M
AGNETISM AND
E
LECTRON
T
RANSPORT IN
M
AGNETORESISTIVE
L
ANTHANUM
C
ALCIUM
M
ANGANITE
A D
ISSERTATION
S
UBMITTED TO THE
D
EPARTMENT OF
A
PPLIED
P
HYSICS
AND THE
C
OMMITTEE ON
G
RADUATE
S
TUDIES
OF
S
TANFORD
U
NIVERSITY
I
N
P
ARTIAL
F
ULFILLMENT OF THE
R
EQUIREMENTS
FOR THE
D
EGREE OF
D
OCTOR OF
P
HILOSOPHY
G. Jeffrey Snyder
June 1997
ii
© Copyright by G. Jeffrey Snyder 1997
All Rights Reserved
iii
I certify that I have read this dissertation and that in my
opinion it is fully adequate, in scope and in quality, as a
dissertation for the degree of Doctor of Philosophy.
_______________________________________
Theodore H. Geballe
(Principal Adviser)
I certify that I have read this dissertation and that in my
opinion it is fully adequate, in scope and in quality, as a
dissertation for the degree of Doctor of Philosophy.
_______________________________________
Malcolm R. Beasley
I certify that I have read this dissertation and that in my
opinion it is fully adequate, in scope and in quality, as a
dissertation for the degree of Doctor of Philosophy.
_______________________________________
Robert L. White
(Materials Science Department)
Approved for the University Committee on Graduate
Studies:
_______________________________________
v
Abstract
It is the goal of this thesis to understand the physical properties associated
with the large
negative magnetoresistance found in
lanthanum calcium
manganite. Such
large
magnetoresistances have been
reported that
this
material is
being considered for use as a magnetic field sensor.
However,
there are many variables such as temperature, magnetic field,
chemical
composition
and processing that greatly
influence the magnitude of the
magnetoresistance. After introducing the problem in Chapter 1, Chapters 2
and 3 describe the
materials synthesis and physical
property
measurements
used in this work. In Chapter 4, the intrinsic magnetic and electron
transport
properties of
lanthanum
calcium manganite
are distinguished from those
that depend largely on the
chemical synthesis and processing.
Chemical
substitution of
lanthanum by gadolinium, discus
sed in Chapter 5, not
only
induces ferrimagnetism,
but also dramatically alters the
electron transport
because of slight structural changes. The physical mechanisms and empirical
relationships found among the resistivity, magnetoresistance and magnetism
in Chapters 3 and 4 are studied in greater depth in Chapters 6 and 7 and
compared with theoretical predictions. This analysis provides a useful
method
for predicting the magnetoresistance as a f
unction of temperature,
magnetic field and transition temperature. The related perovskite, strontium
ruthenate, proves to be a model compound
for the
study of
metallic
ferromagnets. The results of this work is presented in two appendices, and
compared with the manganite results throughout the text.
vii
Preface
Looking back at the many years at Stanford, there are many people I
would
like to thank for helping me along the long, windy path to a Ph.D. thesis. My
dad, papa
Schneider,
Dr.
Demin,
and Frank
DiSalvo deserve the
credit for
getting me interested in science: chemistry, engineering, materials science and
physics.
The graduate first year classes at
Stanford would have been
far too
unbearable without the support of my first
year
commiserators Weber, Jim
and Shelly. My time at the Max Planck Institute in Stuttgart, Germany
could
not have been more productive or pleasant thanks to Prof. Dr. Arndt
Simon,
the whole Abteilung Simon and foreign student ghetto especially Paul Rauch,
Thomas Braun and Chris Ewels.
Having nothing to do with superconductivity, much of my
work at
Stanford
was
outside the KGB headquarters in Ginzton
Lab. The
materials
synthesis for this project was done at the Center for Materials Research in the
McCullough building. Bob Feigelson and his group deserve a special
thanks
for advice and use of equipment, such as the laser heated
crystal
growth
apparatus. S
ome of the crystal samples
used in this thesis were grown by
Vlad Beffa, a Stanford undergraduate working as a CMR
summer student. I
would also like to thank the CMR support
staff: Tracy T
ingle with the SEM
microprobe, Glen and
Waldo for keeping up the
x-ray
facility, Ann
Marshall
for TEM studies, and
Thomas Carlson
and Mark Gibson for knowing how to
get
everything done in McCullough. I would
especially like to
thank Bob
White, Shan Wang
and their students for teaching me about magnetic and
magnetoresistive materials in their group meetings.
Thanks also to the KGB group, especially Ted and Mac for helping me get
started. K. A. Moler performed most of the experiment
and
much of the
analysis of the heat
capacity
experiment in Appendix B. Lior Klein
was the
viii
inspiration behind the irreversibility line plot in section 3.2.2.2.9. Thanks also
to Khiem, Steve, Daniel & Jenny, Laurent
and the rest of the curry club for
great conversations at lunch.
Much of this work was done in collaboration with Hewlett-Packard in Palo
Alto. The MOCVD films of the
manganites
were made by
Ron
Hiskes and
Steve DiCarolis. The XAFS studies in Chapter 5 were performed at the
Stanford Linear Accelerator by Corwin Booth
and Bud Bridges from U. C.
Santa Cruz.
This work could not have been completed without the support of
friends,
housemates, parents but particularly Sossina — thank you very much.
