.2 Increased cerium doping decreases the c-axis lattice parameter signifi-
cantly in Pr2?xCexCuO4?? as seen by X-ray diffraction [33]. . . . . . . . 13
2.3 ThecoppermagneticmomentsinthePCCOcrystalstructurewiththeout-
of-plane elements suppressed [21] (left) and along the c-axis [36] (right).
The spins align antiferromagnetically along the Cu-O-Cu directions. Ad-
jacent CuO2 planes are rotated 90?. . . . . . . . . . . . . . . . . . . . . 15
2.4 The ab-plane spin structure of Pr2?xCexCuO4?? in (a) zero magnetic field
and (b), (c), (d) applied magnetic fields [35]. In field, the [110] directions
are the easy axes for the collinear spin structure (b) whereas [100] and
[010] are preferred for the non-collinear zero-field spin structure (a). . . . 16
2.5 The hybridization of the copper and oxygen orbitals in the CuO2 planes
[38]. At the edges are the free ion Cu2+ 3d9 (left) and O2? 2p6 (right)
shells. The copper 3d9 orbital is then modified by crystal field effects
due to being embedded in a crystal lattice surrounded by oxygen atoms.
Spherical, octahedral coordination, pyramidal coordination, distorted oc-
tahedral coordination and a planer coordination modify the bare copper
orbital as well as splitting the oxygen orbital. The mixing between the
half-filled copper dx2?y2 band and the oxygen ? bands that result from
the crystal field splitting produces a hybridized half-filled band with a
single free electron on each copper site. . . . . . . . . . . . . . . . . . . 18
2.6 The density of states near the Fermi energy for a na??ve cuprate band struc-
tureandonemodifiedbyCoulombinteractions, aMott-Hubbardinsulator
[38]. (a) Without Coulomb interactions, there is a half-filled antibonding
band (AB) at the Fermi energy that comes from the Cu2+ 3d9 and O2?
2p6 orbitals hybridizing. (b) When Coulomb interactions with an energy
scale U are included, the antibonding band is split into two bands, an
upper Hubbard band (UHB) and a lower Hubbard band (LHB) with the
Fermi energy now lying in a gap between bands. A material with no band
crossing the Fermi energy will be an insulator. (c) In the cuprates addi-
tional bands lie between the UHB and LHB: a bonding (B), non-bonding
(NB), and a Zhang-Rice singlet (ZRS) band. Therefore, the cuprates are
insulators not due to U, but due to the charge-transfer gap, ?. . . . . . . 19
2.7 The density of states of a charge transfer insulator with doping [39]. (left)
The undoped charge-transfer insulator with an energy gap ? between
filled and empty states. When electrons or holes are doped into the sys-
tem, they may either create a new band in the charge transfer gap (A), or
move the chemical potential into either the valance or conduction bands
(B) or (C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
v
2.8 TypicalFermisurfacefortheelectron-dopedcuprates[39]. Atwo-dimesional
cut of the quasiparticle dispersion relation (E(kx,ky)) at the Fermi energy
produces the Fermi surface [42] (right). The magnetic Brillouin zone is
indicated with dashed lines. . . . . . . . . . . . . . . . . . . . . . . . . 21
2.9 Evolution of the Nd2?xCexCuO4?? Fermi surface with doping as seen
by ARPES [43]. The ? point is in the top-left corner of each frame.
(Each frame is only the lower-right quadrant of the Fermi Surface drawn
in Figure 2.8.) Initially electron pockets form at (pi,0) and (0,pi) and
as doping increases hole pockets appear around (pi/2,pi/2). At higher
dopings (not shown) the hole-like Fermi surface closes and appears much
as the schematic in Figure 2.8. . . . . . . . . . . . . . . . . . . . . . . . 22
2.10 Generic doping phase diagram for the cuprates [21]. Either hole doping
(left) or electron doping (right) suppresses AFM order and allows a su-
perconducting dome to appear. On the electron-doped side there is some
disagreement as to the terminus of the AF ordered region. This point
is discussed in Chapter 4. The line labeled T? represents a pseudo-gap
crossover (not discussed here). . . . . . . . . . . . . . . . . . . . . . . . 24
2.11 Superconducting dome for PCCO, NCCO, and LCCO [51]. Optimally
grown LCCO has a higher Tc and is shifted to lower cerium dopings com-
pared to PCCO and NCCO. . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1 Recipe for producing a 15 g, x = .15 Pr2?xCexCuO4?? target from con-
stituent oxides. The atomic weights of Pr, Ce, Cu, and O give the number
of grams per mol (column g/m) of Pr, Ce, Cu, Pr6O11, CeO2, and CuO.
The desired ratio of each element, determined from the desired doping,
translates into a desired ratio for each oxide (column Chemical Ratio).
Fromthisratioandtheoxides?molecularweight, theratioinunitsofmass
is determined (column Mass Ratio) and normalized (by multiplier) for a
total mass in grams of the desired amount. The masses (column Masses)
of each starting oxide is thus determined. . . . . . . . . . . . . . . . . . 30
3.2 The Bragg condition for x-ray diffraction [62]. Only diffraction angles
that produce constructive interference (left) will produce a diffraction
peak. Angles that produce destructive interference (right) will not show
peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3 Typical X-ray diffraction data taken on a x = .17 Pr2?xCexCuO4?? thin
film grown on a SrTiO3 substrate. . . . . . . . . . . . . . . . . . . . . . 40
3.4 Simple four-wire resistance measurement. . . . . . . . . . . . . . . . . . 46
3.5 Film wired in the van der Pauw configuration (see text). Measuring V12
with applied current I34 and the equivalent vertical arrangement allows
extraction of resistivity by Equation 3.2. . . . . . . . . . . . . . . . . . . 48
vi
3.6 Film patterned as a Hall bar. The current leads on the ends maintain a
constant current along the central bridge. Resistance measurements are
performed using consecutive voltage leads on a single side of the bridge
whileHallmeasurementsareperformedusingvoltageleadsoppositeeach
other across the bridge. For Hall effect, the magnetic field is applied into
or out-of the page. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7 A magnetic field, B, applied perpendicular to current flow, I, causes a
voltage, V , to appear perpendicular to both. The Hall resistance is this
voltage divided by the applied current. If the voltage leads are not exactly
aligned there will be an additional component due to magnetoresistance
in the voltage signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.1 Zero field spin structure of Pr2?xCexCuO4?? as seen looking along the
c-axis [36]. The solid and hollow balls are Cu atoms on adjacent CuO
planes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 A patterned thin film rotated in an applied in-plane magnetic field [36].
The angle ? represents the angle between the field, H, and the current, I.
The current direction is along the crystalline a-axis. . . . . . . . . . . . . 59
4.3 Magnetoresistance of Pr2?z?xLazCexCuO4 along the [100] (BbardblCu-O-Cu)
and along the [110] (BbardblCu-Cu) directions [35]. The transition to the
collinear spin state in each direction is denoted by B?c. . . . . . . . . . . . 60
4.4 MagnetoresistanceoscillationsareseeninPr2?xCexCuO4?? atsufficiently
high magnetic fields [36]. Between 4 T and 8 T a four-fold oscillation de-
velops, becoming more pronounced at 14 T. The amplitude of the angular
magnetoresistance oscillations, ??(?,H) = ?(?,H)??(?,H=0)?(?,H=0) , is related to
the film?s antiferromagnetism. . . . . . . . . . . . . . . . . . . . . . . . 62
4.5 Magnetoresistance oscillations are seen in under-doped Pr2?xCexCuO4??
(x = .12) [36]. The N?eel temperature, estimated from where the four-fold
oscillations disappear, is between 105 K and 110 K. . . . . . . . . . . . . 63
4.6 Magnetoresistance oscillations are seen in under-doped Pr2?xCexCuO4??
(x = .13) [36]. The N?eel temperature is between 70 K and 75 K. . . . . . 64
4.7 Magnetoresistance oscillations are seen in under-doped Pr2?xCexCuO4??
(x = .14) [36]. The N?eel temperature is between 60 K and 65 K. . . . . . 65
4.8 MagnetoresistanceoscillationsareseeninoptimallydopedPr2?xCexCuO4??
(x = .15) [36]. The N?eel temperature is between 34 K and 38 K. . . . . . 66
4.9 The amplitude of the magnetoresistance oscillations in Pr2?xCexCuO4??
decrease withtemperature beforedisappearing completely [36]. The N?eel
temperature is the point at which the oscillations disappear. It decreases
systematically with increasing cerium doping. . . . . . . . . . . . . . . . 67
4.10 The N?eel temperature as determined by angular magnetoresistance (cir-
cles) indicates a quantum phase transition at around x = .16 [36]. Dia-
monds and the solid line indicate TN determined by ?SR from [44] and
by INS from [45] respectively. Triangles are optical determinations of a
normal state gap from [67, 68], suggested to be the onset of 2D spin-wave
fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
vii
4.11 Angular magnetoresistance of an oxygenated x = .15 Pr2?xCexCuO4??
thin film [36]. Oscillations are observed to go to zero between 110 K and
120 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.12 Angular magnetoresistance oscillations of a La2?xCexCuO4?? thin films
with cerium dopings from x = .06 to x = .15 [70]. Measurements were
taken at 14 T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.13 (a) Field dependence of magnetoresistance at 35 K for several dopings
[70]. Open and closed symbols are taken with the magnetic field parallel
and perpendicular to the direction of current respectively. (b) Field de-
pendence of magnetoresistance for x = .06 at several temperatures. (c)
The amplitude of the difference in magnetoresistance decreases with in-
creasing temperature. The temperature at which this amplitude goes to
zero is identified as TD. (d) Phase diagram with TD(x) and Tc(x). . . . . 75
4.14 La2?xCexCuO4?? film patterned both with the current along the crystal
axis (e.g., [100]) (a) and along the diagonal (e.g., [110]) (b) for a x = .08
film at 35 K [70]. An angular magnetoresistance signal is seen in both
orientations (c,d) with the minima and maxima at the same angle ? in
each case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.1 Patternedfilmforirradiationmeasurements(above)andoxygenationmea-
surements (below). A constant current is maintained in the central chan-
nel from current leads attached at each end of the film. Voltage leads
are periodically spaced along the channel. The above film was irradiated
in small patches such that consecutive voltage leads could provide resis-
tivity (or Hall) measurements corresponding to a single irradiation dose.
Oxygenated films were patterned similarly (Figure 3.6), but had uniform
oxygen treatment across the entire film. . . . . . . . . . . . . . . . . . . 86
5.2 Resistivity of an optimally grown and annealed x = .12 under-doped
Pr2?xCexCuO4?? film (Tc = 6.4 K) at different doses of irradiation. Irra-
diation levels range from 0 to 6.5?1016 cm?2 of 2 MeV H+. . . . . . . . 89
5.3 Hall effect of an optimally grown and annealed x = .12 under-doped
Pr2?xCexCuO4?? film (Tc = 6.4 K) at different doses of irradiation. Irra-
diation levels range from 0 to 6.5?1016 cm?2 of 2 MeV H+. . . . . . . . 90
5.4 Added oxygen in x = .12 as-grown Pr2?xCexCuO4?? films (blue 230
mTorr O2, green 600 mTorr O2) produces more resistive films compared
withoptimallygrownandannealed(black)andmaximallyirradiated(red)
films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.5 Added oxygen in x = .12 as-grown Pr2?xCexCuO4?? films (green 230
mTorr O2, blue 400 mTorr O2, cyan 600 mTorr O2) strongly drives the
Hall resistivity more negative compared to optimally grown and annealed
films (red). This behavior differs both in magnitude and direction from
irradiated films (black, maximally irradiated). . . . . . . . . . . . . . . . 92
5.6 Resistivity of optimally doped (x = .15) Pr2?xCexCuO4?? films. Op-
timal growth (230 mTorr N2O, vacuum annealing) to high O2 growth
(600 mTorr O2, no annealing). . . . . . . . . . . . . . . . . . . . . . . . 94
viii
5.7 Hall effect of optimally doped (x = .15) Pr2?xCexCuO4?? films. Op-
timal growth (230 mTorr N2O, vacuum annealing) to high O2 growth
(600 mTorr O2, no annealing). . . . . . . . . . . . . . . . . . . . . . . . 95
5.8 Angular magnetoresistance of an oxygenated x = .15 Pr2?xCexCuO4??
thin film [36]. Oscillations are observed to go to zero between 110 K and
120 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.9 Amplitude of AMR oscillations as a percentage of magnetoresistance vs
temperature for oxygenated x = .15 Pr2?xCexCuO4?? films. The tem-
perature where the amplitude first goes to zero corresponds to the N?eel
temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.10 Angular magnetoresistance of an oxygenated x = .12 Pr2?xCexCuO4??
thin film grown in 600 mTorr O2. Oscillations are observed to be present
above 110 K. Optimally grown x = .12 has a N?eel temperature between
105 K and 110 K [36]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.11 Amplitude of AMR oscillations as a percentage of magnetoresistance vs
temperature for a oxygenated x = .15 Pr2?xCexCuO4?? film grown in
600 mTorr O2. The temperature where the amplitude first goes to zero
corresponds to the N?eel temperature. . . . . . . . . . . . . . . . . . . . . 100
5.12 Angular magnetoresistance of an irradiated x = .12 Pr2?xCexCuO4??
thin film. The film received a dose of 4.72 ? 1016 cm?2 of 2 MeV H+
irradiation. This dose corresponds to a Tc suppression of ?8 K (extrapo-
lated). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.13 Angular magnetoresistance of an un-irradiated x = .12 Pr2?xCexCuO4??
thin film. This is the same film as Figure 5.12, but was not irradiated at
this spot (Tc = 6.5 K). . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.14 The amplitude of angular magnetoresistance oscillations (seen in Fig-
ure 5.12) of a heavily irradiated x = .12 Pr2?xCexCuO4?? thin film. Zero
amplitude above 110 K shows a N?eel temperature between 100 K and
110 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.15 The amplitude of angular magnetoresistance oscillations (seen in Fig-
ure 5.13) of a un-irradiated x = .12 Pr2?xCexCuO4?? thin film. Zero
amplitude above 110 K shows a N?eel temperature between 100 K and
110 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.1 Schematic of the superlattice structure grown. Films were grown on
SrTiO3 (STO) substrates with alternating layers of under-doped and over-
doped superconductors. The primary pairings grown and investigated
were in the Pr2?xCexCuO4?? system x = .19 paired with either x = .00,
x = .11, or x = .12 and in the La2?xCexCuO4?? system x = .06 paired
with either x = .17, x = .19, or x = .21. . . . . . . . . . . . . . . . . . 117
ix
6.2 Superconducting transition temperature, Tc, compared to annealing time
for a .00/.19 Pr2?xCexCuO4?? superlattice thin film. The transition tem-
perature is elevated compared to the Tcs of both constituent layers. Tc
is relatively insensitive to annealing time and can be annealed for much
longer than single layer films. The arrows indicate the optimal annealing
times for single-doping x = .15 and x = .19 Pr2?xCexCuO4?? thin films. 120
6.3 Satellite peaks in a .00/.19 Pr2?xCexCuO4?? superlattice thin film. The
main peak is the 006 peak of Pr2?xCexCuO4?? and gives a c-axis lat-
tice constant around 12.18 ?A, suggesting a cerium content of x = .08 to
x = .10. The superlattice film was grown with a nominal superlattice pe-
riodicity of 10 nm. The satellite peaks (labeled?) correspond to a 99.2 ?A
periodicity along the c-axis. This is showing evidence for superlattice
formation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4 Satellite peaks in a .06/.19 La2?xCexCuO4?? superlattice thin film [94].
The 008 and 0010 X-ray diffraction peaks show superlattice satellite
peaks that are due to cerium modulation. . . . . . . . . . . . . . . . . . 123
6.5 TherealcomponentoftheACsusceptibilityofa.00/.19Pr2?xCexCuO4??
superlattice film compared to a .15 film. The superlattice film shows satu-
ratingbehavior similarto thesingle layerfilm. This isindicative ofa large
volume fraction superconductivity and suggests that superconductivity is
a bulk effect in the superlattice films. . . . . . . . . . . . . . . . . . . . 124
6.6 Typical resistance vs temperature curve for a .00/.19 Pr2?xCexCuO4??
superlattice film. The Tc of x = .19 is? 8 K; x = .00 has no Tc. . . . . . 125
6.7 (a) Resistivity of a .19/.06 La2?xCexCuO4?? superlattice film compared
with x = .06, x = .11 (optimal), and x = .19 LCCO superlattice films
[94]. Tc is enhanced relative to constituent dopings. In LCCO this is
observed forseveralx/.06superlattices(b) andfor PCCOthis isobserved
for several x/.19 superlattices (c). The maximum Tc of each of these
superlattice pairings (square) is higher than that of the single-doping, x, films
(triangle). The?is a bi-layer film. . . . . . . . . . . . . . . . . . . . . . . . 127
6.8 (a) I-V curves of a 40-layer .19/.06 La2?xCexCuO4?? superlattice [94].
The critical current densities for x/.06 for x = .19 different numbers of
layers, n, ((b), (c)) and for n = 10 with different over-doped layers (d).
Charge count (PZ) varying along the c-axis (Z) is proposed in (e). . . . . 131
6.9 Electronenergy-lossspectroscopy(EELS)of0.19/0.06La2?xCexCuO4??
superlattice. The intensity is of Ce 3d3/2 which is a measure of cerium
concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.10 La2?xCexCuO4?? Tc as a function of the c-axis lattice parameter as mea-
sured by X-ray diffraction [94]. The superlattice films (?) have Tcs that
depend upon the c-axis lattice parameter in much the same way as single-
dopingfilmsgrownbyvariousmethods(opensymbols). Optimallydoped
films have a c-axis lattice parameter of 12.44 ?A. . . . . . . . . . . . . . . 133
6.11 Hall effect versus field at various temperatures for La2?xCexCuO4?? su-
perlattices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
x
6.12 Hall effect versus temperature for La2?xCexCuO4?? superlattices com-
pared to single-doping optimally doped LCCO films. The superlattices
are similar in magnitude to the single-doping films. . . . . . . . . . . . . 137
6.13 The Hall effect versus temperature for various La2?xCexCuO4?? dopings
[70]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.14 TheangularmagnetoresistanceofaPr2?xCexCuO4?? .11/.19superlattice
film. Oscillations are present, although they disappear at high tempera-
tures. The angular magnetoresistance oscillations disappear at a temper-
ature between the x = .11 and x = .15 N?eel temperatures. . . . . . . . . 139
6.15 Hall effect and resistivity versus temperature of oxygenated optimally
doped (x = .15) Pr2?xCexCuO4?? films. Left: Hall effect of oxygenated
films (Figure 5.7) plotted against several optimally annealed cerium dop-
ings[99]. Right: Resistivityoftheseoxygenatedfilms(Figure5.6)replot-
ted here for comparison. Significant oxygen doping, equivalent to several
.01 of cerium doping, suppresses Tc and notably increases the resistivity
of the film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.1 Susceptibility in BaFe2?xCoxAs2 has been reported to exhibit unusual
linear in T behavior up to 700 K [71]. . . . . . . . . . . . . . . . . . . . 146
7.2 The Mott-Ioffe-Regel limit in several metals [108]. Most metals Mott-
Ioffe-Regel limit and saturate by around a few hundred ???cm. . . . . . . 149
7.3 The Mott-Ioffe-Regel limit is violated in the cuprate superconductors
[108]. The cuprates should have a Mott-Ioffe-Regel limit at around sev-
eral hundred ???cm, yet resistance increases well beyond that range. . . . 151
7.4 Thecrystalstructuresofthepnictidesuperconductors[115]. Iron-arsenide
planes (and some modifications thereof) form the common element be-
tween the systems. Here we restrict our discussion to the SrFe2As2 sys-
tem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
7.5 Pnictide phase diagram and unit cell [116, 117]. . . . . . . . . . . . . . . 153
7.6 Cuprate unit cell and phase diagram [38, 116]. . . . . . . . . . . . . . . . 154
7.7 Pnictide Fermi surface [118]. The pnictides are quasi-2D materials with
cylindrical Fermi surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.8 The ab-plane resistivity versus temperature of optimally doped (x = .15)
and annealed Pr2?xCexCuO4?? films (a73) and Nd2?xCexCuO4?? crystals
[123]: optimally doped (x = .15) and annealed (a71), optimally doped
(x = .15) as-grown (unannealed) (a76), underdoped x = .10 (a77), and
overdoped x = .22 (a78) [124]. Optimal crystals are fit to T2 above Tc and
below 700 K (+). The MIR limit in these materials is around 700 ???cm. 163
7.9 The ab-plane resistivity vs temperature, ?(T), up to 800 K for SrFe2As2
(a71), SrFe1.86Ni0.14As2 (a76), SrFe1.82Ni0.18As2 (a77), and SrFe1.74Co0.26As2
(a78)singlecrystals[124]. Theresistivitysaturatesaround400?700???cm;
the MIR limit is around 600 ???cm. . . . . . . . . . . . . . . . . . . . . 164
7.10 Predicted pnictide resistivity saturation due to spin fluctuations [119].
The T?s are different Fermi liquid temperatures in the model. . . . . . . 169
xi
7.11 The resistance of semimetal graphite up to 450 K [140] (left) and of
semimetal CaB6 up to 1000 K [142] (right). . . . . . . . . . . . . . . . . 173
8.1 A typical heating schedule for metal organic deposition films. . . . . . . 179
8.2 Optimization of PCO films by annealing temperature (left) and annealing
time (right) [52]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
8.3 X-ray diffraction of an x = .15 Pr2?xCexCuO4?? thin film grown by
metal organic deposition (above) and grown by normal pulsed laser de-
position (below). Above: The 004 and 008 Pr2?xCexCuO4?? diffraction
peaks are visible, indicating some epitaxy. 2? is scanned from 25? to 85?.
Below: For high quality films grown by pulsed laser deposition, more
X-ray diffraction peaks are seen. 2? is scanned from 5? to 85?. . . . . . . 182
8.4 PCO film Tc and resistivity versus c-axis lattice constant [52, 147]. . . . 185
8.5 The c-axis lattice constant of several amorphous-PLD grown films. The
red line represents the c-axis lattice parameter for un-annealed x = .00
films grown by normal PLD. The green area is the c-axis lattice parameter
for maximal Tc superconducting Pr2CuO4 (Figure 8.4). The films (+) are
ranked in order of increasing oxygen based upon the aggressiveness of
the films? annealing schedules. . . . . . . . . . . . . . . . . . . . . . . . 186
8.6 Pr2CuO4 thin films grown by pulsed laser deposition under various de-
position conditions. Deposition temperatures were varied between 720 C
(a73) and 850 C (a77) with the pressure constant at 230 mTorr N2O. Deposi-
tionpressureswerevariedbetween200mTorrN2O(a76)and230mTorrN2O
(a78) with temperature constant at 800 C. A x = .05 Pr2?xCexCuO4?? film
(a71) is included for reference. All films were deposited for 30 min and
were ?as-grown? (not annealed). . . . . . . . . . . . . . . . . . . . . . . 187
8.7 Pr2CuO4vacuum annealed for 45 min. The annealed Pr2CuO4 film shows
some metallic (d?/dT > 0) region (insert). The resistivity of the film is
much less than the as-grown films (Figure 8.6). . . . . . . . . . . . . . . 188
8.8 The c-axis lattice parameters of various Pr2CuO4 thin films grown by
pulsedlaserdeposition. Adjustmentofpulsedlaserdepositionparameters
did not seem to consistently produce predictable c-axis lattice parameters. 189
8.9 SrFe2?xCoxAs2 thin film with Tonsetc = 10 K. The resistivity drop is sup-
pressed by several K in a magnetic field (insert) indicating that it is due
to the onset of superconductivity. . . . . . . . . . . . . . . . . . . . . . 194
8.10 ? ?2? X-ray diffraction scans of several FeSe thin films (offset). Films
were deposited at various substrate temperatures from 400 C to 700 C
and show various amounts of epitaxy as indicated by the 00lscript film peaks
indexed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.11 The temperature dependence of resistance for several FeSe thin films.
Films were deposited at various substrate temperatures from 400 C to
550 C and all show Tonsetc ? 12 K. . . . . . . . . . . . . . . . . . . . . . 197
xii
List of Abbreviations
11 compounds related to FeSe
1111 compounds related to LaOFeAs
122 compounds related to SrFe2As2
214 compounds related to RE2CuO4
AC alternating current
AC? AC susceptibility
AFM antiferromagnetism
AMR angular magnetoresistance
ARPES angle-resolved photoemission spectroscopy
BCS Bardeen, Cooper, Schrieffer theory
BZ Brillouin zone
DC direct current
ECCO Eu2?xCexCuO4??
EELS electron energy-loss spectroscopy
FS Fermi surface
INS inelastic neutron scattering
LCCO La2?xCexCuO4??
LSCO La2?xSrxCuO4??
LSGO LaSrGaO4
LYCO La2?xYxCuO4??
MIR Mott-Ioffe-Regel
MOD metal organic deposition
MR magnetoresistance
?SR muon spin resonance
NCCO Nd2?xCexCuO4??
NCO Nd2CuO4
NS neutron scattering
O(1) oxygen in in-plane lattice sites
O(2) oxygen in out-of-plane lattice sites
O(3) oxygen at apical sites
OD over-doped
PCCO Pr2?xCexCuO4??
PCO Pr2CuO4
PLCCO Pr2?z?xLazCexCuO4
PLD pulsed laser deposition
PPMS Quantum Design Physical Properties Measurement System
QCP Quantum Critical Point
QPT quantum phase transition
RE a rare-earth element
SC superconductivity
SCCO Sm2?xCexCuO4??
SCO Sm2CuO4
UHB and LHB
xiii
SDW spin density wave
SL superlattice
Sr-122 SrFe2As2
STO SrTiO3
Tprime and T 214 crystal structures (Figure 2.1)
Tc superconductivity transition temperature
TN N?eel temperature
UD under-doped
UHB and LHB upper and lower Hubbard bands
VDP van der Pauw
XRD X-ray diffraction
YBCO YBa2Cu3O7
xiv
Chapter 1
Introduction
1.1 Introduction to Superconductivity
A superconductor conducts electricity without resistance. This phenomenon was
first discovered in mercury in 1911 by Heike Kamerlingh Onnes [1]. The DC resistance
ofthatmaterialwasobservedtorapidlytransitiontozeroat4.2K.Awiderangeofmateri-
als were subsequently shown to superconduct: chemical elements like lead (Tc = 7.2 K),
alloyslikeNb3Al0.75Ge0.25 (Tc ? 20K),andmanycompounds[2]. Thetransitiontemper-
ature, Tc, slowly increased over the years, but remained at low temperatures, 25 K or less,
for decades [3]. Niobium, with Tc = 9.2 K, is the highest Tc elemental superconductor
at ambient pressure; from 1972, Nb3Ge with a Tc of 23.3 K was the highest Tc recorded
until 1986 [4]. This dramatically changed in 1986 when Bednorz and M?uller reported the
discovery of superconductivity at 35 K, the first high-temperature copper-oxide (cuprate)
superconductor [5]. The maximum cuprate Tc obtainable was rapidly advanced to 90 K in
YBa2Cu3O7 and up to 135 K in related cuprates. More recently, in 2008, a second class of
high-temperature superconductors was discovered with iron arsenide (FeAs) layers [6, 7]
following the discovery of superconductivity in LaFePO [8]. The iron-pnictides now have
Tcs up to 55 K [9]. Although both the cuprates and the iron-pnictides will be discussed in
this thesis, most of the focus is on the cuprates.
Superconductors also expel magnetic fields. This property was discovered in 1933
1
by Walther Meissner and Robert Ochsenfeld [10]. This perfect diamagnetism, the Meiss-
ner effect, makes superconductors different from an idealized perfect conductor with zero
resistance. Superconductors will always expel magnetic flux, even if cooled through Tc
in a magnetic field. Therefore, the Meissner effect demonstrates that the superconducting
state is not an ideal conductor but is rather the result of the material undergoing a thermo-
dynamic phase transition [3]. If the magnetic field grows too large, however, it will kill
superconductivity. Quenching superconductivity by magnetic field also implies that there
is a maximum current that the superconductor can carry due to?? vectorB = ?0 vectorJ [11]. Type
I superconductors have a single critical field, Hc, that suppresses superconductivity. Type
II superconductors have two critical fields, Hc2 above which superconductivity is com-
pletely killed, and Hc1 below which no magnetic flux penetrates. Between Hc1 and Hc2
magnetic flux can pass through the superconductor in normal state vortices surrounded by
superconductor [12]. In this mixed state, magnetic flux lines pass through the center of
individual vortex cores; a superconducting screening current circulates around each core
[11]. All high temperature superconductors are Type II.
Superconductors are understood theoretically through the London equations, the
Ginzburg-Landau theory, and BCS theory (and other more complicated models). The
London equations are phenomenological equations that describe the current density in
superconductors in electric and magnetic fields [12]. H. London and F. London developed
this theory in 1935 [13, 14]. The theory takes the form of a two-fluid model with some
fraction of the conduction electrons taking part in the superfluid while the remaining
electrons form a normal fluid [11]. The London equations roughly capture much of the
basic superconductor phenomenology.
2
The Ginzburg-Landau theory [15] was developed as a phenomeological theory to
describe superconductivity. In this theory, there is an order parameter based on the lo-
cal concentration of conducting electrons that characterizes the superconducting state [3].
Applying the variational method to this pseudo-wavefunction provides a powerful gener-
alization to the London equations [12]. This theory was able to go beyond the London
theory and was eventually shown to be a limiting form of subsequent BCS theory [12].
BCS theory, developed by Bardeen, Cooper, and Schrieffer [16, 17], is the modern
picture of superconductors. In this model, the atoms on lattice sites are allowed some mo-
tion in response to the charged electrons. If this ionic motion ?over-screens? the Coulomb
repulsion, the net result is attractive interaction between electrons [11]. This attractive in-
teraction between electrons is facilitated by large numbers of additional electrons acting
through the Pauli exclusion principle [11].
Roughly, an electron traveling with a momentumvectork drives a lattice vibration which
synchronizes a second electron traveling with momentum ?vectork with the first [18]. This
lattice motion, phonons, causes pairs of quasiparticles (electrons or holes) with opposite
spin to interact and become attracted to each other. These pairs together have slightly
lower energies as a pair than as separate electrons and, therefore, they form a lower energy
state of Cooper pairs. As the pairing is in momentum space, generally there are many
Cooper pairs in the same spatial range [19]. The Cooper pair, then, is in a coherent
ground state below the Fermi energy; there is an energy gap that is the difference between
the Fermi energy and the ground state of the Cooper pairs that is responsible for many
of the superconductor?s properties [3]. While the high temperature superconductors are
probably non-BCS superconductors, the BCS theory still provides a useful framework
3
for thinking about superconductivity. Probably non-BCS in this context is a statement
that the Cooper pairs in the high-temperature cuprate superconductors are unlikely to be
mediated by phonon interactions.
Superconductivity was believed to have been well understood in the 1980s, prior
to the discovery of the cuprates. Since that discovery, the cuprates have been extensively
studied; however, unlike the conventional, low-temperature superconductors the high-
temperature superconductors are not well understood, even after 25 years. It is hoped that
by studying current superconductors a deeper understanding will eventually be developed
that will allow superconductors to be designed with useful properties, like room temper-
ature Tcs. This thesis is an attempt to expand our understanding of superconductivity.
1.2 Introduction to this Thesis
The electron-doped cuprate superconductor Pr2?xCexCuO4?? is the central focus
of this thesis. This system has a maximum Tc of just over 20 K and can be prepared in
thin film form. Pr2?xCexCuO4?? also forms a basis for comparison of related materials
studied: La2?xCexCuO4??, SrFe2As2, and Pr2CuO4.
The basic Pr2?xCexCuO4?? material properties are discussed in Chapter 2. Crystal
structure, magnetic ordering, and electronic configuration are described. The focus of this
thesis is on properties that can be investigated with transport measurements.
Basic thin film growth, preparation, and measurement of Pr2?xCexCuO4?? is cov-
ered in Chapter 3. The films are grown by pulsed laser deposition (PLD), patterned,
and contacted for electronic transport measurements. Much of the experimental data
4
discussed was acquired in a Quantum Design Physical Properties Measurement System
(PPMS).
