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University of South FloridaScholar Commons
Graduate Theses and Dissertations Graduate School
January 2013
Magnetism in Complex Oxides Probed byMagnetocaloric Effect and TransverseSusceptibilityNicholas Steven BinghamUniversity of South Florida, [email protected]
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Scholar Commons CitationBingham, Nicholas Steven, "Magnetism in Complex Oxides Probed by Magnetocaloric Effect and Transverse Susceptibility" (2013).Graduate Theses and Dissertations.http://scholarcommons.usf.edu/etd/4440
Magnetism in Complex Oxides Probed by Magnetocaloric Effect and Transverse
Susceptibility
by
Nicholas S. Bingham
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Department of Physics
College of Arts and Sciences
University of South Florida
Co-Major Professor: Hariharan Srikanth Ph.D.
Co-Major Professor: Manh-Huong Phan Ph.D.
Casey Miller Ph.D.
Sarath Witanachchi Ph.D.
Gerald Woods Ph.D.
Michael Osofsky Ph.D.
Date of Approval
April 8, 2013
Keywords: Manganites, Cobaltites, Frustrated Magnets, Phase Separation, Magnetism
Copyright © 2013, Nicholas S. Bingham
DEDICATION
I dedicate this dissertation to all of my friends and family who have helped and
supported me throughout this process. In particular, my wife Gina Bingham, my siblings
Cynda, Matt, Callie, Sarah, Kayla, Erin and Carl, as well as, their spouses and wonderful
children. I also want to specially recognize my parents Dr. Paul Bingham and Julie
Popick, my step-parents Dr. Edward Popick and Cindy Bingham, my father-in-law David
McIntyre and very special thanks to my late mother-in-law Anita McIntyre. I would not
have been able to accomplish this without the support from all of them.
ACKNOWLEDGMENTS
I would like to extend my utmost gratitude to all of the individuals who have
helped me throughout my research to make this dissertation possible. Of course, I would
like to thank my adviser Professor Hariharan Srikanth for his guidance, constant support,
and patience through the writing of this dissertation and all of my Ph.D. work in general.
Professor Srikanth pushed me to ask questions and taught me how to present my research
in a professional manner. I also want to give special thanks to Dr. Manh-Huong Phan,
whose exuberance for science, physics and education was contagious, not just for me but
for everyone he talks to. I will always be grateful to Dr. Phan, for all of his support,
encouragement and guidance throughout all of the research I have been part of at USF. I
will always be grateful to Dr. Alberto Pique, Dr. Michael Osofsky and Dr. Huengsoo
Kim at the Naval Research Laboratory (NRL). They supported me through my Industrial
Practicum, as well as several summers thereafter. I want to thank Professor Victorino
Franco for all of his help with my research as well as his friendship.
I would like to thank my committee members, Dr. Casey Miller, Dr. Sarath
Witanachchi, Dr. Gerald Woods and Dr. Michael Osofsky for stimulating discussions and
general guidance throughout this dissertation. I would like to also thank our collaborators,
in particular, Dr. Christopher Leighton and Dr. Sang-Wook Cheong for providing
excellent quality samples that greatly helped me throughout my research. I want to give
very special thanks to my lovely wife Gina Bingham, without her constant support I
would have never been able to accomplish any of my research. Also, special thanks to my
former lab mate Dr. Anurag Chaturvedi, who has always been there for me as friend and
colleague. I would like to thank all of my current and former lab-mates as well, in
particular Kristen, Paige, Corey, Monet and Natalie for all of the collaboration and fun
throughout my time at USF.
i
TABLE OF CONTENTS
LIST OF FIGURES………………………………………………………………iv
ABSTRACT…………………….…………………………………………….......ix
CHAPTER 1 INTRODUCTION .............................................................................1
1.1 Overview and Motivation ..................................................................... 1
1.2 Objectives of the Dissertation ............................................................... 2
1.3 Outline of the Dissertation .................................................................... 3
CHAPTER 2. FUNDAMENTAL ASPECTS OF MANGANITES ........................6
2.1 Crystal Structure ................................................................................... 7
2.2 Crystal field splitting and the Jahn-Teller effect................................... 9
2.3 Magnetic Interactions.......................................................................... 11
2.4 Conclusions ......................................................................................... 16
References ................................................................................................. 16
CHAPTER 3. EXPERIMENTAL METHODS .....................................................19
3.1 Magnetocaloric Effect ......................................................................... 19
3.1.1 What is the Magnetocaloric Effect? ....................................19
3.1.2 Theoretical Aspects of MCE ...............................................21
3.2 Magnetocaloric Effect as a Fundamental probe…………..….………29
3.2.1 Order of Transitions and Critical Phenomena…………….
............................................................................................................. 25
3.3 Transverse Susceptibility .................................................................... 29
References ................................................................................................. 33
CHAPTER 4 IMPACT OF REDUCED DIMENSIONALITY ON THE
MAGNETIC AND MAGNETOCALORIC RESPONSE OF
La0.7Ca0.3MnO3 ..........................................................................................36
4.1 Introduction ......................................................................................... 36
ii
4.2 Experiment .......................................................................................... 38
4.3 Results and Discussion ....................................................................... 40
4.4 Conclusions ......................................................................................... 45
References ................................................................................................. 45
CHAPTER 5 INFLUENCE OF Sr DOPING ON THE MAGNETIC
TRANSITIONS AND CRITICAL BEHAVIOR OF
La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05, 0.1, 0.2, AND 0.25) SINGLE
CRYSTALS ...............................................................................................48
5.1 Introduction ......................................................................................... 49
5.2 Experiment .......................................................................................... 50
5.3 Results and Discussion ....................................................................... 51
5.4 Conclusions ......................................................................................... 62
References ................................................................................................. 62
CHAPTER 6 MAGNETIC TRANSITIONS, MAGNETOCALORIC
EFFECT, MAGNETIC ANISOTROPY, CRITICAL
EXPONENTS AND THEIR CORRELATIONS IN Pr0.5Sr0.5MnO3.........68
6.1 Introduction ......................................................................................... 69
6.2 Experiment .......................................................................................... 72
6.3 Results and Discussion ....................................................................... 72
6.3.1 Influence of first- and second-order magnetic phase
transitions on the magnetocaloric effect and refrigerant capacity of
Pr0.5Sr0.5MnO3 ................................................................................72
6.3.2 Magnetic Anisotropy and Magnetization Dynamics in
Pr0.5Sr0.5MnO3 ................................................................................86
6.4 Conclusions ......................................................................................... 91
References: ................................................................................................ 92
CHAPTER 7 PROBING MULTIPLE MAGNETIC TRANSITIONS AND
PHASE COEXISTENCE IN La5/8−xPrxCa3/8MnO3 (x = 0.275)
SINGLE CRYSTALS ................................................................................98
7.1 Introduction ......................................................................................... 99
7.2 Results and Discussion ..................................................................... 100
7.2.1 Phase Coexistence and Magnetocaloric Effect ...................100
7.2.2 Transverse Susceptibility ................................................... 109
7.3 Conclusions ....................................................................................... 112
References: .............................................................................................. 112
iii
CHAPTER 8 MAGNETOCALORIC EFFECT AND TRANSVERSE
SUSCEPTIBILITY OF Pr1-xSrxCoO3 (x =0.3-0.5): IMPACT OF
THE MAGNETOCRYSTALLINE ANISOTROPY-DRIVEN
PHASE TRANSITION ............................................................................116
8.1 Introduction ....................................................................................... 117
8.2 Results and Discussion ..................................................................... 118
8.2.1 Anomalous magnetism and Magnetocaloric effect in Pr1-
xSrxCoO3 (0.3 ≤ x ≤ 0.5) ...............................................................118
8.2.2 Transverse susceptibility as a probe of the coupled
structural/magnetocrystalline anisotropy transition in Pr1-xSrxCoO3
(x = 0.5) ........................................................................................125
8.3 Conclusions ....................................................................................... 129
References: .............................................................................................. 130
CHAPTER 9 A COMPLEX MAGNETIC PHASE DIAGRAM AND
MAGNETOCALORIC EFFECT IN Ca3Co2O6 SINGLE
CRYSTALS .............................................................................................133
9.1 Introduction ....................................................................................... 133
9.2 Results and Discussion ..................................................................... 135
9.3 Conclusions ....................................................................................... 142
References: .............................................................................................. 142
CHAPTER 10 CONCLUSIONS AND OUTLOOK ...........................................145
10.1 Conclusions ..................................................................................... 145
10.2 Outlook ........................................................................................... 148
References: .............................................................................................. 150
APPENDICES .....................................................................................................151
APPENDIX A LIST OF PUBLICATIONS ........................................... 152
APPENDIX B LIST OF CONFERENCE PRESENTATION................ 156
iv
LIST OF FIGURES
Figure 2.1: Idealized cubic perovskites phase: Mn3+
/4+
(green) occupy the center of the
cube, oxygen ions (red) form octahedra around the Mn3+
/4+
ions. And the trivalent rare
earth or divalent alkali earth (blue) forms the corners of the cube. .................................... 7
Figure 2.2: The Pnma unit cell of La1-xCaxMnO3 (taken from [8]) showing general
distortions of the standard cubic lattice. The ions are represented by black (manganese),
grey (La or Ca) and white (oxygen) spheres. ...................................................................... 8
Figure 2.3: Crystal field splits degenerate 3d orbitals into eg and t2g levels, then crystal
distortion due to the Jahn-Teller effect, further splits the degenerate eg and t2g levels
(taken from [10]). .............................................................................................................. 10
Figure 2.4: A schematic representation of the double exchange mechanism showing the
simultaneous transfer of electrons between Mn3+
to O2-
and from the O2-
to Mn4+
ions
taken from [14]. ................................................................................................................ 12
Figure 2.5: Schematic representation showing the arrangement of spins and orbitals in
superexchange taken from [14]. ........................................................................................ 14
Figure 2.6: CE -type charge ordering along ab-plane in La0.5Sr0.5MnO4 taken from
[http://folk.uio.no/ravi/activity/ordering/chargeordering.html] ........................................ 15
Figure 2.7: Various forms of orbital ordering in the manganites taken from
[http://folk.uio.no/ravi/activity/ordering/orbitalordering.html] ........................................ 16
Figure 3.1: Schematic of a working magnetic refrigerator. Image credit Tegus et. al.
Nature 415 (2002). ............................................................................................................ 20
Figure 3.2: The method for calculating the RC from the −SM(T) curve using Eq. (3.13)
for two types of transitions in Pr0.5Sr0.5MnO3. .................................................................. 24
Figure 3.3: (a)Schematic diagram of the transverse susceptibility circuit, (b) schematic
depiction of transverse susceptibility probe , (c) Quantum Design PPMS. ...................... 31
Figure 3.4: Transverse and parallel susceptibility (T and P respectively) for single-
domain magnetic particles. Image from reference [20]. ................................................... 32
Figure 4.1: Phase diagram of La1-xCaxMnO3, showing the subtle balance between
chemical doping and magnetic properties (taken from [2]). ............................................. 37
v
Figure 4.2: Schematic representation of a pulsed laser deposition system. Image credit
Andor Technology. ........................................................................................................... 39
Figure 4.3: Temperature dependence of magnetization recorded on cooling in a field of
500 Oe and normalized to 25 K value. Lines are guide to the eye. Inset: First derivative of
magnetization. ................................................................................................................... 41
Figure 4.4: (a) Comparison of temperature-dependent entropy change in bulk and thin-
film La0.7Ca0.3MnO3 samples under an applied field change of 5T. (b) The refrigerant
capacity as a function of applied magnetic field. .............................................................. 42
Figure 4.5: H/M vs M2 for bulk and thin-film La0.7Ca0.3MnO3 ....................................... 43
Figure 4.6: Universal curve calculations as described in the text for the polycrystalline
bulk (a) and thin-film (b) forms of La0.7Ca0.3MnO3. ......................................................... 44
Figure 5.1: Temperature dependence of magnetization taken at 5 kOe. Inset shows the
dependence of the Curie temperature (TC) on the Sr-doped content. The boundary line
between the orthorhombic (Pbnm) and rhombohedral (R3c) phases is taken at x = 0.15.
From [44]. ......................................................................................................................... 52
Figure 5.2: The H/M vs. M2 plots for representative temperatures around the TC for the
La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05, 0.1 and 0.2) samples. From [44]. ................................ 53
Figure 5.3: Modified Arrott plot isotherms with 1K temperature interval for the
La0.7Ca0.3-xSrxMnO3 (x=0.1, 0.2 and 0.25) samples. From [44] ........................................ 55
Figure 5.4: Temperature dependence of spontaneous Ms (square) and inverse initial
susceptibility 0-1
(circles) for the x=0.2 sample; solid lines are fitting curves to Eqs.
(3.15) and (3.16), respectively. From [44]. ....................................................................... 56
Figure 5.5: The linearity of the M(T = TC) versus H
=H
curves validates the
values of the critical exponents. From [44]. ..................................................................... 57
Figure 5.6: Normalized isotherms of La0.7Ca0.3−xSrxMnO3 (x = 0.1 and 0.2) samples
below and above Curie temperature (TC) using the values of and determined from K-F
method. From [44]. ........................................................................................................... 59
Figure 6.1: Temperature dependence of ZFC and FC magnetizations taken at a field of
0.05 T. ............................................................................................................................... 73
Figure 6.2: Temperature dependence of magnetization taken at different magnetic fields
up to 5T. ............................................................................................................................ 74
Figure 6.3: Isothermal magnetization curves taken at different fixed temperatures
between 65 and 300 K for the Pr0.5Sr0.5MnO3 manganite: (a) around TC and (b) around
TCO. .................................................................................................................................... 75
vi
Figure 6.4: Temperature dependence of magnetic entropy change (−SM) at different
applied fields up to 5 T. .................................................................................................... 76
Figure 6.5: Magnetic field dependence of RC for the cases around TC and TCO (without
and with subtracted hysteretic losses). The inset shows the magnetic field dependence of
magnetization taken at 150 K (below TCO) and at 180 K (below TC). .............................. 77
Figure 6.6: Determination of the critical exponents n (panel a) and Δ (panel b) after
fitting of δs and εr, respectively, as a power law of the reduced magnetic field H/Hf. .... 80
Figure 6.7: Dimensionless renormalized temperature t* or field h* dependence of the
dimensionless temperature renormalized magnetization mt* (a), of the dimensionless
field renormalized magnetization mh* (b in logarithmic scales) ...................................... 81
Figure 6.8: Inverse of the dimensionless isothermal susceptibility jh* ............................ 82
Figure 6.9: Temperature (a) and field (b) dependence of the magnetization, and
temperature dependence of SM (c). The dark sold lines in (a) and (b) and the solid lines
in (c) are fits to the data via the ANEOS .......................................................................... 84
Figure 6.10: (a) Temperature dependence above TC of the inverse of the experimental
isothermal initial susceptibility 0 (solid symbol *), along with the ones offered by Eq.
(6) (open symbol ○) and Eq. (15) (lines). (b) Temperature dependence above TC of the
critical exponent ( )ef T (solid symbol) and the value of ·=1.440 presented in the sample
when the FM clusters and their interactions have disappeared above 300 K (dashed line).
........................................................................................................................................... 86
Figure 6.11: An example of unipolar transverse susceptibility scan of Pr0.5Sr0.5MnO3 (a).
3-D Unipolar scans of transverse susceptibility as a function of magnetic field and
temperature (b). ................................................................................................................. 87
Figure 6.12: Temperature dependence of effective anisotropy field (HK), switching field
(HS), and peak height of transverse susceptibility curves ([T/T]max) ........................... 90
Figure 6.13: Unipolar transverse susceptibility and first magnetization with respect to
applied magnetic field at T=140K. ................................................................................... 91
Figure 7.1: Zero-field-cooled and field cooled M(T) with 10mT applied field, measured
on warming [24]. ............................................................................................................. 101
Figure 7.2: The M(H) curves for some selected temperatures. The arrows indicate the
way in which the virgin, return, and second magnetization curves were measured [24].
......................................................................................................................................... 103
Figure 7.3: Temperature dependence of magnetic entropy change (−∆SM) for LPCMO
for the magnetic field change of 1.5 T and 6 T, respectively [24] .................................. 104
vii
Figure 7.4: (a) Magnetic field dependence of maximum magnetic-entropy change
([−SM]max) for LPCMO at 75 K; (b) the magnetic hysteresis loop M(H) measured at 75K
[24]. ................................................................................................................................. 106
Figure 7.5: (a) Magnetic field dependence of maximum magnetic-entropy change
([−SM]max) for LPCMO at 205 K; (b) the magnetic hysteresis loop M(H) measured at
205 K [24]. ...................................................................................................................... 108
Figure 7.6: (a-d): Bipolar TS scans below TC (a) and above TC (b-d). .......................... 110
Figure 7.7: New phase diagrams for LPCMO developed from TS vs HDC (a) Positive and
negative switching field as a function of temperature. (b) Maximum change in TS at
HDC=0 as a function of temperature. ............................................................................... 111
Figure 8.1: Temperature dependence of the magnetization of Pr1−xSrxCoO3 (x=0.3, 0.35,
0.4, and 0.5) compounds when a magnetic field 0H=5 T is applied. Inset: Temperature
dependence of the magnetization at low field (0H=1 mT) and intermediate field
(0H=0.1T) in the x=0.5 sample. .................................................................................... 119
Figure 8.2: Field dependence, from 5 K to 320 K in 5 K increments, of the magnetization
of the polycrystalline Pr0.5Sr0.5CoO3 compounds. The magnetization curve is marked
(open symbol) at the Curie temperature of the sample TC(x=0.5)=230 K. ..................... 120
Figure 8.3: Temperature dependence of the magnetic entropy change for 0H=5 T of the
Pr1−xSrxCoO3 (x = 0.3, 0.35, 0.4, and 0.5) compounds. Solid arrows indicate the
temperatures (TA) of the second phase transition that occurs at low temperature Inset:
Reduced temperature dependence of the magnetic entropy change near TC .................. 121
Figure 8.4: Field dependence of the maximum magnetic entropy change (panel a) and
the refrigerant capacity (panel c) in the studied polycrystalline Pr1−xSrxCoO3 (x=0.3, 0.35,
0.4, and 0.5) compounds. Dimensionless field dependence of the dimensionless
maximum magnetic entropy change s (panel b), and dimensionless refrigerant capacity
rc (panel d). The non-collapse into two master curves indicates that the exponents n1 and
n2 are composition dependent. ........................................................................................ 123
Figure 8.5: Bipolar transverse susceptibility scans of Pr0.5Sr0.5CoO3 as a function of
applied field for 20K (a), 95K (b), 110K (c), and 225K (d). On 8.5(a) the arrows indicate
the sequence of measurement and the anisotropy (Hk), crossover (Hcr), and switching (HS)
peaks are labeled [22]. .................................................................................................... 125
Figure 8.6: Unipolar transverse susceptibility scans for several different temperature
plotted on two plots depicting the two different ferromagnetic phases ((a) is FM1 and (b)
is FM2). The signal intensity appears in arbitrary units as soon of the curves have been
shifted upward or downward for clarity [22]. ................................................................. 126
viii
Figure 8.7: Temperature dependence of the peaks positions in the transverse
susceptibility measurement. (a) Anisotropy field (+HK) (b) Switching field (HS) (c)
Crossover field (Hcr) [22]... ............................................................................................. 128
Figure 9.1: Temperature dependence of (a) dc-magnetization at an applied field of 100
Oe (b) ac susceptibility with small ac magnetic field ~10 Oe at a variety of frequencies.
Also, magnetic field dependence of magnetization at 25K (c) and 5K (d). .................... 136
Figure 9.2: Isothermal magnetization vs applied field, for a temperature range of 120K-
5K with a temperature interval of 5K, and magnetic field from 0-7T. ........................... 137
Figure 9.3: Change in magnetic entropy as a function of temperature, calculated using
the thermodynamic Maxwell relation (Eqn. 3.9). ........................................................... 138
Figure 9.4: Change in magnetic entropy as a function of applied field at various constant
temperatures, (a) 30K, (b) 20K, (c) 15K and (d) 10K. ................................................... 140
Figure 9.5: (a) First derivative of the field dependent change in entropy. (b) Magnetic
phase diagram derived from the field and temperature dependent change in magnetic
entropy. ........................................................................................................................... 141
9
ABSTRACT
Magnetic oxides exhibit rich complexity in their fundamental physical properties
determined by the intricate interplay between structural, electronic and magnetic degrees
of freedom. The common themes that are often present in these systems are the phase
coexistence, strong magnetostructural coupling, and possible spin frustration induced by
lattice geometry. While a complete understanding of the ground state magnetic properties
and cooperative phenomena in this class of compounds is key to manipulating their
functionality for applications, it remains among the most challenging problems facing
condensed-matter physics today. To address these outstanding issues, it is essential to
employ experimental methods that allow for detailed investigations of the temperature
and magnetic field response of the different phases.