Funding for this research was generously provided by The Fanny and John
Hertz
Foundation, the Air
Force Office of
Scientific Research, and the
Stanford Center for Materials Research under the NSF-MRL program
ix
Table of Contents
Abstract
v
Preface
vii
Table of Contents
i x
List of Figures
xiii
List of Tables
xvii
1. INTRODUCTION
1
1.1 Motivation
2
1.2 AMnO
3
3
1.3 Double Exchange
5
2. MATERIALS SYNTHESIS AND CHARACTERIZATION
9
2.1 Sample Preparation
9
2.1.1 Bulk Polycrystalline Samples
9
2.1.2 Single Crystals
10
2.1.2.1 Flux Growth
11
2.1.2.2 Float Zone
12
2.1.2.3 Thin Films
13
2.1.3 Reactive Samples
13
2.2 Characterization
1 4
2.2.1 Elemental Analysis
14
2.2.2 Structural Analysis
14
2.2.2.1 Neutron diffraction
15
2.2.2.2 X-ray diffraction
15
2.2.2.2.1 Powder X-ray diffraction
16
2.2.2.2.2 Single crystal and films
17
2.2.2.3 X-ray Absorption Fine Structure
17
3. ELECTRONIC AND MAGNETIC MEASUREMENTS
1 9
3.1 Transport Properties
1 9
3.1.1.1 Ohm’s Law
19
3.1.1.2 Magnetoresistance
20
3.1.1.3 Drift velocity, mobility, relaxation time and mean free path
21
3.1.1.4 Hall effects
22
3.1.2 Measurement
22
3.1.2.1 Linearity
23
3.1.2.2 Geometry
24
x
3.1.2.3 Contacts
26
3.1.2.4 Reproducibility
27
3.1.2.5 Apparatus
28
3.1.3 Analysis
29
3.1.3.1 Metals
30
3.1.3.1.1 Impurity scattering
30
3.1.3.1.2 Electron-electron scattering
31
3.1.3.1.3 Electron-phonon scattering
31
3.1.3.2 insulators/semiconductors
31
3.1.3.2.1 Band insulators/semiconductors
32
3.1.3.2.2 Polarons
33
3.1.3.2.3 Diffusive Conductivity
35
3.1.3.2.4 Variable range Hopping
35
3.1.3.3 Poor Metals / Heavily doped semiconductors
37
3.1.3.4 Phase transitions
38
3.2 Magnetism
3 9
3.2.1 Measurement
39
3.2.1.1 Apparatus
39
3.2.2 Analysis
43
3.2.2.1 Diamagnetism and Paramagnetism
44
3.2.2.1.1 Larmor diamagnetism
44
3.2.2.1.2 Conduction electron diamagnetism
46
3.2.2.1.3 Pauli paramagnetism
46
3.2.2.1.4 Curie paramagnetism
47
3.2.2.2 Ferromagnetism
49
3.2.2.2.1 Weiss molecular field model
50
3.2.2.2.2 Itinerant electron Model
53
3.2.2.2.3 Generalized Model
55
3.2.2.2.4 Critical region
59
3.2.2.2.5 Landau mean field theory
60
3.2.2.2.6 Arrott Plot
61
3.2.2.2.7 The Curie temperature
61
3.2.2.2.8 Spin waves
63
3.2.2.2.9 Irreversibility
66
3.2.2.3 Antiferromagnetism
69
3.2.2.4 Ferrimagnetism
71
3.2.2.4.1 Mean field model for Gd
0.67
Ca
0.33
MnO
3
72
3.3 Heat Capacity
7 6
3.3.1 Measurement
77
3.3.1.1 Apparatus
78
3.3.2 Analysis
78
3.3.2.1 Electronic specific heat
78
3.3.2.2 Phonon specific heat
79
4. INTRINSIC ELECTRICAL TRANSPORT AND MAGNETIC
PROPERTIES OF LA
0.67
CA
0.33
MNO
3
AND LA
0.67
SR
0.33
MNO
3
MOCVD
THIN FILMS AND BULK MATERIAL
8 0
4.1 Magnetism
8 1
4.1.1 Low Temperature Excitations
83
xi
4.2 Electronic Transport
8 5
4.2.1 Low Temperature Resistivity
86
4.2.1.1 Temperature independent term
89
4.2.1.2 T
2
dependent term
89
4.2.1.3 Relationship to magnetism
91
4.2.2 High Temperature resistivity
92
4.2.3 Transport Near
T
C
93
4.2.4 Hall effect
94
4.2.5 Crystallographic Phase change
96
4.2.6 Small Polarons
96
4.2.7 Colossal Magnetoresistance
97
4.2.8 Domain Boundary Magnetoresistance
99
4.2.9 Low temperature magnetoresistance
99
4.3 Conclusion
9 9
5. LOCAL STRUCTURE, TRANSPORT AND RARE EARTH
MAGNETISM IN THE FERRIMAGNETIC PEROVSKITE
GD
0.67
CA
0.33
MNO
3
101
5.1 Ferrimagnetism
1 0 2
5.1.1 Low temperature moment
103
5.1.2 High temperature susceptibility
104
5.1.3 Low temperature susceptibility
105
5.1.4 Near
T
C
magnetism
107
5.1.5 Magnetism model
108
5.1.5.1 Mean Field Model
108
5.1.5.2 Canted antiferromagnetism
109
5.1.5.3 Spin glass magnetism
110
5.1.5.4 Related Compounds
111
5.2 Electronic Transport
1 1 2
5.2.1 Magnetoresistance
113
5.2.2 Small Polaron Hopping
113
5.2.3 Variable Range Hopping
114
5.3 X-ray Absorption Fine Structure
1 1 4
5.3.1 Relationship of structure to CMR
116
5.4 Conclusion
1 1 6
6. MAGNETOCONDUCTIVITY IN LA
0.67
CA
0.33
MNO
3
118
6.1 Anisotropic magnetoresistance
1 1 8
xii
6.2 Magnetoresistance models
1 1 9
6.2.1 General Model
120
6.2.1.1 Magnetoconductivity model
121
6.2.1.1.1 T >
T
C
regime
123
6.2.1.1.2 T <
T
C
regime
124
6.2.1.1.3 Anisotropic magnetoresistance
125
6.2.1.1.4 Hall Effect
126
6.3 Conclusion
1 2 7
7. CRITICAL TRANSPORT AND MAGNETIZATION OF
LA
0.67
CA
0.33
MNO
3
128
7.1 Magnetism near T
C
130
7.1.1 Spontaneous magnetization exponent
132
7.1.2 Susceptibility exponent
134
7.1.3 Positive nonlinear susceptibility
135
7.1.4 Additional magnetic interaction
137
7.2 Magnetoresistance
1 3 9
7.2.1 Magnetoresistance scaling above
T
C
142
7.2.2 Magnetoresistance scaling below
T
C
144
7.2.3 Magnetoresistance scaling at
T
C
148
7.2.4 Relation to low temperature magnetoresistance
149
7.3 Conclusion
1 5 0
Appendix A. Critical Behavior and Anisotropy in Single Crystal SrRuO
3
152
Appendix B. Magnetic Excitations and Specific Heat in SrRuO
3
173
References
182
xiii
List of Figures
Figure 1-1 The Perovskite structure AMnO
3
where A is a mixture of rare earth and
alkaline earth elements
e.g.