The investigations contained herein all involve Pr2?xCexCuO4??. Firstly, a mea-
surement technique, in-plane angular magnetoresistance, that investigates magnetoresis-
tance as a function of applied magnetic field angle, was used to investigate the anti-
ferromagnetism in Pr2?xCexCuO4?? and La2?xCexCuO4??. The N?eel temperature as
a function of doping was mapped. Secondly, the oxygen content of Pr2?xCexCuO4??
was studied. A comparison between oxygenated and irradiated films was made and
oxygen doping was investigated. The role of annealing was also addressed. Thirdly,
layered structures of alternating dopings were investigated in the Pr2?xCexCuO4?? and
La2?xCexCuO4?? systems. A Tc enhancement due to charge redistribution was found.
Fourthly, Pr2?xCexCuO4?? and Nd2?xCexCuO4?? were used as a comparison in the in-
vestigation of the high-temperature resistive behavior of the SrFe2As2 system. Pnictide
resistivity was found to saturate around the Mott-Ioffe-Regel limit. Finally, other related
systems, like Pr2CuO4, were investigated. These projects are still works-in-progress.
In the first investigation discussed, transport measurements were used to investi-
gate the antiferromagnetism in Pr2?xCexCuO4?? and La2?xCexCuO4??. The first half
of Chapter 4 discusses the Pr2?xCexCuO4?? results and the second half focuses on the
La2?xCexCuO4?? results. In Pr2?xCexCuO4??, four-fold in-plane angular magnetoresis-
tance oscillations were observed; their disappearance coincided with the N?eel tempera-
ture and suggested that antiferromagnetism persists in that system up to optimal doping.
This is suggestive of a quantum phase transition behind the superconductivity dome. In
La2?xCexCuO4??, two-fold oscillations were observed. With the exception of reduced
5
symmetry, these oscillations were seen to behave similarly to the angular magnetoresis-
tance in Pr2?xCexCuO4??. Magnetic data in La2?xCexCuO4?? has been difficult to obtain
and these measurements provide evidence for antiferromagnetism in this system.
Next, Pr2?xCexCuO4?? investigations of the role of oxygenation are discussed in
Chapter 5. A series of over-oxygenated under- and optimally-doped films were prepared.
An under-doped irradiated Pr2?xCexCuO4?? film was used as a comparison by providing
a template for disorder effects. It was observed that while resistivity data show significant
disorder in oxygenated films, Hall effect data show that oxygen has a significant doping
effect. Additionally, angular magnetoresistance data support the doping dependence seen
in the Hall effect by examination of the N?eel temperature evolution with oxygen doping.
Also, this study advances the discussion of the role of annealing in the electron-doped
cuprates by favoring removal of apical oxygens over other competing models.
Superlattices formed by layering under-doped and over-doped layers were studied
in Chapter 6. In both the Pr2?xCexCuO4?? and La2?xCexCuO4?? systems, significant Tc
enhancement was found. Critical current measurements were performed to demonstrate
that the superconductivity enhancement was not due to an interface effect, but, rather,
was due to charge redistribution. Investigation of these superlattices by Hall effect and
angular magnetoresistance support charge redistribution. Hall effect and angular magne-
toresistance measurements further suggest that charge redistributes to form superlattice
thin films that are slightly net-under-doped films.
Penultimately, the high temperature resistivity behavior of the SrFe2As2 system
was investigated in Chapter 7 by comparison to Pr2?xCexCuO4?? and Nd2?xCexCuO4??.
Pr2?xCexCuO4?? and Nd2?xCexCuO4?? are shown to strongly violate the Mott-Ioffe-
6
Regel limit. This is consistent with other high-temperature superconducting cuprates and
is evidence for strong correlations in the Pr2?xCexCuO4?? and Nd2?xCexCuO4?? sys-
tems. The strength of correlations in the pnictide high-temperature superconductors is
still an open question. The high-temperature resistivity of the SrFe2?x(Co,Ni)xAs2 sys-
tem was measured and observed to saturate at around the expected Mott-Ioffe-Regel limit
in these materials. Although spin-fluctuations prevent certain identification of the re-
sistivity saturation as being a Mott-Ioffe-Regel limit, this rules out strong, cuprate-like
correlations.
The final experimental chapter, Chapter 8, addresses some additional projects that
have, as-yet, been less fruitful. An attempt was made to synthesize superconducting
Pr2CuO4, the parent compound of Pr2?xCexCuO4??. The new experimental techniques
used and the status of the project are discussed. Similar attempts to grow thin films
of the iron-based superconductors SrFe2?xCoxAs2 and FeSe1?xTex are also discussed.
The pulsed laser deposition techniques necessary for pnictide and chalcogenide thin films
differ somewhat from growing oxide films like the cuprates.
Together,thesechaptersformaninvestigationintotheworkingsofhigh-temperature
superconductivity. Studying Pr2?xCexCuO4?? and related compounds has advanced the
state of knowledge with respect to high temperature superconductivity. It is hoped that
this knowledge continues to advance.
7
Chapter 2
Cuprate Background
2.1 Introduction
The experimental works covered in this thesis focus on transport measurements in
Pr2?xCexCuO4?? and related compounds. For example, the electrical resistance measure-
ments, discussed in all experimental chapters (Chapters 4, 5, 6, 7, and 8), and the Hall
effect measurements, discussed in Chapters 5 and 6, depend upon the band structure near
the Fermi energy. The angular magnetoresistance measurements, discussed in Chapters
4, 5, and 6, depend upon the system?s magnetic structure. The formation of superlattices
(Chapter6)and, moregenerally, thegrowthofhigh-qualitythinfilmsofPr2?xCexCuO4??
(Chapter 3) used throughout this thesis depend upon knowledge of the RE2CuO4 crystal
structure. In order to understand Pr2?xCexCuO4?? transport, some basic properties of the
system must first be made familiar to the reader.
The crystal structure of Pr2?xCexCuO4?? consists of layers of CuO2 planes; these
planes are necessary for superconductivity. Magnetic moments on the copper atoms in
these planes introduce a spin structure in the compound and strong Coulomb interactions
cause the band structure to be gapped at the Fermi energy. While Pr2?xCexCuO4?? is
a superconductor for some dopings, Pr2CuO4is not. The parent compound is generally
believed to be an antiferromagnetically ordered Mott insulator, although recent proposals
have questioned this picture [20] (Chapter 8). Doping suppresses the antiferromagnetism
8
in the system and introduces charge carriers. Superconductivity in this system arises
between x = .12 and x = .19 doping levels.
Related systems discussed in this thesis are discussed in their individual chapters
andasnecessary. NotablyLa2?xCexCuO4?? hasmanysimilarpropertiestoPr2?xCexCuO4??
and can, in many cases, be treated as a similar material save for a slightly higher Tc and
a slightly lower optimal doping. The La2?xCexCuO4?? system is less explored than the
Pr2?xCexCuO4?? system. Also of note is the SrFe2?xMxAs2 system, with M either Co
or Ni. This system deserves mention in its own right and is discussed in the SrFe2As2
section of Chapter 7.
2.2 Crystal Structure
The properties of materials ultimately depend upon their crystal structure. Crys-
tal structure, for example, determines the spectrum of the phonons that mediate Cooper
pairing in BCS superconductors. While the high-temperature cuprate superconductors
are almost certainly non-BCS, superconductivity is quite sensitive to the details of the
crystal structure. Both the cuprate family of high-temperature superconductors and the
newer ferropnictide family have planes of atoms that are critical to superconductivity. In
eachcase, superconductivityappearsafterdopinganantiferromagneticallyorderedparent
compound.
All of the cuprate high temperature superconductors have similar crystal structures;
they contain layers of copper oxide planes. Many also have tetragonal unit cells, or are
at least orthorhobic. Some of the simpler cuprate crystal structures are found in the 214
9
family of cuprate superconductors. This family, whose members have RE2CuO4 formula
units, contains the electron-doped cuprates, Pr2?xCexCuO4?? and La2?xCexCuO4??, dis-
cussed in this thesis. The crystal structure varies slightly depending on the choice of rare
earth element, RE. For example, a hole-doped 214, LSCO (La2?xSrxCuO4??), crystal-
izesintheT phase(Figure2.1)whereasanelectron-doped214,NCCO(Nd2?xCexCuO4??),
crystalizes in the Tprime phase [21]. Thin films of both PCCO (Pr2?xCexCuO4??) and LCCO
(La2?xCexCuO4??) are formed in the Tprime phase; due to the larger size of the La3+ ion,
LCCO will only crystalize in the Tprime phase in thin film preparations where the crystal
lattice of the substrate stabilizes the film?s crystal structure [22].
In each phase, the copper oxide layers form planer square lattices separated by
charge reservoirsof theremaining elements. Oxygen is inboth planer andreservoir lattice
sites. The former are labeled O(1) and the latter O(2). In addition to these regular lattice
sites, the Tprime phase also often incorporates additional oxygen in interstices directly above
and below the copper atoms. These particular interstitial sites are called apical sites and
frequently do contain oxygen atoms. This site corresponds, in the T phases, to the apex of
the octahedral arrangement of oxygen sites that places atoms above and below the copper
sites. These apical sites are O(2) sites in the T phase and are not filled in the Tprime phase.
This is for an ideal crystal. In real materials there is some amount of impurity oxygen at
the apical sites in the Tprime phase. These oxygens are labeled O(3). The apical sites in the
Tprime crystal structure are convenient locations for interstitial defects to occur in the crystal
lattice; it is relatively easy for O(3) oxygens to be present. Oxygen incorporated at O(3)
disorders the crystal structure and alters the electronic properties.
For high quality samples, these apical oxygens are a common issue. Oxygen re-
10
Figure 2.1: The Tprime (left) and T (right) crystal structures [21]. The major difference be-
tween the two structures is the placement of the oxygen atoms. The T structure surrounds
the copper atoms with oxygens, forming CuO6 octahedra, while the Tprime structure forms
CuO2 planes.
11
duction (or addition) by high temperature annealing provides some experimental control
over the oxygen concentration. Excess oxygen will tend to fill apical sites as O(1) and
O(2)willbefullypopulated; oxygendeficienciescancomefromO(1), O(2), orO(3)sites.
Electron-doped films and crystals need to be reduced in order to exhibit superconductivity
and are, therefore, annealed in a low partial pressure of oxygen. This annealing removes
oxygen; however, it is a long-standing question in the electron-doped cuprates as to from
where exactly oxygen is being removed during annealing. It has been suggested that oxy-
gen reduction effects the number of charge carriers, i.e., acting as a dopant [23], that it
decreases disorder and impurity scattering [24, 25, 26, 27], that it suppresses long-range
ordered antiferromagnetism [28, 29, 30], or that it repairs copper vacancies in the CuO2
planes [31]. This issue has not been resolved in thin films or crystals due to the difficulty
in determining the oxygen content. The presence of apical O(3) oxygens disorders the
films. Likewise, removing oxygen from O(1) would tend to disorder the CuO2 planes.
Either case should harm superconductivity. The bond between the O(2) oxygens and the
rare earth elements is stronger than the bonds between the O(1) oxygens and the copper
atoms and should be affected by annealing less than O(1) or O(3) oxygens [32]. Further
discussion of the role of oxygenation in PCCO can be found in Chapter 5.
In addition to oxygen, the Pr2CuO4 crystal structure also responds to the substi-
tution of cerium for praseodymium. The Tprime crystal structure is tetragonal with lattice
parameters of a = b ? 3.96 ?A and c ? 12.15 ?A in optimally doped Pr2?xCexCuO4??
[21]. Doping from x = .00 to x = .19 shrinks the c-axis by ? 0.15 ?A (Figure 2.2). This
change in lattice spacing is easily measurable by X-ray diffraction and offers a useful
check of the doping level. Above x = .19, PCCO thin films do not grow reliably as a
12
single phase.
Figure 2.2: Increased cerium doping decreases the c-axis lattice parameter significantly
in Pr2?xCexCuO4?? as seen by X-ray diffraction [33].
The La2?xCexCuO4?? system is quite similar to Pr2?xCexCuO4?? in these respects,
althoughwiththecaveatthatLCCOpreferstheT structuretotheTprime structure. Thegrowth
of Tprime-LCCO is stabilized in thin films through the lattice strain induced by the substrate.
Even with this strain stabilization, only doped LCCO preparations are stable; the film
will not form for x < .06 in the Tprime phase. Below this doping the T-phase of LCCO has
been synthesized with low concentrations of cerium [34]; however, these films are quite
resistive and are contaminated with Tprime phase over x ? .05. The Tprime-phase of LCCO is
necessary in order to exhibit superconductivity when doped with cerium.
13
2.3 Spin Structure
Pr2CuO4 has an antiferromagnetic ground state that is slowly suppressed with dop-
ing. In this system, the largest magnetic moments lie on the copper atoms and have a
non-collinear spin structure (Figure 2.3). In zero magnetic field the spins align along the
[100] and [010] directions. These directions are along the copper-oxygen-copper bonds
in the CuO2 planes. At higher fields the spins align collinearly [35]. In the collinear
structure, the spins are all aligned along the same axes, the direction determined largely
by the magnetic field (Figure 2.4). The [110] directions are the easy axes for the collinear
structure; these are along the copper-copper directions. High field behavior is discussed
in Chapter 4.
This spin structure is slowly suppressed in the electron-doped cuprates by spin-
dilution. Doping an antiferromagnet can suppress magnetic structure by replacing mag-
netic elements with non-magnetic ones [37]. With fewer lattice sites participating in the
spin structure, the strength of the antiferromagnetic interactions is weakened. Dopants,
therefore, suppress the N?eel temperature and eventually destroy the spin ordering. The
N?eel temperature is the temperature where the antiferromagnetic (AFM) order is sup-
pressed; it is like the Curie temperature, but for antiferromagnetism rather than for ferro-
magnetism. This happens in Pr2?xCexCuO4??, where doping cerium onto praseodymium
lattice sites suppresses antiferromagnetism. Although in PCCO the copper lattice sites
are the source of the antiferromagnetic structure, it turns out that electrons doped into the
system go on the copper sites, where they dilute the spin structure [38].
14
Figure 2.3: The copper magnetic moments in the PCCO crystal structure with the out-of-
plane elements suppressed [21] (left) and along the c-axis [36] (right). The spins align
antiferromagnetically along the Cu-O-Cu directions. Adjacent CuO2 planes are rotated
90?.
15
Figure 2.4: The ab-plane spin structure of Pr2?xCexCuO4?? in (a) zero magnetic field and
(b), (c), (d) applied magnetic fields [35]. In field, the [110] directions are the easy axes for
the collinear spin structure (b) whereas [100] and [010] are preferred for the non-collinear
zero-field spin structure (a).
16
2.4 Band Structure
In the cuprate system, the spin structure is on the copper atoms, despite copper
normally being non-magnetic; this is due to the electronic structure of the compounds
[21]. If Pr2CuO4 were considered ionically, neglecting covalency, the praseodymium
atoms form Pr3+ ions and the oxygens are O2?. This requires, then, that copper is in the
compound as Cu2+ [38]. When Pr2?xCexCuO4?? is doped, cerium substitution, as Ce4+,
adds extra electrons converting Cu2+ ions to Cu+ ions. The ions are, however, embedded
in a crystal structure that modifies their electronic properties (Figure 2.5). The Cu2+ 3d9
and O2? 2p6 orbitals are modified due to crystal field effects and hybridize [39]. The
result of this process is that Pr2CuO4 ought to be metallic due to having a half-filled band
populated with one electron per copper atom.
Although the band structure in Figure 2.5 predicts metallic behavior, Pr2CuO4 is,
instead, a Mott insulator (Figure 2.6). This type of insulator ?should? be a metal, but
is an insulator due to strong Coulomb interactions that dominate the transport properties
[40, 41]. These interactions split the Cu dx2?y2 band into an upper and lower Hubbard
band, neither of which crosses the Fermi energy. This band splitting creates a Mott-
Hubbard insulator.
While Coulomb interactions do, in fact, do this in Pr2CuO4, there are additional
bands between the upper Hubbard band (UHB) and lower Hubbard band (LHB). There-
fore, the gap in the band structure that causes PCO to be an insulator is due to the charge-
transfer gap, ? (Figure 2.6). The charge-transfer energy, ?, is the energy required to
move a charge between copper and oxygen sites. Because of this PCCO is more correctly
17
Figure 2.5: The hybridization of the copper and oxygen orbitals in the CuO2 planes [38].
At the edges are the free ion Cu2+ 3d9 (left) and O2? 2p6 (right) shells. The copper 3d9
orbital is then modified by crystal field effects due to being embedded in a crystal lattice
surrounded by oxygen atoms. Spherical, octahedral coordination, pyramidal coordina-
tion, distorted octahedral coordination and a planer coordination modify the bare copper
orbital as well as splitting the oxygen orbital. The mixing between the half-filled copper
dx2?y2 band and the oxygen ? bands that result from the crystal field splitting produces a
hybridized half-filled band with a single free electron on each copper site.
18
called a charge-transfer (or Mott-like) insulator rather than a Mott-insulator [38].
This has implications for the magnetic properties as well as the electrical proper-
ties. The Coulomb repulsion that splits the copper dx2?y2 band into an upper and lower
Hubbard band results in localizing an electron on the copper site. The result is a magnetic
moment on the copper atoms in addition to insulating behavior.
Figure 2.6: The density of states near the Fermi energy for a na??ve cuprate band structure
and one modified by Coulomb interactions, a Mott-Hubbard insulator [38]. (a) Without
Coulombinteractions, thereisahalf-filledantibondingband(AB)attheFermienergythat
comes from the Cu2+ 3d9 and O2? 2p6 orbitals hybridizing. (b) When Coulomb interac-
tions with an energy scale U are included, the antibonding band is split into two bands,
an upper Hubbard band (UHB) and a lower Hubbard band (LHB) with the Fermi energy
now lying in a gap between bands. A material with no band crossing the Fermi energy
will be an insulator. (c) In the cuprates additional bands lie between the UHB and LHB:
a bonding (B), non-bonding (NB), and a Zhang-Rice singlet (ZRS) band. Therefore, the
cuprates are insulators not due to U, but due to the charge-transfer gap, ?.
This charge-transfer insulator description of the cuprates describes the parent com-
pounds; however, the superconducting cuprates are doped systems. At light dopings the
19
charge-transfer band structure is only slightly modified to begin to have a partially filled
band at the Fermi energy (Figure 2.7). With some non-zero density of states at the Fermi
energy, the doped electron-doped cuprates have a Fermi surface (FS) (Figure 2.8).
Figure 2.7: The density of states of a charge transfer insulator with doping [39]. (left)
The undoped charge-transfer insulator with an energy gap ? between filled and empty
states. When electrons or holes are doped into the system, they may either create a new
band in the charge transfer gap (A), or move the chemical potential into either the valance
or conduction bands (B) or (C).
The magnetic Brillouin zone (BZ) indicated by dashed lines in Figure 2.8 is due to
antiferromagnetic ordering. Because the spins on the copper atoms alternate directions,
the real space lattice vectors? lengths should double to account for the periodicity of the
magnetic lattice. This halves the reciprocal space lattice vectors, resulting in a smaller
20
antiferromagnetic Brillouin zone. Therefore the Fermi surface should be folded along the
dashed lines in Figure 2.8; X and ? are the same point. This creates electron pockets
around the M points and hole pockets around the center of the edges of the magnetic
Brillouin zone.
Figure 2.8: Typical Fermi surface for the electron-doped cuprates [39]. A two-dimesional
cut of the quasiparticle dispersion relation (E(kx,ky)) at the Fermi energy produces the
Fermi surface [42] (right). The magnetic Brillouin zone is indicated with dashed lines.
21
TheFermisurfaceretainsthesebasicfeaturesasitevolveswithdoping, asshownby
Angle-ResolvedPhotoemissionSpectroscopy(ARPES)measurementsonNd2?xCexCuO4??
(Figure 2.9). ARPES is a probe of the Fermi surface that takes advantage of the photo-
electric effect to map the momentum states near the Fermi energy where quasiparticles
are found. Electron doping first causes electron pockets to form at the M points, (pi,0)
and (0,pi). This is the Fermi surface for the under-doped side of the electron-doped
cuprate phase diagram. Near optimal doping, hole pockets appear near (pi/2,pi/2). On
the over-doped side, antiferromagnetism has been suppressed; there is no longer a mag-
neticBrillouinzoneandtheFermisurfaceclosestoonehole-likeorbitaroundtheXpoint,
(pi,pi).
Figure 2.9: Evolution of the Nd2?xCexCuO4?? Fermi surface with doping as seen by
ARPES [43]. The ? point is in the top-left corner of each frame. (Each frame is only the
lower-right quadrant of the Fermi Surface drawn in Figure 2.8.) Initially electron pockets
form at (pi,0) and (0,pi) and as doping increases hole pockets appear around (pi/2,pi/2).
At higher dopings (not shown) the hole-like Fermi surface closes and appears much as
the schematic in Figure 2.8.
22
2.5 Phase Diagram
The magnetic moments on the copper atoms exhibit non-collinear antiferromag-
netic ordering. In the electron doped cuprates, the parent compound N?eel temperature is
between 200 K and 400 K (? 250 K in NCCO) [44]. The antiferromagnetism (AFM)
in Pr2CuO4 (PCO) is commensurate and persists to similar temperatures as in NCCO,
? 250 K [21]. Commensurate antiferromagnetic ordering is periodic with rational mul-
tiples of lattice parameters. Doping electrons into PCO has the effect of suppressing this
AFM state via spin dilution. In this process, replacing some fraction of Pr3+ with Ce4+,
the electrons added to the system primarily reside on the copper sites, transforming some
3d9 coppers into spin-less 3d10 coppers. With fewer atomic sites available to support an-
tiferromagnetism, the long-range antiferromagnetic ordering weakens with electron dop-
ing. This is observed as a decrease in the N?eel temperature with increased cerium content
(Figure 2.10).
In Figure 2.10, the AFM order is clearly not suppressed symmetrically on the hole-
and electron-doped sides of the cuprate phase diagram. This is due to spin dilution being
the mechanism for spin suppression only in the electron doped system. Hole doping in
the cuprates effectively introduces a competing ferromagnetic interaction between copper
sites, suppressingantiferromagnetismduetospinfrustration. Thisprocessismorerapidly
destructive to the AFM state than spin dilution is on the electron-doped side of the phase
diagram [21].
In addition to suppressing the N?eel temperature, TN, substituting cerium atoms
for praseodymium atoms also induces superconductivity over a range of dopings. In
23
Figure2.10: Genericdoping phasediagramfor thecuprates[21]. Eitherholedoping (left)
or electron doping (right) suppresses AFM order and allows a superconducting dome to
appear. On the electron-doped side there is some disagreement as to the terminus of the
AF ordered region. This point is discussed in Chapter 4. The line labeled T? represents a
pseudo-gap crossover (not discussed here).
24
Pr2?xCexCuO4??, superconductivity is observed from x = .12 up to x = .19. The max-
imum Tc of around 22 K is obtained for x = .15. Above x = .19, cerium cannot be
reliably incorporated into the crystal lattice. Angular magnetoresistance measurements
(see Chapter 4) suggest that the AFM phase persists up to x = .16; however, AFM disap-
pearance at lower dopings has been reported by other techniques [45, 46]. There is some
disagreement, however, among various groups [44, 45, 47, 48, 49, 50]. The optimal Tc
depends upon proper annealing procedures at each cerium doping. This is due to oxygen
excesses or deficiencies respectively hole- or electron-doping the material. Oxygen con-
tent can also affect the N?eel temperature. Oxygen?s role in PCCO is discussed in detail in
Chapter 5.
Superconductivity in related Tprime cuprates follows similar trends. Several of the rare
earth elements with 3+ valences can form 214 cuprates that can be electron-doped to
induce superconductivity. For example, Pr2?xCexCuO4?? and Nd2?xCexCuO4?? both
behave quite similarly, while the phase diagram for La2?xCexCuO4?? is shifted toward
lower dopings and presents a somewhat higher optimal Tc (Figure 2.11). The shift in
optimal doping between LCCO and PCCO or NCCO is not well understood. Both Pr3+
and Nd3+ have similar ionic radii while La3+ is larger. It is possible that the different
lattice spacing slightly adjusts the band structure so that doping causes a hole pocket to
appear in LCCO before PCCO or NCCO. The decrease in optimal Tc with decreasing
rare earth radius continues for Sm2?xCexCuO4?? and Eu2?xCexCuO4?? [51]. Similar
behavior between LCCO and PCCO is also seen in antiferromagnetism; however, LCCO,
unlike PCCO and NCCO, can only be prepared as a thin film in the Tprime phase, making
magnetic measurements more difficult. The N?eel temperature in PCCO and LCCO is
25
further discussed in Chapter 4.
Figure 2.11: Superconducting dome for PCCO, NCCO, and LCCO [51]. Optimally
grown LCCO has a higher Tc and is shifted to lower cerium dopings compared to PCCO
and NCCO.
It has been reported [32, 52, 53, 54] that the electron-doped cuprates can be made
superconducting solely with the careful control of oxygen in the crystal structure and
without cerium doping. Our efforts along these lines are discussed in Chapter 8, but it
should be noted here that this method of inducing supercondutivity in the RE2CuO4 fam-
ily may imply that future revisions of the phase diagram are necessary. This result, how-
ever, would suggest that the parent compounds, RE2CuO4, are not Mott insulators, but
rather (very) poorly optimized band metals. However, this picture is disputed. Nominally
26
undoped Tprime cuprates can also be synthesized through iso-valent doping by substitution of
Y3+ for La3+. La2?xYxCuO4?? (LYCO) is found to superconduct over a range of yittrium
dopings; transport data indicate that it is a Mott-like insulator that is electron-doped by
oxygen reduction [55]. It is possible, therefore, that superconducting Pr2CuO4 is, in fact,
doped by O2 like LYCO. This issue requires further investigation (see Chapter 8).
27
Chapter 3
Preparation of Pr2?xCexCuO4?? Thin Films and Electronic Transport
Measurements
3.1 Introduction
All measurements depend upon the preparation of quality samples. In the case of
the electron-doped cuprates, good samples can be prepared as either single crystals or thin
films. Thin films of materials often are a convenient form to study transport properties.
Pr2?xCexCuO4?? is no exception. Careful control of growth parameters allows for high
qualityuniformepitaxialfilms. Here,PCCOispreparedbypulsedlaserdeposition(PLD).
This technique allows for rapid and flexible sample preparation and has had good results
in the growth of the cuprate superconductors.
3.2 Pulsed Laser Deposition
The pulsed laser deposition technique ablates a stoichiometric target with a focused
high-energylaser. Thisejectsaplasmaofthetargetmaterialthatdepositsontoasubstrate.
Typicallythisproceduremustbeperformedinsideofavacuumchamberwiththesubstrate
mounted on a heater in order to control the deposition atmosphere and temperature. The
substrate choice, deposition temperature, and chamber atmosphere determine the ability
of the deposited material to form into a thin film of the correct phase and can affect
28
the final properties of the film quite dramatically. In the case of oxides, the chamber
atmosphere is particularly important as the low vapor pressure of oxygen relative to the
other elements in the material requires that the chamber atmosphere be responsible for the
film?s oxygen content. This frequently necessitates a post-deposition annealing procedure
to optimize film properties.
3.2.1 Target Making
In order to grow PCCO thin films by PLD, the target consists of polycrystaline
PCCO synthesized by solid state chemical reactions. The process starts with commercial
oxide powders of praseodymium, cerium, and copper between 4 and 5.5 9?s pure. These
oxides, Pr6O11, CeO2, and CuO, are mixed to form the proper ratio of Pr:Ce:Cu, as de-
termined by weight. For example, a 15 gram target of optimally doped Pr2?xCexCuO4??
(x = .15) requires just over 11 grams of Pr6O11, just under 1 gram of CeO2, and just
under 3 grams of CuO (Figure 3.1).
These numbers can be obtained from the desired doping, desired mass, and the
atomic and molecular weights of the constituent atoms and oxides, summarized in Fig-
ure 3.1. The atomic masses in grams per mol are Pr = 140.9077, Ce = 140.12,
Cu = 63.546, and O = 15.9994, giving molecular masses of Pr6O11 = 1021.4396,
CeO2 = 172.1188, and CuO = 79.5454 for the starting oxides. An optimally doped
Pr2?xCexCuO4?? target (x = .15) needs praseodymium, cerium, copper, and oxygen to
be in a ideal ratio of Pr : Ce : Cu : O = 1.85 : 0.15 : 1.00 : 4.00. In order to synthesize
Pr2?xCexCuO4??, however, the ratio Pr : Ce : Cu : O = 1.85 : 0.15 : 1.03 : N/A is used
29
Figure 3.1: Recipe for producing a15g,x = .15Pr2?xCexCuO4?? target from constituent
oxides. The atomic weights of Pr, Ce, Cu, and O give the number of grams per mol
(column g/m) of Pr, Ce, Cu, Pr6O11, CeO2, and CuO. The desired ratio of each element,
determined from the desired doping, translates into a desired ratio for each oxide (column
Chemical Ratio). From this ratio and the oxides? molecular weight, the ratio in units of
mass is determined (column Mass Ratio) and normalized (by multiplier) for a total mass
in grams of the desired amount. The masses (column Masses) of each starting oxide is
thus determined.
30
as copper has a tendency to be slightly deficient in the finished target and oxygen concen-
tration is controlled by the synthesis atmosphere as oxygen in the target is able to freely
exchange with the O2 in air. This desired ratio of elements requires that the oxides be
mixed in a ratio of Pr6O11 : CeO2 : CuO = 0.308?3 : 0.15 : 1.03, based upon the number
of non-oxygen elements per formula unit. This ratio is then converted into units of mass
that can be measured on a laboratory scale. With the molecular masses, the ratio becomes
Pr6O11 : CeO2 : CuO = 314.9439 : 25.8179 : 81.9318 (grams), which can be then
scaled with a multiplier to Pr6O11 : CeO2 : CuO = 11.1763 : 0.9162 : 2.9075 (grams),
foratotalweightof15g, whichisausefulamountofmaterialforcreating1inchdiameter
targets of approximately half a centimeter thickness.
Both Pr6O11 and CeO2 will absorb moisture from the air. Therefore, the con-
stituent oxides are first separately heated to 800 C for 12 hours in order to dry them
before weighing. In all bakings, the ramp rate is between 250 and 300 C/hour. Powders
are weighed to within 500 ?g of the target weight; the target weights both maintain the
proper Pr : Ce : Cu ratio and produce a total weight of the finished target of? 15 g. The
mix is intentionally slightly copper rich (3 %) due to copper having a slight tendency to
leach out of the target during baking. There is also some evidence that copper rich targets
produce higher quality films [56]. Oxygen stoichiometry is not controlled and will auto-
matically adjust itself as the PCCO forming reaction is carried out in ambient atmosphere.
Unlike the other elements present, oxygen concentration in films grown is not determined
by target stoichiometry, but rather by the partial pressure of oxygen during pulsed laser
deposition.
Combiningtheweighedpowders, themixtureisfinelygroundfirstbymanualgrind-
31
ing with mortar and pestle followed by an hour of ball milling. Manual grinding is ef-
fective for breaking up large chunks of material and the ball milling step produces a fine
powder that maximizes surface contact for the subsequent chemical reaction. The mixed
powder is then fired twice in a furnace, once at 950 C for 12 hours, and then at 1050 C
for 12 hours. Manual grinding and ball milling steps are performed after each bake. This
baking procedure fully reacts Pr6O11, CeO2, and CuO to Pr2?xCexCuO4??. The reacted
powderisthentransferredintoa1-inchinner-diameterpelletpressandsubjectedtoapres-
sure of 25 klbs. This pellet is then sintered at 1080 C for 12 hours and finally mounted
with silver paint on a metal stand designed for target mounting in the PLD chamber. The
final target is a non-superconducting polycrystaline PCCO puck of the desired cerium
concentration. Targets are stable for (at least) several years and can be used repeatedly
for film depositions, with minimal sanding to maintain a uniform surface. Cerium can be
reliably incorporated into Pr2?xCexCuO4?? from x = .00 up to x = .19. Targets are gen-
erally synthesized at each .01 of cerium doping over the superconducting dome (roughly
x = .12 to x = .19) and at larger intervals at lower dopings.