In this PhD dissertation, I will demonstrate the relatively unconventional
experimental methods of magnetocaloric effect (MCE) and radio-frequency transverse
susceptibility (TS) as powerful probes of multiple magnetic transitions, glassy
phenomena, and ground state magnetic properties in a large class of complex magnetic
oxides, including La0.7Ca0.3-xSrxMnO3 (x = 0, 0.05, 0.1, 0.2 and 0.25), Pr0.5Sr0.5MnO3, Pr1-
xSrxCoO3 (x = 0.3, 0.35, 0.4 and 0.5), La5/8−xPrxCa3/8MnO3 (x = 0.275 and 0.375), and
Ca3Co2O6.
First, the influences of strain and grain boundaries, via chemical substitution and
reduced dimensionality, were studied via MCE in La0.7Ca0.3-xSrxMnO3. Polycrystalline,
single crystalline, and thin-film La0.7Ca0.3-xSrxMnO3 samples show a paramagnetic to
10
ferromagnetic transition at a wide variety of temperatures as well as an observed change
in the fundamental nature of the transition (i.e. first-order magnetic transition to second
order magnetic transition) that is dependent on the chemical concentration and
dimensionality.
Systematic TS and MCE experiments on Pr0.5Sr0.5MnO3 and Pr0.5Sr0.5CoO3 have
uncovered the different nature of low-temperature magnetic phases and demonstrate the
importance of coupled structural/magnetocrystalline anisotropy in these half-doped
perovskite systems. These findings point to the existence of a distinct class of phenomena
in transition-metal oxide materials due to the unique interplay between structure and
magnetic anisotropy, and provide evidence for the interplay of spin and orbital order as
the origin of intrinsic phase separation in manganites.
While Pr0.5Sr0.5MnO3 provides important insights into the influence of first- and
second-order transitions on the MCE and refrigerant capacity (RC) in a single material,
giving a good guidance on the development of magnetocaloric materials for active
magnetic refrigeration, Pr1-xSrxCoO3 provides an excellent system for determining the
structural entropy change and its contribution to the MCE in magnetocaloric materials.
We have demonstrated that the structural entropy contributes significantly to the total
entropy change and the structurally coupled magnetocrystalline anisotropy plays a crucial
role in tailoring the magnetocaloric properties for active magnetic refrigeration
technology.
In the case of La5/8−xPrxCa3/8MnO3, whose bulk form is comprised of micron-sized
regions of ferromagnetic (FM), paramagnetic (PM), and charge-ordered (CO) phases, TS
and MCE experiments have evidenced the dominance of low-temperature FM and high-
11
temperature CO phases. The “dynamic” strain liquid state is strongly dependent on
magnetic field, while the “frozen” strain-glass state is almost magnetic field independent.
The sharp changes in the magnetization, electrical resistivity, and magnetic entropy just
below the Curie temperature occur via the growth of FM domains already present in the
material, even in zero magnetic field. The subtle balance of coexisting phases and kinetic
arrest are also probed by MCE and TS experiments, leading to a new and more
comprehensive magnetic phase diagram.
A geometrically frustrated spin chain compound Ca3Co2O6 provides an interesting
case study for understanding the cooperative phenomena of low-dimensional magnetism
and topological magnetic frustration in a single material. Our MCE studies have yielded
new insights into the nature of switching between multi-states and competing interactions
within spin chains and between them, leading to a more comprehensive magnetic phase
diagram.
1
CHAPTER 1.
INTRODUCTION
1.1 Overview and Motivation
Materials that exhibit a coupling among magnetic, structural and electronic degrees
of freedom have been the center of focus for many years now from, an applications point
of view, as well as for a fundamental understanding. Research of complex oxide
materials exploded in 1986 with the discovery of the high critical temperature (high-TC)
cuprate superconductors [1]. Since then a whole host of oxide compounds have been
discovered with a seemingly endless number of interesting phenomena. These
phenomena range from all types of magnetism, i.e. ferromagnetism (FM), ferrimagnetism
(FIM), antiferromagnetism (AFM), paramagnetism (PM), canted-AFM etc. [2-10].
Electronic properties such as ferroelectricity, charge/orbital ordering, metallic, insulating,
semiconducting, superconductivity, spin-state transitions etc. all occur in a wide variety
of structures, which can cause localized lattice distortions leading to phase-separation and
geometrical magnetic frustration among other phenomena [3]. All of these properties are
greatly influenced by external fields (such as magnetic, electric, temperature and external
pressure), as well as internal forces induced by chemical doping [2, 5-8, 10].
Interestingly, most of the properties listed above can exist in a single material when
there is a strong coupling amongst all of the degrees of freedom, leading to complex
2
phase diagrams. All of the aforementioned properties in oxides have been studied in great
detail; however, there is still not a generalized theory on the mechanism causing such
complex behavior. For example, high-TC superconductivity and colossal
magnetoresistance have been under debate for more than 20 years, now.
The properties of complex oxides can be realized for a wide variety of potential
applications, ranging from spintronic devices, sensors, MOSFETS (metal-oxide-
semiconductor field-effect transistors), magnetic refrigeration, etc. However wide the
applications are for this class of materials, one could imagine a seemingly endless
number of applications, if the nature of the materials was fully understood.
1.2 Objectives of the Dissertation
The overall objectives of this dissertation are to explore the fundamental nature of
magnetic phase transitions in complex correlated electron oxides with the magnetocaloric
effect (MCE) and transverse susceptibility (TS) probes.
Specific objectives are:
1. To implement MCE and TS as fundamental probes for magnetic, electrical and
structural properties of complex oxide materials synthesized in the Functional
Materials Laboratory at the University of South Florida or acquired from our
collaborators.
2. To systematically investigate, by chemical doping or size reduction, the influence
of first/second- order magnetic phase transitions on MCE.
3. To investigate complex phenomena related to the coupling of the crystalline
structure and magnetocrystalline anisotropy.
3
4. To use MCE and TS probes to study materials that exhibit multiple magnetic and
electronic phenomena simultaneously, known as phase-separation.
5. To investigate geometrically-induced magnetic frustration and related
phenomena, using MCE, in Ca3Co2O6.
1.3 Outline of the Dissertation
The present dissertation aims to provide a comprehensive understanding of MCE
and TS effects on complex magnetic oxide materials, as well as provide a detailed
description of the fundamental nature of magnetic phase transitions in these materials.
For these reasons, this dissertation will be presented in the following chapters:
Chapter 1 gives an overall overview of the motivation of this Ph.D. research
work.
Chapter 2 discusses the fundamental properties, currently known, in doped R1-
xMxMnO3 (where R is a trivalent rare-earth, M is a divalent alkaline earth metal)
manganite compounds.
Chapter 3 gives an overview of the experimental methods used throughout this
dissertation, namely, MCE and TS.
Chapter 4 shows the influence of reduced dimensions on the magnetocaloric
properties of La0.7Ca0.3MnO3 bulk polycrystalline and thin-film samples.
Chapter 5 provides a detailed description of the effects of Sr doping in the
La0.7Ca0.3-xSrxMnO3 manganite on the magnetic phase transitions, as well as the critical
phenomena.
4
Chapter 6 discusses the influence of a first/second- order magnetic transitions on
MCE, as well as the influence of a structural transition on the magnetic properties in
Pr0.5Sr0.5MnO3, probed by TS.
Chapter 7 presents a systematic study on the subtle balance between multiple
phases coexisting in the same temperature regime in phase-separated La5/8−xPrxCa3/8MnO3
(x = 0.275 and 0.375) single crystals.
Chapter 8 demonstrates very strong coupling between structure and
magnetocrystalline anisotropy and its impact on the MCE in Pr1-xSrxCoO3 (x = 0.3, 0.35,
0.4, and 0.5).
Chapter 9 demonstrates the overall usefulness of the MCE as a fundamental
probe, when a new phase diagram is presented in the very complicated, geometrically
frustrated, Ca3Co2O6 single-crystal.
Chapter 10 summarizes all of the important results presented throughout the
dissertation, as well as various plans for future implementation of the MCE and TS
probes.
References
[1] J.G. Bednorz, K.A. Muller, Possible High-Tc Superconductivity in the Ba-La-Cu-O
System, Z Phys B Con Mat, 64 (1986) 189-193.
[2] E. Dagotto, Open questions in CMR manganites, relevance of clustered states and
analogies with other compounds including the cuprates, New J Phys, 7 (2005).
[3] E. Dagotto, Complexity in strongly correlated electronic systems, Science, 309 (2005)
257-262.
5
[4] M.H. Phan, N.A. Frey, M. Angst, J. de Groot, B.C. Sales, D.G. Mandrus, H. Srikanth,
Complex magnetic phases in LuFe2O4, Solid State Commun, 150 (2010) 341-345.
[5] M.H. Phan, S.C. Yu, Review of the magnetocaloric effect in manganite materials, J
Magn Magn Mater, 308 (2007) 325-340.
[6] C.N.R. Rao, B. Raveau, Colossal magnetoresistance, charge ordering and related
properties of manganese oxides, World Scientific, Singapore ; River Edge, N.J., 1998.
[7] P.A. Sharma, S. El-Khatib, I. Mihut, J.B. Betts, A. Migliori, S.B. Kim, S. Guha, S.W.
Cheong, Phase-segregated glass formation linked to freezing of structural interface
motion, Phys Rev B, 78 (2008).
[8] P.A. Sharma, S.B. Kim, T.Y. Koo, S. Guha, S.W. Cheong, Reentrant charge ordering
transition in the manganites as experimental evidence for a strain glass, Phys Rev B, 71
(2005).
[9] Y. Tokura, N. Nagaosa, Orbital physics in transition-metal oxides, Science, 288
(2000) 462-468.
[10] Y. Tokura, Y. Tomioka, Colossal magnetoresistive manganites, J Magn Magn
Mater, 200 (1999) 1-23.
6
CHAPTER 2.
FUNDAMENTAL ASPECTS OF MANGANITES
The discovery of colossal magnetoresistance (CMR) in doped manganites with
the general formula R1−xMxMnO3 (R = La, Pr, Nd, Sm, and M = Sr, Ca, Ba, and Pb) has
stimulated intense research into their physical properties [1]. The relationship between
the ferromagnetism and conductivity (e.g. the relationship between the metal–insulator
(MI) transition and the ferromagnetic-paramagnetic (FM-PM) transition) in several CMR
materials has continued to generate interest and reveal new insights, primarily due to the
complexity of the systems [2-7].
It has been experimentally shown that while the parent compound RMnO3 is an
insulating antiferromagnet, substitution of the trivalent R3+
ion by a divalent M2+
ion
leads to coexistence of Mn3+
and Mn4+
ions and, at sufficiently high doping levels (x), the
material becomes a conducting ferromagnet [1]. The metallic ferromagnetic state in
doped manganites was widely interpreted using the double-exchange (DE) mechanism
[8]. According to this model, the transfer of an itinerant eg electron between the
neighboring Mn sites (local t2g spins) via the O2−
ion results in a ferromagnetic interaction
due to the on-site Hund’s rule coupling. This model is effective for certain types of
manganites, but, it leaves a lot to be desired. In particular, the understanding of the
complex nature of phase transitions, phase coexistence and separation, and the
magnetostructural coupling phenomena in several mixed-valent manganite systems has
7
remained elusive. By using the magnetocaloric effect (MCE) and transverse
susceptibility (TS) measurements, we hope to gain deeper physical insights into the
ground state magnetic properties and magnetic field-induced phenomena in these
complex materials.
2.1 Crystal Structure
R1−xMxMnO3 belongs to the general perovskite family, ABO3. The Mn ions
occupy the B-site at the center of the unit cell, while oxygen ions coordinate around the
Mn ion, forming MnO6 octahedra. The R3+
and M2+
ions are then distributed randomly
over the A-sites in the crystal. The high temperature (~1000 K) cubic phase can be seen
in figure 2.1.
Figure 2.1: Idealized cubic perovskites phase: Mn3+
/4+
(green) occupy the center of the
cube, oxygen ions (red) form octahedra around the Mn3+
/4+
ions. And the trivalent rare
earth or divalent alkali earth (blue) forms the corners of the cube.
At lower temperatures, the MnO6
octahedra become distorted, thereby reducing
the symmetry of the structure. This distortion from the idealized cubic structure can be
simply parameterized via the Goldschmidt tolerance factor (t):
8
⟨ ⟩
√ ( ),
(2.1)
where ⟨ ⟩ (1.21 Ǻ) and (Mn3+ = 0.58 Ǻ, Mn
4+=0.53 Ǻ) [9], are the
average radii of the A-site cation, oxygen, and manganese ions, respectively. For the
idealized cubic case presented in Figure 2.1, t = 1, however, stable values range from 0.8
< t < 1.
Cubic: t = 1
Rhombohedral: 0.96 ≤ t <1
Orthorhombic: t < 0.96
Figure 2.2: The Pnma unit cell of La1-xCaxMnO3 (taken from [8]) showing general
distortions of the standard cubic lattice. The ions are represented by black (manganese),
grey (La or Ca) and white (oxygen) spheres.
Generally, the size of the A-site cations differs greatly from the idealized cubic
model (a linear variation from 1.32Ǻ to 1.25Ǻ for x = 0 and x = 1, respectively), this will
lead the MnO6 octahedra to rotate or distort to improve packing. This distortion in the
9
MnO6 leads this class of perovskites to have a true orthorhombic Pnma unit cell, as
shown in figure 2.2.
Electrical conduction and magnetic ground states are greatly influenced by the
distortion of the MnO6 octahedra. A conduction band is formed in the manganites via the
overlap of Mn 3d and O 2p orbitals. Therefore, by distorting the MnO6 octahedra, there
will be lengthening or bending of the Mn-O-Mn bond, thereby reducing orbital overlap
and hopping amplitude of the itinerant eg electrons. Further evidence for the importance
of chemical doping will be discussed throughout this thesis.
2.2 Crystal field splitting and the Jahn-Teller effect
In the idealized cubic perovskite structure, the five-fold degeneracy of the Mn 3d
orbitals is split into two levels (t2g triplet and eg doublet) by the octahedral crystal field.
The electron state will be defined from Hund’s rules:
1. Maximize spin angular momentum |S|
2. Maximize orbital angular momentum |L|
3. If an orbital is less than half-filled, the total angular momentum (J) is
J=|L-S|. If the orbital is more than half-filled, J=|L+S|. If the orbital is
half-filled then L=0 via rule 1 and the Pauli Exclusion Principle.
Therefore the three 3d electrons in Mn4+
are strongly spin aligned in the lower t2g
level, forming a “core” spin S=3/2. Meanwhile, Mn3+
has an extra electron, which, due to
Pauli Exclusion Principle and strong Coulomb repulsion, resides in the eg level. Due to
Hund’s coupling the eg electron is spin coupled to the “core” S=3/2 electrons.
10
Figure 2.3: Crystal field splits degenerate 3d orbitals into eg and t2g levels, then
crystal distortion due to the Jahn-Teller effect, further splits the degenerate eg and t2g
levels (taken from [10]).
The Jahn-Teller (JT) theorem [10] states that degenerate orbital ground state
levels are generally unstable, which requires decreased symmetry to lift the degeneracy.
Therefore, the MnO6 octahedra spontaneously distorts, further splitting the eg and t2g
energy levels; this distortion is known as the JT effect. A schematic is shown in figure
2.3. The JT effect is only energetically favorable if either of the t2g
or eg
states is partially
occupied. Therefore, Mn3+
, which has an electronic configuration of 3d4, leads to a single
electron in the eg
level, which leads to a very strong deformation in the MnO6 octahedra
in order to lift the degeneracy.
Electrical conduction and magnetic properties of these manganite materials are
primarily attributed to the Mn-O bonds. In the MnO6 octahedral environment, the Mn t2g
triplet orbitals (3dxy, 3dyz and 3dzx) have very little overlap with the oxygen 2p orbitals
11
and are strongly localized. The eg orbitals (3d3z2
-r2 and 3dx
2-y
2) on the other hand, are
farther reaching and are oriented towards the oxygen 2p orbitals. The probability of
overlap between the Mn eg and O 2p orbitals is large enough for electron hopping, thus
forming a method of conduction. By shortening the distance between Mn-O, there will be
an increased probability of orbital overlap, thus a larger occurrence of electron hopping,
and in turn enhancement of ferromagnetic properties. The overall length and angle of the
Mn-O-Mn bond depends strongly on the radii of the A-site cations. The A-site cations
will determine the ratio of Mn3+
to Mn4+
ions in the system. For example, a doped
manganite of the form R(1-x)MxMnO3 will exhibit a Mn4+
/ Mn3+
ratio as:
(2.2)
The ideal ratio for a ferromagnetic-metal ground state has been shown to be x=1/3
[1], however, by changing the ratio, one can observe competition between various
magnetic ground states, as well as charge and orbital ordering, which will be discussed
throughout this dissertation. An eg electron can hop between nearest-neighbor Mn ions,
causing JT lattice distortion. The strong coupling between the eg electron and the lattice
distortions is known as a polaron. In the paramagnetic state, polarons are free to move
about the lattice, thus creating a polaronic liquid [11].
2.3 Magnetic Interactions
The A-site (A = R, M) doping has been shown to control an effective one electron
bandwidth (W), which primarily governs the magnetic and magnetotransport properties
of a material [1-7]. Manganites are generally separated into three classes, namely large,
intermediate and low bandwidth manganites. Larger W, leads to a larger probability of
12
electron hopping, hence large conductivity, and a more stabilized ferromagnetic (FM)
phase. As W is reduced, FM state tends be less prominent and there is a larger probability
of phase separation. W can be tuned by applying external pressure, internal strain due to
chemical doping, etc., thus creating a wide variety of magnetic and structural ground
states in which to investigate.
2.3.1 Double Exchange
Double exchange (DE), first coined by Zener [12], involves the simultaneous
transfer of one electron from the Mn3+
eg orbital to an oxygen 2p orbital, and from that
oxygen 2p orbital to a neighboring Mn4+
eg orbital, as shown in figure 2.4.
Figure 2.4: A schematic representation of the double exchange mechanism showing
the simultaneous transfer of electrons between Mn3+
to O2-
and from the O2-
to Mn4+
ions taken from [14].
The hopping of the itinerate electrons via DE leads to the main conduction channel
in the manganites. The two electrons involved in the DE process must have the same spin
i.e. ferromagnetic coupling, due to Hund’s coupling and the Pauli Exclusion Principle.
The strength of the DE mechanism is defined by the charge transfer integral [13]:
( ) (2.3)
where is the relative angle between local spins. As a magnetic field is applied to the
material, it will force the local t2g spins to align thus reducing spin scattering (i.e.
13
resistivity decreases) and enhancing the ferromagnetic phase. The DE theory has been
shown to accurately describe the properties of the metallic ferromagnetic state in doped
manganites with relatively large W, such as La0.7Sr0.3MnO3 [13]. However, it alone
cannot explain the features of the MI transition and CMR observed in manganites with
narrow W such as La0.7Ca0.3MnO3 [3],
where other effects such as collective JT
distortions and antiferromagnetic (AFM) interactions coexist and strongly compete with
the ferromagnetic phase.
2.3.2 Superexchange
In general, exchange interactions between magnetic ions are short-range
interactions, occurring only when electrons’ spatial wave functions overlap. The range of
these interactions can be slightly extended by the transfer of electrons that do not
contribute to the overall magnetic behavior; this is called superexchange (SE). In the SE
model, magnetic interactions between adjacent ions are mediated by an intermediate non-
magnetic ion. This is a common interaction in insulating oxides, such as the manganites.
If partially-filled and fully-filled orbitals on nearest-neighboring ions point towards each
other, then an electron can be shared between the two ions. For the case of the
manganites, if a vacancy in the eg orbital and the fully occupied O 2p orbital point
towards each other, an electron from the O 2p will be shared between the two ions, as in
the schematic shown in figure 2.5.
SE interactions can produce ferromagnetic or antiferromagnetic states, depending
on the occupancy of Mn orbitals. There are two possible options for SE to occur in
manganites, namely Mn3+
-O2-
-Mn3+
(figure 2.5(a)) and Mn4+
-O2-
-Mn4+
(figure 2.5(b)).
For the Mn3+
(figure 2.5(a)) case, there is an extra electron in the eg state which is spin-
14
aligned to the t2g electrons via Hund’s rules, so the “shared” spin with the oxygen will be
anti-aligned to the eg electron due to the Pauli Exclusion Principle. However, for the
Mn4+
case (figure 2.5(b)), the t2g electrons will align parallel to the O 2p electron. Unlike
the DE mechanism discussed previously, SE will always result in an insulating state.
Figure 2.5: Schematic representation showing the arrangement of spins and orbitals
in superexchange taken from [14].
2.3.3 Charge and Orbital Ordering
In A-site doped manganites, the substitution of a trivalent rare-earth ion with a
divalent alkaline earth metal introduces excess holes (or electrons) into the material. At
relatively high temperatures (>300 K) the excess holes (or electrons) are largely
distributed randomly throughout the crystal, however, as the material is cooled, the
excess holes (or electrons) may arrange in a periodic lattice due to repulsive Coulomb
interactions between them; this ordered state is known as charge order (CO). The pattern
of the ordering can be drastically influenced by the choice of doping, as well as the
doping concentration. The CO state is often accompanied by slight localized lattice
distortions, thereby making it directly observable, although this observation can be rather
difficult. Generally the CO state can be characterized by large changes in the transport
and magnetic properties due to localized charges disrupting the conduction channel
15
leading to the CO state being associated with the AFM (or PM) insulating magnetic state.