La
0.67
Ca
0.33
.3
Figure 1-2 Double exchange and the electronic structure of AMnO
3
.6
Figure 3-1 Effect of changing the scan length for magnetization measurements. A
YIG crystal is used. The three data reduction schemes are also compared. The
results for the full scan algorithm with scan length less than 5 cm are off scale.41
Figure 3-2 Magnetization of YIG sample as it is rotated along the field axis.
4 3
Figure 3-3 Diamagnetic magnetic susceptibility of typical substrates. The increase
in the susceptibility at low temperatures is due to paramagnetic impurities.
4 5
Figure 3-4 Paramagnetic susceptibility and hysteresis loop of a paramagnetic Fe
containing organometallic compound [78].
4 8
Figure 3-5 Effective paramagnetic moment of Fe in the organometallic compound
[SC(CH
3
)
2
C(CH
3
)NCH
2
CH
2
CH
2
]
2
N
-
FePF
-
6
showing a spin transition [78].
4 9
Figure 3-6 Calculated inverse magnetic susceptibility of SrRuO
3
using the molecular
field model.
50
Figure 3-7 Mean field magnetization calculated in various fields for SrRuO
3
with
T
C
=
165K. Inset show the very small field dependence of the magnetization (forced
magnetization) in this model.
5 2
Figure 3-8 Energy spectrum of magnetic excitations. Spin wave excitations have a
one-to-one dispersion relation while excitations in the Stoner continuum (shaded
region) do not. The intensity of excitations in the Stoner continuum is strongest
where the spin waves meet the continuum.
5 6
Figure 3-9 The inflection
T
C
measured for a SrRuO
3
pellet. For
H
< 1 Tesla the
inflection
T
C
is within 1 K of the Arrott
T
C
= 163 K. At higher
H
the inflection
T
C
increases by only a few degrees.
6 3
Figure 3-10 Correction factor to the
T
3/2
contribution of the magnetization in the spin
wave theory due to a magnetic field
H
.64
Figure 3-11 Correction factor to the
T
3/2
contribution of the heat capacity in the spin
wave theory due to a magnetic field
H
.65
Figure 3-12 SrRuO
3
showing spin-glass like irreversibility of zero-field-cooled and
field-cooled measurements in a small field. The field cooled curve may look
saturated, but is actually less than 1/10 saturated at low temperatures. A small
peak is observed in the zero-field-cooled measurement when the reversibility
point is reached.
6 6
Figure 3-13 Initial magnetization of SrRuO
3
pellet at 5 K, after cooling in zero field.
The magnetization follows a “S” shaped curve providing an inflection point.
6 7
Figure 3-14 Magnetic irreversibility line for polycrystalline SrRuO
3
. Above the line
the magnetization is reversible, below it is irreversible. The irreversibility
exponent is about 1.5.
6 8
Figure 3-15 Time dependent magnetization of SrRuO
3
pellet at 5 K. The field was
increased from 0 to 100 Gauss. The magnetization follows a Log(time)
dependence.
70
Figure 3-16 Magnetic susceptibility of a Pt containing “CaRuO
3
” crystal. The
crystal was aligned with its 2-fold symmetric axis parallel to the applied field has
a susceptibility characteristic of antiferromagnetic moments aligning parallel to
the field, while the 3-fold axis appears to have moments perpendicular to the
field.
71
Figure 3-17 Temperature - tolerance factor phase diagram from reference [100], with
the position of Gd
0.67
Ca
0.33
MnO
3
indicated.
7 3
Figure 3-18 Calculated Arrott Plot for Gd
0.67
Ca
0.33
MnO
3
using the mean field model
with
T
C
= 83.3 K.
7 5
xiv
Figure 3-19 High field differential susceptibility for Gd
0.67
Ca
0.33
MnO
3
calculated using
the mean field model. The maximum is at 11.5 K which is near
T
Comp
= 14.2 K in
this model.
76
Figure 4-1 Magnetization of La
0.67
Sr
0.33
MnO
3
polycrystalline pellet at 10kOe. Inset a,
magnetization at 100Oe used to determine
T
C
= 375K. Inset b, full hysteresis
loop at 5 K.
81
Figure 4-2 Magnetization of La
0.67
Sr
0.33
MnO
3
film (LSM1) on LaAlO
3
at 5kOe. Inset,
full hysteresis loop at 5 K of film and (diamagnetic) substrate.