3.2.2 Film Growth
Pulsed laser deposition of thin films is a quite versatile technique for producing
thin films. Any description of the process, therefore, will be general in nature, with
specific films possibly deviating from this process described here in significant ways.
Nevertheless, the procedure for growing a typical PCCO film provides a good scaffolding
onto which modifications can be applied.
32
The most important part of the pulsed laser deposition process is cleaning and
preparing the chamber, target, and substrates. The chamber is responsible for maintaining
the atmosphere necessary for PLD growth, which typically ranges from a few hundred
mTorr of N2O or O2 to vacuum depending upon details of growth. In this discussion,
vacuum typically implies P < 3?10?5 Torr for good PCCO growth, although pressures
of 10?7 Torr are preferred.
The target provides the source material for films produced by the PLD process.
Synthesized prior to pulsed laser deposition, the target should be sanded prior to depo-
sition with a fine grit sand paper, usually 600 grit, to present a uniform surface for laser
ablation. Non-uniformities in the target surface have the effect of reducing the quality of
the plume of material ejected with each laser pulse. Plume quality primarily determines
the rate of film growth, with higher energy densities per pulse ejecting more material.
Typical growth rates for high quality thin films are around 0.3 ?A per pulse and 10 pulses
per second.
The substrate is what ultimately determines the quality of the film?s epitaxy by
seeding the growth of the film?s crystal lattice. Therefore, substrate surface preparation
has a large effect on the ability of the PLD process to grow quality thin films. Substrates
are cleaned three times, first with acetone, then with methanol, and finally with ethanol.
In each case, a small glass beaker is rinsed and then partially filled with the solvent. The
substrate is submerged and ultrasonicated for 5 to 7 minutes, then rinsed and blown dry
with a nitrogen gun. The ultrasonication serves to rinse the substrates well and ensure
that dirt on the film will be removed by the solvent. The substrates are then blown dry in
order to minimize residue remaining on the film due to the evaporation of solvent. This
33
also accounts for the three washes; the acetone cleaning most strongly removes dirt and
the subsequent rinses remove remaining residues.
Substrates are then affixed with silver paint to the chamber?s heater, previously
sanded clean. To attach the backs of the substrates to the PLD chamber?s heater, silver
paint is used due to its good thermal conductivity. Silver paint is applied generously to
the heater and the substrate is then pressed into the liquid. Pressing the substrate insures
uniform thermal contact (and therefore uniform substrate temperature during deposition).
It also has the effect of driving out any tiny air bubbles in the silver paint from behind
the substrate. If air bubbles are allowed to remain, the trapped gas inside the bubbles
will expand during heating, due to the ideal gas law, and will pop the substrate off of the
heater. Prior to insertion into the chamber, the heater is set to 100 C to dry the silver paint.
The choice of substrate, substrate temperature, and chamber atmosphere are the
most important variables in determining whether or not a film composition, established
by a target, will form. The substrate acts to ?seed? the growth of the film?s crystal struc-
ture; therefore, it is necessary for the substrate to have lattice parameters that are well
matched to the film?s. For PCCO the in-plane lattice constants are a = b ? 3.953 ?A. Typ-
ically, PCCO is grown on (100) oriented single crystal SrTiO3 (STO), which is a cubic
perovskite with a lattice constant of a = 3.905 ?A [57] purchased from CrysTec GmbH.
This is a lattice mismatch of only ? 1.2% and seeds c-axis oriented epitaxial PCCO
growth. As PLD growth increases the film thickness, this orientation ultimately produces
films with the c-axis normal to the film surface and the ab-planes stacked parallel to the
surface. STO also has the advantage of being quite resistive; this allows transport mea-
surements to not be contaminated by parallel current paths through the substrate. PCCO
34
will tolerate use of other substrates with larger lattice mismatches. For example, tetrago-
nal LaSrGaO4 (LSGO) with a = 0.384 nm [57] is preferred for far-infrared optical trans-
mission experiments where the frequency dependence of the substrate phonon modes is
a concern [58, 59]. However, if the lattice mismatch is too great, the resulting film will
not be epitaxial and single-phase. For example, attempting to grow Pr2?xCexCuO4?? on
silicon, with a lattice constant of 0.543 nm [57], produces a film where the PCCO 00lscript
X-ray diffraction peaks are not seen.
Provided that the substrate seeds the correct lattice orientation, the temperature is
primarily responsible for the Pr, Ce, and Cu atoms forming in the correct crystalographic
phase. The atmosphere provides the correct oxygen concentration. Deposited at 800 C,
PCCO prefers to form in the Tprime phase. This is the phase in which electron-doped super-
conductivity is found. Substrate temperature is measured by a thermocouple cemented to
the back of the heater and is also monitored separately by an infrared thermometer. Tem-
perature stability is not of great concern for PCCO as the Tprime crystal structure will form at
a range of temperatures around 800 C.
The chamber?s atmosphere is necessarily maintained at a fixed partial pressure of
oxygen in order to grow PCCO. It is a general problem of laser deposition techniques that
the plume of ablated material from the target does not handle well the elements with low
vapor pressures. For example, in the growth of SrFe2?xCoxAs2 and FeSe thin films, ar-
senic and selenium deficiencies in the final films are a concern (Chapter 8). In the case of
oxides, oxygenmustbebledasagasintothevacuumchamberinconcentrationssufficient
to allow its incorporation into the crystal lattice. For PCCO, oxygen is introduced either
as elemental oxygen (O2) or as nitrous oxide (N2O) at a few hundred mTorr of pressure.
35
For optimally grown films, 230 mTorr of N2O is used; however, optimally grown films
can also be prepared in an O2 atmosphere. Oxygen is ultimately, however, adjusted after
growth in an in situ post-deposition annealing step described below.
After fixing temperature, pressure, atmosphere, and substrate choice, the length of
deposition determines the thickness of the film. The laser is pulsed at 10 Hz at an energy
density that produces a growth rate of around 0.3 ?A per pulse. This is typically achieved
by optimally focusing the laser on the target and operating the laser at 700 mJ/pulse
although these laser parameters can be varied significantly to obtain similar energy densi-
ties on the target. In order to maintain the target under this level of ablation, the target is
rotated such that laser pulses trace out a circular annulus rather than ablate the same loca-
tion. This prevents local over-heating of the target. Deposition time is set such that films
are typically grown to between 1000 and 3000 ?A. Thicker films tend to be less uniform at
the surface and thinner films have degraded transport properties.
After the film is deposited, PCCO must be annealed in order to achieve maximal Tc.
This annealing process is designed to reduce the films? oxygen content and is therefore
carriedoutinvacuum. Forannealing, thetemperatureisreducedto720Candthepressure
is held between 10?4 < P < 3?10?5 Torr, with the lower pressures preferred. Annealing
time varies slightly depending upon cerium concentration, reflecting the fact that more
highly cerium-doped films are harder to reduce. Typically, optimal films (maximalTc) are
obtained by annealing at these conditions for one minute per .01 of cerium concentration.
For example, an under-doped x = .12 film is annealed for 12 minutes and an over-doped
x = .19 film is annealed for 19 minutes. It is not clear if this rule-of-thumb holds for more
under-doped films as there is no Tc to optimize. However, recent work on PCO suggests
36
that it does not hold [32, 52, 53, 54].
It is advised that the annealing temperature and pressure be reached as quickly as
possible as the transition period will somewhat anneal the film. This accounts for the
pressure range (10?4 < P < 3?10?5 Torr) used in annealing; the time that the vacuum
pumptakestoreachthebottomofthatrangecannotbeignored. Annealingtimeiscounted
from when 720 C and 10?4 Torr are first attained. Following annealing, heater power is
cut and the films are cooled at a constant atmosphere until below 420 C at which point
little further annealing occurs. Films are only removed from the PLD chamber once they
have cooled to room temperature. A razor blade is used to break the silver paint gluing
the substrate to the heater.
3.2.3 Characterization
Prior to measurements, film quality is assessed by X-ray diffraction, AC suscepti-
bility, and two-probe room-temperature resistance. Thickness and surface roughness are
measured by a Dectak profiler. If future measurements permit contacts to be attached,
resistivity from room temperature down is also measured to characterize the film.
ForcharacterizationpurposesthefilmsaretypicallycheckedusingthevanderPauw
method [60, 61] in either a Quantum Design Physical Properties Measurement System
(PPMS) or a dip-probe setup in a storage dewar. Resistance is measured from 300 K to
2 K in the former or room temperature to? 4 K in the latter. Resistance is then converted
into resistivity using the film thickness obtained by profilometry. Film quality is assessed
by the superconducting transition temperature and transition width, the magnitude of the
37
normal-state resistivity, the presence and strength of a low temperature resistivity up-turn,
and any non-standard transport properties that may be present.
Crystal structure in grown films is checked by X-ray diffraction. Here at Maryland,
X-ray diffraction (XRD) measurements are performed in either a Bruker D8 or a Siemens
D5000 X-ray diffractometer. The technique in each machine is similar. X-rays are gen-
erated at a fixed energy (Cu K?, ? = 1.5406 ?A) and are focused on the thin film. The
X-rays diffract off of the crystal lattice planes at specific angles that satisfy the Bragg
condition, n? = 2dsin? (Figure 3.2). The film and detector can be rotated in ? and peaks
are observed where constructive interference happens.
Figure 3.2: The Bragg condition for x-ray diffraction [62]. Only diffraction angles that
produce constructive interference (left) will produce a diffraction peak. Angles that pro-
duce destructive interference (right) will not show peaks.
In order to characterize thin films, X-ray diffraction measurements are typically
performed as ??2? scans. In this mode the sample is rotated to sweep through a range of
incident angles, ?, between the sample and the x-ray beam. The detector is co-rotated at
an angle of 2? so that it will only detect x-rays that scatter off of crystallographic planes
38
parallel to the film surface, the CuO2 planes in PCCO. Bragg diffraction then gives the
spacing between unit cells along the c-axis, the c-axis lattice parameter.
Thus, the inter-plane spacing, d, can be extracted from the position of the Bragg
peaks. This provides a useful characterization of the thin film because the film should
grow epitaxially, therefore, the only planes participating in the Bragg diffraction are the
ab-planes. Consequently, only the [001] peaks should be seen (Figure 3.3). Weak [001]
peaks, or additional peaks indicate defects in the crystal lattice. In PLD grown PCCO,
there is always a spurious peak at around 2? = 32? that is believed to be caused by
an impurity cerium oxide phase. It is reported that residual resistivity is lower in films
without this peak [56]. Looking at the [001] film peaks, d is a measure of the c-axis lattice
constant. By this, the cerium concentration in the PCCO thin films can be verified [33].
The film?s Tc and ?Tc, the superconducting transition temperature and transition
width thereof, are measured by AC susceptibility (AC?) [38]. This dip-probe fits in a
liquid helium storage dewar and thus can measure from room temperature to ? 4 K. AC
susceptibility works by driving a small current through a coil to produce a small magnetic
field that then induces a small current in a second coil. The production of the drive
coil signal and the detection of the pick-up coil signal are both handled by a Princeton
Applied Research 5210 lock-in. When a thin film is placed between the drive and pick-
up coils, the magnetic field must pass through the sample. Upon cooling the setup, the
temperature will eventually fall below Tc and the thin film will enter the Meissner state.
Superconductors expel all magnetic fields so the onset of superconductivity will screen
the drive coil from the pick-up coil. Where a resistive transition only requires a single
current path to be superconducting, good magnetic screening requires a large volume
39
Figure 3.3: Typical X-ray diffraction data taken on a x = .17 Pr2?xCexCuO4?? thin film
grown on a SrTiO3 substrate.
40
fraction of superconductivity.
3.3 Film Patterning
In order to extract useful parameters from electronic transport measurements, it
is important to understand the path through which the current flows. This is typically
achieved by patterning the thin films into convenient shapes. Films are typically patterned
into an Hall bar geometry that allows for both resistivity and Hall effect measurements
(Figure 3.6). This patterning forces the current to flow down the central bridge of constant
width with the voltage being sampled at fixed locations. Depending upon the positioning
of the voltage leads either the Hall effect or (magneto)resistance is measured.
Films can most quickly be patterned into this shape with a diamond tipped scribe,
although other techniques are more precise. Scribing the film in this manner digs into
the substrate and removes film material in the process, creating a barrier to current. As
the film is only a few thousand ?angstr?oms thick, very little material must be removed;
the scribe typically penetrates well into the substrate. Because of this, the success of
this technique depends more upon the substrate being sufficiently soft to easily scratch
without the application of enough force to break the substrate.
In order to pattern films more precisely, shadow masks are manufactured out of
metal in the desired geometry for patterning. These masks are designed to cover the parts
of the film intended to remain after patterning and allow exposure of the remaining film to
some processing. This processing can be either chemical or mechanical in nature. PCCO
films are patterned with both acid etches or ion milling.
41
A more careful technique than scribing, yet still relatively quick technique is to use
acid to etch the film. Hydrochloric acid (HCl) will etch PCCO at a rate that is on the
order of a kilo?angstr?om per minute for a ? 15 % acid solution. This same technique is
also appropriate for LCCO; however, in that system the etch rate is significantly faster.
This difference is probably due to LCCO films being less stable; the Tprime phase cannot be
synthesized in bulk crystals. In order to prepare the film for acid etching, the film is first
spin-coated in a Headway Research PWM32 photoresist spinner with positive photore-
sist. For positive photoresist, the part exposed to ultraviolet light is etched; for negative
photoresist, the unexposed part is etched. Here Shipley 1813 photoresist is used. The
photoresist is left to harden on the film by subjecting it to a mild (100 C) heat for an hour.
A shadow mask is then overlayed on the film and the film is exposed to UV light supplied
by a Quintel mask aligner. Photoresist developer is then used to remove the exposed pho-
toresist from the film. Next, the film is submerged in acid. HCl is diluted with distilled
water to ? 15 % in order to keep the rate of etching manageable. The etch is halted by
transferring the film from the acid bath to a bath of distilled water. The films are then
blown dry with a nitrogen gun. Complete etching of the film can be observed visually
as STO is white and both PCCO and LCCO are black. Using a multimeter to measure
two-wire resistance can verify full etching as both PCCO and LCCO have kilo-ohm re-
sistances while STO is a good insulator with greater than megaohm resistance. Once the
films are satisfactorily etched, the protective photoresist is removed by ultrasonicating
the film in an acetone bath; acetone dissolves Shipley 1813 photoresist. This procedure
typically produces good quality etches; however, care must be taken to ensure that no
defects in the protective photoresist layer are present as this will translate into defects in
42
the patterning.
For delicate patterning jobs, where very fine features are required, ion milling offers
the most defect-free method of patterning with the sharpest edges. The films are covered
with the shadow mask and mounted inside of the ion mill, which is then pumped down to
vacuum. A beam of argon atoms illuminates the sample with sufficently high energy to
knock material off of the surface. Films are milled until all of the PCCO is removed and
the ion mill is milling into the substrate itself. This procedure creates quite fine patterns;
however, it is quite slow as the ion mill needs to pump down to vacuum.
After the films are patterned (by any method), they are visually checked under an
optical microscope for defects in the patterning. Because the patterned films force current
down a narrow channel, inhomogeneities in this bridge especially need to be avoided as
this will negatively affect the quality of the measurement. If the patterning is satisfactory,
wire leads are then contacted onto the films for transport measurements.
3.4 Electronic Transport Measurements Introduction
Electronic transport is an important tool in understanding material properties. In
this thesis electronic transport measurements are primarily measurements of resistivity,
the Hall effect, and magnetoresistance. The ability of materials to carry current under
different conditions depends upon the underlying physics of the system. Resistivity, for
example, is influenced by scattering from various sources like disorder or phonons. The
numberofchargecarriersinfluencestheHalleffect, andmagneticmaterialsbehavediffer-
ently from non-magnetic ones in magnetoresistance. All transport measurements, how-
43
ever, require the understanding of a few basic experimental techniques discussed here.
3.5 Resistance Measurements
Transport measurements, ultimately, require contacts to be made to the films. For
electronictransport,four-wiremeasurementsarepreferred. Four-wiremeasurementshave
an advantage over two-wire measurements due to the removal of contact resistance from
the measurement. Four-wire resistance measurements consist of two current leads (I+
and I?) and two voltage leads (V+ and V?) electrically connected to the sample. A
constant current is maintained between I+ and I? and voltage is measured between
V+ and V?. Contact resistance on the current leads can be neglected because the current
source is tasked with outputting a constant current. Resistive contacts will require a larger
voltage drop between current leads; this voltage is not the measurement voltage. Contact
resistance on the voltage leads can be neglected due to their being at an equipotential
and with no current flowing through them because of the high input impedance of the
voltmeter. This picture does break down with sufficiently bad contacts, and neglects
related potential issues like resistive heating due to contact resistance; however, for well-
made contacts, four-wire electronic transport measurements measure sample resistance
only and ignore contact resistance.
3.6 Measurement Geometry
Using a four-wire measurement scheme, a constant current is applied, the voltage is
measured, and Ohm?s Law, V = IR, is ultimately used to extract a resistance. Frequently,
44
however, resistivity is the more useful quantity, where R = ?t parenleftbigLwparenrightbig relates the two. The
resistance, R, is an extrinsic property and depends upon the size and shape of the sample:
the length, L; width, w; and thickness, t. Therefore, ?, the resistivity, which does not
depend upon sample geometry but is rather an intrinsic property of the material, is more
useful. It is necessary to know the geometry of the sample, and it is frequently useful to
modify the sample geometry for measurement convenience.
The simplest geometry is to put the contacts in a line on the sample with the current
leads on the outside and the voltage leads on the inside (Figure 3.4). Here it is often
useful for the contacts to extend the width of the sample in order to have the most uniform
current flowing down the length of the sample. The relevant length for the measurement
is the spacing between voltage contacts. This geometry is conceptually simple, but not
preferred for films, as contacts are typically not fully uniform and substantial uncertainty
in geometric factors can be present. Films can typically be easily patterned into more
convenient shapes. Nevertheless, this is often a useful arrangement for samples, like
crystals, that are difficult to pattern. When this method is used on crystals, the current
contacts typically are made such that they completely cover the ends of the crystal in
order to ensure uniform contact.
It is worth noting here another technique for measuring resistivity on unpatterned or
irregular samples: the van der Pauw technique. It has been demonstrated that an arbitrary
arrangement of four-wire contacts on the edges of a uniform, isotropic sample can be
used to extract resistivity data, provided a series of steps are performed [60, 61]. The
optimal configuration for van der Pauw measurements is for the leads to be at the corners
of the film (Figure 3.5). A resistance is measured by running a current along one edge
45
Figure 3.4: Simple four-wire resistance measurement.
and measuring the voltage drop along the other, for example, R12,34 = V34I12 . Resistance
is also measured in the perpendicular direction (R14,23). Re-naming the former Rvertical
and the latter Rhorizontal, the sheet resistance, RS, can be calculated by the van der Pauw
formula:
e
?piRvertical
RS + e
?piRhorizontal
RS = 1. (3.1)
The sheet resistance is related to the resistivity by ? = RSt , where t is the film
thickness. For a uniform film, R12,34 = R34,12 and, likewise, R14,23 = R23,14. Likewise,
reversingthepolarityshouldalsoproducethesameresult, e.g.R12,34 = R21,43. Averaging
of various equivalent Rkl,nm can produce more refined values of Rvertical and Rhorizontal.
The van der Pauw formula has the disadvantage in that it typically can only be solved
numerically; however, in the case of square films, a significant simplification exists. If
46
Rvertical = Rhorizontal = R, then Equation 3.1 reduces to:
RS = piRln2. (3.2)
The film?s resistivity, ?, can then be easily calculated from there by dividing by the film?s
thickness. As most of our thin films are grown on 5 mm?5 mm substrates, Equation 3.2
is a convenient simplification.
The van der Pauw method has the advantage of preserving most of the surface of
the film for measurements that may require a large pristine surface area. Contacting a
film for a van der Pauw resistivity measurement also often tends to be significantly faster
than other methods, making this technique quite useful for rapid characterization of film
quality and properties. The size of the contacts, however, can be an issue as the van der
Pauw formula assumes that the contacts are on the edge of the film and large contacts can
introduce error.
The best measurements are obtained from patterned films. Patterning is typically
done in a Hall bar pattern that allows for both resistivity and Hall effect measurements
(Figure 3.6). The current leads, at each end of the film, force the current to flow down the
narrow bridge in the center. Voltage leads then sample the voltage at specific locations,
depending upon the type of measurement.
Resistance measurements rely on Ohm?s Law and have the voltage leads separated
by a distance along the length of the bridge. This has the advantage of having the length
and width fixed by patterning; the thickness of the thin film is already fixed. This geome-
try is also used for magnetoresistance measurements.
47
Figure 3.5: Film wired in the van der Pauw configuration (see text). Measuring V12 with
applied current I34 and the equivalent vertical arrangement allows extraction of resistivity
by Equation 3.2.
48
Figure 3.6: Film patterned as a Hall bar. The current leads on the ends maintain a constant
current along the central bridge. Resistance measurements are performed using consecu-
tive voltage leads on a single side of the bridge while Hall measurements are performed
using voltage leads opposite each other across the bridge. For Hall effect, the magnetic
field is applied into or out-of the page.
Magnetoresistance is the change in resistance in a magnetic field compared to the
zero-field resistance. In a non-magnetic material the magnetoresistance should always be
positive (the magnetoresistance is larger than the zero-field resistance). A very simple
picture for why this happens is that in a magnetic field the Lorentz force causes charge
carries to follow a curved path. This curved path is longer than the straight path. As long
as the difference is larger than the mean free path of the charge carriers, there are more
scattering events, hence more resistance. More detailed treatment of magnetoresistance
can be found in Reference [4]. Much more complicated behaviors can occur in mate-
rials containing magnetic elements; in these situations, magnetoresistance can be either
positive or negative.
To measure magnetoresistance, resistance is measured, but in a magnetic field. In
anisotropic materials like the cuprates it is important to distinguish between in-plane and
49
out-of-plane magnetic fields. In particular, in PCCO and LCCO, it has been observed that
there is an anisotropy in the in-plane magnetoresistance when the film is rotated such that
the applied external magnetic field remains confined to the ab-plane. This is described
further in Chapter 4.
Patterning of thin films is most useful for Hall effect measurements. The Hall effect
is a transverse voltage that develops in response to current flowing through a magnetic
field (Figure 3.7). A charge moving through a magnetic field feels a force perpendicular
to its direction of motion, vectorF = qvectorv?vectorB. This force separates negative and positive charges,
creating a voltage perpendicular to current flow that can be measured by voltage leads
positioned on opposite sides of the sample. As this voltage is quite small compared to the
longitudinal voltage, patterning greatly helps Hall measurements by aligning the voltage
leads to minimize longitudinal separation.
Figure3.7: Amagneticfield,B, appliedperpendiculartocurrentflow,I, causesavoltage,
V , to appear perpendicular to both. The Hall resistance is this voltage divided by the
applied current. If the voltage leads are not exactly aligned there will be an additional
component due to magnetoresistance in the voltage signal.
50
Nevertheless, the raw Hall signal measured is typically a combination of Hall re-
sistance, Rxy = VyIx , and resistance, Rxx = R
parenleftBig
= VxIx
parenrightBig
. In order to separate these two
resistances, it is noted that the sign of Rxy depends upon the direction of the magnetic
field, due to the vectorI? vectorB term. Therefore, by measuring the Hall effect twice, and reversing
the magnetic field direction in between measurements, two resistivities can be obtained:
R+ = Rxx +Rxy and R? = Rxx ?Rxy. From these, one sees that Rxx and Rxy can then
be extracted by ?
??
?
Rxx
Rxy
?
??
? =
1
2
?
??
?
1 1
1 ?1
?
??
?
?
??
?
R+
R?
?
??
?.
The average of the two measurements will cancel the Hall signal, Rxx = R++R?2 , and the
Hall signal can similarly be extracted by Rxy = R+?R?2 . The Hall coefficient, RH = EyjxB,
then follows from Rxy. The Hall effect has the useful feature that RH = ?1ne, i.e. its
magnitude depends on the number of charge carries, n, and its sign depends upon the
sign of the charge carriers, e. This allows, for example, measurement of the actual doping
level in a sample. However, this interpretation of the Hall effect (a simple Drude model)
is only valid for a one-band systems. If there are multiple charge carriers in the system
the interpretation of Hall data is significantly more complicated.
3.7 Contacts
Transport measurements all rely upon making good contacts to the material. For
Pr2?xCexCuO4??, contacts are typically made by soldering gold wires onto the films with
an indium-based solder, either pure indium metal or an indium/silver alloy. ?Normal? sol-
51
der, a lead/tin eutectic mix, is not preferred. Pr2?xCexCuO4?? films are damaged by the
flux. The high temperatures needed to melt the lead/tin solder can thermally stress and, in
some cases, crack the SrTiO3 substrate if contacts must be remade frequently. Addition-
ally, high temperatures can locally anneal Pr2?xCexCuO4??, changing the oxygen content
and, therefore, transport properties. Indium?s low melting point of 430 K (157 C, 314 F)
combats this. Additionally, indium is able to wet glasses and ceramics, helping to make
good electrical contact, and is quite ductile, making the contacts less likely to break. For
patterned films, indium is soldered to the film to maximally cover the current or voltage
pad; then the gold wire is soldered onto the indium. This creates a large contact with low
contact resistance that is unlikely to heat the film. Larger contacts are also less delicate.
When contacting unpatterned films, additional concerns regarding the size and shape of
contacts must also be considered. Contacts are generally made by hand under an optical
microscope. With practice, wires can be soldered to sub-millimeter-square contact areas
by hand.
Occasionally, indium is not optimal for making contacts. In these cases, silver paint
is often used. This conductive paint flows easily and can be applied with a paint brush
or similar utensil. However, given the typical dimensions of samples, a wooden Q-tip,
broken to create a long thin splinter, offers the best choice for fine control. Allowing
the silver paint to dry slightly before application increases its viscosity and allows for
more precise paint positioning. The silver paint contacts are then allowed to dry; gently
heating the sample (T lessorsimilar 100 C) can hasten this process. Silver paint contacts have the
disadvantage of being quite brittle; poor contacts can fail due to thermal stresses during
measurement runs. However, silver paint can contact very delicate samples more gently
52
than indium. Silver paint contacts will also survive at high temperatures, for example,
for transport measurements well above the melting temperature of solder. This specific
application will be discussed in detail in Chapter 7 of this thesis in the context of high
temperature resistivity measurements.
53
Chapter 4
Angular Magnetoresistance (AMR)
4.1 Introduction
The crystal structure of the cuprate superconductors consists of planes of copper
and oxygen atoms sandwiching doping layers, usually consisting of rare earth elements.
In the specific case of the 214 electron-doped cuprate superconductors, the unit cell is
tetragonal and crystalizes in the Tprime structure. In this crystal structure, the copper atoms
form square lattice planes that are staggered between layers. It has long been known that
the cuprate superconductors have parent compounds with an antiferromagnetic (AFM)
ground state that is suppressed with doping and that, in this state, the magnetic moments
are on the copper atoms. The mechanism by which the magnetism is suppressed is not
symmetric with doping: hole doped materials suppress magnetism by spin frustration,
whereas electron doped materials suppress magnetism by spin dilution. One of the conse-
quences of these differing mechanisms is an asymmetry in the phase diagram. Unlike in
hole doped systems where the AFM state is rapidly suppressed well before superconduc-
tivity appears, electron doped cuprates exhibit a much more gradual suppression of AFM,
leading to questions of competition and/or coexistence (either one being either macro-
scopic or microscopic) in under-doped superconducting samples. Evidence for magnetic
ordering has come from neutron scattering (NS) and muon spin resonance (?SR) in crys-
tals [44, 45, 47, 48, 49, 50].
54
Although neutron scattering techniques have been applied to magnetic thin films
[63], in general, antiferromagnetism in the cuprates has not been measureable in thin
films by these techniques. Spin-sensitive scattering measurements in the cuprates have
used crystals. It has been assumed that the magnetic structure of electron doped cuprates
like Pr2?xCexCuO4??, Nd2?xCexCuO4??, or Sm2?xCexCuO4?? is the same in both single
crystal and thin film preparations.
Here, we used transport data to demonstrate detection of the antiferromagnetic
phase in PCCO (Pr2?xCexCuO4??) thin films. These results compare well with what
has been observed by NS and ?SR in that system. In PCCO, we find that there is evi-
dence for AFM order up to optimal doping. Its disappearance suggests a quantum phase
transition inside of the superconducting dome. We subsequently used transport data to
detect AFM in thin film preparations of Tprime LCCO (La2?xCexCuO4??), an electron doped
cuprate superconductor that can only be prepared as a thin film.
The zero-field spin structure of the electron doped cuprates is noncollinear antifer-
romagnetism. The spins are aligned antiferromagnetically, alternating between the a and
b crystallographic axes between adjacent CuO2 layers (Figure 4.1). At sufficiently high
magnetic fields applied in the plane there is a transition between the noncollinear AFM to
a collinear spin-flop state. In this state, the antiferromagnetic structure in adjacent planes
is no longer perpendicular; it has become parallel. In the zero field noncollinear AFM
state, the spins prefer to align along the crystal axes, i.e. [100] and [010]. In the spin-flop
state, the easy axes become the [110] directions and have a slightly lower magnetoresis-
tance than when the spins are forced to lie along one of the [100] directions. This has been
observedexperimentallyinPr2?z?xLazCexCuO4 (PLCCO)[35]. Antiferromagnetismcan
55
be detected due to a slight angular dependence of magnetoresistance.
PLCCO, PCCO, and LCCO (in thin film form) are all the same Tprime crystal structure
and it is expected that the magnetic structure is also the same. The Tprime phase of LCCO
can only be stabilized as a thin film, which makes spin sensitive scattering experiments
difficult. In PCCO, neutron scattering and ?SR have been performed, yet there is some
disagreement as to the phase diagram. An antiferromagnetic quantum phase transition
(QPT) has been suggested for dopings from x = .13 [45] to x = .16 [64, 65]. These
differing placements of the AFM QPT have correspondingly different interpretations as
to whether AFM order coexists with superconductivity. Quantum critical points (QCP) in
the cuprates at these dopings have been debated [66].
4.2 Experiment
In order to perform the angular magnetoresistance (AMR) measurement, it is nec-
essary to have high quality thin films due to the small amplitude of the AMR oscillations.
The thin films of Pr2?xCexCuO4?? and La2?xCexCuO4?? were grown on (100) oriented
SrTiO3 (STO) or LaSrGaO4 (LSGO) substrates by pulsed laser deposition (PLD) using a
LambdaPhysik KrF excimer laser with a 248 nm wavelength. The films were grown to
a nominal thickness of 300 nm and were annealed in situ immediately after deposition
by adjusting the substrate temperature and the chamber pressure to annealing conditions.
Films were then characterized by x-ray diffraction, AC susceptibility, and resistivity prior
to angular magnetoresistance measurements.
A large magnetic field placed in the ab-plane will force the copper magnetic mo-
56
Figure 4.1: Zero field spin structure of Pr2?xCexCuO4?? as seen looking along the c-axis
[36]. The solid and hollow balls are Cu atoms on adjacent CuO planes.
57
ments to switch to a collinear AFM state in the direction of the applied field. This was
accomplished by mounting the films in a Quantum Design Physical Properties Measure-
ment System (PPMS) capable of applying magnetic fields up to 14 T. The samples were
mounted on a rotator stage that allowed 360? of rotation with the axis of rotation parallel
with the c-axis of the crystal structure (Figure 4.2). As the magnetic field was rotated
through the CuO2 plane, the copper spins were alternately aligned along the easy and
hard axes, [110] and [100] respectively.
The epitaxial nature of the pulsed laser deposition growth of both the films forces
the crystallographic a- and b-axes to align with the substrate a- and b-axes. In the Tprime crys-
tal structure, and in SrTiO3, the a- and b-axes are the equivalent due to lattice symmetry.
The films were patterned such that the current path was along thea-axis (I bardbl[100]) unless
stated otherwise. The films were mounted on the PPMS rotator stage such that the ? = 0?
position is where H ?[100].