Interestingly, regions in the material that are not associated with CO can be ferromagnetic
and metallic in nature, therefore CO manganites can have alternating regions of FM
metallic and AFM insulating regions, which is known as phase separation.
Figure 2.6: CE -type charge ordering along ab-plane in La0.5Sr0.5MnO4 taken from
[http://folk.uio.no/ravi/activity/ordering/chargeordering.html]
Figure 2.6 shows a schematic of CE-type charge order of the half-doped
La0.5Sr0.5MnO4. In this figure, the Mn3+
ions automatically arrange themselves in a
checkerboard type configuration. Another interesting ordering process in the manganites
comes from the lack of spherical symmetry in the Mn 3d orbitals, where the symmetry of
the local environment will determine the most favorable orbital ground-state, therefore
affecting the orientation of the orbitals throughout the crystal. The crystal-field splitting
and JT effect discussed earlier can lead to orbitals aligning into periodic patterns; this
effect is known as orbital ordering (O-O). The O-O can also arrange itself in several
ways; figure 2.7 shows a few orientations, signifying the complex nature of this behavior.
16
Figure 2.7: Various forms of orbital ordering in the manganites taken from
[http://folk.uio.no/ravi/activity/ordering/orbitalordering.html]
2.4 Conclusions
Manganites exhibit a wide range of magnetic, electronic and structural properties,
all of which depend heavily on the chemical composition. Small changes in the A-site, B-
site or oxygen stoichiometry can lead to extraordinarily altered physical properties,
ranging from a simple shift in magnetic transition temperature to a completely different
structure. This class of materials gives scientists a relatively endless supply of complex
phenomena to investigate.
References
[1] Y. Tokura, Y. Tomioka, Colossal magnetoresistive manganites, J Magn Magn Mater,
200 (1999) 1-23.
[2] P.G. Radaelli, D.E. Cox, M. Marezio, S.W. Cheong, P.E. Schiffer, A.P. Ramirez,
Simultaneous Structural, Magnetic, and Electronic-Transitions in La1-xCaxMnO3 with x =
0.25 and 0.50, Phys Rev Lett, 75 (1995) 4488-4491.
[3] Y. Lyanda-Geller, et. al., Charge transport in manganites: Hopping conduction, the
anomalous Hall effect, and universal scaling, Phys Rev B, 63 (2001).
17
[4] E. Dagotto, Open questions in CMR manganites, relevance of clustered states and
analogies with other compounds including the cuprates, New J Phys, 7 (2005).
[5] H.Y. Hwang, S.W. Cheong, P.G. Radaelli, M. Marezio, B. Batlogg, Lattice effects on
the magnetoresistance in doped LaMnO3, Phys Rev Lett, 75 (1995) 914-917.
[6] V.B. Shenoy, C.N.R. Rao, Electronic phase separation and other novel phenomena
and properties exhibited by mixed-valent rare-earth manganites and related materials,
Philos T R Soc A, 366 (2008) 63-82.
[7] J. Tao, D. Niebieskikwiat, M. Varela, W. Luo, M.A. Schofield, Y. Zhu, M.B.
Salamon, J.M. Zuo, S.T. Pantelides, S.J. Pennycook, Direct Imaging of Nanoscale Phase
Separation in La0.55Ca0.45MnO3: Relationship to Colossal Magnetoresistance, Phys Rev
Lett, 103 (2009).
[8] W.E. Pickett, D.J. Singh, Electronic structure and half-metallic transport in the La1-
xCaxMnO3 system, Phys Rev B, 53 (1996) 1146-1160.
[9] R.D. Shannon, Revised Effective Ionic-Radii and Systematic Studies of Interatomic
Distances in Halides and Chalcogenides, Acta Crystallogr A, 32 (1976) 751-767.
[10] H.A. Jahn, E. Teller, Stability of polyatomic molecules in degenerate electronic
states. I. Orbital degeneracy, Proc R Soc Lon Ser-A, 161 (1937) 220-235.
[11] M. Ziese, C. Srinitiwarawong, Polaronic effects on the resistivity of manganite thin
films, Phys Rev B, 58 (1998) 11519-11525.
[12] C. Zener, Interaction between the D-Shells in the Transition Metals .2.
Ferromagnetic Compounds of Manganese with Perovskite Structure, Phys Rev, 82 (1951)
403-405.
18
[13] P.W. Anderson, H. Hasegawa, Considerations on Double Exchange, Phys Rev, 100
(1955) 675-681.
[14] James Christopher Chapman (2005) Phase Coexistence in Manganites (Doctoral
Dissertation)
19
CHAPTER 3.
EXPERIMENTAL METHODS
3.1 Magnetocaloric Effect
3.1.1 What is the Magnetocaloric Effect?
The magnetocaloric effect (MCE) describes the isothermal change in entropy (or
adiabatic change in temperature) of a magnetic material through the application and
removal of an external magnetic field. MCE is best known for its contribution to industry
via magnetic refrigeration (MR)[1].
Figure 3.1 is a schematic representation of an MR; the general operation works as
a magnetic material, initially demagnetized, is at a temperature T. The material is then
adiabatically magnetized, thus decreasing the magnetic entropy of the material, which in
turn increases the entropy of the lattice, therefore leading to an increase in the material’s
temperature (T+T). Then, the small increase in temperature (T) is removed, bringing
the temperature of the material back to its original state (T). Finally, the material is
demagnetized, therefore increasing the magnetic entropy, which decreases the lattice
entropy, and the material’s temperature. Vapor-compression refrigerators are the most
widely used thus far; they are based on the compression and expansion of greenhouse
gases, such as chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs). This
refrigeration process is not very efficient, with an efficiency of just 5–10% of the ideal
20
Carnot cycle as opposed 30–60% for MR. Refrigeration accounts for 25% of residential
and 15% of commercial power consumption; therefore, new technology is needed to
reduce these numbers.
Figure 3.1: Schematic of a working magnetic refrigerator. Image credit Tegus et. al.
Nature 415 (2002).
The concept of MCE itself is very old with magnetic cooling for producing ultra-low
temperatures dating back to the 1920’s. However, recently, complex oxides have shown
promise in MR due to large MCE and tunable phase transitions.
There has been a lot of work on MCE-based MR as an alternative to conventional
gas compression (CGC) methods. The MR technology has several advantages over the
CGC technology, such as:
Magnetic refrigerators can be more compactly built when using solid
substances as working materials.
MR does not use ozone-depleting or global-warming gases, and therefore is
considered an environmentally friendly cooling technology.
21
MR has found wide applications in energy-intensive industrial and
commercial refrigerators such as large-scale air conditioners, heat pumps,
supermarket refrigeration units, waste separation, chemical processing, gas
liquefaction, liquor distilling, sugar refining, grain drying, and so forth.
Even though MCE is known, primarily, as an application-based tool, it also can be
utilized as a particularly good probe for studying fundamentals of magnetic, structural
and electronic phase transitions in magnetic materials. For example, doped manganites
with a general formula of R1−xMxMnO3 (R=La, Pr, Nd, etc., and M=Sr, Ca, Ba, etc.)
exhibit a rich variety of phenomena such as colossal magnetoresistance [2] and large
MCE [3]. From the nature of the measurement, MCE can probe into the coupling of
magnetic- and temperature-induced transitions, which is of utmost importance in these
types of materials. Manganites and the MCE measurement process will be discussed in
further detail in subsequent sections.
3.1.2 Theoretical Aspects of MCE
The thermodynamics of a magnetic material in an applied magnetic field (H), at a
temperature (T) and pressure (p) can be completely described via the Gibbs free energy:
(3.1)
where U is the internal energy, S is the total entropy, V is the volume and M the
magnetization of the material. V, M and S are given by taking the first derivative of G:
( ) (
)
(3.2)
( ) (
)
(3.3)
( ) (
)
(3.4)
22
The specific heat can then be described as the second derivative of G:
( ) (
)
(3.5)
By the definition of phase transitions, if the first derivative of the Gibbs free energy is
discontinuous, the transition is of the first order. Second order transitions occur when the
second derivative of the Gibbs free energy is discontinuous.
The total change in entropy of a magnetic material can be described by:
( ) ( ) ( ) ( ) (3.6)
where Sl,SM, Se are the lattice, magnetic and electronic entropy, respectively. When a
magnetic material is subjected to a sufficiently high magnetic field, the magnetic
moments of the atoms become reoriented, therefore decreasing the magnetic entropy. If
the magnetic field is applied adiabatically, the system must make up for the decrease in
SM by increasing Sl, thus the temperature of the material rises. By running this process
in reverse, we can achieve a decrease in the sample temperature. This warming and
cooling in response to the application and removal of an external magnetic field is called
the MCE. Since entropy is a state function, the total differential can be expressed as:
(
) (
)
(
)
(3.7)
Isobaric (dp=0) and isothermal (dT=0) measurements will lead to a measurement of the
magnetic entropy change alone. The change of dS of a magnetic material upon the
application of an H is related to M with respect to T through the thermodynamic Maxwell
relation:
(
) (
)
(3.8)
23
The magnetic entropy change, ΔSM (T,H), is then calculated by:
( ) ( ) ( ) ∫ (
)
(3.9)
It is interesting to note that since ΔSM (T,H) depends directly on the derivative of the
M(T), this measurement is inherently more sensitive for studying phase transitions than
standard magnetometry. For magnetization measurements made at discrete field and
temperature intervals, ΔSM (T,H) can be approximately calculated by the following
expression:
( ) ∑
( ) ( )
(3.10)
Alternatively, ΔSM (T,H) can be obtained from calorimetric measurements of the field
dependence of the heat capacity and subsequent integration:
( ) ∫
( ) ( )
(3.11)
where C(T,H) and C(T,0) are the values of the heat capacity measured in a field, H, and
in zero field (H = 0), respectively. Therefore, the adiabatic temperature change (ΔTad) can
be evaluated by integrating Eq. (3.11) over the magnetic field, which is given by:
∫
(
)
(3.12)
The refrigerant capacity (RC), is defined as the heat transferred from the cold end (T1) to
the hot end (T2) of an ideal thermodynamic refrigeration process. The RC of a
magnetocaloric material can be, in simple cases, evaluated by considering the magnitude
of ΔSM and its full-width at half maximum (δTFWHM):
( ) ∫ ( )
(3.13)
24
Figure 3.2 shows the method of calculating RC from the -SM curve. From this
figure the RC corresponds to the hatched area under the curve. Immediately following
from equations (3.8–3.11), materials whose total entropy is strongly influenced by a
magnetic field and whose magnetization vary rapidly with temperature are expected to
exhibit an enhanced MCE, i.e. around a magnetic phase transition temperature such as TC
or TN in a conventional ferromagnet or antiferromagnet respectively.
Figure 3.2: The method for calculating the RC from the −SM(T) curve using Eq. (3.13)
for two types of transitions in Pr0.5Sr0.5MnO3.
However, according to the Ehrenfest classification of phase transitions [4], since a
first-order magnetic transition (FOMT) is accompanied by a discontinuity in the first
derivative of the free energy (SM or M), care must be used when calculating SM. For
this kind of phase transition, the ΔSM values obtained from Eq. (3.9) are often much
higher than the ones obtained from pure magnetic contribution alone [5, 6].
3.2 MCE as a Fundamental Research Tool
From equation (3.9) we note that SM(T) is directly related to the first derivative
of magnetization with respect to temperature (M/T), so the MCE is expected to be
25
inherently more sensitive for probing magnetic transitions than conventional
magnetization and resistivity measurements. A very small change in M can give rise to a
more pronounced effect in SM(T) than in M(T) or resistivity measurements. More
importantly, the sign of SM, which is determined by the slope change of the dM/dT
curve, can allow probing the magnetic transitions further to better understand the nature
of the different phases in a material with a rich and complex H-T magnetic phase diagram
[10-13]. Following the convention in MCE analysis, the value of -SM is positive for
materials exhibiting an FM transition, because of the fully magnetically ordered
configuration with the application of an external magnetic field [9, 10]. Meanwhile,
negative values of -SM are found in AFM ordering systems due to orientational disorder
of the magnetic sublattice anti-parallel to the applied magnetic field [11, 12]. An
excellent example of this is the Pr0.5Sr0.5MnO3 system as shown in Figure 3.2, where the
material undergoes a transition from the paramagnetic to ferromagnetic state and a
second transition from the ferromagnetic to antiferromagnetic phase. Recently, von
Ranke et al. [13] have theoretically investigated the implications of positive and negative
MCE in antiferromagnetic and ferromagnetic arrangements. In this dissertation, I will
demonstrate the usefulness of the MCE method for probing the nature of phase
transitions, phase coexistence, magnetic ground states, and the subtle balance of
competing phases in phase separated manganite systems such as Pr0.5Sr0.5MnO3, La5/8-
xPrxCa3/8MnO3 (x = 0.275 and 0.375) and half-doped cobaltites Pr0.5Sr0.5CoO3.
3.2.1 Order of Transitions and Critical Phenomena
Understanding the nature of phase transitions and critical magnetic behaviors near
these transitions is essential to access the underlying origins of the magnetic field induced
26
phenomena such as colossal magnetoresistance (CMR) and the magnetocaloric effect
(MCE). Below, we show the methods used for the analysis of second-order magnetic
transitions and critical exponents of the material systems studied in this PhD research
work.
It has been shown that for materials that exhibit a second-order magnetic
transition (SOMT), the Kouvel–Fisher (K–F) method [14] can be used to precisely
determine the critical exponents of these samples. This method consists of an iterative
procedure which starts by constructing the Arrott–Noakes (A–N) plot (i.e. the plot of M2.5
vs. (H/M)0.75
). From it, the values for M0(T) are computed from the intercepts of various
isothermal magnetization vs. field curves on the ordinate of the plot (for temperatures
below TC). The intercept on the abscissa (for temperatures above TC), allows calculating
0(T). Once the M0(T) and 0(T) curves have been constructed, two additional parameter
data sets, X(T) and Y(T), may be determined:
( )
(
)
(3.15)
( ) (
)
(3.16)
In the critical region, both X(T) and Y(T) should be linear, with slopes that give
the values of the critical exponents, and intercepts of the temperature axis, which
correspond to TC. The values of the critical exponents are refined by using an iterative
method: once Eqs. (3.15) and (3.16) produce the values of the critical exponents, a
generalized A-N plot (M1/
vs. (H/M)1/
) is constructed and used to calculate new M0(T)
and 0(T) curves, which are subsequently input into Eqs. (3.15) and (3.16), resulting in
27
newer values for and . The procedure terminates when the desired convergence of the
parameters is achieved. TC is obtained as the intercept on the abscissa of both X and Y
lines.
According to Widom’s scaling hypothesis [15], for SOMT materials, the
spontaneous magnetization M(,0) below the TC, the critical magnetization M(0,H), the
isothermal initial susceptibility ( ,0),T and the maximum magnetic entropy change
0,MS H possess the following power-law dependences:
0( ,0) ( ) ( 1, ) ;0 0M M M
(3.17)
1/(0, ) ( ) 0 0, ) ;( 1CM H M H M H
(3.18)
0
0
0
;(1,0) 0( ,0) ( )
( 1,0) ; 0T
(3.19)
(0, ) (0,1)M M
nS H S H (3.20)
where /C CT T T is the reduced temperature, M(1,0), M(0,1), 0(1,0) , 0( 1,0) ,
and Δ (0,1)MS are the critical amplitudes, and , , , and n are the critical exponents.
The Widom scaling hypothesis also allows for the determining of the equations of
state of a magnetic system; they can be expressed as [16]:
1/ 1/
( , )( )t
M Hm t
H H
(3.21)
( )h
M Hff m h
(3.22)
28
where 1/( , ) /tm M H H is the renormalized temperature dependence of the
magnetization, 1//t H is the renormalized temperature, is the temperature scaling
function, /hm M
is the renormalized field dependence of the magnetization,
/h H
is the renormalized field, f+ (for T > TC) and f (for T < TC) are the field
scaling functions, and is the so-called gap exponent. According to Eq.
(3.21), if appropriate values of the critical exponents (, , and ) and TC are used to plot
mt versus t, all experimental data points will collapse onto one universal curve, . On the
other hand, according to Eq. (3.22), all experimental data of the plot of mh versus h will
collapse onto two universal curves: f+ (for T > TC) and f (for T < TC). This is an
important criterion to validate the reliability of the procedure used to obtain the critical
exponents. In addition, from Eq. (3.19) the plot of the renormalized field dependence of
the isothermal susceptibility, ( , ) /Thj H
versus h, will collapse onto two
universal curves ( )hj g h : one above TC (g+) and another below TC (g), and from Eq.
(3.20). The plot of the renormalized temperature dependence of the magnetic entropy
change, Δ ( , ) /M
n
ts S H H versus t, will collapse onto one universal curve st=·(t)
[17-20].
Recently, it has been shown theoretically [19] and experimentally [20] that the
latter universal behavior can be obtained without knowledge of the critical exponents,
and that the magnetic field dependence of ΔSM ·can be represented as [18, 21]:
,Δ , Δ ,1
T H
M M
nS T H S T H (3.23)
29
where the amplitude, ,1MS T , is T-dependent, and the exponent n generally depends
on temperature and field, taking the asymptotic values n = 1 and n = 2 when the values of
T are quite far below and above TC, respectively. At T = TC (or at the temperature that
ΔSM attains its maximum value Δ M
pkS , T = Tpk), the exponent n is field-independent and
can be expressed in terms of the other critical exponents, as:
( ) ( )
( )
(3.24)
Since only two critical exponents (n and ) are independent, it is then possible to
completely define the critical exponents using a non-iterative method [22]. The exponent
n can be obtained from the fitting of the Δ M
pkS values as a power law of the magnetic
field using Eq. (3.20), while the exponent , according to Eq. (3.21), can be obtained
from the fitting of the reference temperatures (selected as that corresponding to a certain
fraction of ΔSM in the ΔSM vs. T representation) as a power law of the field 1/r H
or, alternatively, according to Eq. (3.22), as the fitting of the reference fields (selected as
that corresponding to a certain fraction of ΔSM in the ΔSM vs. H representation) as a
power law of the temperature rH
.
3.3 Transverse Susceptibility
Resonant based measurements are advantageous when it comes to probing
relatively minor changes in the physical properties of a material. An easy way to perform
resonant measurements on magnetic materials is based on an LC tank circuit, where a
material is placed inside of the capacitor or the inductor as is the case in this study.
Therefore, any change in material properties will induce a change in the capacitance (C)
30
or inductance (L), which in turn changes the resonant frequency of the circuit. Thus,
measurement of the frequency shift results in a direct correlation in the electronic,
dielectric, or magnetic response of the material [23]. Here we introduce the radio
frequency (RF) transverse susceptibility as a very powerful probe of magnetic anisotropy,
switching fields and spin dynamics in strongly correlated electron magnetic systems such
as complex oxides, as discussed throughout this dissertation.
The transverse susceptibility measurement is an LC tank circuit that is driven at a
constant resonance by supplying the circuit with external power (driven by a tunnel diode
oscillator (TDO)) to compensate for dissipation. This arrangement makes a self-resonant
circuit as the power supplied by the TDO maintains continuous oscillation of the LC tank
circuit operating at a frequency given by the expression [24].
LC
1 (3.25)
Inserting a sample into the inductive coil will produce a small change in the coil
inductance ΔL. If ΔL/L <<1, one can differentiate equation (3.25) and obtain the
expression:
L
L
2
(3.26)
Since ΔL is the related to material properties. For magnetic materials, this is
proportional to the real part (µ′) of the complex permeability.
µ = µ′-iµ″ (3.27)
In this setup, the sample is encapsulated in a gel cap, which can be placed inside
the inductive coil. The entire coil is inserted into the sample chamber of a Physical
Property Measurement System (PPMS) by Quantum Design (Fig. 3.3). The advantage of
31
inserting the probe into the PPMS is that we gain control over a wide range of
temperatures (1.8K – 350K) and magnetic fields (±7 T). Since the LC circuit is driven at
resonance there is a small oscillating RF field (HRF) produced by the inductor, which is
oriented perpendicularly to the DC field (HDC), produced by the PPMS, therefore giving
us transverse geometry.
Figure 3.3: (a)Schematic diagram of the transverse susceptibility circuit, (b) Schematic
depiction of transverse susceptibility probe , (c) Quantum Design PPMS.
In this configuration, the change in inductance is determined by the change in
transverse permeability, µT, of the sample. The TS ratio can be written as:
ΔχT/χT (%) =
sat
T
sat
TT H
100)( (3.28)
where χTsat
is the TS at the saturating field, Hsat. Since this is a measure of the overall
change in TS, there is no dependence on the geometrical parameters, therefore proving to
be useful for many systems [24].