8 2
Figure 4-3 Magnetization of La
0.67
Ca
0.33
MnO
3
film (LCM15) on LaAlO
3
at 5kOe.
Inset, full hysteresis loop at 5 K of film and (diamagnetic) substrate.
8 3
Figure 4-4 Magnetization of La
0.67
(Ca/Sr)
0.33
MnO
3
films and polycrystalline samples
showing the
T
2
dependence of the magnetization. Inset, same data as a function
of
T
3/2
for comparison.
8 4
Figure 4-5 Comparison of the magnetization of La
0.67
Sr
0.33
MnO
3
with the
T
3/2
term
found at low temperatures, and various fits to the magnetization.
8 5
Figure 4-6 Magnetoresistance of La
0.67
Sr
0.33
MnO
3
polycrystalline pellet and Film
(LSM1). Inset, simultaneous magnetization and resistivity of the film at
20Oersted, along with the magnetoresistance [R(
H
= 0 kOe)-R(
H
= 70 kOe)].
8 6
Figure 4-7 Magnetoresistance of La
0.67
Ca
0.33
MnO
3
film (LCM17). Inset, simultaneous
magnetization and resistivity at 20Oersted, along with the magnetoresistance
[R(
H
= 0kOe) - R(
H
= 70kOe)].
8 7
Figure 4-8 Low temperature resistivity (in zero field) of La
0.67
(Sr/Ca)
0.33
MnO
3
films
(LSM1 and LCM10). Solid lines are the fit to R
0
+ R
2
T
2
+ R
4.5
T
4.5
up to 250K
and 200K for LSM and LCM respectively. The dashed lines show the constant
and
T
2
terms of the best fit.
9 0
Figure 4-9 High temperature resistivity (warming and cooling) of La
0.67
Ca
0.33
MnO
3
film
(LCM17) and crystal in zero field. Inset a, same data with different abscissa to
compare small polaron and semiconductor models. Inset b, DSC trace of
polycrystalline La
0.67
Ca
0.33
MnO
3
showing the heat of the high temperature
structural transition.
9 2
Figure 4-10 High temperature resistivity (warming and cooling) of La
0.67
Sr
0.33
MnO
3
film (LSM1) in zero field. Inset, same data displayed as in Figure 4-9.
9 3
Figure 4-11 Resistance as a function of field La
0.67
(Ca/Sr)
0.33
MnO
3
films (LSM1 and
LCM19) in the Hall effect configuration at 5 K. The Hall effect is calculated
from the slope of the line indicated (see text).
9 5
Figure 4-12 Colossal magnetoresistive La
0.67
Ca
0.33
MnO
3
film from [21, 127].
9 7
Figure 4-13 Simultaneous magnetization and resistivity in a magnetic field of
La
0.67
Sr
0.33
MnO
3
polycrystalline pellet at 5 K. Data for both increasing and
decreasing field are shown. Inset, Magnetoresistance of La
0.67
Ca
0.33
MnO
3
film
(LCM10) at 5 K.
9 8
Figure 5-1 Low temperature magnetization of Gd
0.67
Ca
0.33
MnO
3
measured in a 5 kOe
field and zero field after cooling in a large field (remnant).
1 0 3
Figure 5-2 Inverse magnetic susceptibility of bulk Gd
0.67
Ca
0.33
MnO
3
. Solid line is the
high temperature fit to
χ
=
μ
eff
2
/(8(
T
-
Θ
)) described in the text.
1 0 5
Figure 5-3 Low temperature and high-field magnetic susceptibility,
χ
= (
M
(60 kOe)-
M
(40 kOe))/20kOe, of Gd
0.67
Ca
0.33
MnO
3
crystal. Inset, hysteresis loop at 5 K. 1 0 6
Figure 5-4 Arrott plot of polycrystalline Gd
0.67
Ca
0.33
MnO
3
pellet.
1 0 7
Figure 5-5 Magnetization and inverse magnetic susceptibility calculated for
Gd
0.67
Ca
0.33
MnO
3
using the simplified mean field theory described in the text and
T
C
= 83 K,
T
Comp
= 17 K. The contribution to the magnetization of each sublattice is
shown in dashed lines.
1 0 8
Figure 5-6 High temperature resistivity during heating and cooling a Gd
0.67
Ca
0.33
MnO
3
film,
ln
(
ρ
/
T
) vs. 1/
T
. Inset a, comparison with
ln
(
ρ
) vs. 1/
T
. Inset
b
,
comparison with
ln
(
ρ
) vs. 1/
T
1/4
.
111
xv
Figure 5-7 Low temperature resistivity of Gd
0.67
Ca
0.33
MnO
3
crystal,
ln(
ρ
) vs. 1/
T
1/4
.
Inset
a
, comparison with
ln
(
ρ
/
T
) vs. 1/
T
. Solid lines show linear best fit to the
data shown. Inset
b
, magnetoresistance of a film at 200 K and 300 K; solid line
is the quadratic fit.
1 1 2
Figure 5-8 Fourier transform of
k
χ
(
k
) from (a) Mn
K
-edge and (b) Gd
L
III
-edge data on
Gd
0.67
Ca
0.33
MnO
3
. The solid lines are data collected at
T
= 69 K, while the
triangles (
∆
) are data collected at
T
= 40 K. Agreement between data above and
below
T
C
is well within the errors of the experiment. Transform ranges for the
Gd edge data are from 3.5-12.5 Å
-1
and Gaussian broadened by 0.3 Å
-1
. Transform
ranges for the Mn edge data are from 3.2-12.5 Å
-1
and Gaussian broadened by 0.3
Å
-1
.