In PLCCO it has been observed experimentally that the magnetoresistance takes on
measurably different values, depending upon whether the collinear AFM is aligned along
the Cu-Cu direction, [110], or along the Cu-O-Cu direction, [100]. This difference can
be seen at the largest applied fields in Figure 4.3, although the origin of the anisotropic
scattering leading to these different values is not well understood. Rotation of the film
through 360?, at fixed applied magnetic field, causes the resistance to alternate between
the high and low resistance directions. Due to the tetragonal symmetry of the crystal this
should happen four times per 360? rotation.
These oscillations in magnetoresistance are due to an underlying magnetically or-
dered state and therefore their observation is an indication of the magnetic structure of
58
Figure 4.2: A patterned thin film rotated in an applied in-plane magnetic field [36]. The
angle? represents the angle between the field, H, and the current, I. The current direction
is along the crystalline a-axis.
59
Figure 4.3: Magnetoresistance of Pr2?z?xLazCexCuO4 along the [100] (BbardblCu-O-Cu) and
along the [110] (BbardblCu-Cu) directions [35]. The transition to the collinear spin state in
each direction is denoted by B?c.
60
the crystal lattice. The angular magnetoresistance oscillation?s relationship to the crys-
tal?s magnetic structure is further strengthened by comparison to neutron scattering data.
In Pr2?z?xLazCexCuO4 (Figure 4.3), B?c is related to the end of the spin-flop transition as
seen by neutron scattering. Neutrons have a magnetic moment and therefore are sensitive
to the magnetic, as well as the structural, Brillouin zone.
Theseoscillationsaregenerallyquitesmall; typicallythechangeinresistanceisless
than 1% of the average resistance value. The angular magnetoresistanceis measured as
a change in magnetoresistance with angle, typically either ??(?,H) = ?(?,H)??(?,H=0)?(?,H=0) ,
or this value normalized by setting the minimal ??(?,H) to zero, e.g., ??prime(?,H) =
??(?,H)???(?Rmin,H) with ?Rmin = 180? normally. For this study, the most important
feature of the angular magnetoresistance signal is the temperature where the amplitude of
oscillations goes to zero; the numerical value of the angular magnetoresistance oscillation
amplitude does not enter into the analysis.
4.3 Pr2?xCexCuO4?? Results
Thinfilmsofunder-dopedPr2?xCexCuO4?? showfour-foldmagnetoresistancemod-
ulation when a sufficiently high magnetic field is rotated in the ab-plane (Figure 4.4). The
signal develops between 4 T and 8 T, indicating that the spin-flop transition in PCCO is
in this field range and that above 8 T, the spins are in a collinear arrangement. At higher
fields the signal is more pronounced.
The largest magnetic field that was accessible for these measurements was 14 T.
Subsequent measurements were performed at that field in order to maximize signal am-
61
Figure 4.4: Magnetoresistance oscillations are seen in Pr2?xCexCuO4?? at sufficiently
high magneticfields [36]. Between4T and8T afour-fold oscillation develops, becoming
more pronounced at 14 T. The amplitude of the angular magnetoresistance oscillations,
??(?,H) = ?(?,H)??(?,H=0)?(?,H=0) , is related to the film?s antiferromagnetism.
62
plitude. These measurements were performed on a range of dopings of PCCO.
On the overdoped side of the phase diagram, no angular magnetoresistance was ob-
served. This is consistent with antiferromagnetism not being present at higher dopings.
An AMR signal is seen at under- and optimal dopings (Figures 4.5, 4.6, 4.7, and 4.8). The
underdoped side of the PCCO phase diagram has a signature of AFM and superconduc-
tivity at lower temperature.
Figure 4.5: Magnetoresistance oscillations are seen in under-doped Pr2?xCexCuO4??
(x = .12) [36]. The N?eel temperature, estimated from where the four-fold oscillations
disappear, is between 105 K and 110 K.
It can be seen that the highest observed temperature for AMR oscillations decreases
with increased doping (Figure 4.9). This trend holds across the underdoped side of the
63
Figure 4.6: Magnetoresistance oscillations are seen in under-doped Pr2?xCexCuO4??
(x = .13) [36]. The N?eel temperature is between 70 K and 75 K.
64
Figure 4.7: Magnetoresistance oscillations are seen in under-doped Pr2?xCexCuO4??
(x = .14) [36]. The N?eel temperature is between 60 K and 65 K.
65
Figure 4.8: Magnetoresistance oscillations are seen in optimally doped Pr2?xCexCuO4??
(x = .15) [36]. The N?eel temperature is between 34 K and 38 K.
66
phase diagram and indicates N?eel temperature suppression with increased cerium doping.
The AFM phase seems to disappear at around x = .16.
Figure 4.9: The amplitude of the magnetoresistance oscillations in Pr2?xCexCuO4?? de-
crease with temperature before disappearing completely [36]. The N?eel temperature is
the point at which the oscillations disappear. It decreases systematically with increasing
cerium doping.
Although there is some disagreement between techniques like ?SR and inelastic
neutron scattering (INS) to determine the extent of the AFM phase in PCCO, our mea-
surements indicate that AFM ordering is present up to x = .15 above Tc. AMR does not
allow measurement of TN in the superconducting state; however, the trend from lower
dopings suggests that the AFM QPT is around x = .16 (Figure 4.10). Other studies have
suggested a Quantum Critical Point (QCP) at around this doping [64, 65].
67
Figure 4.10: The N?eel temperature as determined by angular magnetoresistance (circles)
indicates a quantum phase transition at around x = .16 [36]. Diamonds and the solid line
indicate TN determined by ?SR from [44] and by INS from [45] respectively. Triangles
are optical determinations of a normal state gap from [67, 68], suggested to be the onset
of 2D spin-wave fluctuations.
68
4.4 Pr2?xCexCuO4?? Discussion
AFM suppression at around x = .16 is suggestive of a quantum phase transition
inside the superconducting dome. Transport studies [64, 65, 69], ARPES [43], and optical
measurements [67, 68] on PCCO and NCCO have suggested a similar doping for an
AFM QPT. This has been contradicted by INS on NCCO suggesting disappearance of
antiferromagnetism at x = .13 and no coexistence of superconductivity and long range
AFM [45]. It has also been contradicted by ARPES on SCCO suggesting short range
AFM at x = .14 [46]. Neutron scattering and ?SR have produced differing results [44,
45, 47, 48, 49, 50]. AFM extending to x = .16 indicates significant coexistence between
antiferromagnetism and superconductivity.
Therelationshipbetweenangularmagnetoresistanceandantiferromagnetismislargely
empirical. It has been shown that in Pr2?z?xLazCexCuO4, magnetoresistance anisotropy
is related to the long range order antiferromagnetism seen by neutron scattering [35].
Likewise, in Pr2?xCexCuO4?? the angular magnetoresistance signal suggests a TN that
is consistent with some of the other measurements of TN in that system. Antiferromag-
netism due to possible magnetic impurities or magnetic impurity phases in the PCCO
crystal lattice can be ruled out as a source of the angular magnetoresistance oscillations by
considering oxygenated films. The addition of oxygen to optimally doped x = .15 films,
for example, in as-grown or incompletely reduced films, shows that the AMR signal can
be quite enhanced with oxygen addition (Figure 4.11) compared to optimally annealed
films of the same doping (Figure 4.8). Oxygen can be reversibly added to or removed
from Pr2?xCexCuO4?? films after initial growth and is not magnetic; oxygen-driven en-
69
hancement of the angular magnetoresistance signal is not due to magnetic disorder. Fur-
thermore, neither oxygenation nor reduction introduces or removes impurity peaks in X-
ray diffraction data, indicating little oxygen-induced change in impurity phases present
in the film. Therefore, AMR dependence on oxygen suggests angular magnetoresistance
oscillations are a feature of PCCO itself and not any impurity phase. Furthermore, inso-
far as oxygen can be treated as a dopant, the angular magnetoresistance signal depends
on the number of charge carriers much more strongly than on disorder (see Chapter 5).
AFM enhancement, with oxygenation, is consistent with the picture that AFM suppres-
sion, with cerium doping in the electron doped cuprates, is due to spin dilution [21]. The
strong response to oxygen (Figure 4.11), which can easily be adjusted without damaging
the crystal structure, suggests that the AMR signal is responding to AFM intrinsic to the
PCCO crystal and its doping and not to any spurious phase.
ThroughtheobservationofangularmagnetoresistanceoscillationsinPr2?xCexCuO4??,
we were able to show that transport measurements can be used to study antiferromag-
netism in that system. The angular magnetoresistance oscillations in Pr2?xCexCuO4??
are observed to decrease with temperature and doping and are observed to disappear at
the N?eel temperature determined by spin-sensitive scattering experiments, as in PLCCO
[35]. WeobservethattheN?eeltemperaturefoundthroughAMRsupportsaphasediagram
where antiferromagnetism extends up to x = .15 above Tc and suggests disappearance at
x ? .16 behind the superconducting dome (Figure 4.10). This work, therefore, supports
the picture of Quantum Critical Point at around x = .16 [64, 65] and suggests that this
QCP has an antiferromagnetic nature. Additionally, as these experiments are transport
measurements and were performed on thin films, these conclusions further suggest that
70
Figure 4.11: Angular magnetoresistance of an oxygenated x = .15 Pr2?xCexCuO4?? thin
film [36]. Oscillations are observed to go to zero between 110 K and 120 K.
71
angular magnetoresistance is a useful technique for studying antiferromagnetism in sys-
tems that are not amenable to spin-sensitive scattering studies.
4.5 La2?xCexCuO4?? Results
A similar set of experiments was undertaken on La2?xCexCuO4?? (LCCO) thin
films [70]. This electron-doped cuprate system cannot be grown as bulk crystals in the
correct phase, preventing most measurements of magnetic structure. Thin films of LCCO
can be grown in the Tprime phase for a range of cerium dopings. Here LCCO films were
prepared with cerium dopings from x = .06 to x = .15. The x = .06 doping is the most
lightly doped LCCO film that it is possible to synthesize; the parent compound does not
form in the Tprime structure. In this system, optimal doping is around x = .10 or x = .11.
The LCCO system is comparable to the PCCO system so antiferromagnetic ordering is
expected to be present in the system.
Thin films of LCCO show two-fold angular magnetoresistance oscillations (Fig-
ure 4.12). This is in contrast to the four-fold oscillations seen in PCCO. However, like
PCCO?s four-fold oscillations, LCCO?s two-fold oscillations decrease in amplitude with
increasing temperature, eventually disappearing. The temperature at which these oscilla-
tions disappear decreases with cerium doping as well. This doping dependence suggests
that angular magnetoresistance oscillations in La2?xCexCuO4?? follow the N?eel temper-
ature as in Pr2?xCexCuO4??. La2?xCexCuO4?? and Pr2?xCexCuO4?? are thought to be
similar systems.
By comparing the amplitude of the angular magnetoresistance signal 90? apart,
72
Figure 4.12: Angular magnetoresistance oscillations of a La2?xCexCuO4?? thin films
with cerium dopings from x = .06 to x = .15 [70]. Measurements were taken at 14 T.
73
there is a clear difference in magnetoresistance in the two directions that both increases
with increasing magnetic field (Figure 4.13a) and decreases with increasing temperature
(Figure 4.13b). Except for having two-fold rather than four-fold symmetry, this is similar
to the observed behavior of PCCO . The amplitude of the difference in magnetoresistance
between the two directions decreases with increasing temperature, eventually reaching
zero at a doping-dependent temperature (Figure 4.13c). This temperature at which the
angular magnetoresistance oscillations reach zero, TD, is found to trace a line similar to
TN in Pr2?xCexCuO4?? (Figure 4.13d).
One obvious difference between the angular magnetoresistance signal observed for
La2?xCexCuO4?? andPr2?xCexCuO4?? isthereducedsymmetryoftheLa2?xCexCuO4??
oscillations. For Pr2?xCexCuO4??, the four-fold oscillations match the symmetry of the
ab-plane of the crystal lattice; the spins that participate in the antiferromagnetism in the
system are on the copper atoms. In La2?xCexCuO4??, however, it is less clear that
assigning the two-fold oscillations in magnetoresistance to antiferromagnetism is cor-
rect, although two-fold oscillations have been assigned to spin density wave ordering
in the barium 122 ferropnictide system [71, 72]. Furthermore, non-magnetic properties
of La2?xCexCuO4??, like superconductivity or phase fluctuations measured by the Nernst
effect [73,74], do nothave thesame temperatureand doping dependenceasTD. Recently,
the parent compound, Tprime-LaCuO4, has been synthesized in powder form and investigated
by ?SR, finding antiferromagnetism with a N?eel temperature of 115 K [75]. The TD
found by angular magnetoresistance appears to extrapolate to near this value at zero dop-
ing (Figure 4.13d). It is likely, therefore, that the angular magnetoresistance signal found
in La2?xCexCuO4?? is due to antiferromagnetism and its disappearance corresponds to
74
Figure 4.13: (a) Field dependence of magnetoresistance at 35 K for several dopings [70].
Open and closed symbols are taken with the magnetic field parallel and perpendicular
to the direction of current respectively. (b) Field dependence of magnetoresistance for
x = .06 at several temperatures. (c) The amplitude of the difference in magnetoresistance
decreases with increasing temperature. The temperature at which this amplitude goes to
zero is identified as TD. (d) Phase diagram with TD(x) and Tc(x).
75
the N?eel temperature.
In Pr2?z?xLazCexCuO4, anisotropic magnetoresistance was reported as related to
the spins making a non-collinear to collinear transition in field [35]. This picture was used
to understand the four-fold angular magnetoresistance oscillations that were observed in
Pr2?xCexCuO4??. If La2?xCexCuO4?? does not have this transition, and the antiferro-
magnetism stays in the non-collinear state, this may result in a two-fold oscillation due
to some unknown asymmetry between the (00lscript) and parenleftbig00lscript2parenrightbig copper oxide planes. There
is, however, currently no good explanation for the angular magnetoresistance signal in
La2?xCexCuO4?? having two-fold, rather than four-fold, oscillations.
Two-fold oscillations are also seen in Pr2?xCexCuO4??. While there is a four-fold
component to Pr2?xCexCuO4?? angular magnetoresistance, a two-fold signal can also
be clearly seen (Figures 4.6, 4.7). This two-fold PCCO signal seems to be suppressed
with temperature (and doping) in concert with the four-fold antiferromagnetism signal,
suggesting that they are related phenomena. Additionally, the La2?xCexCuO4?? angular
magnetoresistance oscillations further disappear at the same doping as Pr2?xCexCuO4??.
This is suggestive of a common magnetic origin because antiferromagnetism in these sys-
tems is due to spin dilution. The antiferromagnetism would be expected to be suppressed
with roughly the same number of charge carriers in either system.
Additionally, the angular magnetoresistance oscillations do seem to be a property of
the material. La2?xCexCuO4?? films were patterned such that the bridge was both along
the [100] and [110] directions and the in-plane angular magnetoresistance was measured.
The observed magnetoresistance oscillations maintained the angular locations of their
minima and maxima with respect to the underlying crystal structure and not the direction
76
of current flow (Figure 4.14). In each orientation, the angle, ?, was measured relative to
the applied in-plane magnetic field such that ? = 0? occurred when the field was along
the crystallographic b-axis ([010] bardbl H). The film was patterned such that the current
was oriented either along the a-axis (I bardbl [100], I ? H) at ? = 0? (Figure 4.14a) or
such that the current was at 45? to this orientation (I bardbl [110]) at ? = 0? (Figure 4.14b).
In both cases, the resulting angular magnetoresistance oscillations (Figures 4.14c 4.14d)
show matching features at the same orientations, i.e., minima occur at H bardbl [100] and
maxima occur at H bardbl [010]. The features were not shifted 45? as the current bridge
was. This excludes extrinsic effects due to the symmetry of the experimental setup and
suggests that the observed angular magnetoresistance signal is connected to the crystal or
magnetic structure of the material.
Material properties of Tprime La2?xCexCuO4?? are not as well explored as they are in
Pr2?xCexCuO4??, due to lack of non-thin-film samples. Therefore, there can be spec-
ulation of structural distortions like in La2?xSrxCuO4?? [76], magnetic stripe ordering
like in YBa2Cu3O7 [77], or disorder (like apical oxygen) in the films. However, if
these effects were present, they would still be consistent with the picture that TD is re-
lated to the magnetic structure of La2?xCexCuO4??. Even though it is not understood
whythemagneticstructureofLa2?xCexCuO4?? producestwo-foldangularmagnetoresis-
tance oscillations compared to the four-fold angular magnetoresistance oscillations seen
in Pr2?xCexCuO4??, both angular magnetoresistance oscillations are likely tracking the
same property: an antiferromagnetism ordering in the material.
The observation of angular magnetoresistance oscillations in La2?xCexCuO4?? are
seenassimilartotheangularmagnetoresistanceoscillationsobservedinPr2?xCexCuO4??.
77
Figure 4.14: La2?xCexCuO4?? film patterned both with the current along the crystal axis
(e.g., [100]) (a) and along the diagonal (e.g., [110]) (b) for a x = .08 film at 35 K [70].
An angular magnetoresistance signal is seen in both orientations (c,d) with the minima
and maxima at the same angle ? in each case.
78
Compared to Pr2?xCexCuO4??, the angular magnetoresistance oscillations evolve simi-
larly with doping and are fully suppressed at around x = .15. The disappearance of these
oscillations appears to track the N?eel temperature. The La2?xCexCuO4?? system can-
not be explored by spin-sensitive scattering techniques. The oscillations are evidence for
antiferromagnetism in La2?xCexCuO4??.
79
Chapter 5
Disorder and Oxygenation in Pr2?xCexCuO4??
5.1 Introduction
One of the outstanding issues in the electron-doped cuprates is the role that oxy-
genation plays in superconductivity and normal state properties. Oxygen addition can be
considered both a doping and a disordering process. To disentangle these two effects,
disorder can be introduced by irradiating the samples without altering doping. Transport
studies were performed on optimal and under-doped Pr2?xCexCuO4?? films subject to
proton irradiation and oxygenation. This separation of the disorder and doping effects
also sheds light on oxygen reduction effects in electron-doped cuprates.
In the electron-doped cuprates, the as-grown material does not show superconduc-
tivity. It is necessary for PCCO to be annealed in an oxygen-depleted environment; the
details of this reduction step (primarily temperature, oxygen partial pressure, and time)
can greatly influence Tc. However, despite the necessity of low oxygen annealing, it is
not established what effect this reduction has microscopically. Electron-doped cuprates
have the Tprime crystal structure with CuO2 planes sandwiched between layers of rare-earth
atoms. Oxygen can exist at in-plane lattice sites (O(1)), out-of-plane lattice sites (O(2)),
and, potentially, at apical sites (O(3)). It is not clear which oxygens are primarily reduced
by annealing to enhance superconductivity. It is known, that in the parent compound,
there is a significant change in the lattice parameters due to oxygen reduction, suggest-
80
ing significant removal of oxygen [26]. However, this change is not seen in the optimally
doped material. In the cuprate superconductors, superconductivity is quite sensitive to the
quality of the crystal structure, particularly the copper-oxide planes. For example, doping
zinc on the copper sites suppresses superconductivity [78]. Oxygen in these materials is
harder to control and although it is well known that an oxygen reduction step is necessary
to maximize Tc, the origin of the removed oxygen is still unresolved.
The possibility of oxygen acting as a dopant can be understood via an ionic picture
of Pr2?xCexCuO4??, although this picture is quite simplified. In the parent compound,
Pr2CuO4, the praseodymium has a 3+ valence, oxygen has a 2? valence, and charge
balance forces copper to have a 2+ valence: Pr3+2 Cu2+O2?4 . Doping Ce4+ onto the Pr3+
sites adds electrons to the system. Due to Coulomb interactions, this doping is primarily
accomplishedonthecoppersites[38]. WhileaddingCe4+ inplaceofPr3+ addselectrons,
adding O2? at interstitial sites (0 valence) adds holes. Removing O2?, therefore, can be
thought of as adding electrons. If oxygen is acting as a dopant in Pr2?xCexCuO4??, it is
dopingthematerialintheoppositesenseascerium, i.e., addingoxygenactslikeremoving
cerium and removing oxygen acts like adding cerium.
Our group has argued previously that apical oxygens are being removed and that
oxygenprimarilyactsasadopantinPCCO(x = .17)[27]. RecentworkonPr2?xCexCuO4??
and Nd2?xCexCuO4?? crystals report that the 4?? in as-grown compounds is? 4.0 and
the excess oxygens are apical [79]. It has been reported that oxygen reduction does not
change the charge doping significantly and oxygen primarily causes disorder in PCCO
[80]. The parent compounds have also been made superconducting solely by oxygen re-
duction, which is suggestive of a doping effect, but it was reported as due to the effect of
81
perfecting the crystal structure [52].
The possibility of oxygen non-stoiciometry increasing disorder in Pr2?xCexCuO4??
hastotakeintoconsiderationtheeffectsofdisorderonsuperconductivity. Magneticdisor-
der is detrimental to superconductivity; however, oxygen is non-magnetic. Non-magnetic
disorder only weakly suppresses superconductivity in s-wave superconductors, supercon-
ductors where the superconducting order parameter is isotropic. The cuprates, however,
are d-wave superconductors; their superconducting order parameter is not isotropic, but
has nodes. In these d-wave superconductors, and more generally in nodal superconduc-
tors, non-magnetic disorder acts to strongly suppress superconductivity [81]. If oxygen
disorders the Pr2?xCexCuO4?? crystal lattice, superconductivity ought to be quickly sup-
pressed.
Inordertoachievesuperconductivityintheelectron-dopedcuprates,apost-synthesis
annealing step is required. The microscopic details of the annealing process, however, are
debated. In the Tprime cuprates, like Pr2?xCexCuO4??, oxygen is initially incorporated into
the crystal lattice in several locations: at in-plane, O(1), sites; at out-of-plane, O(2), sites;
and at apical, O(3), sites. The apical oxygens are interstitial, lying directly above or below
the copper atoms. Despite the O(3) site being interstitial, it is known to be populated at
the several percent level in Nd2?xCexCuO4?? [24, 26]. Annealing in an oxygen-reducing
environment is then necessary to induce superconductivity. The na??ve answer, therefore,
to the question of the role of annealing the electron-doped cuprates in a reducing environ-
ment is that annealing removes the apical oxygens. As these oxygens occupy non-regular
lattice sites, this reduces the disorder in the crystal lattice. This view has been supported
by neutron scattering [82] and transport [25, 27, 83] measurements. Competing models
82
fortheroleofannealingintheTprime cupratesexist. Ithasbeenarguedthatannealingremoves
the O(1), rather than the O(3), oxygens. In this picture, the apical oxygens are mostly un-
touched by annealing as annealing removes oxygens from the CuO2 planes, and in doing
so, suppresses antiferromagnetism in the material [28, 29]. In this scenario, suppression
of antiferromagnetism is what leads to superconductivity. It has also been proposed that
annealing is primarily not about oxygen, but about copper. This argument suggests that
copper vacancies are detrimental to superconductivity and that annealing allows the cop-
per atoms to migrate and ?heal? the CuO2 planes [31]. This migration would come with
the cost of generating intercalated copper-deficient (RE,Ce)2O3 phases, seen by scatter-
ing experiments [49], in the material. Copper excess growths of Pr2?xCexCuO4?? have
been shown to lack this impurity phase [56]. The role played by the annealing step of
electron-doped curates synthesis is quite varied among these three views; this is still an
open question in the field.
OxygenationinPr2?xCexCuO4?? canhaveseveraleffects. Itcoulddopethesystem,
disorder the system, or do both. Additionally, the related question of the role of anneal-
ing the Tprime cuprates to induce superconductivity has several proposed answers. The first
scenario is that annealing removes apical oxygens from interstitial lattice sites, thereby
reducing disorder and allowing superconductivity. The second scenario is that annealing
removesin-planeoxygensfromtheCuO2 planes, therebysuppressingantiferromagnetism
and allowing superconductivity. The third scenario is that annealing allows migration of
copper atoms, thereby healing defects in the CuO2 planes and allowing superconduc-
tivity. In addition to understanding oxygen?s role in either doping or disordering the
Pr2?xCexCuO4?? system, understanding of the role of annealing in the electron-doped
83
cuprates might be gained by studying oxygenated members of this system.
InordertodisentanglethesetwopossibleeffectsofoxygenationinPr2?xCexCuO4??
and these three possible annealing scenarios, over-oxygenated Pr2?xCexCuO4?? was in-
vestigated. Here we expand upon the work done on x = .17 PCCO at lower dopings with
the goal of better understanding the role of oxygen in the superconducting properties of
the cuprates. Over-oxygenated films of both optimal doping (x = .15) and under-doped
(x = .12) PCCO were prepared as was an optimal x = .12 film that was subsequently
irradiated at a range of doses. In x = .17 it was established that oxygen doping opposes
cerium doping but disorders the material sufficiently to not allow Tc enhancement [27].
On the underdoped side, extra oxygen would be expected to suppress Tc due to both dop-
ing and disorder. However, the underdoped side of the phase diagram does offer some
advantages. It is known that at higher dopings the Hall effect changes sign at low tem-
peratures, indicating two band transport [21]. Doping is therefore easier to understand on
the single band underdoped side of the phase diagram. Also, PCCO has an antiferromag-
netic (AFM) ground state that persists up to near optimal doping that can be observed in
transport data [36]. This allows the use of the N?eel temperature as an independent indica-
tor of doping in the system. Finally, underdoped samples always have a low temperature
resistivity upturn whose origins are not well understood; it has been proposed, however,
that it is due to additional magnetic scattering due to strong correlations causing magnetic
droplets to form around impurities [84]. Studying disorder at these dopings may offer
some new insight into the PCCO system.
84
5.2 Experiment
Three series of PCCO thin films were studied: an irradiated series at x = .12 dop-
ing, an oxygenated series at x = .12 doping, and an oxygenated series at x = .15 doping
(Table 5.1). In all three series, the optimally grown member formed one endpoint, and
oxygen or irradiation was progressively added. In all cases Tc had been fully suppressed
prior to the maximal introduction of oxygen or disorder.
The thin films of Pr2?xCexCuO4?? were grown by pulsed laser deposition (PLD)
using a LambdaPhysik KrF excimer laser (248 nm wavelength) on (100) oriented SrTiO3
substrates. The films were grown to a nominal thickness of 300 nm. Series of samples
were fabricated for irradiation and oxygenation measurements respectively. The former
was grown as a single under-doped film that was optimally grown and annealed. The
latter was grown as a series of films made under various oxygenation conditions.
totally awesome newline
Irradiated x = .12 films Oxygenated x = .12 films Oxygenated x = .15 films
.000?1016/cm2 of 2 MeV H+ 230 mTorr N2O, optimal annealing 230 mTorr N2O, optimal annealing
1.18?1016/cm2 of 2 MeV H+ 230 mTorr N2O, no annealing 230 mTorr N2O, no annealing
2.32?1016/cm2 of 2 MeV H+ 230 mTorr O2, no annealing 230 mTorr O2, no annealing
3.52?1016/cm2 of 2 MeV H+ 400 mTorr O2, no annealing 400 mTorr O2, no annealing
4.72?1016/cm2 of 2 MeV H+ 600 mTorr O2, no annealing 600 mTorr O2, no annealing
6.49?1016/cm2 of 2 MeV H+
Table 5.1: Pr2?xCexCuO4?? film samples used for transport measurements.
For the irradiated film, an atmosphere of 230 mTorr N2O was used during the de-
position process. The target consisted of a polycrystalline Pr2?xCexCuO4?? pellet with
a cerium doping of x = .12. The film was annealed in situ immediately after deposition
by lowering the substrate temperature and the chamber pressure to annealing conditions.
85
Deposition was performed at 800 C. Annealing was at 720 C in vacuum (P < 10?4 Torr).
Thisproducedafilmwithasuperconductingtransitiontemperatureof6.4K.Thefilmwas
patterned such that it contained six consecutive regions prepared for Hall and resistivity
measurements (Figure 5.1). These regions were irradiated with protons with exposures
ranging from zero to 6.5 ? 1016/cm2 spaced at roughly equal intervals (0, 1.18, 2.32,
3.52, 4.72, 6.49 ?1016/cm2 of 2 MeV H+). The regions were irradiated by B. Weaver at
the Naval Research Laboratory. In Pr2?xCexCuO4??, this type of radiation, 2 MeV H+,
should primarily knock oxygen into interstitial sites from lattice sites, particularly from
copper-oxide plane lattice sites [85].
Figure 5.1: Patterned film for irradiation measurements (above) and oxygenation mea-
surements (below). A constant current is maintained in the central channel from current
leads attached at each end of the film. Voltage leads are periodically spaced along the
channel. The above film was irradiated in small patches such that consecutive voltage
leads could provide resistivity (or Hall) measurements corresponding to a single irra-
diation dose. Oxygenated films were patterned similarly (Figure 3.6), but had uniform
oxygen treatment across the entire film.
The oxygenated films were grown at two separate dopings (Table 5.1). A series of
films was grown with a x = .12 cerium concentration ceramic PCCO target and another
86
series was grown using an optimally doped PCCO target of Ce = .15. In each series
the atmosphere and annealing times were varied to produce a range of oxygen concentra-
tions in the final films. The least oxygenated films and the optimally grown films were
annealed in situ following deposition using the above described conditions. Films grown
to contain more oxygen were grown under higher partial pressures of oxygen and were
not annealed. These conditions were 230 mTorr N2O, no annealing; 230 mTorr O2, no
annealing; 400 mTorr O2, no annealing; and 600 mTorr O2, no annealing. In each case,
the films were held at the annealing temperature following deposition but the atmosphere
was not evacuated. After growth and any annealing, films were removed from the PLD
chamber and exposed to air only after they had cooled to room temperature.
In order to prepare the films for measurement, the films were patterned for resistiv-
ity, Hall effect, and angular magnetoresistance (AMR) measurements. Oxygenated films
were patterned either by ion milling or by acid etching. The irradiated film was ion-milled
due to the need for smaller size features in that film.
All films were measured in a Quantum Design Physical Property Measurement Sys-
tem (PPMS) in fields up to 14 T. Measurements were performed using standard four-wire
measurement techniques with contacts made by soldering 50?m gold wires to the film
surface with an silver/indium alloy. The film quality was monitored by characterizing
the films by both AC magnetic susceptibility measurements (where a Tc was present) and
X-ray diffraction.
The PPMS rotation option was used for angular magnetoresistance measurements
with the geometry such that the magnetic field was always in the ab-plane and the film
was rotated about the c-axis. These measurements have been used previously to examine
87
the N?eel temperature in PCCO [36]. All AMR measurements were performed at 14 T.
5.3 Results
Proton irradiation introduces disorder into the Pr2?xCexCuO4?? films. Therefore,
measurements of irradiated films characterize the effects of disorder on PCCO. Resistiv-
ity was measured in the irradiated samples from 2 K to 300 K in zero field across the
range of radiation exposures (Figure 5.2). At low temperatures the measurement was also
performed in field, where necessary, to suppress Tc in order to access the normal state re-
sistance. Increased irradiation increased the resistivity of the PCCO film and suppressed
Tc as well as exaggerating the low temperature resistivity upturn seen in under-doped
PCCO.
Hall effect data was also taken from 2 K to 300 K on the series of irradiated sam-
ples (Figure 5.3). These measurements were performed in a 14 T magnetic field applied
along the c-axis of the PCCO films. The polarity of the magnetic field was applied both
into and out of the plane of the film so that magnetoresistance effects could be removed
from the Hall measurement by subtracting the data sets as described in Chapter 3. Irradi-
ation produced a small suppressive change in the Hall resistivity, making it slightly less
negative. This indicates that the charge carrier concentration remains largely unchanged
due to disorder, and that disordering the film lessens conduction by introducing scattering
defects.
Oxygenatedfilmswerealsomeasuredaccordingtothesameprocedure(Figure5.4).
Both oxygen and irradiation increase the resistivity of the films, enhance the low temper-
88
Figure 5.2: Resistivity of an optimally grown and annealed x = .12 under-doped
Pr2?xCexCuO4?? film (Tc = 6.4 K) at different doses of irradiation. Irradiation levels
range from 0 to 6.5?1016 cm?2 of 2 MeV H+.