The theory of reversible TS was first studied theoretically by Aharoni et al. in
1957 [25]. In his work, the expression for TS was analytically derived for a single-
domain particle based on the Stoner-Wolfarth model. When ΔχT/χT is plotted as a
function of HDC, singularities are observed at the anisotropy fields (±HK), as seen in
(a) (b) (c)
32
figure 3.4. The effective anisotropy constant (K) can be extracted from this through the
relation:
HK = 2K/MS (3.29)
where MS is the saturation magnetization.
Figure 3.4: Transverse and parallel susceptibility (T and P respectively) for single-
domain magnetic particles. Image from reference [20].
Many known coupling phenomena are characterized by an overall increase in
effective anisotropy of the system, with exchange coupling being the best known
example. In these systems, an increase in coercivity is almost always observed [26]. We
have shown how TS can also be used to complement traditional static magnetic
measurements for systems whose effective anisotropy has increased due to the presence
of a phase transition. In the examples outlined in subsequent sections, we explain how the
TS curves, for complicated systems, can probe regions in complex phase diagrams that
general magnetometry cannot.
33
References
[1] A.M.Tishin and Y.I. Spichkin, The Magnetocaloric Effect and its Applications,
Institute of Physics Publishing, Bristol and Philadelphia, 2003.
[2] Y. Tokura, Y. Tomioka, Colossal magnetoresistive manganites, J Magn Magn Mater,
200 (1999) 1-23.
[3] M.-H. Phan, S.-C. Yu, Review of the magnetocaloric effect in manganite materials, J
Magn Magn Mater, 308 (2007) 325-340.
[4] J.M. Yeomans, Statistical Mechanics of Phase Transitions, Claredon Press, Oxford,
1992.
[5] L. Tocado, E. Palacios, R. Burriel, Entropy determinations and magnetocaloric
parameters in systems with first-order transitions: Study of MnAs, J Appl Phys, 105
(2009).
[6] N.A.de Oliveira and P.J.von Ranke, Physics Reports, 489 (2010).
[7] A. Giguere, M. Foldeaki, B.R. Gopal, R. Chahine, T.K. Bose, A. Frydman, J.A.
Barclay, Direct measurement of the "giant" adiabatic temperature change in Gd5Si2Ge2,
Phys Rev Lett, 83 (1999) 2262-2265.
[8] M. Balli, D. Fruchart, D. Gignoux, R. Zach, The "colossal" magnetocaloric effect in
Mn1-xFexAs: What are we really measuring?, Appl Phys Lett, 95 (2009).
[9] M.H. Phan, S.C. Yu, Review of the magnetocaloric effect in manganite materials, J
Magn Magn Mater, 308 (2007) 325-340.
[10] M.H. Phan, G.T. Woods, A. Chaturvedi, S. Stefanoski, G.S. Nolas, H. Srikanth,
Long-range ferromagnetism and giant magnetocaloric effect in type VIII Eu8Ga16Ge30
clathrates, Appl Phys Lett, 93 (2008).
34
[11] A. Biswas, et. al., Observation of large low field magnetoresistance and large
magnetocaloric effects in polycrystalline Pr(0.65)(Ca(0.7)Sr(0.3))(0.35)MnO(3), Appl Phys Lett,
92 (2008).
[12] P. Sande, et.al., Large magnetocaloric effect in manganites with charge order, Appl
Phys Lett, 79 (2001) 2040-2042.
[13] P.J. von Ranke, N.A. de Oliveira, B.P. Alho, E.J.R. Plaza, V.S.R. de Sousa, L.
Caron, M.S. Reis, Understanding the inverse magnetocaloric effect in antiferro- and
ferrimagnetic arrangements, J Phys-Condens Mat, 21 (2009).
[14] J.S. Kouvel, M.E. Fisher, Detailed magnetic behavior of nickel near its curie point,
Physical Review a-General Physics, 136 (1964) 1626-&.
[15] B. Widom, Equation of state in neighborhood of critical point, J Chem Phys, 43
(1965) 3898-&.
[16] R.B. Griffiths, Thermodynamic Functions for Fluids and Ferromagnets near the
Critical Point, Phys Rev, 158 (1967) 176-187.
[17] V. Franco, J.S. Blazquez, A. Conde, Field dependence of the magnetocaloric effect
in materials with a second order phase transition: A master curve for the magnetic
entropy change, Appl Phys Lett, 89 (2006).
[18] V. Franco, A. Conde, M.D. Kuz'min, J.M. Romero-Enrique, The magnetocaloric
effect in materials with a second order phase transition: Are T-C and T-peak necessarily
coincident?, J Appl Phys, 105 (2009).
[19] V. Franco, A. Conde, J.M. Romero-Enrique, J.S. Blazquez, A universal curve for the
magnetocaloric effect: an analysis based on scaling relations, J Phys-Condens Mat, 20
(2008).
35
[20] V. Franco, A. Conde, Scaling laws for the magnetocaloric effect in second order
phase transitions: From physics to applications for the characterization of materials, Int J
Refrig, 33 (2010) 465-473.
[21] T.D. Shen, R.B. Schwarz, J.Y. Coulter, J.D. Thompson, Magnetocaloric effect in
bulk amorphous Pd40Ni22.5Fe17.5P20 alloy, J Appl Phys, 91 (2002) 5240-5245.
[22] V. Franco, A. Conde, V. Provenzano, R.D. Shull, Scaling analysis of the
magnetocaloric effect in Gd5Si2Ge1.9X0.1 (X=Al, Cu, Ga, Mn, Fe, Co), J Magn Magn
Mater, 322 (2010) 218-223.
[23] H. Srikanth, J. Wiggins, H. Rees, Radio-frequency impedance measurements using a
tunnel-diode oscillator technique, Rev Sci Instrum, 70 (1999) 3097-3101.
[24] L. Spinu, C.J. O'Connor, H. Srikanth, Radio frequency probe studies of magnetic
nanostructures, Ieee T Magn, 37 (2001) 2188-2193.
[25] E.H.F. A. Aharoni, S. Shtrikman and D. Treves, Bulletin of the Research Council of
Israel, 6A (1957).
[26] J. Nogues, I.K. Schuller, Exchange bias, J Magn Magn Mater, 192 (1999) 203-232.
36
CHAPTER 4.
IMPACT OF REDUCED DIMENSIONALITY ON THE MAGNETIC AND
MAGNETOCALORIC RESPONSE OF La0.7Ca0.3MnO3
This chapter presents a systematic investigation of dimensionality effects and
grain boundaries on the magnetic and magnetocaloric properties of La0.7Ca0.3MnO3 by
contrasting the behavior of poly-crystalline and pulsed laser-deposited thin-film forms of
the system. The paramagnetic to ferromagnetic transition and saturation magnetization
were found to broaden and shift to lower temperatures in the thin-film sample. These
factors serve to reduce the magnitude of the magnetocaloric response in the thin-film
samples. However, a large broadening of the magnetic entropy change peak in the thin-
film sample leads to enhanced refrigerant capacity (RC) when compared to the bulk
sample. Universal curves, based on re-scaled entropy change curves, tend toward collapse
with reduced dimensionality, indicating a crossover from a first- to second-order
magnetic transition in the thin-film.
4.1 Introduction
La1-xCaxMnO3 (LCMO) is a canonical example of the mixed-valent perovskite
compounds, exhibiting a rich phase diagram (figure 4.1), which has fueled a great deal of
research into these systems over the past two decades [1]. The average radius of the A-
site ion can lead to various magnetic phenomena, such as canted-antiferromagnetism
(CAF), charge-ordering (CO), ferromagnetic metallic/insulator (FM/FI) and
37
antiferromagnetism (AFM). In the doping range 0.25 < x < 0.33, bulk LCMO exhibits a
paramagnetic to ferromagnetic transition between 230 K and 260 K, concurrent with the
metal to insulator (MI) transition.
Figure 4.1: Phase diagram of La1-xCaxMnO3, showing the subtle balance between
chemical doping and magnetic properties (taken from [2]).
This critical temperature and doping range is characterized by colossal magnetoresistance
(CMR) and a large magnetocaloric effect (MCE), prompting many studies focused on
understanding the underlying transport and magnetic properties in thin-films [3-8] and
bulk [9, 10] samples of LCMO.
The properties of thin-films as compared to their bulk counterparts vary widely
depending on thickness, substrate, details of deposition, post annealing, oxygen content,
etc. However the general trend upon thickness reduction is a suppression of the Curie
temperature (TC) and saturation magnetization (MS), and an enhancement of resistivity
and magnetoresistance (MR) [7]. In very thin coherently-strained films, disagreement
38
exists as to whether these effects can be attributed primarily to strain or finite size effects,
[5, 8] due to magnetically dead layers on the surface of the film, as well as at the interface
between the substrate and film. However, in moderately thick films (>100 nm) these
features are likely disorder-induced, as strain relaxation can give rise to extrinsic defects
such as dislocations, stacking faults, cationic vacancies, and grain boundaries.
In this chapter, I will examine the re-structuring of the first-order ferromagnetic
LCMO compound in a thin-film sample and compare the results to a bulk polycrystalline
sample of the same composition. The magnetic and magnetocaloric properties of the
samples are characterized, and it is found that the greater deviation from the bulk
behavior occurs in the thin-film. Universal scaling, based on magnetic entropy change
curves, is applied to understand the impact of reduced dimensionality on the nature of the
ferromagnetic transition in LCMO.
4.2 Experiment
A frequently used method for producing manganite thin-films is pulsed laser
deposition (PLD). A PLD system generally consists of a target holder, a heated substrate,
a vacuum chamber (base pressure 10-6
Torr) and a laser, as seen in the schematic in figure
4.2.
A pulsed laser beam is focused onto a stoichiometric target through a quartz window. The
immense temperature generated from the laser onto the target makes the target molten,
leading to evaporation and ionization of the target. The collection of particles ejected
from the surface, called the plume, is then transported to the substrate. PLD has a few
disadvantages, primarily particulates (up to ~10 m) formed in the plume can be
deposited on to the substrate and the plume is highly directional, therefore, non-uniform
39
film thickness may occur. Rastering the laser across the target helps to ensure uniformity
of the film, by minimizing the development of large droplets on the substrate’s surface.
The deposition is performed off-axis.
Figure 4.2: Schematic representation of a pulsed laser deposition system. Image credit
Andor Technology.
Substrate temperature, oxygen partial pressure, laser energy density and laser
repetition rate greatly affect the quality of the thin-film. Samples of LCMO in various
forms were prepared at the Naval Research Laboratory (NRL). LCMO thin-films (~150
nm thickness) were deposited on MgO (100) substrates, from a commercially purchased
(Kurt J.Lesker Company) stoichiometric polycrystalline target, using a KrF excimer laser
(Lambda Physik LPX 305, = 248nm, FWHM = 30 ns) that was operated at 5Hz and
focused through a lens with a 50-cm focal length onto a rotating target at a 45o angle of
incidence. The energy density of the laser beam at the target surface was maintained at ~2
J/cm2. The target-to-substrate distance was 5.5 cm.
Films were deposited at a substrate temperature of 777 oC in an oxygen pressure
of 300 mTorr followed by in-situ annealing at 600 oC for 30 min in an oxygen-rich
40
background. To minimize the effects of variation in stoichiometry and purity, a portion of
the same target was used as the bulk polycrystalline reference sample, while conducting
magnetic measurements. Profilometry confirmed the thickness of the film to be 150 nm.
Magnetic measurements were carried out from 25 K – 350 K under fields up to 5 T. The
diamagnetic contribution from the MgO substrate was corrected by using a linear fitting
and subtraction.
4.3 Results and Discussion
Figure 4.3 shows the temperature dependence of magnetization in a
polycrystalline bulk, and a thin-film of LCMO. Two effects are immediately obvious
from inspection of the results: first, the sharp paramagnetic to ferromagnetic (PM-FM)
transition that occurs in the bulk material is considerably broadened in the thin-film.
Secondly, the TC – estimated here from the minima in the derivative of magnetization
with temperature – shifts to a lower temperature (~235 K) in the thin-film. The
broadening phenomenon can be attributed to the distribution of TC owing to the local
variation of strain near grain boundaries and defects in the thin-film [3, 6]. In a
percolative system, the distribution in transition temperature is Gaussian with a width that
can be qualitatively linked to the disorder present in the system [6]. A Gaussian fit to the
dM/dT curves in the inset of Fig. 4.3 yields distribution widths of Г=5 K and 35 K for the
polycrystalline and thin-film samples, respectively. The large distribution is indicative of
considerable variation in the local structure of the film. The reduction in the average
value of TC has been observed before in both nanocrystalline and thin-film forms of
LCMO, and is usually attributed to finite size effects and disorder [7, 11]. To evaluate the
magnetic entropy change in the system, isothermal magnetization vs. field (M (H)) curves
41
were recorded around the transition temperature in each sample. The inset of Fig. 4.4
compares the M (H) isotherms at 120 K. The 5 T value of magnetization reached 3.5 µB
and 2.4 µB in the polycrystalline and thin-film samples, respectively.
50 100 150 200 250 300 3500.0
0.2
0.4
0.6
0.8
1.0
150 200 250 300
dM
/dT
T (K)
Poly-crystalline
Thin-Film
M/M
(25
K)
T (K)
Figure 4.3: Temperature dependence of magnetization recorded on cooling in a field of
500 Oe and normalized to 25 K value. Lines are guide to the eye. Inset: First derivative of
magnetization.
The expected spin-only magnetic moment is determined by the Ca2+
-doping-dependent
ratio of Mn4+
(S = 3/2) to high-spin Mn3+
(S = 2), which predicts a value of 3.7 µB in
LCMO. Defects and oxygen off-stoichiometry could reasonably account for the ~5%
discrepancy between the polycrystalline sample and the ideal value.
The entropy change in the system is obtained by integrating between successive
M (H) isotherms according to the thermodynamic Maxwell relation. Under an applied
field change of 5 T, the absolute value of the magnetic entropy change (| |) reaches a
peak value near the TC of 7.7 J/kg K in the polycrystalline sample. This value is in good
agreement with Ref. [12], in which a sol-gel method combined with high temperature
sintering was used to prepare the sample, in contrast to Ref. [10] in which a modified
42
solid state reaction process gave rise to unusually large values of magnetic entropy
change (9.9 J/kg K for µ0ΔH = 5T).
50 100 150 200 250 3000
2
4
6
8
0 1 2 3 4 5
0
50
100
150
200
250(b)
-
S (
J/k
g K
)
T (K)
0H = 5T
(a) Poly-crystalline
Thin-Film
RC
(J/k
g)
0H (T)
Figure 4.4: (a) Comparison of temperature-dependent entropy change in bulk and thin-
film La0.7Ca0.3MnO3 samples under an applied field change of 5T. (b) The refrigerant
capacity as a function of applied magnetic field.
The decline in the peak | | from the bulk sample to the thin-film sample
(approximately one-third of the bulk value) is consistent with the fall-off in the
magnitude of magnetic moment and the broadening of the FM-PM transition that reduces
⁄ .
Figure 4.4 (b) shows the field-dependence of the refrigerant capacity (RC). The
RC, given by ∫ ( )
, where T1 and T2 are the temperatures defining the full
width at half maximum, is a measure of the heat exchanged between the hot and cold
ends of an ideal refrigeration cycle. The RC is considered to be an important figure of
merit in the evaluation of a magnetocaloric material. It has been observed on a number of
occasions that the reduced maximum value of | | that often accompanies broad
magnetic entropy change peaks can be compensated for by the increased width, resulting
43
in an enhanced RC over sharper transitions [13]. It can be seen that this scenario holds
true in the present case, where the RC reaches its largest values in the thin-film, for which
the breadth of the transition overcomes the deleterious effects of the drop in .
0 2500 5000 75000.00
0.05
0.10
0.15
0 1000 2000 3000 4000 50000.0
0.1
0.2
0.3
0.4
Thin film
(b)
0H
/M (
T g
/em
u)
M2 (emu/g)
2
(a)
Bulk
300 K
120 K
300 K
0H
/M (
T g
/em
u)
M2 (emu/g)
2
50 K
Figure 4.5: H/M vs. M2 for bulk and thin-film La0.7Ca0.3MnO3
In general, the order of the magnetic phase transition is determined via the
Banerjee criterion, which using the Landau-Lifshitz theory of first-order transitions [14],
a negative slope in the H/M vs. M2 plot is of first-order, otherwise the transition is
second-order (fig 4.5). The Banerjee criterion has been implemented for a wide variety of
materials, however, controversial reports have emerged for DyCo2 [15]. The first-order
nature of the transition in DyCo2 is not obvious using the Banerjee criterion, due to the
small size of the discontinuity in the first derivative of the free energy. This results in
only positive slopes of the H/M vs. M2 isotherms, leading to the false classification of a
second-order transition. A new criterion for determining the order of a transition has
recently been proposed based on a re-scaling of entropy change curves [16].
Universal behavior manifested in the collapse of ΔSM (T) curves after a scaling
procedure has been established for materials undergoing an SOMT, such as that
described in Chapter 3 of this dissertation.
44
-12 -8 -4 0 40.01
0.1
1
(b)
Thin-Film
S
'
S
'
Polycrystalline
(a)
-4 -2 0 2 4
0.1
1
Figure 4.6: Universal curve calculations as described in the text for the polycrystalline
bulk (a), and thin-film (b) forms of La0.7Ca0.3MnO3.
However, the scaling assumptions that underlie this behavior break down when applied to
an FOMT, and the expected collapse of the modified ( ) curves fails. As a
consequence, whether or not collapse is achieved, the universal curve method can be
applied as a method of distinguishing first and second order magnetic transitions. Figure
4.6 compares the universal curve constructions for each sample by plotting the
normalized entropy change (ΔS') against a reduced temperature (θ), where ΔS'= ΔSM /
Δ is the re-scaled entropy change and θ is the temperature variable defined by:
{ ( ) ( )⁄
( ) ( )⁄
.
Here the reference temperatures and are chosen such that ∆ ( )
∆ ( ) ⁄ . In Fig. 4.6 (a), the divergence of the curves is clear in the
polycrystalline compound, particularly above the TC. In the thin-film there is a clear
collapse of the curves below TC, which is consistent with an SOMT. We note that there is
not perfect agreement of the data above TC, however a check of the Arrott plot
constructions confirms the second order nature of the transition in the thin-film. This
45
suggests that T<TC is the essential region for collapse when applying this criterion. The
presence of quenched disorder is known to force fluctuation-driven FOMTs to become
continuous [17], and this appears to be the case in the thin-film sample.
4.4 Conclusions
The magnetic and magnetocaloric properties of bulk polycrystalline and thin-film
samples of the CMR manganite LCMO were investigated to observe the effects of
reduced dimensionality in the system. Broadened transitions, along with reduced Curie
temperature, magnetic moment, and magnetic entropy change were observed in the
nanocrystalline and thin-film samples. Even though the thin-film exhibited vastly
different properties, there was a minor increase in the RC. The FOMT in bulk LCMO is
converted to a SOMT in the thin-film. In the next chapter the role of Sr-doping on the A-
site of La0.7Ca0.3-xSrxMnO3 will be discussed.
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boundaries in colossal magnetoresistive films, Phys Rev B, 63 (2001) 020402.
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epitaxial La0.7Ca0.3MnO3 films, J Phys-Condens Mat, 18 (2006) 9783-9794.
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study of strained LCMO thin films, J Appl Phys, 97 (2005) 10C102.
46
[6] M. Egilmez, K.H. Chow, J. Jung, Percolative model of the effect of disorder on the
resistive peak broadening in La(2/3)Ca(1/3)MnO(3) near the metal-insulator transition, Appl
Phys Lett, 92 (2008) 162515.
[7] M. Ziese, H.C. Semmelhack, K.H. Han, S.P. Sena, H.J. Blythe, Thickness dependent
magnetic and magnetotransport properties of strain-relaxed La0.7Ca0.3MnO3 films, J Appl
Phys, 91 (2002) 9930-9936.
[8] A. de Andres, J. Rubio, G. Castro, S. Taboada, J.L. Martinez, J.M. Colino, Structural
and magnetic properties of ultrathin epitaxial La0.7Ca0.3MnO3 manganite films: Strain
versus finite size effects, Appl Phys Lett, 83 (2003) 713-715.
[9] D. Kim, B. Revaz, B.L. Zink, F. Hellman, J.J. Rhyne, J.F. Mitchell, Tricritical point
and the doping dependence of the order of the ferromagnetic phase transition of La1-
xCaxMnO3, Phys Rev Lett, 89 (2002) 227202.
[10] A.N. Ulyanov, et.al., Metamagnetic transition and extremely large low field
magnetocaloric effect in La(0.7)Ca(0.3)MnO(3) manganite, J Appl Phys, 103 (2008) 07B328.
[11] T. Sarkar, A.K. Raychaudhuri, A.K. Bera, S.M. Yusuf, Effect of size reduction on
the ferromagnetism of the manganite La1-xCaxMnO3 (x=0.33), New J Phys, (2010)
123026.