115
Figure 6-1 High field (longitudinal) magnetoresistance above and below
T
C
for
La
0.67
Ca
0.33
MnO
3
film. The solid lines show the fit using the indicated equivalent
circuit
123
Figure 6-2 Low field magnetoresistance and magnetization (relative units) of
La
0.67
Ca
0.33
MnO
3
at 0.9
T
C
. The sum of the longitudinal and transverse resistances
minimizes the effect of the anisotropic magnetoresistance.
1 2 4
Figure 6-3 Hall effect of La
0.67
Ca
0.33
MnO
3
below (fully magnetized data only) and
above
T
C
.
126
Figure 7-1.
M
2
vs.
H
/
M
plot for La
0.67
Ca
0.33
MnO
3
float zone crystal. A mean field
ferromagnet has linear isotherms with a positive slope. The negative slope for
T
>
T
C
indicates a faster than linear increase in
M
(inset) due to a highly unusual
positive non-linear susceptibility
χ
3
.
130
Figure 7-2. Data from Figure 7-1 (using the same symbols) scaled with
β
= 0.27 and
γ
= 0.90. According to the scaling hypothesis, all the
T
<
T
C
data should lie on
a single curve while the
T
>
T
C
data should lie on a separate, single curve.
1 3 1
Figure 7-3. Saturation Magnetization,
M
0
as a function of temperature for
La
0.67
Ca
0.33
MnO
3
crystal. At each temperature, the value shown is
M
extrapolated
to
H
= 0 as given by the intercept in Figure 7-1.Solid line is fit to
M
0
(
T
)
∝
(1 -
T
/
T
C
)
β
with
β
= 0.30.
1 3 3
Figure 7-4. Inverse magnetic susceptibility, 1/
χ
0
as a function of temperature for
La
0.67
Ca
0.33
MnO
3
crystal. At each temperature, the value shown is
H
/
M
extrapolated to
H
= 0 as given by the intercept in Figure 7-1. Solid line is fit to
1/
χ
0
∝
(
T
/
T
C
- 1)
γ
with
γ
= 0.7 and
T
C
= 263K.
1 3 6
Figure 7-5. Magnetization in a magnetic field for a La
0.67
Ca
0.33
MnO
3
polycrystalline
pellet at 0.9 and 1.1
T
C
. The solid lines indicate the linear regions in each case.139
Figure 7-6. Magnetoresistance of La
0.67
Ca
0.33
MnO
3
film compared with -
M
2
of a pellet,
both at 0.9
T
C
. The solid line for the magnetoresistance data shows the fit using
the indicated equivalent circuit. The dashed line in the inset compares the
exponential fit.
1 4 0
Figure 7-7. Magnetoresistance of La
0.67
Ca
0.33
MnO
3
film compared with -
M
2
of a pellet,
both at 1.1
T
C
. The solid line for the magnetoresistance data shows the fit using
the indicated equivalent circuit.
1 4 1
Figure 7-8. Fitting parameters
σ
0
and
ρ
∞
for
T
>
T
C
in a La
0.67
Ca
0.33
MnO
3
film. The
temperature dependence of these two parameters reflect the insulating behavior of
the material.
142
Figure 7-9. Fitting parameter
σ
H
2 as a function of temperature in a La
0.67
Ca
0.33
MnO
3
film for
T
>
T
C
. The temperature dependence of
σ
H
2 and the square of the
susceptibility are the same, indicating a relationship between the
magnetoconductance and
M
2
.
143
Figure 7-10. Fitting parameters
σ
0
and
ρ
∞
for
T
<
T
C
in a La
0.67
Ca
0.33
MnO
3
film.
ρ
∞
is
governed by the A + B
T
2
terms in the resistivity while
σ
0
diverges at
T
C
. The
inset shows
σ
0
data fit with a (
T
C
-
T
)
1.8
power law (dashed line), and
σ
∝
exp(
M
/
M
E
)
(solid line). The zero field resistivity
ρ
(
H
= 0) =
ρ
∞
+ 1/
σ
0
is shown
for comparison.
1 4 5
xvi
Figure 7-11. Fitting parameter
σ
H
as a function of temperature in a La
0.67
Ca
0.33
MnO
3
film for
T
<
T
C
. The solid line shows the best fit to the data using a critical
exponent of 0.7.
1 4 6
Figure 7-12. Magnetoresistance of La
0.67
Ca
0.33
MnO
3
film at 262 K
≈
T
C
. The solid line
shows the fit (for the full data on a linear scale) using the indicated equivalent
circuit.
149
Figure A- 1. Magnetization at 5 K of SrRuO
3
single crystal along several
crystallographic directions showing strong cubic but not uniaxial
magnetocrystalline anisotropy. Inset shows the full hysteresis loop of the single
crystal data along with that of a polycrystalline pellet for comparison.
1 5 5
Figure A- 2. Arrott Plot of SrRuO
3
single crystal along easy [110] direction. Inset,
critical isotherm (
T
= 163K
≈
T
C
) on a log scale fit to
M
δ
∝
H
with
δ
= 4.2. 1 5 7
Figure A- 3. Zero field magnetization
M
0
of SrRuO
3
single crystal along easy [110]
direction. Solid line shows the fit to
M
0
(
T
)
∝
(1 -
T
/
T
C
)
β
with
β
= 0.36. Inset
showing the same data on a log plot. The critical exponent
β
appears to change
from Heisenberg-like
β
= 0.39 near
T
C
to Ising-like
β
= 0.32 as
T
decreases.
1 5 8
Figure A- 4. Zero field inverse susceptibility 1/
χ
0
of SrRuO
3
single crystal along
easy [110] direction. Solid line shows the fit to 1/
χ
0
(
T
)
∝
(1 -
T
/
T
C
)
γ
with
γ
=
1.17 and
T
C
= 163.2 K. The inset shows the same data on a log plot.