89
Figure 5.3: Hall effect of an optimally grown and annealed x = .12 under-doped
Pr2?xCexCuO4?? film (Tc = 6.4 K) at different doses of irradiation. Irradiation levels
range from 0 to 6.5?1016 cm?2 of 2 MeV H+.
90
ature resistive upturn, and suppress superconductivity. However, the two treatments show
clearly different behavior in Hall data (Figure 5.5). In a simple Drude model, the Hall
effect, RH = EyjxB = ?1ne, depends only on the number of charge carriers; accordingly
irradiation induced disorder does not have a significant effect on the charge carrier con-
centration in under-doped Pr2?xCexCuO4??, whereas oxygenation does have a significant
effect on the charge carrier concentration. This indicates that oxygenation significantly
dopes the film in addition to disordering it.
Figure 5.4: Added oxygen in x = .12 as-grown Pr2?xCexCuO4?? films (blue 230 mTorr
O2, green 600 mTorr O2) produces more resistive films compared with optimally grown
and annealed (black) and maximally irradiated (red) films.
Similar results were seen in optimally cerium doped films that were also produced
91
Figure 5.5: Added oxygen in x = .12 as-grown Pr2?xCexCuO4?? films (green 230 mTorr
O2, blue 400 mTorr O2, cyan 600 mTorr O2) strongly drives the Hall resistivity more
negative compared to optimally grown and annealed films (red). This behavior differs
both in magnitude and direction from irradiated films (black, maximally irradiated).
92
in a range of oxygen partial pressures (Figure 5.6) from optimal conditions, growth in
230 mTorr N2O followed by vacuum annealing, to highly over-oxygenated films, growth
in 600 mTorr O2 followed by no annealing. On all films, resistance measurements were
performedfrom2Kto300Kinzerofield. Liketheirradiatedfilms,theseover-oxygenated
films also show several behaviors that are indicative of increased disordering in the films?
crystal structure; a large increase in resistivity, a suppressed Tc, and an exaggerated low
temperature resistivity upturn are observed. The Tc is not yet fully suppressed in unan-
nealed samples (red curve, Figure 5.6), indicating that our growth conditions themselves
begin the annealing process since this is not observed in unannealed crystals.
Like for the x = .12 Pr2?xCexCuO4?? films, for optimally cerium doped (x =
.15) films, Hall measurements were performed from 2 K to 300 K in 14 T magnetic
fields (Hbardblc) on the range of film oxygenations grown (Figure 5.7). The Hall data show a
large increase in the magnitude of the Hall coefficient that is comparable to the shift seen
due to decreased cerium doping. Therefore, oxygenation is changing the charge carrier
concentration at a magnitude comparable to cerium doping. Doping is a significant effect
of oxygen concentration in Pr2?xCexCuO4??.
Oxygenation in x = .15 films is consistent with oxygenation in x = .12 films, and
both are consistent with x = .17 films [27]. Across the Pr2?xCexCuO4?? phase diagram,
oxygenadditionactstodopeintheoppositedirectiontoceriumaddition. However, unlike
cerium doping, doping by oxygen is also introducing significant disorder in the process.
The picture of oxygen significantly doping Pr2?xCexCuO4?? can be strengthened
by observing a doping-dependent property unrelated to superconductivity: antiferromag-
netism (AFM). Angular magnetoresistence was measured on oxygenated and irradiated
93
Figure 5.6: Resistivity of optimally doped (x = .15) Pr2?xCexCuO4?? films. Optimal
growth (230 mTorr N2O, vacuum annealing) to high O2 growth (600 mTorr O2, no an-
nealing).
94
Figure 5.7: Hall effect of optimally doped (x = .15) Pr2?xCexCuO4?? films. Optimal
growth (230 mTorr N2O, vacuum annealing) to high O2 growth (600 mTorr O2, no an-
nealing).
95
films according to the procedure given in Chapter 4. For this study, the irradiated films
were all x = .12 films, while the oxygenated films were both x = .12 and x = .15 films.
Films were rotated about the c-axis such that the magnetic field rotated through the ab-
plane. Magnetoresistance was measured from ? = 0? ? 360? and from ? = 360? ? 0?
at each temperature. The geometry of the experiment was constructed such that ? = 0?
was when the magnetic field was parallel to the b-axis (H bardbl [010]) and perpendicular to
the current, constrained to flow along the a-axis (H ? I, I bardbl [100]). This rotation pro-
duces an oscillation in magnetoresistance that is related to the antiferromagnetism of the
cuprates (Chapter 4). The amplitude of the resulting oscillations (Figure 5.8) decreases to
zero at the N?eel temperature (TN).
In oxygenated samples, the AMR signal shows an enhancement of the N?eel tem-
perature with increased oxygenation in x = .15 films (Figure 5.9). This is compared to
< 40 K for optimally grown and annealed x = .15 films (Figure 4.8). This is consistent
with the Hall effect data that show oxygen doping the material in the opposite sense to
cerium. The magnitude of the doping shift due to oxygen is similar between the two mea-
surement techniques. As all of the over-oxygenated films were as-grown (un-annealed),
changes in antiferromagnetism primarily involve adjustment of the oxygen concentration
rather than that of any of the other chemical elements found in Pr2?xCexCuO4??.
Similar to optimally doped Pr2?xCexCuO4??, oxygen addition also enhances the
N?eel temperature in under-doped, x = .12, Pr2?xCexCuO4?? (Figure 5.10). The ex-
act N?eel temperature is difficult to determine due to both increased thermal noise over
? 100 K and increased resistivity of heavily over-oxygenated films. However, weak
AMR oscillations are observable at 140 K, above the 100 K N?eel temperature of opti-
96
Figure 5.8: Angular magnetoresistance of an oxygenated x = .15 Pr2?xCexCuO4?? thin
film [36]. Oscillations are observed to go to zero between 110 K and 120 K.
97
Figure 5.9: Amplitude of AMR oscillations as a percentage of magnetoresistance vs tem-
perature for oxygenated x = .15 Pr2?xCexCuO4?? films. The temperature where the
amplitude first goes to zero corresponds to the N?eel temperature.
98
mal x = .12 films, suggesting consistent behavior between x = .12 and x = .15 over-
oxygenated films.
Figure 5.10: Angular magnetoresistance of an oxygenated x = .12 Pr2?xCexCuO4??
thin film grown in 600 mTorr O2. Oscillations are observed to be present above 110 K.
Optimally grown x = .12 has a N?eel temperature between 105 K and 110 K [36].
The angular magnetoresistance oscillations for Pr2?xCexCuO4?? x = .12 films
grown in 600 mTorr O2 disappear between 140 K and 170 K (Figure 5.11). This is equiv-
alent to a roughly .03 decrease in cerium doping, estimated from Figure 4.10. This is
comparable to the doping change seen in optimally doped x = .15 Pr2?xCexCuO4??
films grown in 600 mTorr O2 (Figure 5.9)
Oxygen enhancement of AFM could be counter-suggestive of oxygen as a disor-
99
Figure 5.11: Amplitude of AMR oscillations as a percentage of magnetoresistance vs
temperature for a oxygenated x = .15 Pr2?xCexCuO4?? film grown in 600 mTorr O2. The
temperature where the amplitude first goes to zero corresponds to the N?eel temperature.
100
dering influence since AFM, being an ordered state, is not disrupted by oxygenation.
However, irradiation does not significantly suppress the four-fold oscillations in AMR,
indicating that the AFM state in PCCO is fairly robust against disorder. Four-fold oscilla-
tions are present in both highly irradiated x = .12 (Figure 5.12) and in the non-irradiated
region of the same film (Figure 5.13). Irradiation induced disorder does not suppress anti-
ferromagnetism. As 2 MeV H+ irradiation primarily knocks oxygen out of in-plane sites
into interstitial sites, removal of planer oxygens does not suppress antiferromagnetism.
Figure 5.12: Angular magnetoresistance of an irradiated x = .12 Pr2?xCexCuO4?? thin
film. The film received a dose of 4.72?1016 cm?2 of 2 MeV H+ irradiation. This dose
corresponds to a Tc suppression of?8 K (extrapolated).
In both the irradiated (Figure 5.14) and non-irradiated (Figure 5.15) regions of the
101
Figure 5.13: Angular magnetoresistance of an un-irradiated x = .12 Pr2?xCexCuO4??
thin film. This is the same film as Figure 5.12, but was not irradiated at this spot (Tc =
6.5 K).
102
x = .12film, the amplitude of the angular dependence of the magnetoresistance decreases
to zero between 100 K and 110 K, indicating a N?eel temperature between these two tem-
peratures. The N?eel temperature seems to vary little with irradiation induced disorder, or
with irradiation induced absence of in-plane oxygens caused by 2 MeV H+ irradiation.
The antiferromagnetism in Pr2?xCexCuO4?? is, however, sensitive to doping by cerium.
Therefore, because the N?eel temperature is largely insensitive to disorder, but sensitive to
doping; oxygen enhancement of TN is a doping effect.
Figure 5.14: The amplitude of angular magnetoresistance oscillations (seen in Fig-
ure 5.12) of a heavily irradiated x = .12 Pr2?xCexCuO4?? thin film. Zero amplitude
above 110 K shows a N?eel temperature between 100 K and 110 K.
103
Figure 5.15: The amplitude of angular magnetoresistance oscillations (seen in Fig-
ure 5.13) of a un-irradiated x = .12 Pr2?xCexCuO4?? thin film. Zero amplitude above
110 K shows a N?eel temperature between 100 K and 110 K.
104
5.4 Discussion
The Hall effect and angular magnetoresistance oscillations show oxygen to be a
significant dopant in Pr2?xCexCuO4??. Resistivity data show significant disordering in
the Pr2?xCexCuO4?? films as well. These positions are supported by comparison with
intentionally-disordered irradiated films, which show significant disordering in resistiv-
ity and little change in Hall effect or angular magnetoresistance data. Annealing is also
shown to be primarily about removing apical oxygen. Irradiation does not suppress anti-
ferromagnetism, despite knocking oxygen out of the CuO2 plane, and antiferromagnetism
inas-grownoxygenatedsamplesbehavesconsistentlywithannealedfilms, despitenotun-
dergoing an annealing step. These two conclusions are discussed below.
PCCOfilmsbecomemoreresistivewithincreasingirradiationanddevelopastronger
low temperature upturn in resistivity. Both of these effects indicate that irradiation adds
disorder to the system. Additionally, Hall effect measurements on irradiated films only
show a small positive shift in the Hall effect, indicating that the total number and sign of
charge carriers remain largely the same with irradiation. Charge carrier concentrations are
not supposed to change in the irradiated films as the main effect of 2 MeV H+ irradiation
is to knock oxygen into interstitial sites from lattice sites, especially in the copper-oxide
plane [85]. Little change due to irradiation is seen in angular magnetoresistance, sug-
gesting nearly no suppression of antiferromagnetism due to disorder. The angular mag-
netoresistance results will be discussed at length below. Irradiating underdoped PCCO
(x = .12) suppresses Tc at a rate of??2 K per 1.2?1016 2 MeV H+/cm2.
It is well known that Pr2?xCexCuO4?? must be annealed after initial growth in order
105
to achieve superconductivity and that this post-annealing step is oxygen-reducing. One
effect of this annealing step ought to be reducing oxygen disorder in the films. Disorder
due to off-stoichiometric oxygen concentration should be detrimental to superconductiv-
ity. Either adding additional oxygen or excessively removing oxygen would then have
similar disordering effects. Explicitly over-annealing PCCO creates more resistive films
with stronger low temperature upturns in resistivity. Tc is also suppressed in these films,
further suggesting a disordering effect. This is consistant with previous work on the
overdoped Pr2?xCexCuO4?? x = .17 system [27]. However, Tc suppression could be
consistent with oxygen as a dopant as well, because, in a simple ionic picture, O2? should
hole dope while Ce4+ electron dopes. Oxygen doping should dope under-doped PCCO
away from optimal doping. Measurements of the Hall effect on over-oxygenated films are
not consistant with oxygen causing disorder like irradiation. Unlike irradiation, oxygen
strongly changes the magnitude of the Hall effect both in magnitude and direction. Hall
data suggest that oxygen dopes the material in the opposite direction of cerium doping.
Additional oxygen should dope Pr2?xCexCuO4?? independent of where it is incor-
porated into the crystal lattice. As-grown (and therefore over-oxygenated) crystals have
excess oxygen initially and need to be reduced toward 4 + ? = 4 for superconductivity,
rather than growing stoichiometrically and being reduced to 4?? < 4 [79]. Therefore,
over-oxygenating the crystal should fully populate all of the oxygen lattice sites in the
CuO2 and PrO layers and start filling apical oxygen sites. In the x = .17 system it was
proposed that this is the dominate source of oxygen-induced disorder [27]. Irradiation
by 2 MeV protons knocks CuO2 plane oxygens into apical sites [86] and produces dis-
order similar to oxygenation. This suggests that a major component of disorder in either
106
irradiated or oxygenated films is the presence of apical oxygens. Optimal annealing to
achieve superconductivity, therefore, is likely removing apical oxygens in order to reduce
the disorder they create.
Additionally, this doping effect due to oxygen seems to be a quite general effect.
The magnetic properties of Pr2?xCexCuO4?? also respond to oxygen as a dopant with
an enhanced N?eel temperature seen in over-oxygenated samples. Oxygen does introduce
some disorder and therefore might be expected to suppress TN, due to AFM being an
ordered state. The enhanced N?eel temperatures seen in over-oxygenated samples suggest
either that oxygen?s disordering effect does little to frustrate antiferromagnetism, or that
oxygen doping overpowers oxygen disorder in PCCO?s magnetic structure. AMR mea-
surements of irradiated films suggest the former. Spin dilution, the mechanism by which
doping suppresses antiferromagnetism in the electron-doped cuprates, could be relatively
insensitive to disorder. Doping in the electron-doped cuprates takes place in the Cu d-
orbital, effectivelychanging3d9 to3d10, whichisspinless[21]. Inthesematerials, Cedop-
ing on the Pr sites does not suppress antiferromagnetism by disorder, but by spin-dilution
where fewer and fewer Cu atoms have a magnetic moment until long range antiferromag-
netism cannot be maintained. Irradiation from 2 MeV protons cause little change in the
total number of charge carriers in the system, as seen in the Hall effect data (Figure 5.3).
The angular magnetoresistance data on irradiated x = .12 Pr2?xCexCuO4?? show that
the N?eel temperature also shows little sensitivity to disorder (Figures 5.14, 5.15). De-
spite AFM being an ordered state, its suppression via spin-dilution depends much more
strongly on the number of charge carriers than on disordering of the crystal lattice.
AFM?s robustness with respect to disorder could, however, be due to the dose of
107
irradiation since X-ray diffraction (XRD) was unable to distinguish between differently
irradiated regions of PCCO. Radiation dose is difficult to translate into a density of point
defects; however, the maximally oxygenated film is significantly more resistive than the
maximally irradiated film (Figure 5.4). A x = .15 film grown in 600 mTorr O2 looks
similar to a x = .11 film in Hall and AMR data. Therefore, oxygen doping in this
study covered a doping range equivalent to several percent cerium doping. Irradiation is
unlikely to introduce a much larger concentration of defects than this level of additional
oxygen as the increased scattering would be seen in resistivity data. On the other hand,
severalpercentceriumdopinghasclearlymeasurableeffectsinthecuprates. Forexample,
the doses of irradiation used in this study were large enough to have significant effect on
Tc, indicating sufficient disorder to disrupt ordered states. Therefore, it is likely that
AFM?s insensitivity to irradiation in PCCO is due to crystal defects contributing little to
spin-dilution.
Both Hall effect and angular magnetoresistance data suggest that oxygen has a sig-
nificant doping effect. This conclusion seems to be at odds with ARPES data on as-grown
and oxygen-reduced films which show no significant change in the electronic filling nor
in the band structure parameters but does show significant reduction of long-range anti-
ferromagnetic order [87]. In that study; however, the comparison was between as-grown
and optimal films, which is a much smaller range of oxygen doping than investigated
here. For example, the green and blue curves in Figure 5.6 are as-grown and optimal
films respectively; this represents a much smaller range of oxygenation than between my
optimal and maximally oxygenated films. The large change in antiferromagnetism seen
by Richard et al. [87] can be understood due to their study?s focus on optimally cerium
108
doped films. Near optimal doping, the N?eel temperature changes rapidly with doping
(Figure 4.10). When vextendsinglevextendsingledTNdx vextendsinglevextendsingle is large, small changes in doping will strongly affect antifer-
romagnetism; theN?eeltemperatureismuchmoresensitivetodopingnearoptimaldoping.
It is likely, therefore, that ARPES would show a significant change in the Fermi surface
due to oxygenation if it were investigated over a larger range of oxygen.
In addition to the question of whether oxygen is primarily doping or disordering
Pr2?xCexCuO4??, the related question of the role of annealing can be addressed by these
measurements. The three scenarios presented were: first, annealing could remove api-
cal oxygens from interstitial lattice sites, thereby reducing disorder and allowing super-
conductivity; second, annealing could remove in-plane oxygens from the CuO2 planes,
thereby suppressing antiferromagnetism and allowing superconductivity; and third, an-
nealing could allow migration of copper atoms, thereby healing defects in the CuO2
planes and allowing superconductivity. These three scenarios are discussed here.
Theideathatannealingremovesapicaloxygensissupportedbytheover-oxygenated
samples. Samples that are strongly oxygenated should have O(1) and O(2) sites fully pop-
ulated andO(3) sites populatedwell above the4% to10% levelsin annealed andas-grown
crystals [24, 26]. Strongly over-oxygenating Pr2?xCexCuO4?? shows that transport prop-
erties, Tc and normal state resistivity, degrade in a consistent manner among annealed,
as-grown, and over-oxygenated films. This indicates that annealing effects are clearly re-
lated to oxygenation effects. As apical sites are non-standard lattice sites, and, therefore,
disorder, it is likely that the oxygen in question is apical. These measurements support
the picture that has been proposed [25, 27, 82, 83] whereby annealing seems to allow su-
perconductivity through a reduction in disorder caused by removing apical oxygens from
109
interstitial lattice sites.
The idea that annealing removes planer oxygens is contradicted by the irradiated
samples. Samples that were irradiated by 2 MeV H+ irradiation should have lattice oxy-
gens knocked into interstitial sites; this irradiation especially targets lattice oxygens in
the copper-oxide plane [85]. Oxygen, therefore, is removed from planer lattice sites by
irradiation. Yet despite this, antiferromagnetism is not suppressed in irradiated films (Fig-
ure 5.15) compared to non-irradiated films (Figure 5.14). As the suppression of antifer-
romagnetism in the electron-doped cuprates is due to spin dilution and is most sensitive
to doping level, no change in antiferromagnetism due to this type of oxygen movement
would be expected in the absence of a special role played by in-plane oxygens. This
indicates in-plane oxygens are not a major influence on antiferromagnetism, unlike as
suggested in the picture [28, 29] where annealing allows superconductivity through the
suppression of antiferromagnetism by removing O(1) oxygens from in-plane lattice sites.
One objection to this argument is that knocking in-plane oxygens into interstitial
sites is, basically, a Frenkel defect. These defects do not change the net composition of
the material, keeping the doping level the same. This might then suggest that there should
be no change in antiferromagnetism because antiferromagnetism suppression by removal
of in-plane oxygens is compensated by antiferromagnetism enhancement due to doping
from the additional interstitial oxygen. This, however, would be a surprising coincidence
if in-plane and out-of-plane oxygens play quite different roles in the antiferromagnetism
in the material. If in-plane oxygens are more significant for antiferromagnetism than out-
of-plane oxygens, the in-plane oxygen vacancies should not be compensated for by equal
numbers of out-of-plane oxygens. Therefore, seems unlikely that the in-plane and out-
110
of-plane oxygens play significantly different roles with respect to antiferromagnetism in
the crystal structure. AFM suppression due to in-plane oxygen vacancies and AFM en-
hancement due out-of-plane oxygen interstices are so well balanced that there is almost
no change in antiferromagnetism between irradiated and non-irradiated films. Removal
of apical oxygen suppresses TN just as much as removal of in-plane oxygen does; how-
ever, apical oxygen removal removes disorder from the crystal lattice whereas in-plane
oxygen removal adds disorder to the crystal lattice. The former would be more helpful to
superconductivity than the latter; there seems to be no distinction for antiferromagnetism
between O(1) and O(3) oxygens. Therefore, it is likely that annealing is not allowing
superconductivity by suppressing antiferromagnetism by removing in-plane oxygens.
The idea that annealing fixes copper vacancies is contradicted by the oxygenated
as-grown films. Samples that were never annealed, but were only deposited in different
atmospheric pressures of oxygen show significantly different doping levels and N?eel tem-
peratures at different oxygen concentrations (Figures 5.5 and 5.9). This implies that an-
nealing is not important for the number of charge carriers or antiferromagnetism because
none of the oxygenated films are annealed and, therefore, that the effects of annealing on
doping and antiferromagnetism are solely due to oxygen. Both in the x = .12 series and
in the x = .15 series there is a continuous evolution of resistivity, Hall effect, and AMR
from annealed to as-grown to over-oxygenated films, indicating that annealing effects are
oxygen effects. This suggests that non-oxygen-related annealing effects are not a major
influence in Pr2?xCexCuO4??, unlike as suggested in the picture [31] where annealing
allows superconductivity through the healing of copper vacancies in the copper-oxide
planes.
111
One complication to the argument is that as-grown films, in otherwise optimal con-
ditions, do have a (low) Tc. This indicates that the deposition process itself is partially
annealing the films as crystals do not behave in this way. However, both x = .12 and
x = .15 films show the same trend in the oxygen series of films in resistivity, Hall effect,
and angular magnetoresistance. The two cerium dopings studied, x = .12 and x = .15,
anneal at different rates, as seen by the 20 to 25% difference in annealing times neces-
sary to produce optimal films. If annealing during growth is significant, the two dopings
should behave in noticeably different ways. In both systems, oxygenation from optimal
to 600 mTorr O2 growth results in a .03 reduction in effective cerium doping in both
Hall effect (Figures 5.7 and 5.5) and angular magnetoresistance data (Figures 5.9 and
5.11 as compared to Figures 4.8 and 4.5 respectively). This indicates that oxygenation
overwhelms any intrinsic annealing; otherwise, an x = .12 film should not be doped by
oxygen the same as an x = .15 film, based upon different annealing rates. Therefore,
intrinsic annealing can be neglected as not significant in the oxygenated films. The dif-
ferences in properties in both of the oxygenated series are therefore due to oxygenation.
The fact that annealed film behavior is consistent with the trend seen in un-annealed as-
grown over-oxygenated films suggests that annealing is an oxygen effect. Therefore, it is
likely that annealing is not allowing superconductivity by healing copper vacancies in the
copper-oxide planes.
Several different scenarios for the role of annealing in leading to superconductiv-
ity in the electron-doped cuprates have been proposed: disorder reduction by removal
of apical oxygens, antiferromagnetism suppression by removal of in-plane oxygens, and
CuO2 plane-healing migration of copper atoms. Scenario two is addressed by angular
112
magnetoresistance measurements on irradiated films. These suggest that removing oxy-
gen from the CuO2 plane does not suppress antiferromagnetism; therefore, this scenario
is unlikely. Scenarios one and three are addressed by over-oxgenated films. These films
are un-annealed and differ only in the growth atmosphere?s oxygen concentration. There-
fore, transport properties in these films evolve due to oxygen concentration. That these
oxygenated and un-annealed films show a consistent trend with annealed films strongly
suggeststhatannealingisanoxygeneffect. Withregardstoscenariothree, thefactthatthe
over-oxgenated films are un-annealed, and behave consistently with annealed films, sug-
gests that annealing is unlikely to have significant non-oxygen-related effects; therefore,
scenario three is unlikely. Regarding scenario one, over-oxygenation should likely fully
populate the oxygen lattice sites, O(1) and O(2), and add significant oxygen to the apical
O(3) site. This suggests that the transport properties of over-oxgenated films evolve due
to apical oxygen concentration. That these oxygenated films show a consistent trend with
annealed films strongly suggests that annealing is not only an oxygen effect, but likely an
apical oxygen effect; therefore, scenario one seems to be the best model to describe our
data. In contrast to models predicting significant changes to the copper-oxide plane dur-
ing the annealing process, our transport data suggest that removal of apical oxygen is the
primary role of annealing and the reduction in crystal disorder do to this removal is then
suggested as the main factor in the emergence of superconductivity in the electron-doped
cuprate superconductors.
In conclusion, both disordering Pr2?xCexCuO4?? thin films as well as oxygenating
them produce a disordering effect as seen by an increase in resistivity and suppression
of Tc. However, oxygenation of PCCO significantly changes the Hall effect resistivity as
113
compared to irradiative disordering. Irradiation shows little change in the Hall resistiv-
ity, consistent with a pure disordering effect. Oxygen does not; it shifts the Hall effect
significantly, indicating a change in the number of charge carriers. While oxygenation of
PCCO does show a disordering effect, oxygen primarily acts as a dopant in PCCO.
Additionally, oxygenation of Pr2?xCexCuO4?? thin films supports the picture that
the annealing step in electron-doped superconducting cuprate synthesis is primarily due
to removing apical oxygen. A lack of irradiation-induced suppression of TN and the
consistent evolution of transport properties between annealed samples and a series of
un-annealed as-grown over-oxygenated samples contradict other proposed models for an-
nealing in the electron-doped cuprates.
114
Chapter 6
Tc Enhancement in Electron-Doped Cuprate Heterostructures
6.1 Introduction
Superconductivity in the cuprates is normally accomplished by doping into the
CuO2 plane. Counterintuitively, another method for inducing higher Tc superconduc-
tivity in the cuprates is to pair under- and over-doped cuprates. The close proximity of
the different dopings contributes to an enhanced Tc. On the hole-doped side of the phase
diagram, it has been shown that there can be an enhancement in Tc by pairing metallic
and insulating cuprates [88, 89]. Similar behavior has been reported at the interface of
different dopings of La2?xSrxCuO4?? (LSCO) [90, 91]. It has been proposed that the Tc
enhancement seen in these cases could arise from a combination of the under-doped side
of the phase diagram providing a large pairing amplitude and the over-doped side of the
phase diagram providing phase stiffness [92, 93].
This effect had not been seen on the electron-doped side of the cuprate phase dia-
gram. The electron-doped cuprates are known to show a phase fluctuation Nernst signal
above Tc on the under-doped side of the superconducting dome [74]. If the picture of
a large under-doped pairing amplitude stabilized by over-doped phase stiffness is cor-
rect, the Nernst fluctuations suggest a Tc enhancement on the electron-doped side as well.
However, this Nernst signal is weaker on the electron-doped side than it is on the hole-
doped side and therefore the enhancement should be much smaller.
115
In order to investigate this effect, several heterostructures of the electron-doped
cuprates, Pr2?xCexCuO4?? and La2?xCexCuO4??, were fabricated. This discussion will
berestrictedtoheterostructuresthattaketheformofsuperlatticethinfilmswheremultiple
layers of under- and over-doped cuprates were stacked. Other heterostructures (e.g., bi-
layers) were not investigated in similar detail, but do seem to exhibit similar physics.
In both Pr2?xCexCuO4?? and La2?xCexCuO4?? superlattice thin films, an unex-
pected large enhancement in Tc was observed; although, the superlattice Tc was never
higher than optimal single-doping Tc [94]. This effect was observed for multiple pair-
ings of under-doped and over-doped layers. Our measurements indicate that the Tc en-
hancement is due to simple charge redistribution rather than any of the theoretical models
mentioned above.
6.2 Superlattice Film Preparation
Superlatticefilmswereproducedaslayersofunder-andover-dopedcuprates. These
layers were layered along the c-axis of the crystal structure, i.e., the ab-planes of the
under- and over-doped layers are coplaner (Figure 6.1). This stacking of the different
film layers was achieved during the pulsed laser deposition (PLD) growth of the thin
films. This required some modification of the pulsed laser deposition process described
in Chapter 3.
For the Pr2?xCexCuO4?? superlattice films discussed here, the over-doped layer
was always x = .19. Less over-doped Pr2?xCexCuO4?? over-doped layers do show some
Tc enhancement, but were not systematically investigated. Less over-doped layers have
116
Figure 6.1: Schematic of the superlattice structure grown. Films were grown on SrTiO3
(STO) substrates with alternating layers of under-doped and over-doped superconductors.
The primary pairings grown and investigated were in the Pr2?xCexCuO4?? system x =
.19 paired with either x = .00, x = .11, or x = .12 and in the La2?xCexCuO4?? system
x = .06 paired with either x = .17, x = .19, or x = .21.
117
higher Tcs themselves; .12/.17 superlattice films have Tcs that are only slightly higher
than those of single-doping x = .17 films.
With the over-doped layer fixed at x = .19, the under-doped layer focused on was
x = .00 and, to a lesser extent, x = .11 and x = .12. The highest Tc obtainable for single
doping films is less than 10 K (0 K for x = .00, 0 K for x = .11, ? 6 K for x = .12, and
? 8 K for x = .19), while the .00/.19, .11/.19, and .12/.19 superlattice films have Tcs of
at least 14 K.
6.2.1 Superlattice Film Growth
The pulsed laser deposition process grows epitaxial thin films with the concentra-
tion supplied by the target. In order to prepare the superlattice films, the PLD chamber
was modified to allow two targets by replacing the original target holder with a carousel
capable of holding up to six targets. Rotation of this carousel allowed any individual tar-
get to be rotated into or out of the path of the ablating laser. The films grow along the
c-axis at a rate of an ?angstr?om per few laser pulses. The targets were alternated such that
each target was (typically) ablated for one minute. At 10 pulses per second, the films
grow roughly 20 ?A in one minute.
One minute per target nominally produces superlattices with 20 ?A layers, although
the necessary time for a given thickness can be quite variable based upon the fluency of
the laser. For example, many of the superlattice films were grown for longer times at
a lower laser power prior to power-boosting laser maintenance. Superlattice films were
grown with a range of layer thicknesses, for example 5 nm, 10 nm, or 20 nm layers,
118
and at a range of total thicknesses, with 20 total layers being the most typical. Generally,
superlatticefilms weregrown withequallythick layersofunder- andover-doped material.
The typical film also was terminated with the over-doped layer, regardless of whether the
initial layer was under- or over-doped.
The top-most layer was over-doped due to the greater conduction in the over-doped
compared to the under-doped layer, especially when the under-doped layers were un-
doped Pr2CuO4 (PCO). The un-doped parent compound is quite insulating and, at low
temperatures, exceedsthemeasurementrangeaccessiblebytheQuantumDesignPhysical
Properties Measurement System (PPMS). When attaching electrical leads to the films,
films are top contacted; by having the top layer be over-doped, an insulating PCO cap
layer could not prevent current from flowing.
Like other films grown by PLD, the oxygen content of the superlattice films was ad-
justed by a post-deposition annealing step. It was found that the annealing conditions ap-
propriate for single-doping films were not optimal for superlattice films (Figure 6.2). The
highest transition temperatures were achieved for anneals that were significantly longer
than either individual layer?s optimal annealing time. This is suggestive of oxygen behav-
ior in the superlattice films differing from the single phase films.
SimilarfilmswerealsopreparedintheLa2?xCexCuO4?? system. InPr2?xCexCuO4??,
the highest doping accessible is x = .19; the under-doped layer is more adjustable. In
La2?xCexCuO4??, the lowest doping accessible is x = .06; the over-doped layer is more
adjustable. A Tc enhancement was also found in this system for combinations of under-
doped and over-doped films.
119
Figure 6.2: Superconducting transition temperature, Tc, compared to annealing time for
a .00/.19 Pr2?xCexCuO4?? superlattice thin film. The transition temperature is elevated
compared to the Tcs of both constituent layers. Tc is relatively insensitive to annealing
time and can be annealed for much longer than single layer films. The arrows indicate
the optimal annealing times for single-doping x = .15 and x = .19 Pr2?xCexCuO4?? thin
films.
120
6.2.2 Superlattice Film Characterization
In order to investigate the Tc enhancement in the electron-doped cuprate superlat-
tice films, it was necessary to verify that the films grown by pulsed laser deposition were,
in fact, layered structures. It could have been that the cerium content could have redis-
tributed and formed a uniform film of intermediate doping. If this were the case it would
probably increase Tc due to the optimal single-doping film having a higher Tc than either
superlattice component.