[12] W. Tang, W.J. Lu, X. Luo, B.S. Wang, X.B. Zhu, W.H. Song, Z.R. Yang, Y.P. Sun,
Particle size effects on La0.7Ca0.3MnO3: size-induced changes of magnetic phase
transition order and magnetocaloric study, J Magn Magn Mater, 322 (2010) 2360-2368.
[13] N.S. Bingham, M.H. Phan, H. Srikanth, M.A. Torija, C. Leighton, Magnetocaloric
effect and refrigerant capacity in charge-ordered manganites, J Appl Phys, 106 (2009)
023909.
47
[14] L.D. Landau, E.M. Lifshits, L.P. Pitaevskii, Statistical physics, Pergamon Press,
Oxford ; New York, 1980.
[15] M. Parra-Borderias, F. Bartolome, J. Herrero-Albillos, L.M. Garcia, Detailed
discrimination of the order of magnetic transitions and magnetocaloric effect in pure and
pseudobinary Co Laves phases, J Alloy Compd, 481 (2009) 48-56.
[16] C.M. Bonilla, F. Bartolome, L.M. Garcia, M. Parra-Borderias, J. Herrero-Albillos,
V. Franco, A new criterion to distinguish the order of magnetic transitions by means of
magnetic measurements, J Appl Phys, 107 (2010) 09E131.
[17] S. Rossler, U.K. Rossler, K. Nenkov, D. Eckert, S.M. Yusuf, K. Dorr, K.H. Muller,
Rounding of a first-order magnetic phase transition in Ga-doped La0.67Ca0.33MnO3, Phys
Rev B, 70 (2004) 104417.
48
CHAPTER 5.
INFLUENCE OF Sr DOPING ON THE MAGNETIC TRANSITIONS AND
CRITICAL BEHAVIOR OF La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05, 0.1, 0.2, AND 0.25)
SINGLE CRYSTALS
This chapter presents a comprehensive study of the ferromagnetic phase
transitions and critical exponent trends near these transitions in La0.7Ca0.3-xSrxMnO3 (x =
0, 0.05, 0.1, 0.2 and 0.25) single crystals. Based on the H/M vs. M2 analyses and using
Banerjee criterion, we demonstrate a transition from the discontinuous FOMT to the
continuous SOMT at x∼0.1. The critical analyses, based on the magnetic data using the
Kouvel–Fisher method, affirm that x∼0.1 is a tri-critical point that separates the FOMT
for x < 0.1 from the SOMT for x > 0.1. Above the tri-critical point (i.e. x ≥ 0.2), the
system exhibits a SOMT with the critical exponents ( = 0.36±0.01, = 1.22±0.01)
belonging to the Heisenberg universality class ( = 0.365±0.003, = 1.336±0.004) with
short-range exchange interactions. This indicates that the magnetic interaction in these
manganites is of a short-range nature. Our results and analyses reveal that while the DE
mechanism and formation of ferromagnetic clusters can account for the canonical MR
and metal-like conductivity in La0.7Ca0.3−xSrxMnO3 with x = 0.2 and 0.25, other effects
such as cooperative Jahn–Teller (JT) distortions and antiferromagnetic (AFM) coupling
are important additions for understanding the nature of the ferromagnetic transition, the
MI transition and CMR in La0.7Ca0.3−xSrxMnO3 with x = 0, 0.05 and 0.1. Our studies
49
provide physical insights into the relationship between the ferromagnetism and
conductivity in doped manganites.
5.1 Introduction
In perovskite manganites, the choice of A-site (A = rare-earth, alkaline earth)
dopants has been shown to control an effective one-electron bandwidth (W), which in
turn governs the magnetic and magneto-transport properties of the materials [1-7]. The
metallic FM state in doped manganites has been widely interpreted in the context of the
DE mechanism; as a magnetic field is applied to the material, the local t2g spins are
forced to align, thus reducing spin scattering (i.e. resistivity decreases). The transfer
integral that dictates the strength of the DE interaction depends on the angle between
these local spins, thus linking ferromagnetism and metallicity. The DE theory provides a
good description of the metallic FM state in large bandwidth manganites such as
La0.7Sr0.3MnO3 [8]. However, it is not sufficient to explain the features of the MI
transition and CMR observed in La0.7Ca0.3MnO3 [3] and other narrow bandwidth
manganites in which collective JT distortions and AFM interactions coexist and compete
with the ferromagnetic phase. Indeed, experimental studies have revealed that the
occurrence of the MI transition and CMR in La0.7Ca0.3MnO3 results mainly from the
combination of the DE interaction between Mn3+
and Mn4+
ions and a strong JT effect [3,
9]. This system has been found to undergo a discontinuous FOMT at TC [10, 11], and the
first-order nature of the transition is associated with a strong electron-phonon coupling
and/or an intrinsic inhomogeneity in the material that gives rise to competing coexisting
ground states [12, 13]. Meanwhile, the La0.7Sr0.3MnO3 system (which is free from JT
lattice distortions) has been found to undergo a continuous SOMT and exhibit a canonical
50
MR behavior.[3, 14] From a crystallographic standpoint, we note that La0.7Ca0.3MnO3
crystallizes in an orthorhombic (Pbnm) structure, whereas La0.7Sr0.3MnO3 possesses a
rhombohedral (R 3c) structure [15-17].
One way to stabilize intermediate phases bridging the two systems is co-
substitution of both Sr and Ca in the lattice. The substitution of large Sr2+
ions for smaller
Ca2+
ions in La0.7Ca0.3−xSrxMnO3 (0≤x≤0.3) manganites leads to a structural change from
the orthorhombic to rhombohedral structure which consequently induces a change in the
physical properties of the materials.[3, 15, 17] Notably, Tomioka et al.[3] reported that
with increasing Sr content, the sharp MI transition and CMR behavior for La0.7Ca0.3MnO3
(x = 0) were transformed to the metallic state and exhibited canonical MR behavior for
La0.7Sr0.3MnO3 (x = 0.3). However, the physical origin of the observed phenomena is still
not fully understood. Particularly, the mechanism of a metal-like conductivity in the PM
region in La0.7Ca0.3−xSrxMnO3 compounds with x > 0.1 remains an open question [3]. In
addition, it is unclear how the magnetic interactions are renormalized near the PM–FM
transition range and what universality class governs the PM–FM transitions in these
systems.
To address these important issues, we have conducted a comprehensive study of
the FM phase transitions and critical exponents near these transitions in La0.7Ca0.3-
xSrxMnO3 (x = 0, 0.05, 0.1, 0.2 and 0.25) single crystals. The samples were provided by
Professor Nan Hwi Hur group at Sogang University, South Korea.
5.2 Experiment
Single crystals of La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05, 0.1, 0.2, 0.25) were prepared by
the floating-zone method using an infrared radiation convergence-type image furnace that
51
consist of four mirrors and halogen lamps; details of the growth conditions can be found
elsewhere.[18] The starting polycrystalline ceramic feed rods were obtained from the
solid-state reaction of a stoichiometric mixture of La2O3, CaCO3, SrCO3 and MnCO3
were ground, pelletized, and calcined at 1000 °C for 20 h. Sintering was carried out in air
at 1300 °C for 80 h with intermediate regrinding. The feed rod was treated at 1300 °C for
20 h in air. The crystal growth apparatus (Crystal Systems Inc.) is an infrared radiation
convergence type image furnace that consists of four mirrors and four halogen lamps.
The input power for the halogen lamp is 1000 W. The temperature of the image furnace
was measured by detecting blackbody radiation of a graphite rod with a pyrometer. X-ray
diffraction (XRD) data and electron-probe microanalysis confirmed the quality of the
crystals. The XRD analyses indicated that the crystal structure is orthorhombic for x = 0,
0.05 and 0.1 compositions and is rhombohedral for x = 0.2 and 0.25 compositions. These
results are fully consistent with those reported in previous works. [15-17]
5.3 Results and Discussion
Figure 5.1 shows the temperature dependence of magnetization taken at an applied
field of 5 kOe for the La0.7Ca0.3−xSrxMnO3 (x=0, 0.05, 0.1 and 0.25) samples. It is
observed in Figure. 5.1 that all of the samples undergo a PM–FM transition and this
transition broadens gradually with increasing Sr doping. The TC of each sample, defined
by the minimum in dM/dT, are plotted as a function of Sr-doping, as shown in the inset of
Figure. 5.1. In connection with the crystal structure of the samples, one can see clearly in
the inset of Figure. 5.1 that with increasing Sr doping, the TC increases at a rate faster in
the orthorhombic phase (x = 0, 0.05 and 0.1) than in the rhombohedral phase (x = 0.2 and
0.25). The boundary line between these two crystalline phases is taken at x = 0.15, which
52
corresponds to a tolerance factor t = 0.92 as determined from previous studies [3, 17, 19].
It has been noted in doped manganites that cooperative JT distortions are present in the
orthorhombic phase but are not allowed due to the higher symmetry of the MnO6
octahedra in the rhombohedral phase [20-22].
0 50 100 150 200 250 300 350 4000.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.3210
240
270
300
330
360
M
/MS
T (K)
x=0
x=0.05
x=0.10
x=0.25
R3c
Pbnm
TC (
K)
x
Figure 5.1: Temperature dependence of magnetization taken at 5 kOe. Inset shows the
dependence of the Curie temperature (TC) on the Sr-doped content. The boundary line
between the orthorhombic (Pbnm) and rhombohedral (R3c) phases is taken at x = 0.15.
From [44]
This leads to a general expectation in the present case that the JT effect is significant in
La0.7Ca0.3−xSrxMnO3 with x = 0, 0.05 and 0.1 but is negligible in La0.7Ca0.3−xSrxMnO3 with
x = 0.2 and 0.25. Since JT distortions decrease and the Mn–O–Mn bond angle increases
(and W increases) with Sr doping, the DE interaction is strengthened and the metallic FM
state is stabilized in the samples with larger Sr doping [3, 15]. This clearly explains the
increase of TC with increasing Sr doping (see Figure. 5.1). This also explains a faster
increase in the rate of TC with Sr addition in the orthorhombic phase than in the
53
rhombohedral phase (see the inset of Figure. 5.1). To determine the order of the magnetic
phase transition in the La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05, 0.1, 0.2 and 0.25) samples, we
have analyzed H/M vs. M2 curves (which were constructed from the isothermal M(H)
data) using Banerjee criterion [23], the results of which are presented in Figure. 5.2.
0 1000 2000 3000 4000 5000 6000
200
400
600
800
0 500 1000 1500 2000 2500 3000 3500
100
200
300
400
0 500 1000 1500 2000
100
200
300
400
500
600
0 1000 2000 3000 4000 5000 6000 7000
500
1000
1500
2000
La0.7
Ca0.3-x
SrxMnO
3
(a) x = 0
224K220K 214K 208K
228K
232K
236K
H/M
(O
e.g
/em
u)
M2 (emu/g)
2
(c) x = 0.1
280K283K286K
289K292K
295K
298K
301K
H/M
(O
e.g
/em
u)
M2 (emu/g)
2
(d) x = 0.2
320K323K
326K329K
332K
335K
338K
341K
H/M
(O
e.g
/em
u)
M2 (emu/g)
2
(b) x = 0.05
230K240K250K
260K270K
280K
290K
300K
H/M
(O
e.g
/em
u)
M2 (emu/g)
2
Figure 5.2: The H/M vs. M2 plots for representative temperatures around the TC for the
La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05, 0.1 and 0.2) samples. From [44]
According to this criterion, the magnetic transition is of the second-order if all of
the H/M vs. M2 curves have a uniformly positive slope [24]. On the other hand, if some of
the H/M vs. M2 curves shows a negative slope at some point, the transition is of first-
order [24, 25]. It can be observed in Figure. 5.2 that the H/M vs. M2 curves of the x = 0
54
and 0.05 samples show a negative slope at T > TC, indicating a FOMT for these samples.
However, the H/M vs. M2 curves of the x = 0.1, 0.2 and 0.25 samples have only positive
slopes, implying that these samples belong to the class of SOMT materials. Nevertheless,
a closer examination of the H/M vs. M2 curves at low magnetic fields for x = 0.1 reveals
that this sample is not a purely SOMT material and some degree of FOMT may be still
present in the material. It has been noted, in chapter 4, that a precise determination of the
type of magnetic transition using the Banerjee criterion becomes difficult when the
magnetic transition is a mixture of FOMT and SOMT [26]. Our study shows that the Sr
doping in La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05, 0.1, 0.2 and 0.25) suppresses the FOMT but
favors a SOMT and a FOMT to SOMT transition occurs at x∼0.1. A similar trend has
been reported on polycrystalline La2/3(Ca1−xSrx)1/3MnO3 (x = 0, 0.05, 0.15 and 0.3)
manganites [22-24].
Figure. 5.3 shows the A–N plots of the La0.7Ca0.3−xSrxMnO3 (x = 0.1, 0.2 and
0.25) samples with optimized critical exponents ( and ) obtained from the K–F method.
Figure. 5.4 shows the K–F plot for one representative sample (x = 0.2). The best fits yield
the values of TC = 289 K, = 0.26 ± 0.01 and = 1.06 ± 0.02 for the x = 0.1 sample; TC =
326 K, = 0.36 ± 0.01 and = 1.22 ± 0.01 for the x = 0.2 sample; TC = 344 K, = 0.42 ±
0.02 and = 1.14 ± 0.05 for the x = 0.25 sample. Using the Widom scaling relationship
[27], + =, the critical exponent () is determined to be 5.1 ± 0.2, 4.4 ± 0.2 and 3.7 ±
0.2 for x = 0.1, 0.2 and 0.25 compositions, respectively. This relationship has been tested
by plotting M(T = TC) versus H/()
=H1/
and checking the linearity of the curve as
shown in Figure. 5.5. The reliability of the obtained exponents and Curie temperatures
can also be ascertained by checking the scaling of the magnetization curves.
55
50 100 150 200 250 3000
1
2
3
4
5
6
50 100 1500
1
2
3
4
50 100 150 2000
2
4
6
8
= 1.222
300K
M1/ (
10
6 (
em
u/g
)1/)
(H/M)1/
(Oe g/emu)1/
(a)
x = 0.1
280K
= 0.260
= 1.064
x = 0.25
340K
= 0.363
x = 0.2
(b)M
1/ (
10
4 (
em
u/g
)1/)
(H/M)1/
(Oe g/emu)1/
320K
= 0.417
= 1.142
355K
341K(c)
M1/ (
10
3 (
em
u/g
)1/)
(H/M)1/
(Oe g/emu)1/
Figure 5.3: Modified Arrott plot isotherms with 1K temperature interval for the
La0.7Ca0.3-xSrxMnO3 (x=0.1, 0.2 and 0.25) samples. From [44].
According to Eq. (3.21), if the appropriate values for the critical exponents and for the TC
are used, the plot of M/H1/
versus ε/H1/
should correspond to a universal curve onto
which all experimental data points collapse. Two different constructions have been used
in this work, both based on the scaling equation of state discussed in chapter 3.2.1.
56
315 318 321 324 327 330 3330
5
10
15
20
25
30
35
0
2
4
6Kouvel-Fisher method
=1.222
TC=326.793
=0.363
TC=326.710
Y(K
)=M
S(d
MS/d
T)-1
T (K)
X(K
)=
0
-1(d
0
-1/d
T)-1
Figure 5.4: Temperature dependence of spontaneous Ms (square) and inverse initial
susceptibility 0-1
(circles) for the x=0.2 sample; solid lines are fitting curves to Eqs.
(3.15) and (3.16), respectively. From [44].
Alternatively, Eq. (3.22) indicates that M/|ε| versus H/|ε|
should result in two
universal curves, one for ε > 0 (T > TC) and the other for ε < 0 (T < TC). For a more
convenient visualization of the results, this plot is usually represented in logarithmic
scale. However, this second representation tends to cover the small deviations of the
experimental data with respect to the universal curves caused by an inappropriate choice
of the parameters. Using the values of and TC obtained from the K–F method, the
scaled data are plotted in Figure. 5.6 for the x = 0.1 and 0.2 samples, respectively. In the
case of scaling using Eq. (3.22), it can be observed that all of the experimental points fall
on two curves, one for T < TC and the other for T > TC. This clearly indicates that the
obtained values of and TC for these samples are reliable and in agreement with the
scaling hypothesis. A less perfect overlap of the data points has been observed for the x =
0.1 sample in comparison with the x = 0.2 sample (see Figure. 5.6a and b). This agrees
57
with our previous observation (Figure. 5.2c) and argument that this sample is not a purely
SOMT material and some degree of FOMT is still present in it.
0.7 0.8 0.9 1.0
25
30
35
x = 0.2M
(T
)
H1/
(T0.23
)
0.7 0.8 0.9 1.0
30
35
40
45
x = 0.1
H1/
(T0.20
)
La0.7
Ca0.3-x
SrxMnO
3
Figure 5.5: The linearity of the M(T = TC) versus H
=H
curves validates the
value of the critical exponents. From [44].
It has been argued that in homogeneously magnetic systems the universality class
of the magnetic phase transition should depend on the range of the exchange interaction,
J(r) [28]. If J(r) decays with distance (r) at a rate faster than r−5
then the Heisenberg
exponents ( = 0.365 ± 0.003, = 1.336 ± 0.004) are valid for a 3D isotropic ferromagnet
[29]. However, if J(r) decays at a rate slower than r−4.5
then the mean-field exponents (
= 0.5, =1) are valid. According to the DE theory, the effective FM interaction is driven
by the kinetics of the electrons which favor extended states. Therefore, one could expect
the critical exponents in the DE model to be described within the framework of the mean-
field theory [30, 31]. However, computational studies have demonstrated that the critical
exponents in the DE model are consistent with those expected for the 3D Heisenberg
model [32]. It has also been theoretically shown that PM–FM transitions may become
discontinuous, depending on doping level and competition with superexchange AFM
58
interactions [33]. The values of the critical exponents of La0.7Ca0.3−xSrxMnO3 (x = 0.1, 0.2
and 0.25) samples are in agreement with those predicted by the latter models. [32, 33] It
is clear that the critical exponents of the x = 0.1 sample ( = 0.26 ± 0.01, = 1.06 ± 0.02)
match well with those derived from the tricritical mean-field model ( = 0.25, = 1). The
existence of this tricritical point (x∼0.1) clearly sets a boundary between FOMT (x < 0.1)
and SOMT (x > 0.1) within the range of compositions under study (0≤ x ≤0.25). A similar
case has also been reported on La1−xCaxMnO3 (0.2≤ x ≤0.5) polycrystalline manganites,
where the tricritical point is found at x∼0.4 [29].
To further confirm that the PM–FM transition becomes a conventional SOMT
above the tricritical point, the critical exponents of the samples with x > 0.1 are expected
to match those predicted for the 3D Heisenberg model [34]. The values of the critical
exponents of the x = 0.2 sample ( = 0.36 ± 0.01, = 1.22 ± 0.01) are close to those
expected for the 3D Heisenberg model ( = 0.365 ± 0.003, = 1.336 ± 0.004). For the x =
0.25 sample, the value of = 0.42 ± 0.02 is relatively larger than that expected for the 3D
Heisenberg model ( = 0.365 ± 0.003) but is consistent with that of La0.7Sr0.3MnO3 ( =
0.45±0.02) reported previously by Ziese[35] and Taran et al.[36] using the Arrott-Noakes
method and by Lofland et al. [14], using microwave absorption methods.
The critical exponent of the x = 0.25 sample ( = 1.14 ± 0.05) is smaller than that
of the x = 0.2 sample ( = 1.22±0.01). It has been argued that for a true SOMT the critical
exponents are independent of the microscopic details of a system due to the divergence of
correlation length and correlation time close to a transition point and hence their values
are almost the same for a transition that may occur in different physical systems [37].
However, one must note secondary effects on the PM–FM transition (hence on the
59
critical exponents) of a system due to magnetic anisotropies or dipolar long-range
couplings of FM clusters [38-41]. It has been pointed out that a Mn-ion triplet containing
an Mn3+–Mn
4+–Mn
3+ cluster has significant binding energy of about half the binding
energy of the bulk [42].
-0.5 0.0 0.5 1.0 1.5
2
4
6
8
10
105
106
107
108
101
102
-2 -1 0 1 2 3
1
2
3
4
5
6
105
106
107
108
109
101
102
x = 0.1
MH
-1/ (
em
u g
-1 O
e-0
.20)
H-1/(+)
(10-4 Oe
-0.75)
(a)
-M
(e
mu
g-1)
-(+)
H (Oe)
x = 0.1
(b)
MH
-1/ (
em
u g
-1 O
e-0
.23)
H-1/(+)
(10-4 Oe
-0.63)
x = 0.2
(c)
-M
(e
mu
g-1)
-(+)
H (Oe)
x = 0.2
(d)
Figure 5.6: Normalized isotherms of La0.7Ca0.3−xSrxMnO3 (x = 0.1 and 0.2) samples
below and above Curie temperature (TC) using the values of and determined from K-F
method. From [44].