1 5 9
Figure A- 5. Scaled Arrott Plot of SrRuO
3
single crystal along easy [110] direction
with
β
= 0.36 and
γ
=1.17. Symbols are the same as those used in Figure A- 2.160
Figure A- 6. Magnetization as a function of temperature of SrRuO
3
single crystal
along easy [110] direction. Inset shows the approximate
T
2
dependence of the
magnetization.
161
Figure A- 7. Inverse magnetic susceptibility (1/
χ
=
M
/
H
) at
H
= 10 kOe of
polycrystalline SrRuO
3
compared to the single crystal data from Figure A- 4.
The solid line is the straight-line fit with
T
C
= 165K which demonstrates the
slightly positive curvature of the data.
1 6 4
Figure A- 8. Variation of the
T
3/2
parameter in fitting the magnetization data of single
crystal SrRuO
3
to
M
=
M
S
(1 -
AT
3
/
2
-
BT
2
) as the fitting range is increased. The
upper inset shows the correlation of the
A
and
B
parameters. In the region where
A
is relatively stable (around
T
max
= 60 K),
A
decreases as
T
max
is lowered. The
symbols are the same as those used in Figure A- 9.
1 6 6
Figure A- 9. Variation of the
T
2
parameter in fitting the magnetization data of single
crystal SrRuO
3
to
M
=
M
S
(1 -
AT
3
/
2
-
BT
2
) as the fitting range is increased. In
the region where
B
is relatively stable (around
T
max
= 60 K),
B
increases as
T
max
is
lowered.
167
Figure A- 10. Variation of the
T
2
parameter in fitting the magnetization data of
single crystal SrRuO
3
to
M
=
M
S
(1 -
BT
2
) as the fitting range is increased. The
parameter
B
for this fit is more stable and constant than that shown in Figure A-
8. Inset, variation of
Θ
2
in a magnetic field.
1 6 9
Figure A- 11. Variation of
A
and
B
fitting parameters in the hypothetical case where
the true magnetization is given by
T
3/2
and
T
5/2
terms.
1 7 0
Figure B- 1 Heat capacity of SrRuO
3
cooled in zero field (zfc), in an 8 T magnetic
field, and in zero field after being magnetized (rem). Inset, difference between the
heat capacity measured after cooling in zero field with that in 8 T and the
remnant magnetized state.
1 7 4
Figure B- 2. Zero field heat capacity data fit with two free parameters,
γ
and
β
. Solid
line, including the
T
3/2
contribution expected theoretically for spin waves (see
text). Dashed line, without any
T
3/2
contribution.
1 7 5
Figure B- 3. The linear term of the heat capacity
γ
as a function of magnetic field.
Each circle is from a single
c
P,H
datum between 4.3 and 5 K with phonons
subtracted:
γ
(
H
) = (
c
P,H
(
T
) -
β
T
3
)/
T
with
β
= 0.191 mJ/mol·K
4
.
γ
(
H
) for each
square was determined by fitting 15-20 data points between 6 and 12 K to:
c
P,H
(
T
)
xvii
=
γ
T
+
β
T
3
. The triangles are calculated from the magnetization data of a single
crystal.
176
List of Tables
Table 3-1 Theoretical 3-dimentional critical exponents for different models and
selected experimental values [86, 87].
6 0
Table 4-1 Physical Properties of Polycrystalline Pellets
8 2
Table 4-2 Magnetoresistance of Annealed Films.
8 9
Table 5-1 Transition Temperatures for Gd
0.67
Ca
0.33
MnO
3
.
107
1
M
AGNETISM AND
E
LECTRON
T
RANSPORT IN
M
AGNETORESISTIVE
L
A
0.67
C
A
0.33
M
N
O
3
1. Introduction
The development of
new materials for technological applications has
opened many doors to
innovation in
the 20
th
century. New electronic and
magnetic materials in particular have helped
bring about the
information
revolution. Much of
the progress is due to
materials processing.
Technological applications often have st
rict
compositional and
microstructural requirements
for their materials. An integrated circuit for
instance must have several compatible semiconductor, dielectric, and
metallic materials with
specific properties in precise
locations.
Improvements
using well understood materials such as these are
usually
incremental.
A risky but potentially
more revolutionary method
for
advancing
technologies is to find a different materials which have
inherent properties
superior to those currently in use. There are many
known materials
which
need to be better understood before it would be clear that their use would be a
significant advancement. In some
cases a
previously unknown
class of
compounds (such as the cuprate superconductors) may have to be discovered.
It is also important to consider other aspects of the material, such as
chemical
and thermal stability, toxicity and availability.
The study of
new materials
physics can
have different emphasis.
Many
physicists are interested in new materials
because they can be used to study a
new physical
phenomenon. An
example of this is the
study of
heavy
fermion metals
and superconductors which
have little potential application
2
Chapter 1
in themselves,
but the physics learned
from their
study may be quite
useful.
Conversely, one can use
physics to help
understand new materials for
potential applications. The
physics may be well established but will give
valuable insight into the uses and
limitations of
the material. The
emphasis
of this dissertation is on the latter: what physics can
reveal about a
material
as opposed to what the material can tell you about physics.
1.1 Motivation
This dissertation has been motivated by the desire to understand the
basic
transport and magnetic properties and the physics behind
them in
metallic,
ferromagnetic perovskite oxides. The manganites in particular show a wealth
of complex properties. It has been useful to characterize these properties as
either
common to
ferromagnetic metals in general or unique to the
manganites. For this reason, the
study of
SrRuO
3
has been quite useful i n
understanding the properties of the manganites. For example,
SrRuO
3
and
the manganites shows similar magnetic critical behavior
and low
temperature magnetic excitations. It has also been advantageous to
further
classify
the properties of the manganites as those which
are
intrinsic to the
material and those
affected by processing. The physics of the
intrinsic
properties are easier to study,
while the extrinsic properties can be easily
modified. Once the
inherent
properties of the material
are
understood,
properties which depend strongly on processing can then be tuned for used i n
a device with particular characteristics.