The superlattice films were characterized by X-ray diffraction after growth. These
measurements were primarily ? ?2? scans on a Bruker D8 X-ray diffractometer. It was
observed that, in addition to the expected Pr2?xCexCuO4?? X-ray diffraction peaks, there
were additional satellite peaks around the main 00lscript peaks. These were observed in both
Pr2?xCexCuO4?? (Figure 6.3) and in La2?xCexCuO4?? (Figure 6.4). These satellite peaks
are due to additional periodicity along the c-axis and correspond to the expected layer
thicknesses of the superlattice films grown by pulsed laser deposition.
Satellite peaks arise due to the modulated structure in the superlattice and their
presence is evidence for the formation of distinct superlattice layers. The periodicity of
the superlattice, ?, can be calculated by ? = ?/2(sin?i ?sin?i+1), where i indexes the
satellite peaks [95, 96, 97, 98]. The periodicity is due to different c-axis lattice parameters
in the under-doped and over-doped layers. X-rays fully penetrate these thin films; there-
fore, all planes are participating in constructive (or destructive) interference. If there are
small changes in lattice spacings between layers, the interference peaks between one pair
of crystal planes will be at a slightly different angle than those of another pair. Typically,
121
this causes a broadening of X-ray diffraction peaks as all of these slight angle differences
are uncorrelated and cluster closely around the average value, producing a sharp peak
with some non-zero full-width half-max value. In superlattice heterostructures, the slight
differencesinspacingbetweenlayersarenotuncorrelated; thesatellitepeaksareevidence
of regular deviations from the average c-axis lattice spacing.
Figure 6.3: Satellite peaks in a .00/.19 Pr2?xCexCuO4?? superlattice thin film. The
main peak is the 006 peak of Pr2?xCexCuO4?? and gives a c-axis lattice constant around
12.18 ?A, suggesting a cerium content of x = .08 to x = .10. The superlattice film was
grown with a nominal superlattice periodicity of 10 nm. The satellite peaks (labeled ?)
correspond to a 99.2 ?A periodicity along the c-axis. This is showing evidence for super-
lattice formation.
The films were also characterized by AC susceptibility (AC?). The superlattice
films show magnetic screening comparable to the single layer films as seen in the real
122
Figure 6.4: Satellite peaks in a .06/.19 La2?xCexCuO4?? superlattice thin film [94]. The
008 and 0010 X-ray diffraction peaks show superlattice satellite peaks that are due to
cerium modulation.
123
component of AC? (Figure 6.5). These measurements were performed in a dip-probe in
a liquid helium storage dewar.
Figure 6.5: The real component of the AC susceptibility of a .00/.19 Pr2?xCexCuO4??
superlattice film compared to a .15 film. The superlattice film shows saturating behavior
similar to the single layer film. This is indicative of a large volume fraction superconduc-
tivity and suggests that superconductivity is a bulk effect in the superlattice films.
Resistivity of the superlattice films was also measured (Figure 6.6). Even films with
insulating x = .00 Pr2?xCexCuO4?? layers show metallic behavior and an elevated Tc.
The normal state resistance indicates that either the over-doped layer is shorting out the
more insulating under-doped layer or some charge redistribution has occurred and the su-
perlattice is behaving like some intermediate doping. According to the X-ray diffraction
124
data (Figure 6.3), the most ?average? doping is in the range x = .08 to x = .10. This
is due to the X-rays diffracting off of all layers, so slight variations in the c-axis lattice
parameter between layers get smeared out, and the main peak corresponds to the average
c-axis lattice constant. Single phase films of these dopings however, are not supercon-
ducting and have large low-temperature resistivity upturns. For .11/.19 and .12/.19 su-
perlattice films, the ?average? doping is closer to x = .15 or x = .16; however, .00/.19
does not behave substantially differently.
Figure 6.6: Typical resistance vs temperature curve for a .00/.19 Pr2?xCexCuO4?? super-
lattice film. The Tc of x = .19 is? 8 K; x = .00 has no Tc.
125
6.3 Results
ItwasfoundthatsuperlatticefilmsdoshowanenhancedTc,butthisTc-enhancement
is probably due to charge redistribution rather than the interface effect of the various theo-
retical proposals. The superconducting transition temperatures in both Pr2?xCexCuO4??
and La2?xCexCuO4?? superlattices are enhanced relative to the Tcs of the constituent
dopings. This was found in both Pr2?xCexCuO4?? (Figure 6.6) and in La2?xCexCuO4??
(Figure 6.7a). In neither system, however, did the superlatticeTc ever surpass theTc of the
single-doping optimally doped film. The possibility of using superlattices to surpass the
optimal Tc of a material was reported in La2?xSrxCuO4?? bi-layers [90]. More recently,
however, that result was not reproduced, although a more modest Tc enhancement was
seen [91].
In the PCCO and LCCO systems, different pairings of dopings were used. For
LCCO, the under-doped layer was held constant at x = .06 and the over-doped layer
was varied, x = .17,.19,.21 (Figure 6.7b). LCCO cannot be doped more lightly than
x = .06 as contaminant T phase LCCO is preferred, but it can be doped beyond the
superconducting dome. This system was, therefore, used to investigate the dependence
ontheover-dopedlayerforsuperlatticesuperconductivity. Thechoiceofover-dopedlayer
matters little for the superlattice Tc. For PCCO, the over-doped layer was held constant
at x = .19 and the under-doped layer was varied, x = .00,.11,.12 (Figure 6.7c). PCCO
cannot be doped more heavily than x = .19, but can be doped below the superconducting
doping range. This system was, therefore, used to investigate the dependence on the
under-doped layer for superlattice superconductivity. The choice of under-doped layer
126
matters little for the superlattice Tc.
Figure 6.7: (a) Resistivity of a .19/.06 La2?xCexCuO4?? superlattice film compared with
x = .06, x = .11 (optimal), and x = .19 LCCO superlattice films [94]. Tc is enhanced
relative to constituent dopings. In LCCO this is observed for several x/.06 superlattices
(b) and for PCCO this is observed for several x/.19 superlattices (c). The maximum Tc
of each of these superlattice pairings (square) is higher than that of the single-doping, x, films
(triangle). The?is a bi-layer film.
6.4 Discussion
In each system, the superlattice Tc was also found to be insensitive to the thick-
ness of individual layers, from 5 nm to 20 nm. This observation suggests that possible
127
strain enhancement of Tc is unlikely. Thin films are strained relative to bulk crystals due
to lattice mismatch with the substrate. (In the case of LCCO in particular, this substrate
strain effect allows the superconducting Tprime phase to be stabilized.) Strain-induced super-
conductivity could be an explanation for superlattice superconductivity as there are more
interfaces for potential lattice mismatches. However, this picture is unlikely due to the
fact that layer thickness did not significantly alter superlattice Tc. Interface strain effects
ought to decrease farther away from the interface, implying stronger effects for thinner
layers than for thicker ones. This trend was not seen.
In each system, superlattice Tc was also found to be insensitive to the number of
individual layers, from 6 to 40. This suggests that the Tc enhancement seen in the super-
lattice films may not be an interface effect between the two layers, but is rather caused
by some long-range charge distribution. Our critical current measurements (discussed
below) prove this is true. Varying the number of layers varies the number of interfaces.
If the highest Tc were only found at the interfaces (or in a narrow region around the in-
terfaces), the effective thickness of the superconducting regions of the films would be
thinner. This would not affect the Tc seen by resistivity as any superconducting path
between contact leads would short out non-superconducting regions; however, it would
limit the total current that could pass through the film, reducing the critical current of the
superlattice.
The critical current, Ic, was determined for La2?xCexCuO4?? superlattices of dif-
ferent layer thicknesses by measuring the current (I) - voltage (V) characteristics of the
superlattice thin films (Figure 6.8a). In the superconducting state, current flow does not
produce a voltage drop. This can be seen directly from Ohm?s Law, V = IR, when
128
R = 0 ? as in a superconductor. Too much current, however, will destroy supercon-
ductivity; the critical current is the current that completely suppresses superconductivity.
The critical current can be thought of as a consequence of the upper critical field, Hc2. A
current, I, will produce a tangential magnetic field H = I/2pir; if H > Hc2, the field
produced by the current will suppress superconductivity.
The critical current density, Jc = Ic/(w ? t), where w and t are respectively the
width and thickness of the current bridge on the patterned films, was measured for several
different numbers of layers, n (Figures 6.8b, 6.8c). Jc does not depend upon the number
of layers in the superlattice; therefore, the superconductivity cannot be confined to the
interface between over-doped and under-doped layers. If superlattice superconductivity
were an interfacial effect, then it would be expected that Jc = n ? Jinterfacec because
parallel conduction paths divide current.
The superlattice Jcs are, however, less than the single phase film with comparable
Tc, x = .11(Figure 6.8d). If charge is redistributed in some fashion similar to Figure 6.8e,
some sub-region of the film is locally nearly optimally doped. This highest Tc region
of the film then determines Jc and occupies some fraction of the total film thickness:
Jc = 1m ? Jprimec(Tmaxc ). Jc does depend moderately on the choice of over-doped layer
(Figure6.8d). Thisdependenceontheover-dopedlayerdopingsuggeststhatthelargerthe
doping range, the smaller the nearly optimally doped fraction of the film. This fraction,
1/m, does not depend upon the number of layers because charge redistributes spatially
over the entire layer. If the total thickness is constant, a .21/.06 superlattice film with
any number of layers gives the same total thickness of both x = .21 and x = .06 regions
as any other number of layers. The range of doping that charge has to redistribute over
129
matters more than the spatial range that charge has to redistribute over.
The spatial range of charge redistribution suggests that charge redistribution may
not be uniform or that it may involve migration of dopants like oxygen. The Thomas-
Fermi screening length in the cuprates is estimated to be 6 ?A [89] to 10 ?A [94]; our
superlattice results suggest charge redistribution occurs over at least 20 nm. This anoma-
lously long charge redistribution length is not well understood. Long charge redistribu-
tion lengths may suggest that superlattice films do not redistribute to a single doping,
but rather continue to have some variable charge concentration with depth (Figure 6.8e).
Long charge redistribution lengths could also suggest that there is some physical migra-
tion of dopant atoms in the superlattice films; this would likely suggest oxygen movement
during annealing.
Because Jc does not depend upon the number of interfacial layers, the possibility
of surface superconductivity at the interface is excluded. This suggests some manner
of charge redistribution as the mechanism for superlattice superconductivity. Charge re-
distribution is unlikely to be due to cerium redistribution because the X-ray diffraction
satellite peaks (Figures 6.3, 6.4) require a structural periodicity in the crystal lattice. This
modulation is also seen more directly through electron energy-loss spectroscopy (EELS)
(Figure 6.9). X-ray diffraction data also show that the c-axis lattice parameter for the su-
perlatticefilmsapproachesthatoftheoptimallydopedsingle-dopingfilmswithincreasing
Tc (Figure 6.10). This suggests that charge redistribution occurs with some effect similar
to cerium substitution in single-phase films.
Charge redistribution can also be investigated by Hall effect and angular magne-
toresistance measurements. The Hall effect can give the number of charge carriers and is
130
Figure 6.8: (a) I-V curves of a 40-layer .19/.06 La2?xCexCuO4?? superlattice [94]. The
critical current densities for x/.06 for x = .19 different numbers of layers, n, ((b), (c))
and for n = 10 with different over-doped layers (d). Charge count (PZ) varying along the
c-axis (Z) is proposed in (e).
131
Figure 6.9: Electron energy-loss spectroscopy (EELS) of 0.19/0.06 La2?xCexCuO4??
superlattice. The intensity is of Ce 3d3/2 which is a measure of cerium concentration.
thus sensitive to the overall doping of the material. Observation of angular magnetoresis-
tance oscillations indicates magnetic ordering and, therefore under-doped regions due to
an antiferromagnetic quantum phase transition in Pr2?xCexCuO4?? near optimal doping.
If there were strong charge redistribution, the films should behave electronically as
though there is a single conduction channel of intermediate doping due to charge redistri-
bution diluting the over-doped layer and fortifying the under-doped layer such than they
have a single effective doping. Therefore, if the charges were fully redistributed between
the layers, i.e., the x = .00 and x = .19 layers redistributed to form a single x ? .10
layer, this would cause the film to behave as a single layer film of x ? .10. A film with
this ?average? doping would be identifiable in both Hall effect and angular magnetoresis-
tance data. The Hall effect would, therefore, see a x ? .10 film in a single-band picture,
132
Figure6.10: La2?xCexCuO4?? Tc asafunctionofthec-axislatticeparameterasmeasured
by X-ray diffraction [94]. The superlattice films (?) have Tcs that depend upon the c-axis
lattice parameter in much the same way as single-doping films grown by various methods
(open symbols). Optimally doped films have a c-axis lattice parameter of 12.44 ?A.
133
i.e., RH = ? 1ne. Additionally, strong angular magnetoresistance oscillations would be
expected with a N?eel temperature of around 150 K (Figure 4.10). A single doping film
of ?average? doping, the expectation for strong charge redistribution, should be readily
observable in Hall and angular magnetoresistance data.
If, however, the charges were well separated in the over- and under-doped layers,
the film should behave as though there were two parallel conduction channels, one over-
dopedchannelandoneunder-dopedchannel. ThisshouldalsobeobservableinHalleffect
and angular magnetoresistance data. A two-band Hall effect suggests what might be seen
where the under- and over-doped layers provide independent conduction channels. For
two-bands,
RH = 1?
1 + ?2
parenleftbigg?
1q1?1
m?1 +
?2q2?2
m?2
parenrightbigg
,
in the low-field limit [38]. In this model, RH will be most strongly influenced by the
more conductive channel, i.e., if ?1 greatermuch ?2 then RH(?1,?2) ? RH(?1). In the case of
under-doped/over-doped cuprate superlattices, the over-doped layer is significantly more
conductivethantheunder-dopedlayer. Thissuggeststhatthemoreconductiveover-doped
layers would tend to short out the less conductive under-doped layers and the Hall effect
should be similar to the Hall effect of the over-doped layer. As angular magnetoresistance
is a magnetoresistance measurement, 1R = 1R1 + 1R2 suggests that with two parallel con-
duction channels in cuprate superlattices, angular magnetoresistance will, like the Hall
effect, also behave similarly to the more conductive over-doped layer. As with the Hall
effect the more conductive over-doped layer will tend to short out the under-doped layer.
However, in these cuprate systems there are no angular magnetoresistance oscillations
134
to measure above x ? .15, so the dominate over-doped layer will contribute no signal,
and the angular magnetoresistance signal should show a N?eel temperature comparable to
the under-doped layer (? 250 K in Pr2CuO4). These behaviors in Hall effect and angu-
lar magnetoresistance data should be clearly distinguishable from the single conduction
channel of the strong charge redistribution case.
Together, the Hall effect and angular magnetoresistance oscillations can provide a
strong probe of charge redistribution in these under-doped/over-doped cuprate superlat-
tices. A strongly charge redistributed sample will appear to have a doping level half way
between the nominal under-doped and over-doped layer doping levels and will appear as
such an ?average? film in both Hall effect and angular magnetoresistance measurements.
A superlattice without charge redistribution will appear, in contrast, to have conflicting
doping levels reported by Hall effect and angular magnetoresistance measurements; the
Hall effect will show a very over-doped film and the angular magnetoresistance oscil-
lations will show a very under-doped film. By observing how well the doping levels
recorded by these two measurements agree or disagree, the character of the charge redis-
tribution can be investigated.
The Hall effect was measured on two La2?xCexCuO4?? superlattices (Figure 6.11).
It was found that the Hall effect of these superlattice thin films is of a similar magnitude
to that of the single-doping films (Figure 6.12). Na??vely, .17/.06 and .21/.06 superlattice
films should either be like x ? .115 and x ? .135 films if charge is well distributed
or like x ? .17 and x ? .21 films if charge is not well distributed. The superlattice
films are reasonably similar to the optimally doped (x = .11) single-doping thin films.
In La2?xCexCuO4??, the Hall effect is positive at high dopings like x = .17 or x = .21,
135
whereas the lower dopings are negative (Figure 6.13). The superlattice films are more like
the ?average? doping films, suggesting again, that there is significant charge redistribution
in the superlattices.
Figure 6.11: Hall effect versus field at various temperatures for La2?xCexCuO4?? super-
lattices.
Superlatticestructurecouldalsobeinvestigatedviaangularmagnetoresistancemea-
surements. These measurements, discussed in Chapter 4, probe the magnetic ordering of
the thin film. The antiferromagnetism in both Pr2?xCexCuO4?? and La2?xCexCuO4??
is known to be an under-doped phenomenon, disappearing in over-doped films. The an-
gular magnetoresistance of Pr2?xCexCuO4?? superlattice films does exhibit oscillations,
136
Figure 6.12: Hall effect versus temperature for La2?xCexCuO4?? superlattices compared
to single-doping optimally doped LCCO films. The superlattices are similar in magnitude
to the single-doping films.
137
Figure 6.13: The Hall effect versus temperature for various La2?xCexCuO4?? dopings
[70].
138
indicating that an under-doped region is present (Figure 6.14).
In the electron-doped cuprates, antiferromagnetism is suppressed by spin-dilution;
the N?eel temperature is sensitive to the doping level, rather than cerium concentration.
This is seen, for example, in the antiferromagnetism enhancement due to oxygen doping
discussed in Chapter 5. Therefore, oscillations seen in superlattice films suggest that
the charge redistribution in the superlattice thin films may be incomplete or that charge
redistributes to a slightly under-doped doping level.
Figure 6.14: The angular magnetoresistance of a Pr2?xCexCuO4?? .11/.19 superlattice
film. Oscillations are present, although they disappear at high temperatures. The angular
magnetoresistance oscillations disappear at a temperature between the x = .11 and x =
.15 N?eel temperatures.
139
As angular magnetoresistance is a resistance measurement, the most conductive
part of the film will tend to carry the bulk of the current. Therefore, if there is incomplete
charge redistribution, the angular magnetoresistance measurement would preferentially
sample the over-doped region. The observation of angular magnetoresistance oscilla-
tions, however, comes from under-doped regions as there is no angular magnetoresis-
tance signal in Pr2?xCexCuO4?? above x ? .15 (Chapter 4). Hall effect measurements
on La2?xCexCuO4?? superlattices indicate significant charge redistribution to a doping
level near the average of the under-doped and over-doped doping levels; however, the
Pr2?xCexCuO4?? angular magnetoresistance data suggests that the most conductive, i.e.,
most highly doped, part of the superlattice film to show antiferromagnetism is, in fact,
slightly under-doped. Based on angular magnetoresistance, the TN of the .11/.19 super-
lattice thin film is comparable to that of an x = .13 or x = .14 single-doping film. As
angular magnetoresistance oscillations are observed in optimally doped Pr2?xCexCuO4??
(Figure 4.8), the TN defined from the superlattice angular magnetoresistance signal indi-
cates that a x = .15 region in the charge-redistributed film is not present and the su-
perconductivity Tc is determined by slightly under-doped regions with effective doping
levels around x = .13 or x = .14. The Tcs of these superlattice films are also compara-
ble with single films at around this doping range. The Hall effect on La2?xCexCuO4??
superlattices is consistent with slightly under-doped superlattices (Figure 6.12).
The highest-Tc regions in the superlattice films are due to charge redistribution. If
these regions are indeed slightly under-doped, this would provide a natural explanation
for the superlattice Tc. Although it is not clear why charge redistribution creates slightly
under-doped regions rather than optimally doped regions as its maximal-Tc regions, I
140
speculate here that it may be due to the doping effect of oxygen in the superlattice, based
upon investigation of annealing superlattice films. Further experiments are needed to
investigate the plausibility of this explanation.
Itisknownthatsuperlatticefilmsrequiredifferentannealingproceduresthansingle-
doping films (Figure 6.2), suggesting that oxygen behaves differently in superlattice and
single-doping films. As oxygen can function as a dopant in Pr2?xCexCuO4?? (Chapter 5),
the superlattice is doped by the under-doped layers, the over-doped layers, and oxygen in
both types of layers. Therefore, the ?average? doping that might be expected from charge
redistribution, e.g., x ? .15 for a .11/.19 superlattice, could be modified by oxygen
doping. However, na??vely adding oxygen doping to the model proposed for charge re-
distribution (Figure 6.8e) would suggest that the whole doping profile would shift, for
example, rather than redistributing between x = .11 and x = .19, a .11/.19 superlattice
may have charge redistribution between effective cerium dopings x = .10 and x = .18.
If this is happening, however, there should still be some fraction of the superlattice at
optimal doping as x = .15 still lies within the range covered by charge redistribution.
The possibility that a slightly under-doped maximal Tc is due to oxygen doping shifting
the whole doping region to below optimal doping, for example, a .11/.19 superlattice is
oxygen doped to a .06/.14 superlattice, is unlikely due to the large amount of disorder
that such aggressive oxygen doping would induce (Figure 6.15). If oxygen were doping
the superlattice films that significantly, Tc would be suppressed and the superlattice films
would be quite resistive. In order to have the highest-Tc region be non-optimally doped,
the continuity of the doping in this model would seem to need to be broken by this oxygen
doping.
141
Figure 6.15: Hall effect and resistivity versus temperature of oxygenated optimally doped
(x = .15) Pr2?xCexCuO4?? films. Left: Hall effect of oxygenated films (Figure 5.7)
plotted against several optimally annealed cerium dopings [99]. Right: Resistivity of
these oxygenated films (Figure 5.6) replotted here for comparison. Significant oxygen
doping, equivalent to several .01 of cerium doping, suppresses Tc and notably increases
the resistivity of the film.
Uniform oxygen behavior in the superlattice films would not disrupt the continuity
ofceriumdopingsuggestedby(Figure6.8e). However, oxygenconcentrationisnoteasily
determined in Pr2?xCexCuO4?? thin films and there is no reason to believe that oxygen is
behaving identically in the over-doped and under-doped layers. Therefore, let us specu-
late that there is some intrinsic oxygen diffusion from over-doped to under-doped layers
in superlattice thin films. This oxygen movement would effectively over-anneal the over-
doped layers and over-oxygenate the under-doped layers. If this happens in the superlat-
tice films, it pulls both layers away from optimal doping as oxygen dopes in the opposite
sense as cerium (Chapter 5). Oxygen depletion in the over-doped layers would add more
electrons to the system, over-over-doping the over-doped layers, and oxygen concentra-
tion in the under-doped layers would remove electrons from the system, under-under-
doping the under-doped layers. With this oxygen profile, the fact that superlattice anneal-
142
ing times are significantly longer than single-doping film annealing times (Figure 6.2)
can be understood. The longer annealing times further over-anneal the over-doped layer,
but they also over-anneal the over-oxygenated under-doped layer. The most over-doped
regions would most likely be degraded and not participate significantly in transport. How-
ever, this longer annealing time would also over-anneal the over-oxygenated under-doped
layers, thereby removing the excess oxygen and pulling the under-doped regions back to
their Figure 6.8e behavior, even while the over-doped layers are over-annealed and are
shifted to higher dopings. This picture would therefore have the region of highest Tc be
slightly to the under-doped side of optimal doping.
This explanation is speculative and would require further experimental investiga-
tion. OxygenconcentrationisquitedifficulttodetermineinthinfilmsofPr2?xCexCuO4??,
and even more difficult at the nanometer scale resolution probably needed to investigate
its profile in these superlattices; however, this picture would also suggest a significant
increase in disorder in the over-over-doped layers that might be detectable with careful
X-ray diffraction investigation. Bi-layer films may provide an alternate method for in-
vestigating this possibility as ion milling could remove the top layer after film synthesis
allowing film properties to be investigated on a more layer-by-layer basis.
Using ion milling or similar technique to slowly remove layers of bi-layer, or re-
duced layer superlattice, films may provide additional useful information on the nature
of charge redistribution in the cuprate superlattices. If the charge redistribution is related
to the film?s structure, i.e., attached to the crystal lattice as synthesized and set by the
details of that synthesis, ion milling to remove the top layer of a Tc-enhanced bi-layer
film might preserve the elevated Tc. In such a study, comparing under-doped/over-doped
143
to over-doped/under-doped bi-layers might shed light on the most important regions of
the superlattice films. At the very least, such a study should be able to determine whether
charge redistribution is generally structural and static in nature, or more electronic and
dynamic in nature.
6.5 Conclusion
Interface effects in heterostructures of electron-doped cuprate supercondutors were
proposed as a mechanism for enhancing Tc. This investigation of Pr2?xCexCuO4?? and
La2?xCexCuO4?? superlattices found significantTc enhancement by creating films of lay-
ered under-doped and over-doped cuprates. However, the enhancement of Tc in superlat-
tices of Pr2?xCexCuO4?? and La2?xCexCuO4?? is not due to interface effects because
critical current measurements reveal the superconductivity to be independent of the num-
ber of interfaces. The enhanced superconductivity appears to be a consequence of charge
redistribution. The Hall effect and angular magnetoresistance measurements on superlat-
tice films suggest that charge redistribution produces superlattice films with an effective
doping that is somewhat less than optimal-doping. The Tc was enhanced in superlattice
films relative to the constituent single-phase films; however, the possible interface effects,
that initially motivated this study, seem unlikely to be present.
144
Chapter 7
High Temperature Resistivity Measurements
7.1 Introduction
The new iron-pnictide family of superconductors is often compared to the cuprate
superconductors. Both families have similar phase diagrams with magnetic ordering in
the parent compounds that is suppressed by doping; further doping yields a superconduct-
ing dome with quite high transition temperatures. However, the cuprate superconductors
are doped Mott-Hubbard insulators with strong Coulomb interactions, whereas the pnic-
tide parent compounds are metallic, suggesting that the pnictides might be more weakly
correlated than the cuprates. Supporting this picture, resistivity saturation has been re-
ported in PrFeAsO crystals as evidence for electron-phonon scattering [100]. However,
magnetic susceptibility in BaFe2?xCoxAs2 has been observed to show unusual linear tem-
perature dependence up to 700 K (Figure 7.1), described as indicating strong magnetic
fluctuations [71]. This susceptibility data suggest interesting physics above room temper-
ature. Magnetic fluctuations have also been observed in neutron scattering [101, 102] and
nuclear magnetic resonance (NMR) [103, 104] results.
145
Figure 7.1: Susceptibility in BaFe2?xCoxAs2 has been reported to exhibit unusual linear
in T behavior up to 700 K [71].
7.2 Mott-Ioffe-Regel Limit
The Mott-Ioffe-Regel limit is a resistivity saturation at high temperatures. This sat-
uration is due to the details of charge transport. In metals, where there are free conduction
electrons, the electrons will move in response to an applied electric field. This movement,
however, takes place in the context of a crystal lattice and is hindered by the electrons
interacting with and being deflected by their local environment. At low temperatures this
scattering can be accomplished by a number of things: crystal defects, other electrons,
lattice vibrations. At high temperatures, however, the lattice vibrations dominate. These
phonon modes are stronger at higher temperatures, causing much more frequent electron-
phonon scattering.
For a wide range of temperatures, the resistivity of most metals is dominated by
146
phonons. In typical (weakly correlated) metals, high temperature resistivity depends on
charge carriers scattering off of phonons. In these materials, ?(T) is described by the
Bloch-Gr?uneisen theory:
?ph(T) = A
parenleftbigg T
?D
parenrightbigg5integraldisplay ?D/T
0
x5dx
(ex ?1)(1?e?x).
This phonon-mediated resistivity is predicted to be linear above the Debye temperature,
?D, up to high temperatures [2].
This linear resistivity cannot continue indefinitely in real crystals as pointed out by
Ioffe and Regel [105] and Mott [106] due to the finite size of the crystals? interatomic
spacing. More electron-phonon scattering means more resistivity as the mean free path,
lscript, the distance between successive scattering events, decreases. Therefore, the resistivity
increases with increasing temperature. However, phonons are lattice vibrations; they are
displacements of atoms off of the lattice site. There is no phonon in the empty space
between lattice sites, and, therefore, the mean free path cannot shrink to less than the
interatomic spacing, a, in the crystal. This implies that there is a minimum mean free
path in phonon-dominated metallic transport and, therefore, a maximum resistivity due to
electron-phonon scattering. As electron-phonon scattering dominates the transport prop-
erties at high temperatures for normal metals, the resistivity as a whole will tend to satu-
rate and no longer increase. The Mott-Ioffe-Regel limit occurs when this happens.
The Mott-Ioffe-Regel limit is due to electron-phonon coupling because phonons are
the dominant scatterers at high temperature. Although several models have been proposed
historically to explain why phonons lead to a restriction on kFlscript ? 1, phonons couple
147
to the hopping matrix elements that describe electron transport [107]. The phonons are
atomicdisplacementstoanotherwiseperiodiccrystallattice, andthereforeeffectivelyadd
to disorder in the system at high temperatures. Increased lattice vibrations in this model
cause the electronic states to have less well defined wave vectors and the current depends
less on individual states and more on the average [107]. Here, rather than the kF being
a good quantum number to describe the electronic states, the states mix together due to
interactions with the phonons. The resistivity, then, is no longer described by the Bloch-
Gr?uneisen theory mentioned above, but is more linear: ? ? Adn where d is the interatomic
spacing and n is the orbital degeneracy [107]. This leads to an apparent mean free path of
lscript ? cn1/3d. Scattering then tends to occur on this length scale and the apparent mean free
path in this picture is then related to the nearest neighbor distance, lscript ? d, the Ioffe-Regel
condition.
The Mott-Ioffe-Regel limit (Figure 7.2) occurs in a wide variety of materials, in-
deed in the vast majority of metals. This is due to phonons being present in every solid
material and their general dominance in high-temperature transport. For a 3D system with
a spherical Fermi surface, the MIR limit is given [108] by ? = 3pi2planckover2pi1e2k2
Flscript
. For a 2D system,
which is more appropriate for the cuprates and pnictides, a cylindrical Fermi surface gives
a MIR limit of ? = 2piplanckover2pi1ce2k
Flscript
where c is the inter-planar spacing [108]. Typically, metals have
a MIR limit around 100?1000 ???cm; this behavior has been observed in many ordinary
metals [109].
It is worth noting that the Ioffe-Regel criterion, lscript < a, affects resistivity domi-
nated by charge carriers scattering off of bosonic excitations. Generally this is electron-
phonon scattering; however, bosonic magnetic scatterers, like electron-magnon scattering
148
Figure 7.2: The Mott-Ioffe-Regel limit in several metals [108]. Most metals Mott-Ioffe-
Regel limit and saturate by around a few hundred ???cm.
149
in ??Fe80?xNixCo20, can also show Ioffe-Regel resistive saturation [110]. Any electron-
boson scattering will produce a MIR saturation; however, scattering from other processes
that do not depend on boson excitations will not MIR limit if the scatterers do not depend
on the lattice spacing, such as electron-electron interactions in highly correlated systems
[109].
These Mott-Ioffe-Regel limit violating materials are typically highly correlated
systems as the electrons are scattering off of something that is stronger than electron-
phonon interactions at high temperatures. The cuprate family of superconductors is a
well known example of Mott-Ioffe-Regel limit violation. These materials are, indeed,
highly correlated doped Mott insulators (Figure 7.3). The strong Coulomb interactions
in La2?xSrxCuO4 (LSCO) allow the t-J model to predict resistive saturation well above
the MIR limit due to scattering caused by electronic interactions [108]. Experimentally,
MIR limit violation is known to occur in the high-Tc cuprates like LSCO [111, 112] and
YBa2Cu3O7 (YBCO) [113, 114].
The high-temperature ferropnictide superconductors are believed to be correlated
systems, although more weakly correlated than in the cuprates. Because MIR limit vi-
olating behavior is typical in strongly correlated systems, high-temperature resistivity
measurements are important for understanding the charge carrier dynamics in the ferrop-
nictides.
150
Figure 7.3: The Mott-Ioffe-Regel limit is violated in the cuprate superconductors [108].
The cuprates should have a Mott-Ioffe-Regel limit at around several hundred ???cm, yet
resistance increases well beyond that range.