The large spin moments of these FM clusters are expected to enhance the dipole–dipole
interaction in the case of the 3D Heisenberg model thus resulting in larger values of the
critical exponents than those predicted by this model [36, 42]. Recently, magnetization
and electron paramagnetic resonance (EPR) studies have revealed that FM clusters
persisting, even in the paramagnetic region, have significant influence on the magnetic
60
order parameters (i.e. the critical exponents) in doped manganites, such as Pr0.5Sr0.5MnO3
which will be discussed in great detail in the following chapter.
In the case of La0.7Ca0.3−xSrxMnO3 (x = 0.1, 0.2 and 0.25) samples, the x = 0.1
composition is in the crossover region of FOMT→SOMT. A crossover in the MI
transition is also observed in this composition (for x < 0.1 the MI transition is well
defined, but is largely suppressed and instead a metal-like conductivity is observed in the
PM region for x > 0.1) [3]. This concurrence clearly demonstrates a coherent correlation
between the magnetism and conductivity in the doped manganites. Furthermore, we note
the nonlinearity of the modified Arrott plots (Figure. 5.3), signaling the presence of FM
clusters in the La0.7Ca0.3−xSrxMnO3 samples. Therefore, it can be proposed that it is the
formation of FM clusters that leads to a percolation mechanism for conduction and
metallic behaviors observed at T > TC in the PM region for the x = 0.2 and 0.25 samples.
A recent study has shown that the PM–FM transition of a (Sm0.7Nd0.3)0.52Sr0.48MnO3
manganite transforms from a FOMT to a SOMT when subjected to an external pressure
[43]. It has been argued that the presence of external pressure at a certain level can
suppress the polaronic state, increase the bandwidth of the system, and as a result the
FOMT converts to SOMT [43]. In the case of La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05, 0.1, 0.2
and 0.25) manganites, we argue that the substitution of large Sr2+
ions (<rA>∼1.31Ǻ ) for
smaller Ca2+
ions (<rA>∼1.18Ǻ ) introduces chemical (internal) pressure without
affecting the valency of the Mn ions (the ratio of Mn3+
/Mn4+
is unchanged i.e. there is no
change of electronic density) [16, 17]. It has been shown that the chemical pressure
modifies local structural parameters such as the Mn–O bond distance and Mn–O–Mn
bond angle, which directly influence the probability of electron hopping between Mn ions
61
[1, 3, 16, 17]. Therefore, the change of internal pressure with Sr addition is expected to
increase W which consequently increases the TC and converts the FOMT into SOMT at a
threshold pressure (which corresponds to a Sr-doping level, x = 0.1). Above the critical
point (x > 0.1), the system shows a SOMT with the critical exponents belonging to the
Heisenberg universality class. The change in nature of the PM–FM transition with
chemical (internal) pressure (Sr doping) clearly points to a strong coupling between the
magnetic order parameter and lattice strain in these doped manganites [43].
Furthermore, the theory predicts that the PM–FM transition of La1−xMxMnO3 (M=
Ca, Sr) becomes continuous or discontinuous, depending upon the change in the relative
strength of the DE interaction (i.e. the FM interaction) and AFM coupling [33]. In the
present study, we note that the ground state of La0.7Ca0.3MnO3 (x = 0) is FM, but the
AFM phase is also present and competing with the FM phase [12, 13]. The substitution of
Sr for Ca in La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05, 0.1, 0.2 and 0.25) suppresses the AFM
tendency and enhances the FM phase. As a result, the PM–FM transition changes from
discontinuous to continuous at x∼0.1. In addition, we recall that strong JT lattice
distortions are possible in the x = 0, 0.05 and 0.1 samples that crystallize in an
orthorhombic structure, whereas this effect is negligible in the x = 0.2 and 0.25 samples
possessing a rhombohedral structure. These important observations, coupled with the
magnetic, magnetotransport and critical exponent analyses, clearly suggest that in
addition to the DE interaction, cooperative JT effects and AFM coupling are important
ingredients for assessing the nature of the FM transition and the MI transition including
CMR in La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05 and 0.1) manganites. While the DE model is
sufficient to explain the canonical MR behavior in La0.7Ca0.3−xSrxMnO3 (x = 0.2 and 0.25)
62
samples where AFM interactions are weak and JT lattice distortions are negligible, the
formation of FM clusters likely leads to a percolation mechanism for the conduction and
metallic behavior observed in the PM region for these samples.
5.4 Conclusions
The FM phase transitions and critical behavior of La0.7Ca0.3−xSrxMnO3 (x = 0,
0.05, 0.1, 0.2 and 0.25) single crystals have been studied systematically. Using the
Banerjee criterion and Kouvel–Fisher method, we show that x∼0.1 is a tricritical point
that separates a FOMT for x < 0.1 from a SOMT for x > 0.1. Above the tricritical point,
the system exhibits a SOMT with critical exponents belonging to the Heisenberg
universality class with short-range exchange interactions. The change of the PM–FM
transition with chemical (internal) pressure introduced by substitution of larger Sr ions
for smaller Ca ions points to the strong coupling between the magnetic order and
structural parameters in these doped manganites.
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68
CHAPTER 6.
MAGNETIC TRANSITIONS, MAGNETOCALORIC EFFECT, MAGNETIC
ANISOTROPY, CRITICAL EXPONENTS AND THEIR CORRELATIONS IN
Pr0.5Sr0.5MnO3
In the previous chapter, we discussed the influence on the nature of the
paramagnetic (PM) to ferromagnetic (FM) transition on Sr doping in the La0.7Ca0.3-
xSrxMnO3 system. However, by changing the doping concentration from the ideal (in
terms of stabilized FM-metallic nature) x=1/3, to x=1/2 (where there are an equal number
of Mn3+
and Mn4+
ions) there are new phases that arise in addition to FM ordering,
namely antiferromagnetic (AFM) order, charge/orbital ordering (CO/OO), and in some
cases phase-separation i.e. competition among all aforementioned states.
In this chapter, we present systematic studies of the influence of a first-order
magnetic transition (FOMT) and a second-order magnetic transition (SOMT) on the
MCE and RC of charge-ordered (CO) Pr0.5Sr0.5MnO3 (PSMO). Our results reveal that
while the FOMT at TCO induces a larger MCE, it is restricted to a narrow temperature
range resulting in a smaller RC. The SOMT at TC induces a smaller MCE but with a
distribution over a broader temperature range, thus resulting in a larger RC. In addition,
hysteretic losses associated with the FOMT are very large below TCO and, therefore,
detrimental to the RC, whereas these effects are very small or negligible below TC due to
the nature of the SOMT.
69
In addition to the existence of deleterious magnetic and thermal effects on RC, the
Maxwell relation used to calculate SM is suspect due to the discontinuous nature of a
first-order transition. Because PSMO exhibits two fundamentally different transitions,
well-separated in temperature, we were able to deconvolute the two transitions, therefore
allowing the critical analyses of the SOMT in order to understand the type of magnetic
order and interactions of the FM phase in PSMO. The results obtained reveal the
existence of a short-range ferromagnetic order at T < TC and the presence of
ferromagnetic clusters in the paramagnetic region (T > TC).
To probe the magnetic anisotropy and its correlations with the MCE and critical
exponents in this material, transverse susceptibility measurements were performed. These
experiments reveal an abrupt change in magnetic anisotropy field (HK) at the FM to AFM
transition (TCO ~150 K), which is associated with a simultaneous structural phase
transition from tetragonal to orthorhombic symmetry. This provides evidence of strong
coupling between the magnetism and the lattice in Pr0.5Sr0.5MnO3. The data also clearly
indicate the presence of HK in both the PM and AFM states, pointing to the importance of
the d(x2-y
2)-type orbital order and the orbital-order-induced intrinsic phase separation in
the A-type AFM. The polycrystalline sample was synthesized using standard solid-state
reaction method and provided by Professor Christopher Leighton at the University of
Minnesota.
6.1 Introduction
As we discussed in Chapter 3, the refrigerant capacity (RC) is considered to be
the most important factor for assessing the usefulness of a magnetic refrigerant material
[1-3]. The RC depends not only on the magnitude of ∆SM, but also on the temperature
70
dependence of ∆SM (e.g. the full width at half maximum of the ∆SM(T) peak) [1, 3]. A
good magnetic refrigerant material with large RC requires both a large magnitude of ∆SM
as well as a broad ∆SM(T) curve. Most previous studies on charge-ordered manganites [4-
9] were focused mainly on exploring large MCE (large magnitudes of ∆SM) around TCO
and did not consider the issues of refrigerant capacity and hysteretic losses in detail.
Thus, from fundamental and practical perspectives, it is essential to understand the
influence of the nature of magnetic phase transitions on both the MCE and RC in these
materials.
We also note that although the use of the Maxwell relation has been validated
over the years for determining SM of SOMT materials [1, 10], its applicability to FOMT
materials still remains under debate [11-18]. Gschneidner, Jr. et al.[11] calculated the
SM of Gd5Ge2Si2 from M(H) measurements using the Maxwell relation and showed its
excellent agreement with that calculated from the heat capacity (C) data. However,
Giguere et al. [19] later argued that the use of the Maxwell relation overestimated the
value of SM for this FOMT compound and suggested an alternative approach using the
Clausius-Clapeyron equation. In a recent study, Liu et al. [20] have shown that the use of
the Maxwell relation yields huge “spike” peaks of SM in the FOMT compounds MnAs,
Mn1-xFexAs, and La0.7Pr0.3Fe11.5Si1.5, in which both PM and FM phases coexist in the
vicinity of TC. Those authors proposed an alternative “geometric” solution for removing
these spurious SM peaks. De Oliveira and von Ranke have reformulated the Maxwell
relation showing its limitation for the calculation of SM in FOMT materials. Having
theoretically studied the effect of magnetic irreversibility on estimating the SM from
M(H) measurements, J.S. Amaral and V.S. Amaral argue that the spurious SM peaks
71
arise mainly from the presence of magnetic irreversibility or a mixed-phase regime that is
not considered in the Maxwell relation [21]. In this case, the authors suggest that if the
Landau theory or the mean field model is applied to experimental (nonequilirium) data
then the equilibrium M(H) curves can be estimated and the true value of SM can be
consequently obtained [21, 22]. Very recently, Cui et al. [23] have proposed a simple
modification to the Maxwell relation by taking into account the mass variations in FM
and PM phases on temperature in the two-phase region for MnAsCx, (Mn,Al)As, and
Mn0.994Fe0.004As compounds, which in effect eliminates the unphysical SM peaks. While
previous studies were focused mainly on magnetocaloric materials with a first-order PM-
FM transition [13, 19-24], an interesting question emerges regarding the validity of using
the Maxwell relation for calculation of SM in magnetocaloric materials with a first-order
FM-AFM transition.
Furthermore, it has been noted that there exists a static d(x2-y
2)-type orbital order,
which mediates the FM coupling within the OO planes while favoring the AFM coupling
perpendicular to the OO planes, thus resulting in an overall A-type AFM spin state in
PSMO [25-29]. This implies that OO-induced magnetic anisotropy could play an
important role in the magnetism of the material. Indeed, torque magnetization and
electron paramagnetic resonance (EPR) studies have recently revealed strong OO-
induced magnetic anisotropy in the FM state, and the signature of magnetic anisotropy
detected in the PM and AFM state suggests FM clusters persisting within these states
[28]. Despite the light this study could shed on the phase separation problem, a clear
understanding of the magnetic anisotropy and its correlations with the magnetic entropy
and critical exponents in this material is lacking.
72
In order to address the outstanding issues we have conducted a systematic study
of the magnetism, MCE and TS of PSMO. Our results clear-up some of the discrepancies
on the nature of first- and second-order phase transitions and their influences on the MCE
and highlight the important role of magnetic anisotropy and its correlations with the MCE
and critical exponents in mixed phase manganite systems like PSMO.
6.2 Experiment
Polycrystalline samples of Pr0.5Sr0.5MnO3 were fabricated from Pr2O3, SrCO3, and
MnO using standard solid-state reaction methods. The starting powders were thoroughly
ground and then reacted in air for 10 days at 1500 °C with several intermediate grindings.
The reacted powders were then cold pressed into disks of 1.5 mm thickness and sintered
in air for 1 day at 1500 °C. The final sintered samples were slow cooled over a period of
40 h to room temperature. Temperature-dependent X-ray diffraction (XRD)
measurements were performed on the sample over a wide temperature range of 100 to
300 K. The XRD patterns reveal a structural transition from the tetragonal (I4/mcm) to
orthorhombic (Fmmm) symmetry. This result is consistent with what was reported
previously for the same composition [30, 31].
6.3 Results and Discussion
6.3.1 Influence of first- and second-order magnetic phase transitions on the
magnetocaloric effect and refrigerant capacity of Pr0.5Sr0.5MnO3
Figure 6.1 shows the temperature dependence of magnetization (M(T)) taken at a
field of 0.05T. It can be observed that the PSMO system undergoes a SOMT from the PM
73
to FM state at TC ~250 K followed by a FOMT from the FM charge-disordered to AFM
CO state at TCO ~152 K.
0 50 100 150 200 250 3000
20
40
60
PMFM
M
(e
mu
/g)
T (K)
ZFC
FC
AFM
Pr0.5
Sr0.5
MnO3
Figure 6.1: Temperature dependence of zero-field cooled (ZFC) and field-cooled (FC)
magnetizations taken at a field of 0.05 T.
To investigate the effect of magnetic field on the SOMT and FOMT, M(T) curves
were measured in different magnetic fields (µ0H = 1 T, 2 T, 3 T, 4 T, and 5 T), the results
of which are displayed in Figure 6.2. It can be observed that the SOMT at TC continues to
broaden as the magnetic field is increased, whereas the FOMT at TCO remains reasonably
sharp even at fields of up to 5 T due to the strong coupling between the magnetism and
the lattice in the vicinity of the TCO [32]. Due to the sharp change in the M(T) we expect
to observe a very large MCE in the FOMT region.
74
Figure 6.2: Temperature dependence of magnetization taken at different magnetic fields
up to 5T [49].
In order to evaluate the MCE, the isothermal magnetization curves of the sample
were measured with a field step of 0.05 T in a range of 0-5 T and a temperature interval
of 3 K in a range of temperatures around the TC and around the TCO. Such families of
M(H) curves are shown in Figure 6.3(a) and (b), respectively. As expected from Figure
6.1, there is a more drastic change of the magnetization around the TCO (see Figure
6.3(b)) than around the TC (see Figure 6.3(a)), indicating a larger magnetic entropy
change in the vicinity of the TCO. It is worth mentioning here that around the TCO the
sample shows S-shape magnetization, which is typical for metamagnetic materials[33]. It
is believed that the metamagnetism arises mainly from the coexistence of the competing
AFM/CO and FM phases and the collapse of the AFM/CO state that occurs in the
presence of an applied magnetic field [32].
75
0 1 2 3 4 5 60
10
20
30
40
50
60
70(b)
T=65K
T=300K
T=165K
0H (T)
M (
em
u/g
)
M (
em
u/g
)
0H (T)
T=165K(a)
0 1 2 3 4 5 60
10
20
30
40
50
60
70
Figure 6.3: Isothermal magnetization curves taken at different fixed temperatures
between 65 and 300 K for the Pr0.5Sr0.5MnO3 manganite: (a) around TC and (b) around
TCO [49].
Figure 6.4 shows the temperature dependence of SM calculated using the
Maxwell relation at different magnetic fields ranging from 0.15 T to 5 T. It can be
observed that the Pr0.5Sr0.5MnO3 system exhibits large magnetic entropy changes around
the TC and around the TCO. As expected from the M(T) and M(H) data, the SM around
the TCO is much larger than that around the TC. For µ0ΔH = 5 T, the magnitude of ∆SM (-
7.5 J/kg K) at the TCO is about twice that (3.2 J/kg K) at the TC. We note from Figure 6.4
that the large ∆SM peak around the TCO is concentrated in a narrow temperature range,
whereas the ∆SM peak around the TC is spread over a broader temperature range raising
the possibility of an enhanced RC.
We have calculated the RC for both cases around the TC and around the TCO using
the method described in Chapter 3.2, and plotted the results as a function of magnetic
field in Figure 6.5. It can be observed that in both cases the RC increases with the applied
magnetic field. An important fact to be emphasized here is that the magnitude of RC is
larger around the TC than around the TCO for µ0H < 3.7 T, which belongs to the magnetic
76
field range useful for practical use of magnetic refrigerators. As shown previously in Ref.
[1], in the same refrigeration cycle, a material with higher RC is preferred, because it
would support transport of a greater amount of heat in a real refrigeration cycle.
Figure 6.4: Temperature dependence of magnetic entropy change (−SM) at different
applied fields up to 5 T [49].
Therefore, for the case of Pr0.5Sr0.5MnO3, a larger value of RC around the TC indicates
that magnetic refrigeration in the vicinity of the TC is more effective than that around the
TCO.
Furthermore, we recall that hysteretic losses (magnetic and thermal hysteresis) are
often involved in FOMT [33]. Because these hysteretic losses are the costs in energy to
make one cycle of the magnetic field, they must be considered when calculating the
usefulness of a magnetic refrigerant material being subjected to cyclic fields [2].
77
1 2 3 4 5 6 7
50
100
150
200
250
300
RC
(J/k
g)
0H (T)
TC
TCO
(hysteresis)
TCO
(subtracted hysteresis)
Figure 6.5: Magnetic field dependence of RC for the cases around TC and TCO (without
and with subtracted hysteretic losses). The inset shows the magnetic field dependence of
magnetization taken at 150 K (below TCO) and at 180 K (below TC).
To evaluate possible hysteretic losses involved in the magnetic phase transitions
in Pr0.5Sr0.5MnO3, we measured the M(H) loops at temperatures around the TC and the
TCO. The inset of Fig 6.5 shows, for example, the M(H) curves measured at 180 K (below
TC) and at 150 K (below TCO). It can be seen that the hysteretic losses (the area mapped
out by the increasing and decreasing field curves) are very large below the TCO, whereas
they are very small or negligible below the TC. To be precise, we have subtracted the
average hysteretic losses from the RC values calculated without considering hysteretic
losses. For comparison, the RC obtained after subtracting the average hysteretic losses for
the case around the TCO are also included in Figure 6.5. In the range of magnetic fields
investigated, the superiority of the RC around the TC is even more pronounced after
78
accounting for hysteresis around the TCO. This clearly indicates that the hysteretic losses
involved in a FOMT significantly reduce the RC and are, therefore, undesirable for use in
a real magnetic refrigeration cycle.
An important fact that emerges from the present study is that the comparison of
MCE among magnetocaloric materials [34] by considering the magnitude of SM only is
inadequate. Instead, a proper estimation should be made with the use of RC, with
attention paid to the fact that magnetic hysteresis losses must be estimated and subtracted
from the RC calculation. In addition, this comparison should be made only in the same
temperature range. From a device standpoint, it is believed that not only FOMT materials
but also SOMT materials are promising candidates for active magnetic refrigeration
applications. Some SOMT materials with zero hysteretic losses are even more
advantageous. An example of this is Gd – the best magnetic refrigerant candidate
material to date for practical use in sub-room-temperature magnetic refrigerators [35].
Considering the fact that SOMT materials with a large magnetic entropy change over a
broad temperature range usually possess large refrigerant capacity [35, 36], it would be
worthwhile to search for enhanced RC in materials that undergo multiple magnetic phase
transitions [9, 37, 38]. From this perspective, the MCE research in magnetic
nanocomposites with a SOMT may be of great interest [37].
We now turn our focus to the complete description of the SOMT near TC in
PSMO, including the critical exponents and equation of state, based on analyses of the
family of SM curves. As previously noted in Chapter 3, only two critical exponents (n
and ) of the SOMT are independent. We have used the non-iterative procedure to obtain
the other related critical exponents (, , and ) using the following relationships:
79
1 Δ Δ; 1 2 ; 1/ 1/ Δ 1n n n (6.1)
In order to obtain the critical exponent n as outlined in Eq. 3.20, the experimental
Δ pk
MS values normalized to their corresponding maximum values,
s=Δ ( ) / Δ ( )M M
pk pkfS H S H , have been fitted as a power law of the magnetic field H in the
whole experimental magnetic field range. The fitting yields a value of the critical
exponent n = 0.670, as presented in Figure 6.6(a). Alternatively, the reference
temperature ( ) /r r C CT T T , where r CT T is chosen such that
( ) ( )⁄ , is also expected to show a power law dependence on H
with the exponent equal to Δ. This fitting, as shown in Figure 6.6(b), yields a value of the
gap exponent 1.835 (1/ 0.545 ). In this fitting procedure magnetic fields higher
than 1.4 T have been used, to ensure technical saturation.
In order to validate the reliability of the critical exponents obtained according to
this procedure, the temperature and field dependence of the normalized magnetization
and isothermal susceptibility (mt, mh and jh respectively) has been plotted versus the
renormalized temperature, t, and field, h, respectively.