In this chapter some background on the manganites is presented,
focusing
in the recent interest in “Colossal magnetoresistance” (CMR). Chapter 2
briefly summarizes the materials synthesis and characterization. In chapter 3
the magnetism
and transport
experimental
procedures are given as well as
the pertinent analysis and theory. In chapter 4 the results of the
intrinsic
electrical and magnetic properties of La
0.67
Ca
0.33
MnO
3
are presented. I n
chapter 5 the ferrimagnetism
and structure-transport correlations are shown
Introduction
3
for the related
compound Gd
0.67
Ca
0.33
MnO
3
. Chapter 6 introduces the
magnetoconductivity
analysis of the magnetotransport
phenomena
studied
here. In Chapter 7 this analysis is used to
examine the relationship bewteen
the magnetization and the magnetoresistance.
1.2 AMnO
3
The R
1-
x
A
x
MnO
3
perovskite manganites, where R and A are some
rare
earth and alkaline earth
elements respectively
and 0.2 <
x
< 0.5, display the
unusual property of being paramagnetic insulators at high temperatures and
ferromagnetic metals at low temperatures [1-4]. Perovskite is the name of the
structure
type,
Figure 1-1,
containing corner sharing MnO
6
octahedra.
Both
end members of La
1-
x
A
x
MnO
3
are antiferromagnetic insulators
[5],
but become
Mn
A
Oxygen
Figure 1-1 The Perovskite structure
AMnO
3
where A is a
mixture of rare earth and alkaline earth elements
e.g.
La
0.67
Ca
0.33
.
4
Chapter 1
ferromagnetic metals upon doping. The theory of double exchange
[6-8],
described in
section 1.3, has been developed in order to explain
this
phenomenon
and correctly predicts
x
= 1/3 to be
optimal doping
[9]. R e c e n t
calculations show that a second mechanism such as a J
ahn-Teller distortion
may be required to explain the magnetoresistance within the double exchange
model [10-12].
Until recently,
much of the experimental
work on the manganites has
been motivated by their utility as a cathode materials in solid oxide fuel
cells
[13].
Thus many compounds of the
type R
1-
x
A
x
MnO
3+
δ
have been st
udied i n
polycrystalline form [14-1
7].
Much has been learned about their
defect
chemistry and high temperature electronic and ionic conductivity. Most of
these compounds are not
metallic above room temperature
but
have
electronic conductivity, presumably due to (small) polaron
hopping,
sufficient to make good electrodes.
Interest in the perovskite manganites has expanded since their
fabrication
as epitaxial thin films [18, 19]. Some films have shown the insulator to
ferromagnetic metal transition at lower temperatures with a large
magnetoresistance near this transition [20, 21].
∆
R/R(H) of greater
than 10
6
%
has been reported for fields of several Tesla [
22-25].
Since Giant
Magneto
Resistance (GMR) films have a
∆
R/R(H) of typically 20% (which saturates in a
few
thousand
Oersted), the
manganite films have been
proposed as possible
replacements for GMR
read heads in the magnetic recording
industry.
However, since magnetic recording devices work at room temperature
with
low magnetic fields, the temperature range and field sensitivity of the
manganites in their present
state do not make
them competitive with GMR
materials. Nevertheless, the rather imprecise term "Colossal
Magneto
Resistance" (CMR) has been coined for this phenomenon.* However, since it
* It should be noted however, that such a large magnetoresistance is not
Introduction
5
has been widely adopted it will be employed it here where CMR is defined as
∆
R/R(
H
) > 10. CMR materials often refers to all manganite perovskites.
Although the films are quite
stable and the
measurements reproducible
even
after several
months, it is
clear that growth and
annealing
conditions
greatly influence the properties of the manganite films [27].
Furthermore, the
electrical and magnetic properties of the CMR films are often very
different
than those of the materials
produced by bulk ceramic techniques or
single
crystals
with the same
nominal composition.
Thus, in order to
understand
these materials, one should distinguish between the properties intrinsic to
perfect crystalline R
1-
x
A
x
MnO
3
and those caused by
microstructure,
strain,
disorder and/or compositional variations.
From the work
described in chapter 4, it is
concluded that the low
temperature, CMR ph
enomenon is
not intrinsic to the
thermodynamically
stable phases with composition La
0.67
Sr
0.33
MnO
3
or La
0.67
Ca
0.33
MnO
3
.
In chapter 5 the effect of the rare earth
magnetism is shown
for the
case
R = Gd in Gd
0.67
Ca
0.33
MnO
3
. The possibility of structural distortions at
T
C
are
considered for this compound.
1.3 Double Exchange
The theory of double exchange is concerned with the exchange process
involving
d
-band carriers in a mixed valent oxides. First postulated by
Zener
[6] to
explain the properties of
()(
La
A
Mn
Mn )O
3+
1
2
1
34
3
−
+
−
++
xx
x
x
[1, 2, 4],
the theory of
double exchange was
formulated by Anderson
and Hasegawa
[7] a n d
DeGennes
[8]. The compo
unds at the
two ends of the series are
unique to the manganates. Doped EuO and EuS show magnetoresistances
of 10
4
%, using the above definition, and therefore can be considered a
CMR material. Furthermore, it has been shown that in some Chevrel
phase compounds [26], a magnetic field makes the material
superconducting - which would make them “super-magnetoresistance”
(SMR) materials.