151
7.3 SrFe2As2 Background
Pnictides are compounds that contain elements from the nitrogen column of the
periodic table (and chalcogenides are compounds that contain elements from the oxy-
gen column of the periodic table). Superconductivity in several iron based pnictide and
chalcogenide compounds has been recently discovered (since 2008). Since then, super-
conducting transition temperatures in this family have reached up to 55 K. The common
building block in this family is planes of iron and arsenic atoms (Figure 7.4), although
significant modifications can be made to this basic form, for example by substituting ar-
senic for another pnictide or a chalcogenide. Between these planes there are (often) some
other element or elements and the system can be doped by atomic substitution on most
lattice sites.
Figure 7.4: The crystal structures of the pnictide superconductors [115]. Iron-arsenide
planes (and some modifications thereof) form the common element between the systems.
Here we restrict our discussion to the SrFe2As2 system.
152
SrFe2As2 belongs to the 122 family of ferropnictide superconductors. It is metallic
with a spin density wave ground state. Doping suppresses this antiferromagnetism and
induces superconductivity. This doping can be accomplished by a wide range of elements
on all lattice sites; here we focus on cobalt and nickel doping. Substitution of some
fraction of iron for either element produces a superconductor.
The pnictide family of superconductors can be compared to the cuprate family. The
phase diagrams for the pnictides (Figure 7.5) and the cuprates (Figure 7.6) seem to have
quite similar structure. It is tempting, therefore, to suspect that the pnictides also possess
other cuprate properties.
Figure 7.5: Pnictide phase diagram and unit cell [116, 117].
It is also useful to point out another way that the pnitides are similar to the cuprates:
both are quasi-2D materials. The 2D nature of the cuprates can be seen not only in the
crystal structure, but also in the Fermi surface (Figure 2.9). The pnictides are similar in
153
Figure 7.6: Cuprate unit cell and phase diagram [38, 116].
that they also have quasi-2D Fermi surfaces (Figure 7.7), although the pnictides are not
as 2D as the cuprates. However, as the Mott-Ioffe-Regel limit depends upon the size and
shape of the Fermi surface, the quasi-2D nature of the pnictide FS is interesting.
This comparison between high-Tc superconductor families is perhaps more sugges-
tive that actual. In the cuprates, the strong Coulomb interactions that are present account
for many of this family?s unusual properties. The pnictides, unlike the cuprates, are not
Mott insulators; they are metals. Therefore, it is not correct to assume that the pnictides
and cuprates are analogues. In the many cuprates, strong Coulomb interactions can be
seen in the fact that the cuprates violate the Mott-Ioffe-Regel limit. Here, the electron-
doped cuprates Nd2?xCexCuO4?? and Pr2?xCexCuO4?? are observed to behave similarly.
Saturating behavior is observed in the Sr-122 pnictides, suggesting much weaker elec-
tronic correlations in that system than in the cuprates. This resistivity saturation around
154
Figure 7.7: Pnictide Fermi surface [118]. The pnictides are quasi-2D materials with
cylindrical Fermi surfaces.
155
the MIR limit in the SrFe2As2 (Sr-122) system contrasts with a MIR limit violation that
is seen in the electron-doped cuprates. These results qualitatively support the picture of
modest correlation strength in the ferropnictides. In addition, it is supportive of a re-
cent prediction that pnictide transport can be explained in terms of magnetic interband
coupling [119].
7.4 Experimental Detail
Resistivity was measured at elevated temperatures for cuprate and pnictide samples.
The experimental methods used in this experiment required some work beyond the stan-
dard resistivity measurements of Chapter 3. Construction of a specialized experimental
apparatus was necessary. Electrical continuity and signal noise reduction also needed to
be addressed. These details of the experimental apparatus and contacts are briefly dis-
cussed prior to the experimental results.
7.4.1 Experimental Apparatus
In order to measure PCCO and Sr-122s at high temperatures it was necessary to
design a system that could reach those temperatures without destroying the films and
crystals. This required both a heater and the ability to control the atmosphere. Sr-122s
will be oxidized at high temperatures and destroyed if oxygen is present. The cuprates
will be annealed if the oxygen concentration is too high or too low.
A chamber used for pulsed laser deposition was modified for this purpose. The
pulsed laser deposition process already requires high temperatures and a controlled at-
156
mosphere. By pumping the chamber down to vacuum and slowly leaking either argon or
oxygen gas into the chamber, the films could be maintained in the necessary atmosphere.
For the cuprates, the flow rate of oxygen had to be regulated in order to neither add nor
remove oxygen from the crystal lattice. The pnictides only needed an inert atmosphere; a
low pressure of flowing argon was used to exclude oxygen.
The temperature was controlled using the pulsed laser deposition heater and ther-
mometer. These were controlled by a Neocera temperature controller. The heater is
a resistive heater and the thermometer is a calibrated thermocouple. Additional wires
were attached to the thermocouple so that the temperature could also be read by a GPIB-
enabled voltmeter. This simplified computer logging of temperature data.
The resistance was measured as a standard four-wire measurement and was accom-
plished by modifying a low temperature dip-probe resistivity setup. Two major modifica-
tions were necessary to the system. First, the vacuum chamber required a feed-through
for the wires. This was accomplished by modifying a spare heater flange and using the
heater and thermometer feed-throughs to carry measurement wires across the vacuum
chamber wall. Inside the pulsed laser deposition chamber, 50 ?m diameter gold wires
were soldered to the film or crystal and then mechanically secured to the chamber wall
taking care to keep the wires away from the heater as much as possible to avoid melting
insulation.
Second, the electronics needed to be modified in order to make good measurements.
The high temperatures of the measurement produced a lot of thermal noise compared to
low temperature ones and the feed-throughs required several wire-wire solder points that
added to the resistance of the measurement leads. These were combated by switching
157
the measurement from DC to AC. The low temperature resistivity dip-probe uses a DC
measurement setup: a current source produces a known, fixed current and a voltmeter
measures it. With the high temperature setup, this produced excessively noisy data. High
temperature measurements were performed with a Princeton Applied Research 5210 dig-
ital lock-in. The lock-in both produced the reference voltage and measured the signal
voltage. The reference voltage was first passed through a large resistor (large compared
to the sample resistance) in order to function as a current source.
Data were collected by a LabView VI written to sample the lock-in output and the
voltmeter measurement of temperature. The state of the pulsed laser deposition chamber
was controlled using techniques standard to pulsed laser deposition. For example, thermal
control and ramping were provided by the Neocera temperature controller and gas flow
was regulated by a needle valve between the argon or oxygen bottle and the pulsed laser
deposition chamber.
7.4.2 Contacts
While contacts are always an important issue in transport measurements, at elevated
temperatures, they become especially critical. This is due, primarily, to the failure of
standard low temperature techniques and requires that extra care be taken in order to
achieve the desired results. In both high and low temperature applications there are two
types of contacts that must be considered. Electrically conducting contacts are used for
the actual transport measurements and connect the sample to the wires used to probe the
system. Thermally conducting contact also has to be made between the sample and the
158
heater or cold head in order to maintain good temperature control. This contact generally
has to be electrically insulating in order to avoid shorting out the measurement through
the temperature control setup. These two types of contacts must be made for either low
or high temperature measurements.
Whilegoodthermalcontactcanbeasignificantexperimentalissueforlowtempera-
ture measurements, in the PPMS, good thermal contact at low temperatures is often fairly
straightforward. Samples are mounted on a PPMS puck with a dab of vacuum grease. The
grease is electrically insulating and pressing the sample into the grease provides a good
degree of thermal contact between the sample puck and the film or crystal to be measured.
Above several hundred degrees centigrade, however, the grease does not survive. Charred
vacuum grease is no longer sticky and allows the crystals or films to fall off of the heater.
In order to measure resistivity, wires must be connected to the sample. The most
common technique is to solder gold wires to the film or crystal with indium solder. In-
dium solder is generally preferred over lead-tin eutectic solders due to its low melting
temperature. Here, however, this feature is a liability. In order to measure resistivity up to
1100 K, the contacts cannot melt below this temperature. Therefore, neither indium nor
lead-tin solder can be used in this application.
In the pulsed laser deposition process, silver paint is used to affix the substrate
to the heater. Silver paint hardens at elevated temperatures and provides good thermal
contact. This technique is appropriate for attaching films to the heater by silver painting
the back of the substrate; the substrate itself is an insulator and isolates the film from the
electrically conductive silver paint. Silver paint cannot, however, be used to thermally
contact crystals to the heater as it will short out the crystal electrically.
159
Electrical contacts that will withstand elevated temperatures can, however, be cre-
ated with silver paint. The silver paint must be allowed to dry well prior to measurements
as it has but little mechanical strength and can easily be broken. It does, however, main-
tain itself at high temperatures and thus allows electrical contacts to be made that can
survive up to 1100 K. Gold wires, typically used for low temperature measurement con-
tact leads, were found to be adequate at high temperatures as well and were used to make
leads to the samples.
Thethermalcontactbetweenthecrystalsandtheheaterturnedouttobebestachieved
by using GE varnish. At high temperatures the varnish hardens into a black resin that is
difficult to remove. At lower temperatures GE varnish is frequently used to add insula-
tion to bare wires that might accidentally touch. For small and/or delicate crystals, the
crystal can be GE varnished to a bare film substrate that is subsequently affixed to the
heater with silver paint. This can be more convenient as silver paint is easier to control
than GE varnish and most of the more difficult sample mounting can then be done under
microscope.
7.5 Experimental Details
High temperature resistivity measurements were performed on the electron-doped
cuprates, Nd2?xCexCuO4?? (NCCO) and Pr2?xCexCuO4?? (PCCO), as well as on Ni and
Co doped SrFe2As2. NCCO single crystals were prepared by self-flux with a typical
size of 0.5 mm ? 0.5 mm ? 0.03 mm as described elsewhere [120]. Crystals were then
reduced in a low oxygen anneal to achieve superconductivity. PCCO thin films were
160
grown by pulsed laser deposition (PLD) using a LambdaPhysik KrF excimer laser on
5 mm ? 10 mm STO substrates as described in Chapter 3. The films were grown to a
nominal thickness of 300 nm and were vacuum annealed to maximize superconductivity.
Single crystals of SrFe2?x(Ni,Co)xAs2 were prepared by self-flux, as described by Saha
et al. [121], with a typical dimension of 2 mm?0.5 mm?0.1 mm.
Low temperature measurements were performed before and after the high tempera-
ture measurements to be certain that the crystals and films of both types of materials were
not damaged by thermal cycling up to 800 K. Neither cuprates nor pnictides decompose at
these high temperatures provided that they are maintained in an inert environment. When
such damage did occur due to non-inert atmosphere contaminants, it would manifest itself
in significant hysteresis between the up and down temperature sweeps. These incidents
are obvious and also result in visual decomposition of the crystals, for example, color
change. Any damage due to thermal cycling in properly maintained atmospheres was
minimal and did not affect our measurements because the resistivity did not change when
sweeping up and down in temperature.
For Pr2?xCexCuO4?? elevated temperatures suggest annealing, which changes the
sample properties. At 500 C, these measurements are in the regime where PCCO is being
annealed; however, this is the lower end of that range and annealing is consequently quite
slow and a small amount of oxygen, roughly controlled, maintains the films. Sweeping
down in temperature immediately after reaching the maximum temperature minimized
the time spent at high temperatures and did not significantly over-anneal the PCCO films.
Cuprate measurements, at higher temperatures, however, do require a controlled oxygen
atmosphere to maintain proper oxygen stoichiometry.
161
The samples were contacted to gold wires by electrically conductive silver paint
that maintained its bonding at high temperatures as described above and were heated by
a Neocera substrate heater designed for pulsed laser deposition of films. The sample and
heater were enclosed in a vacuum chamber and the atmosphere was maintained between
8 and 10 Torr of flowing argon to minimize the possibility of oxidation. The crystal
geometry allowed a four-probe resistivity measurement; a 100 Hz, 1 mA current was
applied and was measured by a Princeton Applied Research 5210 lock-in amplifier. Phase
data were also collected on the high temperature measurements as a way to monitor the
system. Jumpsinphasesignaledproblemsinthemeasurementlikecontactsbreaking. For
problem-free measurements, the phase was stable to less than a degree. Measurements
below 300 K were performed in a Quantum Design PPMS.
The PPMS can measure up to 400 K. On some of the samples this was done to
ensure good matching of data between the PPMS and the high temperature experimental
setup. With the data sets overlapping across a 100 K temperature range, the two systems
had to be well calibrated against each other.
7.6 Results
As shown in Figure 7.8, the ab-plane resistivity of optimally doped PCCO and
NCCO violates the MIR limit with T2 behavior up to 700 K and linear behavior at higher
temperatures [122]. This trend is consistent with previous work on NCCO which showed
resistivity increasing up to 600 K [67]. The MIR limit in these materials should be around
700 ???cm, similar to LSCO [108]. Optimally-doped NCCO can be fit reasonably well
162
Figure 7.8: The ab-plane resistivity versus temperature of optimally doped (x = .15)
and annealed Pr2?xCexCuO4?? films (a73) and Nd2?xCexCuO4?? crystals [123]: optimally
doped (x = .15) and annealed (a71), optimally doped (x = .15) as-grown (unannealed)
(a76), underdoped x = .10 (a77), and overdoped x = .22 (a78) [124]. Optimal crystals are
fit to T2 above Tc and below 700 K (+). The MIR limit in these materials is around
700 ???cm.
to ? = ?0+AT2 between Tc and 700 K; above 700 K resistivity is linear in T with a slope
of? 5 ???cm/K. The meaning of this T2 behavior is not understood; at low temperatures
T2 dependence is often electron-electron scattering, but 700 K is much too hot to expect
electron-electron scattering.
The ab-plane resistivity of some 122 Fe-pnictides up to 800 K is shown in Fig-
ure 7.9. The SrFe2As2 parent compound and x(Ni) = 0.14, x(Ni) = 0.18, and x(Co) =
163
Figure 7.9: The ab-plane resistivity vs temperature, ?(T), up to 800 K for SrFe2As2 (a71),
SrFe1.86Ni0.14As2 (a76), SrFe1.82Ni0.18As2 (a77), and SrFe1.74Co0.26As2 (a78) single crys-
tals [124]. The resistivity saturates around 400 ? 700 ???cm; the MIR limit is around
600 ???cm.
0.26 dopings are shown. The two nickel dopings are under-doped and over-doped sam-
ples; the cobalt doping is near optimal. The resistivity increases smoothly above the SDW
transition or Tc and saturates at high temperatures. Above 650 K the resistivity maintains
a constant value of between 400 and 700 ???cm depending on doping.
164
7.7 Discussion
In the electron-doped cuprates, the MIR limit is strongly violated with ? ? T2 up
to 700 K as shown in Figure 7.8. A ? ? T2 above Tc and up to? 250 K has been known
for many years but its exact origin is not known [21]. For typical Fermi liquid metals,
a resistivity proportional to T2 usually comes from electron-electron scattering, but this
is not expected to be observed above ? 20 K. At higher temperatures electron-phonon
scattering, or electron scattering off of other bosons, usually dominates the resistivity. At
high temperatures (T > ?D) T-linear behavior from electron-phonon scattering usually
dominates. This picture, however, assumes a lack of strong correlations and would pre-
dict MIR limit saturation. The lack of resistivity saturation rules out dominant phonon
scattering for the electron-doped cuprates.
In many strongly correlated metallic systems, the MIR limit has been shown to be
violated, as in, La1?xSrxMnO3 [109, 112], Li2VO4 [109, 125], Srn+1RunO3n+1 [126],
and the hole-doped cuprate high temperature superconductors (Figure 7.3). For exam-
ple, neither YBa2Cu3O7 nor La2?xSrxCuO4 show resistivity saturation up to 1100 K and
LSCO still shows resistivity increasing linearly at those temperatures, well beyond the
Ioffe-Regel resistivity [127]. Additionally, in many cuprates, the Ioffe-Regel criterion is
violated below room temperature due to their high resistivity. The Ioffe-Regel condition
assumes noninteracting electrons, so the electron-doped cuprates? lack of ?(T) saturation
suggests strongly correlated behavior consistent with hole-doped high-Tc cuprates.
In the cuprates, the t-J model has been used to explain the normal state behavior
in terms of strongly correlated electrons in doped antiferromagnets [128]. MIR limit
165
violation consistent with this picture has been reported in LSCO at similar temperatures
[108]. Derived from the Hubbard model, the t-J model describes a system of strongly
correlated electrons with antiferromagnetic interactions associated with a Mott-Hubbard
insulator state at zero doping [128]. This model has been used to analyze LSCO where
the MIR limit is violated but resistivity still saturates, although at a higher resistance,
?sat ? 0.07cx(1?x) m??cm where c is the inter-CuO2-plane spacing and x is the doping [108,
129]. Unfortunately, for PCCO and NCCO the saturation value in this model is around
3500 ???cm and 1100 K is not high enough to test this model. It would be instructive to
look for saturating behavior up to 1300 K; however, it is doubtful that this could be done
without complications due to oxygen loss and the crystal melting. In summary, strong
correlations seem to dominate the PCCO and NCCO ab-plane charge transport because
of the MIR limit violation.
Incontrasttothecuprates, theSr-122pnictidesdoshowresistivitysaturationathigh
temperatures. This superficially resembles the picture expected for electron-phonon scat-
tering in typical metals, which would suggest weak correlations in the ferropnictides. It
has been suggested that the Fermi-liquid picture can explain the pnictide transport behav-
ior [130]. However, there have been observations of non-Fermi-liquid [131] and quantum
critical [132] behavior in the pnictides. Additionally, high temperature resistivity satura-
tion has been proposed by Prelov?sek and Sega as a signature of a two-band model with
spin fluctuation coupling [119]. In this model, electron and hole bands are coupled by
strong spin fluctuations that give rise to the transport properties.
A MIR limit often does suggest a typical band metal picture. If that picture holds,
the electron-phonon coupling constant should be a meaningful quantity. The roughly
166
linear ?(T) from ? 200 K to ? 400 K has a slope of 0.5?0.9 ???cm/K, about a tenth
that of NCCO, and suggests correspondingly weaker electron-phonon scattering. From
transport data, this value can be calculated [100] by ?tr = planckover2pi1?2p8pi2k
B
d?
dT . For SrFe2As2, the
plasma frequency has been measured [133] to be ?p = 1.4 ? 104 cm?1. This gives
a ?tr ? 0.12 for SrFe2As2. This is too small to reproduce the Tc of the 122s. This
mismatch between the electron-phonon coupling constant?and the expectedTc is similar
to calculations done on several 1111 pnictides where ? ? 0.17?0.21 predict a Tc of a
few Kelvin at most [134]. A ?tr ? 0.12 is also much smaller than the ?tr = 1.53 reported
for PrFeAsO [100].
A stronger indication of charge carrier coupling to phonon excitations is the ob-
servation of a MIR limit. Depending upon the size, shape, and dimensionality of the
Fermi surface, the Mott-Ioffe-Regel limit can take on many different values. Quasi-two-
dimensional, the Fermi surface of the 122s is better approximated as a cylinder than as a
more 3D shape (Figure 7.7). With kFlscript ? 1, the MIR limit condition gives several hun-
dred ???cm as a reasonable estimate for the MIR limit in a quasi-2D system such as the
Sr-122s.
SrFe2As2 has a c-axis lattice parameter of 12.32 ?A [121]. If it is assumed to be a
2D system, a cylindrical Fermi surface gives a MIR limit of ? = 2piplanckover2pi1ce2k
Flscript
where c is the
inter-planar spacing [108]. Taking half the c-axis lattice parameter value as the inter-
planer spacing and lscript ? a gives a MIR limit of ?MIR2D = 634 ??.cm. If a spherical Fermi
surface is assumed instead, the MIR limit is given by ? = 3pi2planckover2pi1e2k2
Flscript
. With kF =
parenleftBig
3pi2N
V
parenrightBig1/3
,
?MIR3D = 2560 ??.cm. A spherical Fermi surface is clearly a poorer approximation than
cylindrical for the 122s but indicates that a cylindrical FS underestimates the MIR limit.
167
It should be noted that the value of the MIR limit can vary significantly depending upon
MIR criteria used; kFlscript ? 1, lscript ? a, and kFlscript ? 2pi are all used in the literature. Taking
the 2D estimate as a lower bound on the Sr-122?s MIR limit, saturation is expected by
around 650 ???cm or so in order to not rule out electron-phonon coupling. The measured
resistivity saturation is 400?700 ???cm.
Although any calculation of the MIR limit is somewhat approximate, the Sr-122s
saturate near the expected MIR limit for that system of ? 650 ???cm. Electron-phonon
scattering, therefore, could explain the value of the resistivity saturation in the 122s and
would suggest that electron correlations do not play an important role in the scattering for
transport.
Recently, however, a model has been proposed by Prelov?sek and Sega where strong
spinfluctuationscoupletheelectronandholebandsinthesystemandproduceasaturating
?(T) (Figure 7.10) [119]. In this model, the magnitude of the resistivity is primarily
tuned by the spin-fermion coupling constant, g0. A g0 of order unity corresponds to ?
saturating at around 1000 ? 1500 ???cm; this compares to our measured value of ?
400 ? 700 ???cm. The measured resistivity saturation is a factor of ? 2 ? 4 less than
predicted by the model; this implies a larger spin-fermion coupling, g0 greatermuch 1, and the
possible breakdown of the model [119]. This model, however, is only a two-band model
where the 122 system is known to be more complicated; therefore, some discrepancy in
magnitude cannot rule out relatively strong spin-fermion coupling in the 122s. As the
pnictides are known to show spin fluctuations from neutron scattering [101, 102] and
NMR [103, 104] results, coupling to spin fluctuations could produce MIR-like resistivity
saturation in the pnictides.
168
Figure 7.10: Predicted pnictide resistivity saturation due to spin fluctuations [119]. The
T?s are different Fermi liquid temperatures in the model.
169
Similar models predict ?(T) saturation due to two bands with unequal scattering
[135]. The pnictides are known to be multi-band systems (Figure 7.7) and this may con-
tribute significantly to their transport properties. If the two bands have different transport
parameters, themoreconductivebandcan?shunt?thelessconductiveband, saturatingthe
high temperature resistance. The more conductive band, therefore, would begin to dom-
inate transport properties and the material would appear less resistive. This is similar to
the argument made in Chapter 6 to argue that cuprate superlattices have significant charge
redistribution; there the more conductive layer was not observed to dominate transport,
indicating a lack of distinct bands. In the case of the pnictides, Golubov et al. propose that
the two bands of interest are a stronger interaction band consisting of a combination of the
two electronic pockets and the inner hole pocket around the ?-point and a weaker inter-
action band consisting of the remaining outer hole pocket [135]. If the first band is quite
clean, with a low scattering rate, and the second band is quite dirty, with a high scatter-
ing rate, this could result in high temperature saturation of resistivity [135]. While there
could still be a MIR limit in this model, it would not be the primary cause of resistivity
saturation.
In similar systems to the 122s, much higher resistivity values have been reported in
high temperature measurements on the 1111 oxypnictides. Large resistivities have been
observed in the NdFeAsO [136] and LaFePO [137] systems and a resistivity saturation at
2500?3000 ???cm has been reported in PrFeAsO crystals as evidence for a MIR limit
[100]. This saturation is significantly higher than the 100 ? 1000 ???cm seen in most
MIR limited materials. Low carrier concentrations can produce a large MIR limit [108]
or a small spin-fermion coupling constant could produce a resistivity saturation at high
170
values [119].
An additional complication in interpreting the pnictide data is that resistivity satu-
ration could also be due to the fact that the arsenides are semimetals. Semimetals can be
thought of as indirect band gap semiconductors with a slightly negative band gap. As such
a picture suggests, adding thermal energy, kBT, to the system will activate more charge
carriers at high temperatures. In the pnictides, the energy scale for this type of thermally
activated behavior is Eh = 300 K, so semimetal behavior should describe transport above
? 100 K [138].
The distinct behavior of semimetals is due to the fact that they have energy bands
quite near the Fermi energy that can be thermally excited to participate in transport. Co-
and Ni-doping may be expected to significantly influence this behavior by making the
material more n-type and more metallic with respect to properties depending upon band
structure. Hall effect measurements has argued that, with sufficient Co-doping, Ba-122
transport is dominated by a single charge carrier [139]. Having only a single dominate
charge carrier would suppress much of the distinction between a semimetal and a metal,
and might suggest differing behavior in the parent, and doped materials due to thermal
excitation of charge carriers. Like the spin fluctuations model by Prelov?sek and Sega that
was discussed, the similarity in resistivity saturation between the undoped SrFe2As2 and
the Co- and Ni-doped samples indicates a lack of doping dependence of the saturation
mechanism, suggesting that either thermal activation of charge carriers near the Fermi
energy does not change at high temperatures with doping, or that the resistivity saturation
may be MIR-limited.
High temperature resistivity measurements ultimately cannot resolve this issue. For
171
metallic systems, MIR limited behavior is nearly universal with few exceptions. The tem-
perature dependence of semimetals at high temperature does not have such clear expecta-
tions. The MIR limit criterion (lscript ? a) would still be in effect in these systems; however,
the expression of that limit may be obscured by large changes in the number of charge
carriers. For example, elemental tungsten has a significant reduction in phonon frequen-
cies at high temperatures that would substantially increase resistance in the absence of a
MIR limit; the MIR limit makes this resistivity increase only moderate [108].
In semimetal systems that have been measured at high temperatures, resistivity ex-
hibits diverse behaviors. At elevated temperatures (Figure 7.11), semimetal resistivity
can, indeed, show saturation and even decrease as in the case of semimetal graphite [140]
and graphene [141]. However, increase without limit is seen in semimetal CaB6 [142].
Also, bismuth?s resistivity increases with no saturation up to its melting point of 544 K
[143]. Although pnictide semimetal behavior could describe the high temperature resis-
tivity saturation seen, it is difficult to draw conclusions regarding semimetal behavior in
the 122s from high temperature resistivity.
Thermal activation of charge carriers near the Fermi surface could influence the
high temperature resistivity saturation in the Sr-122s. High temperature resistivity, how-
ever, is inconclusive on the ultimate mechanism for the observed saturation. The resis-
tivity value of the saturation is suggestive of a MIR-limit; however, influences due to
thermally activated behavior or spin-fluctuations cannot be ruled out with these measure-
ments.
MIR limited behavior in a weakly coupled system, resistive saturation due to rela-
tively strong spin-fermion coupling, or thermally activated charge carriers could explain
172
Figure 7.11: The resistance of semimetal graphite up to 450 K [140] (left) and of
semimetal CaB6 up to 1000 K [142] (right).
the high temperature resistive saturation in the Sr-122s. Saturating resistivity in the Sr-
122s does rule out strong electronic correlation effects like those in the cuprates. In the
Sr-122s, however, the resistivity saturation cannot by itself provide a conclusive picture
of pnictide charge dynamics.
Finally, the similarity in resistivity saturation between undoped SrFe2As2 and Co-
and Ni-doped samples reveals a lack of doping dependence of the saturation mechanism.
If spin fluctuations are responsible, as in the model of Prelov?sek and Sega or more gener-
ally as the bosonic scatterer, it may be expected that the suppression of AFM order with
doping should result in a modification of this scattering and therefore a change in the re-
sistivity saturation. Similarly, semimetal behavior is often quite sensitive to doping and
may be expected to lessen with doping. However, the lack of change in the saturation tem-
perature of ?(T) suggests that either the spin fluctuation spectrum or thermally activated
behavior does not change at high temperatures with doping, or that phonon-scattering is
indeed dominant at high-temperatures in the iron pnictides.
173
7.8 Conclusions
Wemeasuredtheab-planeresistivityofseveralSr-122superconductorsandelectron-
doped cuprates. The electron-doped cuprates strongly violate the Mott-Ioffe-Regel limit
while the 122s saturate at around 400 ? 700 ???cm at high temperatures. Strong elec-
tronic correlations can explain the cuprate behavior; however, pnictide saturation can be
explained either by electron-phonon scattering, by coupling between spin fluctuations and
charge carriers, or by thermally activated charge carriers. The observed high temperature
resistivity saturation in the Sr-122s supports both the picture of more weakly correlated
physics in the ferropnictides than in the cuprates and recent predictions of magnetic inter-
band coupling in the pnictides.
174
Chapter 8
Other Projects
8.1 Introduction
Significant time was spent on several film-growth projects that were ultimately less
successful. Attempting to synthesize superconducting Pr2CuO4 by careful control of oxy-
gen, the resistivity of Pr2CuO4 was decreased significantly and some metallic behavior
(d?/dT > 0) was obtained. These results are promising, but incomplete. Additionally,
attempts were made to synthesize thin film preparations of iron-based superconductors,
with some preliminary success. Neither of these projects, however, were taken to comple-
tion due to competing demands of more quickly productive projects. The partial results
obtained are here briefly discussed.
8.2 Superconductivity in Pr2CuO4?
The investigation into potentially oxygen doping Pr2CuO4 into a superconducting
state extends the Pr2?xCexCuO4?? oxygen doping work performed in Chapter 5. As oxy-
gen removal in Pr2?xCexCuO4?? has a similar doping effect to adding cerium, Pr2CuO4??
might be made superconducting if introduction of disorder can be minimized during the
oxygen reduction. Here, the experimental techniques attempted and some of the more
promising results obtained are described in the hope that this project may be revived in
175
the future.
8.2.1 Introduction
ThecupratesuperconductorsaredopedMott-like(charge-transfer)insulators(Chap-
ter 2). This well-established picture has, however, recently been called into question, in
particular, on the electron-doped side of the phase diagram. It has been proposed that,
unlike the T-phase cuprates, the Tprime-phase cuprates are not Mott insulators. Rather, lack-
ing apical oxygens, they are Slater insulators; their insulating behavior is due to their
long range antiferromagnetism ordering [20, 144]. The apical oxygens in the Tprime-phase
introduce significant disorder into the crystal structure; it has been proposed that they in-
duce the copper magnetic moments which then act as Kondo (magnetic) scatterers [145].
Indeed, removing O(3) oxygens, the apical impurities, was reported to allow supercon-
ductivity to appear at lower dopings in Pr2?xCexCuO4?? [146]. If this is the case, remov-
ing apical oxygens fully would suppress antiferromagnetism, which, in turn, would allow
superconductivity. This was reported to happen [52]. Increased oxygen concentration,
presumably on the apical sites, does increase antiferromagnetism in Pr2?xCexCuO4??
(Chapter5). Theacceptedelectron-dopedcupratephasediagramhasanantiferromagnetic
parent compound that is then doped to induce superconductivity. It has been claimed,
however, that Pr2CuO4 (PCO) is not a Mott insulator, but rather a 30 K superconductor
[32, 52, 53, 54]. The Mott-like insulating state, therefore, is not intrinsic to the material,
but is rather due to disorder.
In the Tprime cuprates, the charge-transfer gap is significantly smaller than in the T
176
phase cuprates and may even close [52]. As the main difference between the T and Tprime
phases is the apical oxygen, O(3) oxygens (apical oxygen disorder in the Tprime phase) seem
to increase the ?Mott-like? nature of the Tprime-RE2CuO4 system. Apical oxygen can act as
a scatterer, frustrating superconductivity and making a normal band metal insulating.
If oxygen plays such a sensitive role in determining the properties of the electron-
doped cuprates, the amount and location of oxygen, especially O(3) oxygen, is quite
important. However, oxygen content and location cannot be measured accurately in thin
films and there could be impurity oxygen at the apical sites. If so, oxygen reduction might
induce superconductivity by clearing apical oxygen.
Synthesis of these films was attempted at Maryland. Films were grown both by
pulsed laser deposition (PLD) and metal organic deposition (MOD). However, the pa-
rameters necessary to obtain superconductivity were not found.
8.2.2 Film Growth
The reported superconducting thin films of PCO were grown either by MOD or by
Molecular Beam Epitaxy (MBE). MBE is a technique for film growth similar to PLD, but
with greater control over the layers of atoms being deposited. Here, films were grown by
PLD, by MOD, and by PLD with PLD attempting to replicate the MBE or MOD growth.
8.2.2.1 Metal Organic Deposition
Theprocessofgrowingthinfilmsbymetalorganicdepositionisquitedifferentfrom
pulsed laser deposition techniques. MOD deposition is a process in which the metallic
177
elements in the film are delivered in solution to the substrate. Rather than control the
stoichiometry of metallic elements by PLD target synthesis, the metals are chemically
bound to larger organic molecules. These organic molecules are then dissolved into a
solvent in the proper ratios to maintain stoichiometry. The resulting solution is then spin-
coated onto a clean substrate.