Figure 6.7 shows the dimensionless mt* vs. t*, Ln(mh*) vs. Ln(h*) and Figure 6.8
shows Ln(jh*)-1
vs. Ln(h*) representations, where mt*, mh*, jh*, t*, and h* are the
corresponding dimensionless magnitudes obtained according to the relationship x*=x/xo,
where x=mt, mh, jh, t, h, and xo is in the units of x. It can be observed that the experimental
data fall on the same curve, in the mt* vs. t* representation (Figure 6.7(a)), and on the
two curves f+ (for T>TC) and f (T<TC) in the Ln(mh*) vs. Ln(h*) representation (Figure
6.7(b)).
80
0.25
0.50
0.75
1.000.00 0.25 0.50 0.75 1.00
0.50 0.75 1.000.50
0.75
1.00
(H/Hf)
0.670
s
a.
b.
r
(H/Hf)
0.545
Figure 6.6: Determination of the critical exponents n (panel a) and Δ (panel b) after
fitting of δs and εr, respectively, as a power law of the reduced magnetic field H/Hf.
This fact indicates that the obtained values of the critical exponents, = 0.394 and =
4.651, of PSMO are reliable. These values are close to those reported previously by A. K.
Pramanik and A. Banerjee for the same composition [29].
By combining Eqs. (3.21) and (3.22), it is possible to find relationships between
the critical amplitudes M(0,1) and M(1,0), and the values of the temperature and field
scaling functions for ·(t=0) and f·(h=0), respectively:
(0,1) (0)M , (6.2)
(0) 0; (0) ( 1,0)f f M , (6.3)
81
as has been presented in Figs. 6.7(a) and 6.7(b), 0,1 32.264M emu g1
T1/
and
( 1,0) 98.962M emu g1
, respectively.
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.40
10
20
30
40
50
60
70
-12 -8 -4 0 4 80
50
100
150
200
250
mt*
t*
M(0,1)
=(t*)
(a)
mt*=(t*)
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
-4
-2
0
2
4
6
-5 0 5 10
f+
f-
T=TC
T>TC
T<TC
Ln
mh*
Ln h*
Ln(M(-1,0))
f=(h*)1/
(b)
mh*=f
-(h*)
mh*=f
+(h*)
Figure 6.7: Dimensionless renormalized temperature t* and field h* dependence of
the dimensionless temperature renormalized magnetization mt* (a), of the
dimensionless field renormalized magnetization mh* (b in logarithmic scales)
Additionally, taking into account the value of the critical exponent = 1.440, the
representation Ln(jh*)-1
vs. Ln(h*) has been plotted in Figure 6.8 showing that the
experimental data fall on two curves g+ (for T>TC) and g (T<TC), which gives further
evidence of the validity of the fitting procedure used to obtain the critical exponents.
Similarly, by combining the equation jh=g(h) and Eq. (3.19) it is possible to obtain the
relationships between the critical amplitudes 0(1,0) and 0( 1,0) , and the values of the
field scaling functions for 0g h :
(0) (1,0); (0) ( 1,0)o og g , (6.4)
as has been presented in Figure 6.8, 0 1,0 1.716 T emu1
g. In Figs. 6.7(b) and 6.8 it
can be seen that the asymptotic (or critical) values of mh* and jh* evolve as power-law of
82
field with critical exponents 1/ (according to Eq. (3.18)) and
, respectively. To
achieve as much information about the FM state as possible we need to separate the two
transitions.
-2 0 2 4 6 8 10 12
0
1
2
3
4
5
6
7
g=(h*)- /
g-
g+
Ln(o(1,0))
Ln
(j h
*)-1
Ln h*
T<TC
T>TC
T=TC
Figure 6.8: Inverse of the dimensionless isothermal susceptibility jh*.
In order to be able to de-convolute the field- and temperature-dependent ,SOM T H
curves of the SOMT, subsequently used to obtain their deconvoluted Δ ,SO
MS T H
curves, the Arrott–Noakes equation of state (ANEOS) has been used [39]:
1
1/
/
( )Ca T T bH
MM
,
(6.5)
where the parameters a and b are related to the critical amplitudes of the isothermal initial
susceptibility ( 0(1,0) ), the spontaneous magnetization ( ( 1,0)M ), and critical
magnetization (M(0,1)), along with the critical exponents (, , and ) and Curie
83
temperature (TC). These relationships can be obtained using Eqs. (3.17), (3.18), (3.19)
and (6.5), according to:
1/(1,0)o
C
aT
, (6.6)
/(0,1)b M , (6.7)
1/( 1,0)
C
M ba
T
,
(6.8)
Recently, it has been shown that the ANEOS is able to reproduce the universal
curve σ for amorphous alloys [18], and also allows predicting of the shape of the ΔSM
curves [40] when the parameters a and b have been obtained from nonlinear fit of the
experimental data, and the critical exponents β and γ from the Kouvel–Fisher iterative
method. Using Eq. (6.5) with the directly obtained parameters a = 6.055 10-3
emu1/
g1/
K1
T1/
, and b = 1.343 10-5
emu/(·)
g/(·)
T1/
predicted by the universal behaviors, the
critical exponents and , and the TC value, the thermomagnetic response of the
deconvoluted SOMT in the magnetic field range up to a value of 0 5 TfH in 10 mT
increments, and in the temperature range from 30 K to 400 K in 0.1 K increments, has
been simulated. To compare with the experimental data, the corresponding simulated data
have been presented with solid lines in Figure 6.9 (a-c). Good agreement between the
experimental and simulated data has been found, which indicates that the ANEOS can be
used to represent the thermomagnetic response of manganites in the vicinity of their TC.
Figure 6.9(c) shows the deconvoluted magnetocaloric response of the SOMT,
Δ ,SO
MS T H , when the ANEOS is used [18, 40].
84
25 75 125 175 225 275 3250
20
40
60
80
Tf
CO
M (
em
u g
-1)
T (K)
TC
(a)
0 1 2 3 4 5 60
20
40
60
80(b)
T=
30
0 K
M
(e
mu
g-1)
0H (T)
TC=
24
7 K
T=
17
3 K
30 80 130 180 230 280 330 380
0
1
2
3
-S
SO
M (
J K
-1 k
g-1)
T (K)
oH (T)
1
2
3
4
5
Lines: Thoer. data Eq. 15
Symbols: Exp. data
(c)
Figure 6.9: Temperature (a), and field (b), dependence of the magnetization, and
temperature dependence of SM (c). The dark sold lines in (a) and (b) and the solid lines
in (c) are fits to the data via the ANEOS.
We have found good agreement between the experimental and simulated data in the
vicinity of TC, but a noticeable discrepancy for T << TC. This discrepancy likely arises
from the coexistence of AFM and FM phases that are present in the material below the
85
TC. It is also worth noting that for small field changes ( 0 1 TH ) the experimentally
calculated value of Δ ,SO
MS T H is considerably smaller than the theoretically calculated
Δ ,SO
MS T H , but becomes equal for large field changes ( 0 5 TH ). This can be
attributed to the presence of ferromagnetic clusters [28, 41, 42] and their influence on the
magnetic entropy change and critical exponents near the SOMT in PSMO. We propose
that for small applied magnetic fields, the magnetic field response of magnetization is
weak in materials exhibiting FM clusters thus resulting in a small change in magnetic
entropy, while for large applied magnetic fields, all of the magnetic moments are aligned
with the magnetic field resulting in the overall change in magnetic entropy that is close to
the theoretically predicted value. This explains the small values of Δ ,SO
MS T H reported
for magnetocaloric materials with FM clusters present [43].
The experimentally measured 0 (solid symbol ), along with the predictions
offered by Eq. (2.19) (open symbol ○) or by Eq. (3.4) as 0 Ca T T
(lines), are
presented in Figure 6.10(a). The discrepancy between the experimental and theoretical
data is due to the upward deviation of 0( )T above TC,
This deviation once again suggests the existence of FM correlations/clusters in this
compound above TC. This observation has consequences for the critical behavior of the
system and consequently the equation of state. The effects of this FM interaction above
TC can be taken into account either if a temperature dependence of the parameter a(T) of
the ANEOS is introduced, or if an effective critical exponent, ef, is defined. Figure
6.10(b) presents the temperature dependence of the critical exponent ( )ef T obtained
numerically, demonstrating its tendency towards a constant value of ·=1.440, as
86
temperature increases as a result of the disappearance of the FM clusters and their
interactions.
0.00
0.05
0.10
0.15
0.20
250 260 270 280 290 300
1.20
1.25
1.30
1.35
1.40
1.45
(b)
-1 o (
T e
mu
-1 g
)
(a)
T>TC (K)
Figure 6.10: (a) Temperature dependence above TC of the inverse of the experimental
isothermal initial susceptibility 0 (solid symbol *), along with the ones offered by Eq.
(6) (open symbol ○) and Eq. (15) (lines). (b) Temperature dependence above TC of the
critical exponent ( )ef T (solid symbol) and the value of ·=1.440 presented in the sample
when the FM clusters and their interactions have disappeared above 300 K (dashed line).
6.3.2 Magnetic Anisotropy and Magnetization Dynamics in Pr0.5Sr0.5MnO3
In order in confirm these results we have also studied the temperature dependence
of effective magnetic anisotropy field (HK, a measure of ferromagnetic correlations) by
87
using the radio-frequency transverse susceptibility (TS). The HK has been found to persist
in the temperature range TC < T < 300 K, suggesting the existence of FM correlations or
FM clusters in the PM regime and their disappearance above 300 K, which is fully
consistent with the critical analysis and discussions presented above.
As discussed in the introduction, we expect the magnetic anisotropy to provide
considerable additional information on the magnetic interactions in PSMO. Figure 6.11
(a) shows an example of the TS profile of PSMO taken at 160 K. The change in T with
DC magnetic field (Hdc) is expressed from equation (3.28). The plot represents a unique
uni-polar field sweep from positive (+5 kOe) to negative (-5 kOe) fields. As expected,
two symmetric, broad peaks are seen in the scans at the anisotropy fields (HK), while the
sharp peak corresponds to the switching field (HS). Figure 6.11(b) displays a 3D plot of
the magnetic field and temperature dependence of the change in TS for unipolar field
sweeps from positive (+5 kOe) to negative (-5 kOe) fields. It is observed that there are
remarkable changes in peak location (HK) and peak height ([∆/]max) with temperature
(T) at the PM-FM and FM-AFM transition regions.
-4 -3 -2 -1 0 1 2 3 40.2
0.4
0.6
0.8
positive to negative
-HK
HS
HK
(
%)
H (kOe)
T = 160 K
Pr0.5
Sr0.5
MnO3
(a)
Figure 6.11: An example of unipolar transverse susceptibility scan of Pr0.5Sr0.5MnO3 (a).
3-D Unipolar scans of transverse susceptibility as a function of magnetic field and
temperature (b).
-6-4
-2
0
2
4
6
0.0
0.5
1.0
1.5
2.0
2.5
050
100150
200250
300
TC
/
(
%)
T (K)
H (kOe)
TN
(b)
88
To better illustrate these, the temperature dependence of HK, HS, and [∆/]max
are depicted in Figure 6.12. As one can see clearly in Figure 6.12(a), there is a strong
change in HK in the vicinity of the FM-AFM transition and finite values of HK are
detected over a wide temperature range, even above the TC (in the PM region) and below
the TCO (in the AFM region). To understand this dependence, we recall that the crystal
structure of PSMO favors a Jahn-Teller (JT) distortion that likely induces the d(x2-y
2)-
type orbital order even in the PM state. It has been shown that in the PM region, the
dynamic spin fluctuations are anisotropic due to the polarization of the d(x2-y
2)-type
orbital [27, 28]. Below TC, the PSMO system enters the FM state with an enhanced lattice
distortion, resulting in the change of the polarization of the orbital state. Therefore, we
attribute the persistence of magnetic anisotropy in the PM range (Figure 6.12(a)) to the
anisotropic spin fluctuations resulting from the polarization of the d(x2-y
2)-type orbital.
This is fully consistent with the previous observation based on torque magnetization and
EPR [42], suggesting that the existence of FM clusters in the PM region originates from
the d(x2-y
2)-type orbital order. It is likely that the existence of FM clusters in the vicinity
of the PM-FM transition (the role of magnetic anisotropy) governs the critical exponents
of Pr0.5Sr0.5MnO3 [31]. In this case, the change in shape and size of FM clusters above
and below the TC is expected to reduce the effective dimensionality of spin interaction
(D<3). This may provide some important clues for understanding the unusual critical
behaviors reported in a large class of doped manganites [44-46].
With further decrease in temperature from the TC, the HK first increases sharply at
190 K, reaches a maximum at ~150 K (TCO), decreases sharply at ~ 135 K, and finally
decreases gradually at lower temperatures. Based on previous neutron scattering studies
89
[27, 28], the AFM spin correlations are known to develop between orbital-ordered planes
in the FM state and progressively increase below 190 K yielding a weak parasitic A-type
AFM order before the system undergoes a first-order transition at TCO to the pure AFM
phase [27, 28].Therefore, we can attribute the sharp increase in HK at ~190 K to the
progressive development of the AFM phase that may result in the formation of highly
anisotropic FM clusters, while the sharp decrease in HK at ~135 K arises mainly from the
strong decrease of the volume fraction of the FM phase. We recall that a structural
transition from tetragonal to orthorhombic symmetry occurs at the TCO in PSMO [31].
The strong variation of HK coupled with the structural change at the TN clearly suggests a
strong coupling between the magnetism and the lattice in this material. The strong
coupling between the structure and magnetic anisotropy has also been studied in
Pr0.5Sr0.5CoO3, which will be discussed in chapter 8.
As shown in Figure 6.12(a), HK increases in the FM region but decreases in the
AFM region with lowering temperature. The temperature dependence of HS (Figure
6.12(b)) also reveals a remarkable variation around the TCO, where the structural
transition has been documented [31]. This observation once again points to the strong
coupling between the magnetism and the lattice in PSMO. The HS is found to increase
with decreasing temperature in both FM and AFM regions.
As one can see clearly in Figure 6.12(c), [∆]max is small and almost constant
in the AFM range (T < TCO). This is consistent with the small permeability of the AFM
phase. It is worth noting from Figure 6.12(c) that there is a sharp increase in [∆]max
at the TCO, which is associated with the increase in magnetic permeability (µ). In the
temperature range of TCO ≤ T ≤ TC, [∆]max increases rapidly with increasing
90
temperature, as a result of the strong increase in ∆µ. At T ~ TC, a drop in [∆]max is
observed, which is associated with the PM-FM transition. In the PM range, [∆]max is
expected to be zero [29, 47].
0 50 100 150 200 250 3000
300
600
900
1200
0 50 100 150 200 250 3000
1
2
3
0 50 100 150 200 250 3000
100
200
300
400
500
(c)
PM
FM
Hk(O
e)
T(K)
AFM
(a)
PM
FM
AFM
[/
] m
ax (
%)
T (K)
(b)
PM
FM
AFM
Hs (
Oe)
T (K)
Figure 6.12: Temperature dependence of effective anisotropy field (HK), switching field
(HS), and peak height of transverse susceptibility curves ([T/T]max)
However, the non-zero value of [∆]max for Pr0.5Sr0.5MnO3 is retained until T =
300 K (see Figure 6.12(c)). This fully agrees with the temperature dependence of HK and
HS, supporting our argument that FM clusters persist at temperatures above the TC in
PSMO. Finally, we show that the TS is also useful for probing metamagnetic transitions
in PSMO. As one can see clearly in Figure 6.13, a composite plot of the TS and M(H)
data taken at 140 K, the PSMO system is converted from the AFM to the FM state as the
applied magnetic field is increased.
91
-40 -30 -20 -10 0 10 20 30 400.0
0.2
0.4
0.6
/
(
%)
H (kOe)
T = 140 K
0
20
40
60
80
M (
em
u/g
)
-HC1
-HC2
HC2
HC1
Figure 6.13: Unipolar transverse susceptibility and first magnetization with respect to
applied magnetic field at T=140K.
Here, HC1 corresponds to a critical field at which the AFM state begins
transforming into the FM state and HC2 corresponds to the critical field at which the AFM
state fully converts into the FM one.The clear coincidence between the [∆] and
M(H) data demonstrates the ability of this technique for probing magnetic phase
conversion in metamagnetic systems [48].
6.4 Conclusions
We have demonstrated the usefulness of MCE and TS in studying complex phase
transitions and the magnetic anisotropy in half-doped manganites such as Pr0.5Sr0.5MnO3.
First, we have studied the influence of first- and second-order magnetic phase transitions
on the magnetocaloric effect and refrigerant capacity of charge-ordered Pr0.5Sr0.5MnO3. It
is shown that the first-order magnetic transition at TCO induces a larger MCE but confines
92
the peak in a narrower temperature limiting the value of RC, while the second-order
magnetic transition at TC induces a smaller maximum MCE over a broader temperature
range resulting in larger RC. Hysteretic losses accompanying the first-order magnetic
transition are very large below TCO and therefore detrimental to the RC, whereas they are
very small or negligible below TC due to the nature of the SOMT. The Maxwell relation,
and non-iterative critical analysis methods have been used to characterize the MCE and
the nature of phase transitions in phase-separated manganites of Pr0.5Sr0.5MnO3. We show
that around the second-order PM-FM transition the SM can be precisely determined from
magnetization measurements using the Maxwell relation, but around the first-order FM-
AFM transition the values of SM are overestimated by the Maxwell relation in the
magnetic field range where a conversion between the AFM and FM phases occurs. The
presence of AFM and FM phase coexistence as well as FM clusters has a significant
impact on the MCE and critical exponents near the SOMT in phase-separated materials.
With TS it is evidenced that there is an abrupt change in magnetic anisotropy at the FM-
AFM transition, which is associated with the structural phase transition that occurs at the
same temperature. This is clear indication of the strong coupling between the magnetism
and the lattice in Pr0.5Sr0.5MnO3.
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[43] A. Rebello, V.B. Naik, R. Mahendiran, Large reversible magnetocaloric effect in
La0.7-xPrxCa0.3MnO3, J Appl Phys, 110 (2011).
[44] N.A. Frey, S. Srinath, H. Srikanth, M. Varela, S. Pennycook, G.X. Miao, A. Gupta,
Magnetic anisotropy in epitaxial CrO2 and CrO2/Cr2O3 bilayer thin films, Phys Rev B, 74
(2006).
[45] P. Poddar, J.L. Wilson, H. Srikanth, D.F. Farrell, S.A. Majetich, In-plane and out-of-
plane transverse susceptibility in close-packed arrays of monodisperse Fe nanoparticles,
Phys Rev B, 68 (2003).
[46] G.T. Woods, P. Poddar, H. Srikanth, Y.M. Mukovskii, Observation of charge
ordering and the ferromagnetic phase transition in single crystal LSMO using rf
transverse susceptibility, J Appl Phys, 97 (2005).
[47] R.S. Freitas, L. Ghivelder, P. Levy, F. Parisi, Magnetization studies of phase
separation in La0.5Ca0.5MnO3, Phys Rev B, 65 (2002).
[48] H. Srikanth, J. Wiggins, H. Rees, Radio-frequency impedance measurements using a
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Magnetocaloric effect and refrigerant capacity in charge-ordered manganites Journal of
Applied Physics 106, 023909 (2009)
98
CHAPTER 7.
PROBING MULTIPLE MAGNETIC TRANSITIONS AND PHASE
COEXISTENCE IN La5/8−xPrxCa3/8MnO3 (x = 0.275) SINGLE CRYSTALS
In the previous chapters, we have demonstrated the versatility of MCE and TS as
useful tools for studying phase transitions of various origins, however, these probes can
also be utilized to study interesting phenomena such as phase separation. In this chapter,
we will show how the multiple magnetic transitions, phase coexistence, and kinetic arrest
of microscale phase-separated La5/8−xPrxCa3/8MnO3 (LPCMO) manganites are probed by
the MCE and TS techniques. Bulk LPCMO is comprised of micron-sized regions of
ferromagnetic (FM), paramagnetic (PM), and charge-ordered (CO) phases. TS and MCE
experiments have evidenced the dominance of low-temperature FM and high-temperature
CO phases. The “dynamic” strain liquid state is strongly dependent on magnetic field,
while the “frozen” strain-glass state is almost magnetic field independent. In combination
with magnetic, magneto-transport, and magnetic force microscopy (MFM)
measurements, MCE studies provide solid evidence that the sharp change in the
magnetization, electrical resistivity, and magnetic entropy just below the Curie
temperature (TC)occur via the growth of FM domains already present in the material even
in zero magnetic field. The subtle balance of coexisting phases and kinetic arrest are also
probed by MCE and TS experiments, leading to a new and more comprehensive magnetic
phase diagram.
99
7.1 Introduction
La5/8−xPrxCa3/8MnO3 (LPCMO) is a mixture of La5/8Ca3/8MnO3 (x = 0) and
Pr5/8Ca3/8MnO3 (x = 5/8) exhibiting low-temperature ferromagnetic metallic (FMM) and
charge-ordered insulating (COI) ground states, respectively. In this system, the
substitution of smaller Pr ions for larger La ions reduces bandwidth (W), thus leading to
micrometer scale phase separation with multiple phases coexisting in the material [1, 2].