6
Chapter 1
antiferromagnetic insulators. For
x
near
1/3,
the compounds become
ferromagnetic and metallic
below the Curie temperature. This
correlation
can be qualitatively explained with the theory of double exchange.
For
x
= 1, the insulating properties
can be understood assuming a
very
large Hund’s rule, exchange splitting, which is about 3
e
V [28]. The
x
= 1 com-
pounds (CaMnO
3
for example) contain entirely Mn
4+
which has 3
d
electrons.
For a transition metal in an octahedral
environment, as is
the
case in the
perovskites, the five degenerate
d
orbitals are split into a low energy, triply
degenerate
t
2
g
set and a
higher
energy, doubly degenerate
e
g
set (Figure 1-2).
The
t
2
g
and the
e
g
orbitals are split by the crystal or ligand field
(by
about 5
e
V),
while the spin-up and the spin-down halves are
split by the exchange energy
(> 5
e
V). The three Mn
4+
d
electrons entirely fill the spin-up
t
2
g
orbitals
while
leaving the
e
g
and the spin-down
t
2
g
orbitals entirely empty. For large
enough
crystal-field and exchange splittings, there is no overlap with the occupied
spin-down
t
2
g
band, and the material is expected to be an insulator.
e
g
t
2g
CaMnO
3
T<T
N
e
g
t
2g
La
1-x
Ca
x
MnO
3
T<T
C
LaMnO
3
T<T
N
∆
La
1-x
Ca
x
MnO
3
T
≥
T
C
t
t
H
Antiferromagnetic
Insulator
Jahn-Teller
∆
Antiferromagnetic Insulator
θ
Double Exchange
t
2
= cos
2
(
θ
/2
)
Metal
↔
Insulator
Ferromagnetic
Metal
Paramagnetic
Insulator
Figure 1-2
Double
exchange and the electronic structure of
AMnO
3
.
Introduction
7
For
x
= 0, the situation is slightly more complex. Most reports claim
that
stoichiometric LaMnO
3
is an antiferromagnet insulator
[29]. It is
apparently
difficult to prepare
stoichiometric LaMnO
3
which likes to lose oxygen or be
rich in
lanthanum.
Off-stoichiometric LaMnO
3
will contain
mixed-valent
manganese and could then be metallic and ferromagnetic.
Stoichiometric
LaMnO
3
contains entirely Mn
3+
which has 4
d
electrons. The first 3 fill the
spin-up
t
2
g
band, as in
CaMnO
3
, while the
remaining electron half-fills the
spin-up
e
g
band. The
e
g
band is apparently
further split, resulting in an
insulator. There are several ways the band could be split, any or all of
which
may be the cause of the
insulating behavior. First of all, a half-filled
band is
susceptible to splitting due to the Mott correlation
effect – producing a
Mott
insulator. Secondly, the structure is not entirely cubic particularly for the end
members. Such a distortion raises the
degeneracy of the
t
2
g
and
e
g
orbitals.
This is known as a Jahn-Teller splitting. Finally, the unit cell
relevant to the
electronic structure may be doubled, which will split the
e
g
band in half. T h e
magnetic structure, by virtue of the
antiferromagnetism,
has a doubled
cell,
which may affect the electronic structure.
At finite values of
x
there will be
x
holes (or 1 -
x
electrons) in the spi
n-up
e
g
band. These holes should be free to move and provide a large
conductivity.
If,
however, the intra-atomic exchange, which holds the spins of all the
d
electrons on a given ion parallel, is stronger than the “hopping
integral,”
then the hopping can only
take place between pairs of ions on which the
t
2
g
spins (Mn
4+
core) are parallel. Otherwise the two sites have different
energies.
The difference in energy is
proportional to
-cos(
θ
/2),
where
θ
is the
angle
between the neighboring core spins. Since free carriers gain kinetic energy by
being itinerant, this provides a type of exchange
mechanism which
holds the
two core spins parallel. Conversely, the
more parallel the
core spins are
aligned, the easier it is for the carriers to become
itinerant. Since a
magnetic
field has a large effect of aligning
ferromagnetically coupled magnetic spins
8
Chapter 1
near
T
C
(magnetic susceptibility becomes large), the application of a
magnetic
field should increase the conductivity near
T
C
. This gives a simple qualitative
explanation for the large negative magnetoresistance observed near
T
C
.
It has been
suggested
the double exchange mechanism alone
cannot
provide such a large effect on the resistance
[10]. It is
proposed, that the
electron-phonon
coupling which localizes the conduction electrons as
polarons at
T
>
T
C
, augments the double exchange mechanism to provide the
observed effects [11, 12]. This conclusion is not universally accepted [9, 30-32].
The polaronic mechanism alone may account for similarly large
magnetoresistance in ferromagnetic semiconductors [30,
33, 34]. The stable
state of a electron donor in a
ferromagnetic semiconductor
can abruptly
shift
from being a shallow to a deep donor as the
temperature is
raised toward
T
C
.
The increasing spin disorder destabilizes the large-radius donor,
which
collapses into a well localized
small-polaronic donor. The
electron-lattice
interaction plays a pivotal role in this phenomenon. The
magneto-resistance
arises because the
temperature of the donor-state collapse and the
accompanying metal-insulator transition are increased by the application of a
magnetic field. Other explanations for magnetoresistance in
ferromagnetic
materials are discussed in chapter 6.
When superexchange is of comparable magnitude to the double exchange,
a canted an
tiferromagnetic ground
state is expected.
This is because
superexchange favors an antiferromagnetic ground
state with energy
proportional to cos(
θ
) while the double exchange is proportional to
-cos(
θ
/2).
The minimum of these two energies is in general some
θ
≠
0 [8].