The spin-coated thin film is not, however, the correct material. The coated substrate
must first be calcined by firing it at high temperatures. The heat of this step decomposes
the organic molecules carrying the metallic elements, leaving an amorphous film of the
constituent elements. This amorphous film is then baked at a high temperature to allow
the film to crystalize in the proper structure.
TogrowPr2?xCexCuO4?? bymetalorganicdeposition,praseodymiumnitrate,cerium
nitrate,andcoppernitratewereused. Thesethreecompounds,Pr(NO3)3?6H2O,Ce(NO3)3?
6H2O, and Cu(NO3)3 ?212H2O, have atomic weights of 326.92 g/mol, 326.64 g/mol, and
232.59 g/mol respectively. The proper mixture was then determined by weighing, exactly
as is done for oxides during pulsed laser deposition target synthesis (Chapter 3). All three
nitrates are soluble in water. Sufficient water to fully dissolve the three nitrates was nec-
essary; however, the solution will then be spin-coated onto substrates and this process is
more easily done with thicker mixtures.
The spin-coating procedure is modified from the method for spin-coating photore-
sistontothinfilms. AfewdropsoftheMODsolutionarepipettedontoacleanedsubstrate
which is then spun at 4000 rpm to produce a very thin film of the solution. It was found
that modifying the basic solution recipe made this step easier. First, adding glycerol to
the solution greatly increased its viscosity. This allowed the solution to spread out as a
178
thin film on the substrate by suppressing its tendency to be flung off. Second, a small
amount of detergent was added to the solution. SrTiO3 (STO), the substrate of choice for
growing PCCO due to lattice matching, is hydrophobic. Adding detergent to the MOD
solution allowed it to more easily wet STO. The addition of these extra organic molecules
does not affect the final films produced as they will decompose along with the nitrates at
high temperatures. However, one of the decomposition products of glycerol, acrolein, is
toxic, so this step should be performed in a fume hood or properly vented pulsed laser
deposition chamber under vacuum.
Once the solution is spin-coated onto the substrate it is then heated to remove the
organics and to form the PCO film. A typical heating schedule (Figure 8.1) has three
plateaus. The first plateau is to calcine the solution. This removes the organics and
leaves only the PCO precursors. The second plateau synthesizes the compound. This
temperature is determined from the PCO phase stability diagram. The third plateau is for
annealing; this adjusts the oxygen content in the PCO film.
Figure 8.1: A typical heating schedule for metal organic deposition films.
179
The superconducting Pr2CuO4 films reported were calcined in air at 400 C. They
were then heated to between 850 C and 900 C in an oxygen atmosphere between 2 ?
10?4 atm and 1 atm (150 mTorr and 760 Torr). Annealing was the crucial step; varied
time and temperature in vacuum (P <1?10?7 atm?1?10?4 Torr) produced a range of
films shown in Figure 8.2.
Figure 8.2: Optimization of PCO films by annealing temperature (left) and annealing time
(right) [52].
A range of films were produced at Maryland (Table 8.1). All metal organic depo-
sition films grown were highly resistive; the room temperature resistivity was a useful
characterization to track progress. In general, crystalization at 850 C to 900 C was found
to be too high; better results were obtained at 800 C or 750 C. Deposition in an oxygen
atmosphere between 2?10?4 atm and 1 atm (150 mTorr and 760 Torr) was only explored
in the 150 mTorr to 600 mTorr range due to chamber design limitations. The turbo pump
speed is adjustable, the roughing pump is not. Therefore, to control the pressure well,
pressure had to be low enough to not destroy the turbo pump. As lower pressure films
seemed better, this limitation was not too severe.
180
Vacuum annealing was recommended (Figure 8.2) in the range 5 min to 60 min,
with times less than15min preferred and in the temperature range420C to500C. For our
films annealing temperatures significantly higher than this seemed to be better with 650 C
seeming best. Annealing for 15 min was better than shorter anneals; longer annealing was
not fully explored in favor of more promising methods.
Calcining Crystalization Annealing Resistance at 300 K
10 min 15 min 5 min
400 C 900 C in 450 C 1 M?
air 150 mTorr O2 3?10?6 Torr O2
10 min 15 min 5 min
400 C 850 C in 450 C 460 k?
air 150 mTorr O2 1?10?5 Torr O2
10 min 15 min 5 min
400 C 750 C in 450 C 120 k?
air 150 mTorr O2 9?10?7 Torr O2
10 min 15 min 5 min
400 C 750 C in 450 C 650 k?
air 600 mTorr O2 4?10?6 Torr O2
10 min 15 min 15 min
400 C 750 C in 450 C 90 k?
air 150 mTorr O2 6?10?6 Torr O2
10 min 15 min 15 min
400 C 750 C in 720 C 110 k?
air 150 mTorr O2 8?10?7 Torr O2
10 min 15 min 15 min
400 C 750 C in 650 C 40 k?
air 150 mTorr O2 8?10?7 Torr O2
Table 8.1: A sample of heating schedules used for Pr2CuO4 films grown by metal or-
ganic deposition. Room temperature resistance was used to characterize the Pr2CuO4
fims grown by metal organic deposition.
The most significant draw-back of the metal organic deposition procedure to pro-
181
duce thin films was a difficulty in forming single-phase epitaxial thin films. Like in
pulsed laser deposition, epitaxy is supposed to be forced by the substrate (with good
lattice matching between the film and substrate). In pulsed laser deposition, however, the
film grows up off of the substrate. In metal organic deposition, all the material is present
as the crystal is forming. This seems like it allows the substrate less influence over the
crystallization. MOD films grown at Maryland did form in the correct phase as seen in
X-ray diffraction (Figure 8.3). The resultant films were not, however, as high-quality
as are grown by pulsed laser deposition. Further optimization of the MOD technique is
necessary to obtain films comparable in quality to pulsed laser deposition.
Figure 8.3: X-ray diffraction of an x = .15 Pr2?xCexCuO4?? thin film grown by metal
organic deposition (above) and grown by normal pulsed laser deposition (below). Above:
The 004 and 008 Pr2?xCexCuO4?? diffraction peaks are visible, indicating some epitaxy.
2? is scanned from 25? to 85?. Below: For high quality films grown by pulsed laser
deposition, more X-ray diffraction peaks are seen. 2? is scanned from 5? to 85?.
182
8.2.2.2 Amorphous PLD
PLD was, however, adjusted to mirror the MOD technique. Films were grown by
PLD at room temperature so that they would form an amorphous layer. After this step the
films should be equivalent to MOD films after calcining and were subsequently processed
like MOD films. Amorphous films had difficulty forming into the correct phase, however.
The same parameters for crystallization and annealing as used in metal organic de-
position films were taken as a starting point for optimization. A range of films were
produced at Maryland with this amorphous pulsed laser deposition technique (Table 8.2).
While superconducting PCO films have been reported to produce a 30 K Tc when fully
optimized, my films did not superconduct and were still resistive. These films were sig-
nificantly improved over metal organic deposition films, however, and the most useful
characterization used to track progress was the temperature at which the films became
so resistive that the validity of the Quantum Design Physical Properties Measurement
System resistivity measurement started to become questionable (? 1 M?). A dip-probe
resistivity measurement setup was available and was modified to allow reliable resis-
tance measurements up to almost 10 M?; however, the additional information provided
by measurement at higher resistances was rarely needed and only proved useful to dis-
tinguish PPMS measurement artifacts from actual data. The best parameters reported
(Figure 8.2) were not directly transferable to our procedure here. This indicates that there
are important uncontrolled parameters in the MOD growth process.
Films grown by amorphous pulsed laser deposition were significantly less resistive
than metal organic deposition grown films. In addition, they tended to crystalize better.
183
Deposition Crystalization Annealing T(R > 1 M?)
20 min 15 min 5 min
100 C 850 C in 720 C 80 K
230 mTorr N2O 230 mTorr N2O 1?10?5 Torr
30 min 15 min 5 min
100 C 733 C in 720 C 40 K
230 mTorr N2O 230 mTorr N2O 3?10?5 Torr
30 min 15 min 60 min
100 C 800 C in 630 C 20 K
230 mTorr N2O 230 mTorr N2O 5?10?6 Torr
30 min 15 min 45 min
100 C 800 C in 720 C 30 K
230 mTorr N2O 230 mTorr N2O 9?10?6 Torr
Table 8.2: A sample of growth parameters for Pr2CuO4 films grown by amorphous pulsed
laser deposition. For insulating films without a Tonsetc , the temperature where the resistiv-
ity surpassed 1 M? characterized films.
This suggests that calcining the metal organic deposition films may have left a residue
that was harming growth; dirty substrates are known to produce poor-quality films in
traditional pulsed laser deposition growths. Despite being more conductive than metal
organic deposition films, in amorphous pulsed laser deposition films, one difficulty in
optimizing PCO is still the large resistivity of the material. Resistivity is also a rather
rough method of characterization; for an optimally doped Pr2?xCexCuO4?? film grown
by normal pulsed laser deposition, films are optimized by maximizing Tc, which is a
much more sensitive measure. Amorphous pulsed laser deposition films, however, show
stronger X-ray diffraction peaks. It was reported that the c-axis lattice parameter can be
used to optimize superconducting PCO films (Figure 8.4). A narrow window of lattice
parameters around 12.19 ?A gives superconductivity. Here, amorphous-PLD grown PCO
films consistently have c-axis lattice parameters that are too small (Figure 8.5).
184
Figure 8.4: PCO film Tc and resistivity versus c-axis lattice constant [52, 147].
8.2.2.3 Pulsed Laser Deposition
AchievingsuperconductivityinPr2CuO4 thinfilmsshouldbeamatterofcontrolling
oxygen. Therefore, it should be possible to produce superconductivity in Pr2CuO4 via
standard pulsed laser deposition processes. Films grown by the standard pulsed laser
deposition procedure should have better crystallinity than metal organic deposition or
amorphous-PLD films. However, as this procedure is a greater departure from that which
was reported in References [32, 52, 53, 54], it?s not clear that this is the best path to take.
Growing films by pulsed laser deposition should have only a few key parameters,
deposition pressure, temperature, and time, and annealing pressure, temperature, and
time. In order to make films that are less oxygenated, therefore, the films can either be
grown in reduced oxygen or annealed more aggressively. As overly aggressive annealing
can quickly degrade films, film growth in a less oxidizing atmosphere was attempted.
Focusing on deposition conditions, the extremal films are plotted in Figure 8.6. De-
creasing the deposition pressure provoked a small decrease in resistivity; decreasing the
185
Figure 8.5: The c-axis lattice constant of several amorphous-PLD grown films. The red
line represents the c-axis lattice parameter for un-annealed x = .00 films grown by nor-
mal PLD. The green area is the c-axis lattice parameter for maximal Tc superconducting
Pr2CuO4 (Figure 8.4). The films (+) are ranked in order of increasing oxygen based upon
the aggressiveness of the films? annealing schedules.
186
deposition temperature had a much larger effect. At lower deposition pressures, crys-
talline quality was noticeably degraded in X-ray diffraction. Pr2?xCexCuO4?? needs to
be grown in some pressure oxygen. At lower deposition temperatures, the Tprime phase does
not form. Further oxygen reduction must come from annealing.
Figure 8.6: Pr2CuO4 thin films grown by pulsed laser deposition under various deposition
conditions. Deposition temperatures were varied between 720 C (a73) and 850 C (a77)
with the pressure constant at 230 mTorr N2O. Deposition pressures were varied between
200 mTorr N2O (a76) and 230 mTorr N2O (a78) with temperature constant at 800 C. A
x = .05 Pr2?xCexCuO4?? film (a71) is included for reference. All films were deposited for
30 min and were ?as-grown? (not annealed).
With adjustment of the deposition parameters exhausted, the Pr2CuO4 films were
then annealed under various conditions. Beginning with films deposited at 720 C, the
187
films were vacuum annealed at various temperatures for long times. By substantially
lowering the annealing temperature from 720 C to 600 C, it was found that the films were
more resistant to degradation. This allowed the films to be annealed for much longer
times with a net result of greater annealing taking place. In this manner, the resistance of
the Pr2CuO4 films was dramatically lowered by several orders of magnitude at low tem-
peratures; resistivity measurements also suggested the beginnings of metallic behavior,
d?/dT > 0 (Figure 8.7).
Figure 8.7: Pr2CuO4vacuum annealed for 45 min. The annealed Pr2CuO4 film shows
some metallic (d?/dT > 0) region (insert). The resistivity of the film is much less than
the as-grown films (Figure 8.6).
In addition to becoming more metallic, some of the Pr2CuO4 films have shown
188
sharp low-temperature drops in resistivity consistent with partial superconductivity. How-
ever, these possible Tonsetc films have not been consistently reproducible and therefore are
probably more indicative of uncontrolled parameters in the Pr2CuO4 growth/annealing
process than they are indicators of anything else. The superconducting Pr2CuO4 films
reported in the literature all had c-axis lattice parameters within a narrow range around
of 12.194 ?A, reduced from a bulk value of 12.234 ?A [32, 52]. For my PLD-grown films,
adjustment of deposition parameters and extension of annealing time did not seem to
translate in any consistent ways to c-axis lattice parameters (Figure 8.8).
Figure 8.8: The c-axis lattice parameters of various Pr2CuO4 thin films grown by pulsed
laser deposition. Adjustment of pulsed laser deposition parameters did not seem to con-
sistently produce predictable c-axis lattice parameters.
189
8.2.3 Crystals
In addition to growing thin films of Pr2CuO4 for oxygen reduction, reducing parent-
compound crystals was also attempted. Crystals of Pr2CuO4 (PCO), Nd2CuO4 (NCO),
and Sm2CuO4 (SCO) were annealed. These crystals were available already synthesized.
It was reported that in the parent compounds of Pr2?xCexCuO4??, Nd2?xCexCuO4??,
Sm2?xCexCuO4??, Eu2?xCexCuO4??, and even Gd2?xCexCuO4??, there is superconduc-
tivity [53, 52]. It was hoped that reduction might be easier in crystals compared to films
or in the NCO or SCO systems compared to PCO.
In order to anneal cuprate crystals powder and pellets of the same material and
doping are required. The pellets are created identically to pulsed laser deposition targets
(Chapter 3) with the exception of having a 1 cm diameter rather than a 1 inch diameter.
The powder is created in this same process except it is not pressed into a pellet form but
rather finely ball-milled as the final step. To anneal crystals, the crystal is sandwiched
between two pellets of appropriate material and doping. This sandwich is then placed in a
ceramic boat crucible and fully covered in powder. The anneal then takes place in a tube
furnace under flowing argon, flowing at a rate of 1 bubble per second, for 3 days at 920 C.
Additionally, a small amount of elemental titanium was placed in the furnace next to the
Pr2CuO4, Nd2CuO4, or Sm2CuO4 to act as a getter to ensure a non-reactive atmosphere.
The purpose of the pellets and powder is to slow the rate of oxygen diffusion from the
crystals themselves and provide a more uniform environment.
The annealing of crystals proved to be more difficult to control than the annealing
of films. One bubble per second of flowing argon does not allow the atmosphere to be as
190
accuratelycontrolledasinthepulsedlaserdepositionchamber. Additionally, contaminate
atmosphere is easily introduced into the tube furnace resulting in the crystals chemically
reacting, as evidenced by color changes from black to red, green, and blue. The crystals
of PCO, NCO, and SCO were, additionally, several years old. For most measurements,
PCCO films do not significantly degrade over time; however, for delicate measurements,
like tunneling, fresh films are preferred. Films appear to be the more optimal system for
investigating superconducting Pr2CuO4.
8.3 Thin Films of Iron-Based Superconductors
Following the recent discovery of the ferropnictide superconductors and related
superconducting compounds, attempts were made to synthesize thin films preparations of
thesematerials. Thinfilmsareeasierthancrystalsforsomemeasurements, likemeasuring
the Nernst and Hall effects, and allow easier creation of devices. Here, the experimental
techniques attempted and some of the more promising results obtained are described in
the hope that this project may be revived in the future.
8.3.1 Introduction
Thin films are often more convenient than crystals for measurements. This is partic-
ularly true for measurements where geometry is important. The recently discovered pnic-
tide and chalcogenide superconductors have mostly been investigated as crystals; only
a few groups have successfully synthesized thin films of these iron-based superconduc-
tors. Here at Maryland, some effort was expended to synthesize these materials in thin
191
film form. Although this project is currently inactive, several modifications to the stan-
dard cuprate pulsed laser deposition process (Chapter 3) are significant and worth brief
discussion.
8.3.2 SrFe2?xCoxAs2 Films
The 122 pnictides are not oxides. For cuprates, the pulsed laser deposition atmo-
sphere is maintained at some partial pressure of oxygen. This provides the necessary oxy-
gen for Pr2?xCexCuO4?? film growth (and the oxygen still has to be more finely adjusted
via post-deposition annealing). Thin films of the pnictides, in contrast, have to be grown
in vacuum. The requirements for this vacuum are fairly stringent. At P = 10?8 Torr, the
base pressure of a well-sealed pulsed laser deposition chamber must be reached. Cham-
bers reserved for oxide use are generally not this well sealed and often have a base pres-
sure one or two decades higher.
One of the consequences of growing films under these low pressures is that the
plume of material from the laser-ablation of the target is not well columnated compared
to cuprate plumes grown in higher pressure atmospheres. The plume of pnictide material,
therefore, tends to spread out as it is ejected from the target and the deposition rate de-
clines precipitously with increasing distance between the target and the substrate. In order
to compensate for this tendency, the distance between the target mount and the substrate
heater was decreased to < 1 inch and the optical path was modified in order to continue
illuminating the target with laser energy. The laser power was also increased in order to
boost the amount of material being deposited on the substrate.
192
Additionally, the arsenic content of SrFe2?xCoxAs2 proved problematic. The tox-
icity of arsenic required that the chamber vacuum pumps be vented directly into the gas
cabinet exhaust system. This system already vents the gas cabinets containing fluorine
gas and prevents laboratory contamination. Arsenic also is fairly corrosive so the vacuum
pumps have to be checked for degradation. Arsenic in the target itself and the resultant
122 thin films is chemically bound in the 122 crystal lattice; however, in the pulsed laser
deposition process, the plume created by laser deposition is a plasma and will introduce
elemental arsenic into the chamber atmosphere. This is especially likely due to arsenic?s
low vapor pressure.
The low vapor pressure of arsenic creates difficulties for film synthesis as well.
Oxygen in Pr2?xCexCuO4?? is an extreme example of how the pulsed laser deposition
process is affected by low vapor pressure: the oxygen in the target cannot be relied upon
to travel with the rest of the elements in the plasma plume and deposit on the substrate.
Thus, an oxygen atmosphere is required to maintain oxygen in the growing film. Arsenic
is not nearly as bad as oxygen in this regard and an atmosphere of arsene gas is not
necessary. Shrinking the distance between the target and the substrate, already useful to
control for the thinner atmosphere, helps to prevent the arsenic from escaping from the
films too much.
Films of SrFe2?xCoxAs2 (x ? 0.25) were grown. Superconductivity was seen in
these films (Figure 8.9), however, with a lower onset temperature than has been reported
elsewhere [148].
193
Figure 8.9: SrFe2?xCoxAs2 thin film with Tonsetc = 10 K. The resistivity drop is sup-
pressed by several K in a magnetic field (insert) indicating that it is due to the onset of
superconductivity.
8.3.3 FeSe1?xTex Films
Deposition of the 11 chalcogenides has many similarities to that of the 122 pnic-
tides. The 11 chalcogenides are not oxides and must be grown in vacuum; although,
P = 10?6 Torr is sufficient. Selenium creates many of the same problems for pulsed laser
deposition as arsenic. (Tellurium is similar to selenium in the problems that it creates.)
Toxicity and low vapor pressure are dealt with similarly. The chamber pumps are vented
into the gas cabinet exhaust system to address the former issue and the distance between
the target and substrate is decreased to address the latter issue.
There is some question as to the ?correct? stoichiometry of the FeSe system for su-
perconductivity. Ratherthanhavingtheironandseleniumina1:1ratio,superconductivity
is apparently favored in either slightly selenium-deficient (?1:0.88 [149, 150], ?1:0.92
[151], ?1:0.82 [152]) or iron-rich (?1.01:1 [153]) ratios. The difference between these
two cases is a question of vacancies on the selenium sites or irons on interstitial sites.
194
Here, for the most part, FeSe in a 1:1 ratio was prepared. Selenium deficiency was par-
tially investigated by growing combinatorial films.
The FeSe system can also be doped. Doping tellurium into the FeSe system can
increase Tc [154, 155, 156, 157, 158, 159]. Sulphur can enhance superconductivity [160,
161], as can sodium and cobalt doping [162], although cobalt enhancing Tc is disputed
[163]. Some investigation into the tellurium doped iron selenide system was investigated
here by growing combinatorial films.
A commercial FeSe target was purchased and additional targets of FeSe, FeSe0.6,
and FeSe0.5Te0.5 were prepared. Unlike the target preparation of Pr2?xCexCuO4?? (Chap-
ter 3), the targets were not synthesized as polycrystalline powders of the final material.
Instead, elemental iron and selenium powders were mixed together and sintered. The
laser should ablate the target into a plasma of its constituent elements, so this target-
making procedure should not alter the resultant films. This, however, assumes that the
elements are ablated at the same rate. With single-material targets this is less of an issue;
but, the syntheses of the targets themselves are more difficult.
Thin films of FeSe were prepared at a variety of different substrate temperatures.
For many different growth conditions, epitaxially oriented 11 films were growing on
SrTiO3 substrates. EpitaxywasmonitoredbyobservingfilmX-raypeaksinX-raydiffrac-
tion ??2? scans (Figure 8.10). A partial superconducting transition, with Tonsetc = 12 K,
was seen for many different growth conditions (Figure 8.11). A T0c was not, however,
observed. Magnetic screening was not observed in AC susceptibility, although this is ex-
pected for partial superconductivity. However, the partial transition was suppressed by
about 6 K in a 14 T magnetic field indicating that the 12 K drop in resistance is really due
195
to superconductivity.
Figure 8.10: ? ? 2? X-ray diffraction scans of several FeSe thin films (offset). Films
were deposited at various substrate temperatures from 400 C to 700 C and show various
amounts of epitaxy as indicated by the 00lscript film peaks indexed.
TheprimarytargetsthatwerefocuseduponwereFeSe; however,FeSe0.6 andFeSe0.5Te0.5
targets were also synthesized for growth of combinatorial films. In this technique two
targets are mounted on an adjustable carousel, like that which was used for growing su-
perlattice films (Chapter 6). However, rather than simply alternating targets, a motorized
mask is also made to move across the path of the ablated material. This creates a thickness
gradient of the material being ablated. On the mask?s return path, the other target is used.
This creats a thickness gradient of that material as well, but in the opposite direction. The
196
Figure 8.11: The temperature dependence of resistance for several FeSe thin films. Films
were deposited at various substrate temperatures from 400 C to 550 C and all show
Tonsetc ? 12 K.
197
significant difference between these wedge-shaped layers of alternating material and uni-
form superlattice layers is the layer thickness. The superlattice layers were synthesized
every? 5 to? 20 unit cells (5 to 20 nm for 12.2 ?A unit cells). The combinatorial layers,
however, are designed such that each is only a fraction of a unit cell thick. This is con-
trolled by adjusting the shutter speed relative to the laser pulse rate and energy density.
This adjustment must be performed individually for each target. Layers that are thinner
than a unit cell will not produce a heterostructure, but, rather, will be uniformly incor-
porated into a single crystal lattice. Therefore, the net result will be a smooth gradient
between the two end members along the length of the film.
ThiscombinatorialtechniquewasusedtocreategradientsbetweenFeSeandFeSe0.6
to investigate the selenium deficiency needed for optimal superconductivity. It was also
used to create gradients between FeSe and FeSe0.5Te0.5 for similar reasons. If this project
is resumed, combinatorial growth techniques offer a method for rapidly characterizing
doping phase diagrams of material systems.
198
Chapter 9
Summary and Future Directions
9.1 Angular Magnetoresistance
The magnetic structures of Pr2?xCexCuO4?? and La2?xCexCuO4?? were investi-
gated by angular magnetoresistance measurements. Four-fold angular magnetoresistance
oscillations were found in Pr2?xCexCuO4?? and two-fold angular magnetoresistance os-
cillations were found in La2?xCexCuO4??. The disappearance of angular magnetore-
sistance oscillations was found to track the N?eel temperature in Pr2?xCexCuO4?? and
suggested that magnetism in that system persisted up to x = .15. In La2?xCexCuO4??,
angular magnetoresistance oscillations were also observed to evolve similarly with dop-
ing. The disappearance of these oscillations is also believed to track the N?eel temperature
and also occurs around x = .15. The oscillations are evidence for antiferromagnetism in
this system.
In Pr2?xCexCuO4??, these angular magnetoresistance experiments support the idea
of antiferromagnetism terminating at around x ? .16, a proposed Quantum Critical Point.
Quantum critical behavior in the cuprates has been long debated. In La2?xCexCuO4??,
this work was the first to experimentally demonstrate the existence of antiferromagnetism
intheLa2?xCexCuO4?? system. WhileantiferromagnetisminLa2?xCexCuO4?? hadbeen
assumed based on similar systems like Pr2?xCexCuO4?? or Nd2?xCexCuO4??, the lack of
crystal samples of La2?xCexCuO4?? has frustrated spin-sensitive scattering experiments.
199
The angular magnetoresistance measurements avoided this difficulty.
In order to strengthen this conclusion, it would be useful to more carefully inves-
tigate the origins of the angular magnetoresistance signal. It is taken as an observation
that the zeroing of the angular magnetoresistance amplitude coincides with suppression
of antiferromagnetism. More careful understanding of the exact relationship between an-
tiferromagnetism and angular magnetoresistance would be useful. This is especially true
for the La2?xCexCuO4?? system where the angular magnetoresistance has only two-fold
symmetry rather than the four-fold symmetry expected by the Tprime structure.
9.2 Oxygen and Disorder
Over-oxygenated and irradiated Pr2?xCexCuO4?? at x = .12 and x = .15 were
investigated through resistivity, Hall effect, and angular magnetoresistance. Oxygen is
found to act as both a source of doping and disorder in the system. The doping effect is
found to be a significant effect of over-oxygenation. Under- and optimally-doped films
are seen to behave similarly to over-doped films. Oxygen significantly changes the num-
ber of normal state charge carriers in the system. Additionally, oxygen is seen to have a
strong doping effect in a separate probe of charge carrier concentration; N?eel temperature
suppression via spin-dilution can be controlled by oxygen doping and is largely insen-
sitive to disorder. Also, annealing is indicated as an apical oxygen removal process and
several other proposed annealing models are excluded.
The role of oxygen in Pr2?xCexCuO4??, and the influence of annealing on it, have
long been an issue. By over-oxygenating Pr2?xCexCuO4?? films and observing the shift
200
of Hall effect and angular magnetoresistance oscillation data to effectively lower cerium
dopings, oxygen is seen to act as a dopant, in contrast to models suggesting more com-
plicated roles for oxygen in the electron-doped cuprates. This data support the simpler
picture of O2? hole-doping the system, even with the presence of additional disorder due
to introducing excess oxygen. This data also addresses a long-standing uncertainty in
the understanding of the electron-doped cuprates by supporting the picture that anneal-
ing is primarily about removing apical oxygen, while additionally rejecting several other
proposals in the literature.
Oxygen studies in electron-doped cuprate thin films are always complicated, how-
ever, by a long-standing inability to accurately measure the oxygen concentration and po-
sition in the materials. Careful refinement of chemical analysis techniques as they relate
to oxygen would, therefore, be of much use in understanding the behavior of complicated
oxides like the cuprates. Successful work along these lines would greatly strengthen con-
clusions based upon oxygen studies. More careful correlation between oxygen levels due
to oxygenation versus annealing procedures could strengthen this study?s conclusions, as
well as investigating several different annealing levels, annealing oxygenated films, and
possibly irradiation of off-optimally grown films.
9.3 Superlattices
Enhancement of Tc in superlattices of Pr2?xCexCuO4?? and La2?xCexCuO4?? was
investigated. These structures were pairings of under-doped and over-doped layers. Tc
enhancement was found in these structures and was determined to not be an interface
201
effect by critical current measurements. The Tc enhancement was, instead, found to be
due to charge redistribution. Hall effect and angular magnetoresistance measurements
further clarify this position; charge redistribution appears to result in slightly net-under-
doped films.
Interfaceeffectsbetweenunder-dopedandover-dopedcupratesuperconductorswere
hoped to increase Tc. While this work demonstrates that Tc enhancement does occur in
layered cuprate structures, it refutes proposed interface effects. We demonstrated that the
interface between the layers is not critical for the observed Tc enhancement. These results
discourage seeking enhanced Tcs in these materials via interfacial effects.
The critical current measurements suggesting charge redistribution are supported
by Hall effect and angular magnetoresistance measurements. The two former data sets
are not complete due to a blocked impedance in the PPMS at the time of this thesis
writing. These measurements should be completed on a fuller set of doping pairs in
both the Pr2?xCexCuO4?? and La2?xCexCuO4?? systems. Additionally, the observation
of charge redistribution is speculated to be due to the role of oxygen in the superlattice
films; this hypothesis should be investigated. Charge redistribution might also be able
to be investigated more fully in bi-layer, or reduced layer superlattice, films by slowly
removing layers via ion milling or similar technique and observing changes in transport
properties.
202
9.4 High Temperature Resistance
The high temperature resistance of electron-doped cuprates and Sr-122 pnictides
was measured. The electron-doped cuprates were shown to violate the Mott-Ioffe-Regel
limit. This is consistent with the hole-doped cuprates and is evidence for strong corre-
lations in these materials. The Sr-122s show a saturation at high temperatures at several
hundred ???cm. This saturation is consistent with Mott-Ioffe-Regel limited behavior in
these materials or with coupling due to spin-fluctuations. While coupling due to spin-
fluctuations cannot be ruled out, the likely Mott-Ioffe-Regel limit in the Sr-122s sup-
port the view that the new pnictide high-Tc superconductors are not strongly correlated
systems, in contrast to the cuprate high-Tc superconductors. These measurements sug-
gest that the pnictides are probably reasonably typical metals in terms of normal-state
electron-phonon interactions.
These results are the first observation of possible Mott-Ioffe-Regel limited behavior
in the 122s, a system where the strength of correlations is still under debate. Saturation
at the Mott-Ioffe-Regel limit discourages exotic models for pnictide correlations. Ruling
out strong, cuprate-like correlations in the 122s may additionally have implications for
understanding superconducting properties, like the pairing mechanism, in the pnictides.
This work could easily be extended by the investigation of Mott-Ioffe-Regel limited
behavior, an under-studied direction, in other related systems. The 11 and 1111 systems,
for example, are not expected to have the same strength of electronic interactions as the
122s or as each other. The chalcogenides, in particular, have no high temperature resistiv-
ity data and may be the more correlated of the various iron-based high-temperature super-
203
conductor systems. Additionally, the Prelov?sek and Sega model discussed also predicted
specific behavior for thermopower and Hall effect at elevated temperatures. Modification
of the experimental setup to allow these measurements is suggested as a useful continuing
investigation.
9.5 Superconducting Pr2CuO4 and Pnictide/Chalcogenide Thin Films
Several additional film growth projects were attempted, synthesizing superconduct-
ing Pr2CuO4 by careful control of oxygen and growth of pnictide and chalcogenide thin
films by pulsed laser deposition. These projects are still future work as-is, as these
projects are left incomplete. For superconducting Pr2CuO4, the central issue is the ability
to accurately and consistently control oxygen. The pulsed laser deposition chamber many
not be able to provide the required accuracy in its current form. Modification of the cham-
ber or replacement with other equipment for annealing may be productive directions. For
the iron-based superconductor thin films, the growth parameters must be optimized, and
Maryland?s pulsed laser deposition chambers may need modification to allow tighter con-
trol of parameters. For the iron selenide system, combinatorial growth should be fully
developed.
[164] needs to be cited somewhere
204
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