It has been argued that in the presence of quenched disorder induced by the ions of
different radii, the similarity of the free energies leads to the coexistence of the
competing FMM and COI phases [3, 4]. If this is the case, the phase separation should be
static because the phase boundaries are pinned by the disorder sites. However,
experimental studies have revealed that these phase boundaries are not fully pinned in
LPCMO [2, 5-10], and hence the inherent coexistence of the FMM and COI phases at the
micron length scale is inconsistent with the notion of a charge-segregation type of phase
separation [11-13]. It has been suggested that the different crystal structures of the FMM
and COI phases generate long-range strain interactions leading to an intrinsic variation in
elastic energy landscape, which in turn leads to phase separation (PS) in the strain-liquid
and strain-glass regimes [5, 9, 10, 14]. It has also been suggested that phase separated
regions strongly interact with each other via martensitic accommodation strain, which
leads to a cooperative freezing of the combined charge/spin/ strain degrees of freedom [2,
8]. As a result, LPCMO undergoes a transition from the strain-liquid state to the strain
glass state. Since the strain-liquid state shows large fluctuations in resistivity [8, 9] and
can easily be transformed into a metallic state by applying an external field [5, 10], it is
considered a “dynamic” PS. In contrast, effect of electric field is negligible on the frozen
100
strain-glass state thus classifying it as a “static” PS [5, 10]. Despite a number of previous
works [8, 14, 15], the effect of magnetic field on the strain-liquid and strain-glass states
has not been studied in detail. Another emerging issue, still under debate, is the
underlying origin of the sharp increase in the magnetization below TC in the strain-liquid
region. Two different mechanisms have been proposed for interpreting this observation
[1, 5, 6, 8, 10, 14]. In the first scenario, it is proposed that with lowering temperature, the
COI state is spontaneously destabilized to the FMM phase giving rise to a coexistence of
these two phases, and the sharp increase of the magnetization below TC is due to the
melting of the COI state [8, 14]. This is similar to the case of charge-ordered
R0.5Sr0.5MnO3 (R=La, Pr, and Nd) manganites [11, 16, 17]. In the second scenario, it has
been suggested that the increase in magnetization occurs via the growth of FMM domain
regions that are already present in the material even in zero magnetic field [1, 5, 6, 10].
To shed light on these important unresolved issues, it is essential to employ two
experimental methods that allow detailed investigations of the temperature and magnetic
field responses of the different phases. In this study, we use our ideally suited MCE and
TS experiments for this purpose. Our studies were performed on La5/8−xPrxCa3/8MnO3 (x
= 0.275) single crystals, which were grown in an optical floating-zone furnace and
provided by Professor Sang-Wook Cheong at Rutgers University [7, 18].
7.2 Results and Discussion
7.2.1 Phase Coexistence and Magnetocaloric Effect
Figure 7.1 shows the zero-field-cooled (ZFC) and field-cooled (FC)
magnetization curves taken at 10 mT applied field with the data recorded while warming
up. It is observed that the LPCMO system undergoes multiple magnetic transitions. A
101
peak at TCO ~ 205 K is due to the COI transition [8], and a shoulder at a lower
temperature of about 175 K arises from antiferromagnetic (AFM) ordering [14]. As T is
further decreased, the magnetization sharply increases and an FMM transition is observed
at TC ~ 90 K. A drop in magnetization is observed at Tg ~ 30 K, below which the system
enters the frozen strain-glass state from the dynamic strain-liquid state [2, 8, 14, 19]. It
has been shown that Tg is actually the re-entrant COI transition temperature [2, 8].
0 50 100 150 200 250 3000.0
0.3
0.6
0.9
Tg
TC
TN
TCO
ZFC
FC
0H = 10 mT
M (
em
u/g
)
T (K)
Figure 7.1: Zero-field-cooled and field cooled M(T) with 10mT applied field, measured
on warming [24].
The MCE measurement process for LPCMO is slightly different than the previous
samples; it appears that large magnetic irreversibility occurs just below TCO, due to the
coexistence of the FMM and COI phases. Therefore, we measured the M(H) curves using
the following measurement protocol to eliminate any influence from the hysteresis.
Before conducting any M(H) measurements at temperatures below TCO, the sample was
cooled in zero magnetic field from above TCO. At each temperature, the magnetization
was measured as the magnetic field was continuously swept from 0 to 6 T (labeled the
102
virgin M(H) curve); then from 6 T to 0 (labeled the return M(H) curve); and finally from
0 to 6 T (labeled the second M(H) curve). The M(H) data were taken first at 300 K and
subsequently at lower temperatures following the same measurement protocol.
Figure 7.2 shows the M(H) data at selected temperatures with the “virgin,”
“return,” and “second” curves labeled. These data clearly indicate large field hysteresis in
LPCMO. It is worth noting that for T = 75 K, a reversible magnetization is observed as
the applied magnetic field is cycled (i.e., the second M(H) curves coincide with the virgin
M(H) curves). However, for T < 75 K the second M(H) curves do not coincide with the
virgin M(H) curves but coincide with the return M(H) curves below 65 K. Identical
curves are then observed for subsequent field cycles. To capture these intriguing features
from the perspective of MCE, we have calculated the magnetic entropy change from the
M(H) curves taken after completing one cycle of applied field (i.e., the second M(H)
curves). This helps avoid the hysteresis problem (discussed in section 3) when calculating
the magnetic entropy change of LPCMO using equation (1.3).
Figure 7.3 shows the temperature dependence of −SM for the magnetic field
change of 1.5 T and 6 T, respectively. As expected, −SM curves exhibit peaks around
TCO, TC, and Tg. The positive values of −SM around TC and the negative values of −SM
around TCO and Tg (at low applied fields, 0H < 2 T) are consistent with the LPCMO
undergoing the FM, CO and re-entrant CO transitions, respectively.
It is noted in Fig. 7.3 that the −SM has the largest variation at T ~ 75 K (in the
dynamic PS state), while it is comparatively very small at T < Tg (in the frozen PS state).
This indicates that the strain-liquid state is strongly affected by an applied magnetic field,
whereas the strain-glass state is relatively magnetic field independent.
103
0 1 2 3 4 50
20
40
60
80
100
0 1 2 3 4 50
20
40
60
80
100
0 1 2 3 4 50
20
40
60
80
100
0 1 2 3 4 50
20
40
60
80
100
(b) T = 70 K
2nd
(a) T = 75 K
M (
em
u/g
)
0H (T)
0T -> 5T (virgin)
5T -> 0T (return)
0T -> 5T (second)
virgin
2nd
(d) T = 25 K
2nd
virgin
M (
em
u/g
)
0H (T)
2nd
virgin(c) T = 65 K
M (
em
u/g
)
0H (T)
2nd
virgin
M (
em
u/g
)
0H (T)
Figure 7.2: The M(H) curves for some selected temperatures. The arrows indicate the
way in which the virgin, return, and second magnetization curves were measured [24].
In the strain-liquid region, the large variation of −SM (Fig. 7.3) is attributed to the
suppression of dynamic fluctuations (dynamic phase separation) in magnetic fields. The
large variation of −SM in the dynamic PS region (Fig. 7.3) can also be correlated with
the strong increase in the magnetization below TC (Fig. 7.1). The contribution to the
−SM results, in LPCMO, from the low-field magnetization change in the ferromagnetic
phase and the high-field magnetization change related to the fact that the field-induced
metamagnetic transition takes place in the AFM phase.
To clarify, if the strong increase in the magnetization below TC is attributed to the
destabilization of the COI phase [8, 14] or due to the enhancement of pre-existing FMM
domains in the material [1, 5, 6, 10], we plot in Fig. 7.4 the magnetic field dependencies
104
of the maximum magnetic-entropy change (−SMmax
) and the magnetization (M) at 75
K.It is observed in Fig. 7.4(a) that the −SMmax
increases rapidly and quite linearly with
increasing H up to 2.6 T and then remains almost constant for H > 2.6 T. This
dependence of −SMmax
(H) can be correlated with the M(H) dependence. We note that at
75 K the COI and FMM phases coexist and both of them are magnetic field dependent.
0 50 100 150 200 250 300
0
3
6
9
(-)
(+)T
N
TC
TCO
Tg
6.0T
1.5T
-S
M (
J/k
g K
)
T (K)
Figure 7.3: Temperature dependence of magnetic entropy change (−∆SM) for LPCMO
for the magnetic field change of 1.5 T and 6 T, respectively [24].
The change in the FMM phase can be achieved at a lower magnetic field while a
higher magnetic field is needed to change the COI phase. As extracted from the M(H)
curve (Fig. 7.4(b)), HS1 = 1.5 T is a critical magnetic field at which the COI phase starts
to convert into the FMM phase while HS2 = 2.6 T is a critical magnetic field at which the
COI phase converts fully into the FMM phase. Therefore it can be concluded that for H <
HS1 the −SMmax
results solely from the variation of the magnetization in the FMM phase,
105
since the applied magnetic field has a negligible effect on the COI phase. For HS1 < H <
HS2, however, the COI phase converts into the FMM phase, thus also contributing to
−SMmax
. For H > HS2, the constancy of −SMmax
can be attributed to the complete
conversion of the COI phase into the FMM phase. According to this, it is quite natural to
infer, at first glance, that the sharp increase of the magnetization below TC for LPCMO is
due to the destabilization of the COI phase [8, 14].
However, we note that a critical magnetic field needed to fully convert COI into
FMM is often very high for charge-ordered manganites (for example, at T~75 K, HS2 = 12
T for La1−xCaxMnO3 (x = 0.5) (Ref. [1]) and HS2 = 8–17 T for Pr1−xCaxMnO3 (0.3 < x <
0.5) (Ref. [15])). For the case of LPCMO, the volume fraction of the COI phase at 75 K
is large (69%) determined from the M(H) curve in Fig. 7.4(b) (using the same method
employed in Ref. [6]) and the application of a magnetic field of ~2.6 T is unlikely to be
strong enough to convert COI fully into FMM. This can also be reconciled with the fact
that at 75 K the −SMmax
resulting from the variation of the magnetization in the FM
phase (~6.49 J/kg K) is about twice larger than that resulting from the COI→FMM
conversion (~2.44 J/kg K).
These findings clearly suggest that the sharp increase in the magnetization below
TC in LPCMO cannot be due to the destabilization of the COI phase [8, 14], but instead
can be attributed to the enhancement of the pre-existing FMM domain regions [1, 5-7,
10]. The hysteresis appearing below HS2 ~ 2.6 T is the result of the coexistence of the
COI and FMM phases, whereas the application of higher fields (H > 2.6 T) completely
suppresses the COI phase and as a result the FMM phase with no hysteresis is observed at
these magnetic fields.
106
0 1 2 3 4 52
4
6
8
10
0 1 2 3 4 50
20
40
60
80
100
(III)(II)
FM
CO + FM
T = 75 K
Phase coexistence
[-S
M] m
ax (
J/k
g K
)
0H (T)
Hs2
= 2.6 T
CO + FM
Phase coexistence
(I)
(a)
(b)
Hs1
= 1.5 T
Hs2
= 2.6 T
T = 75 K
FMCO + FM
CO + FM
M (
em
u/g
)
0H (T)
Figure 7.4: (a) Magnetic field dependence of maximum magnetic-entropy change
([−SM]max) for LPCMO at 75 K; (b) the magnetic hysteresis loop M(H) measured at 75K
[24].
Finally, we note that the subtle balance between the competing COI and FMM
phases in LPCMO is readily affected by applied magnetic field, and study of such a
balance can be of great importance in elucidating the physical origin of magnetic/electric
field-induced “colossal” effects [5, 9, 10]. Here, we show that the change in magnitude
107
and sign of -SM can be an indicator of the intricate balance between the COI and FMM
phases as seen in the change in sign of -SMmax
at 205 K (~TCO) as the applied magnetic
field is increased. As shown in Fig. 7.5(a), the -SMmax
is negative and first increases in
magnitude with increasing H up to HC1~2.2 T, and then decreases and reaches zero at HC2
~3.1 T. For H > HC2, it is positive and increases gradually with increasing H up to HC3 ~
3.9 T and finally increases rapidly for H > HC3. Here HC1 = 2.2 T is a critical magnetic
field at which the COI phase starts to convert into the FMM phase, HC2 = 3.1 T is a
critical magnetic field at which the half of the COI phase converts into the FMM phase,
and HC3 = 3.9 T is a critical magnetic field at which the COI phase converts fully into the
FMM phase. The magnetic field dependence of -SMmax
can be interpreted as follows. For
H < HC1, the applied magnetic field is not strong enough to convert the COI phase into
the FMM phase, so the negative -SMmax
and its increase with H result from the
contribution of the COI phase. However, for HC1 < H < HC2, the positive contribution to -
SMmax
from the FMM phase becomes significant because the COI phase is partially
converted into the FMM phase. Since the contribution from the FMM phase is opposite
to that from the COI phase, the sum of the two components lead to a decrease in
magnitude of the negative -SM with H in the range HC1 < H < HC2.
In other words, both the COI and FMM phases coexist but the COI phase is
dominant over the FMM phase, since the sign of -SM is negative. At H=HC2, the positive
and negative contributions to -SMmax
from the COI and FMM phases are equal or
compensated and so -SMmax
crosses zero. For HC2 < H < HC3, the COI phase is largely
converted into the FMM phase which now dominates over the COI phase leading to a
positive -SM. For H > HC3, the COI phase is fully converted into the FMM phase leading
108
to a rapid increase in magnitude of positive -SM. The values of HC1, HC2, and HC3
coincide with the critical magnetic fields determined from the M(H) curve (see Fig.
7.5(b)).
Figure 7.5: (a) Magnetic field dependence of maximum magnetic-entropy change
([−SM]max) for LPCMO at 205 K; (b) the magnetic hysteresis loop M(H), measured at
205 K [24].
The hysteresis seen in the M(H) curve between HC1 and HC3 (Figs. 7.2(b) and 7.5(b)) is
fully consistent with the coexistence of the COI and FMM phases as already revealed by
the MCE data (Fig. 7.5(a)). These results provide an important understanding of the
0 1 2 3 4 5 6
-0.4
0.0
0.4
0.8
1.2
+
FM
+ FM
CO
HC3
= 3.9 T
HC1
= 2.2 T
CO
FM
[-S
M] m
ax (
J/kg
K)
0H (T)
T = 205 K
HC2
= 3.1 T
(+)
(-)
CO
(a)
-6 -4 -2 0 2 4 6-100
-50
0
50
100
Hc3
= 3.9 T
Hc2
= 3.1 T
M (
em
u/g
)
0H (T)
T = 205 K
Hc1
= 2.2 T
(b)
109
physical origin of the magnetic/electric field induced “colossal” effects, including
colossal magnetoresistance and large magnetocaloric effects in mixed-phased manganites
[9, 20-22].
7.2.2 Transverse Susceptibility
To understand the magnetization dynamics of LPCMO we have also performed
TS measurements in these LPCMO (x=0.275) single crystals. Figure 7.6 (a-c) shows the
change in T as a function of applied DC field (HDC) below the TCO. As seen from the -
SM data (Fig. 7.2) there is no appreciable dependence of -SM on external field at
temperatures below Tg, due to the system being in the static PS regime. However, when
probing near (and above) TC (Fig. 7.6 (b-f)), in the dynamic PS region, we see the
emergence of a sharp drop in the TS data, associated with the conversion of COI to
FMM, as seen from M(H) and –SM(T) (Figs 7.4, 7.5). At T < TC, the shape of TS spectra
remains almost the same with no field hysteresis as the HDC is swept between +5T and -
5T and vice versa, indicating a magnetic field-assisted kinetic arrest phenomenon as also
reported previously for Gd5Ge2 alloys [23]. It is worth noting that unlike the case of
Gd5Ge2, this kinetic arrest occurs just below TC in the LPCMO system. This finding
points to the important fact that the spin dynamics of the LPCMO system are frozen out
by the applied field even in the dynamic region, as the magnetic energy dominates over
the thermal and strain energies. As the temperature is increased further above TC, the drop
in TS occurs at higher values of HDC, signifying that LPCMO is in an increasingly stable
COI state above TC. It is noted that a largest field hysteresis (the area enclosed by the
increasing (blue) and decreasing (red) TS curves) is observed around 70 K, which is
associated with the perspective of the strongest phase separation that occurs in this
110
temperature range. The field hysteresis is largely suppressed with increasing temperature,
which is consistent with the fact that the COI phase becomes dominant at the expense of
the FMM phase at high temperatures.
Having considered the variation in the magnetization dynamics of the LPCMO
system after the DC magnetic field is cycled, we plot in Fig. 7.7(a) the temperature
dependence of the switching fields (HS+ and HS
-) associated with the conversion between
the COI and FMM phases on increasing and decreasing DC fields, leading to a more
accurate H-T phase diagram in the dynamic and static PS regions at temperatures below
TCO.
Figure 7.6: (a-d): Bipolar TS scans below TC (a) and above TC (b-d).
It can be seen that below TC, after the material saturated, the COI phase is fully
suppressed and its dynamics are kinetically arrested. As a result, the material now
behaves as a soft ferromagnet irrespective of variation in applied field. As temperature
-60 -40 -20 0 20 40 60
0
1
2
3
T
T (
%)
H (kOe)
decreasing
increasingT = 150 K
-60 -40 -20 0 20 40 60
0
2
4
T
T (
%)
H (kOe)
decreasing
increasing
T = 90 K
(c)
-60 -40 -20 0 20 40 60
0
2
4
T
T (
%)
H (kOe)
decreasing
increasing
T = 80 K
(b)
-60 -40 -20 0 20 40 60
0.0
0.7
1.4
2.1
T (
%)
H (kOe)
decreasing
increasing
T = 60 K
(a)
(
c)
(
f)
111
is increased further, the emergence of two competing phases becomes more evident,
where the drastic drop in TT is mainly due to the growth of the FMM domains inside
the COI ones.
Figure 7.7: New phase diagrams for LPCMO developed from TS vs. HDC (a) Positive
and negative switching field as a function of temperature. (b) Maximum change in TS at
HDC=0 as a function of temperature.
Probing even deeper insights into the temperature dependence of TS, we plot the
[TT]max at zero applied DC field (HDC = 0) (Fig. 7.7 (b)) and in so doing, realize a
new temperature dependent phase diagram for LPCMO. At high temperature [TT]max
~ 0, due to the small permeability in the PM region. On decreasing the temperature a
small increase in [TT]max is observed around TCO, signifying the beginning of the
dynamic PS region, where we begin to see FMM clusters forming in the COI region. The
curve dramatically increases to a maximum at TC, followed by a large drop off at Tg. The
dramatic increase below TCO is a signature of FMM domains nucleating in the sample,
followed by the large drop-off associated with the freezing of the PS region. The
strongest variation in [TT]max at T ~ TC reflects the fact that the most robust phase
separation occurs at this temperature. An important consequence that emerges from these
new TS phase diagrams is the absence of peaks associated with effective anisotropy
0 30 60 90 120 150 1800
1
2
3 H
+
S(T)
H-
S(T)
0H
(T
)
T (K)
CO
CO +
FM
FM
(a)
0 50 100 150 200 250 3000
1
2
3
4
5
FS
FM + CO
/
T] m
ax (
%)
T(K)
PM
(b)
112
fields (HK), which are often observed in conventional FM systems such as Pr0.5Sr0.5MnO3
(Chapter 6) and Pr0.5Sr0.5CoO3 (Chapter 8), indicating that the FMM phase is not
stabilized in the bulk form of LPCMO. In other words, the phase separation in the
LPCMO system is dynamic and the phase boundaries are not pinned by the disorder sites.
7.3 ConclusionsIn summary, systematic magnetocaloric measurements on
La5/8−xPrxCa3/8MnO3 single crystals have revealed important insights into the complex
multiple-phase transitions. The system is ferromagnetic at low temperature and becomes
charge ordered at high temperature. The dynamic strain-liquid phase is strongly affected
by an applied magnetic field, whereas the frozen strain-glass phase is nearly magnetic
field independent. The origin of the large MCE in the strain-liquid region arises from the
suppression of dynamic fluctuations in magnetic fields. The MCE data clarify that the
sharp increase in the magnetization below TC may not be due to the destabilization of the
COI phase to the FMM phase, but favors the idea of the growth of pre-existing FMM
domain regions. TS experiments provide evidence for the instability of the FMM phase
and the unusual magnetic field-assisted kinetic arrest of the magnetization in this system.
Overall, MCE and TS have proven to be excellent probes of the magnetic transitions and
ground-state magnetic properties of phase-separated systems like LPCMO.
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Pr1/2Sr1/2MnO3, Phys Rev Lett, 74 (1995) 5108-5111.
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116
CHAPTER 8.
MAGNETOCALORIC EFFECT AND TRANSVERSE SUSCEPTIBILITY OF Pr1-
xSrxCoO3 (x =0.3-0.5): IMPACT OF THE MAGNETOCRYSTALLINE
ANISOTROPY-DRIVEN PHASE TRANSITION
In this chapter we demonstrate that the TS can be used as a powerful probe of the
structurally coupled magnetocrystalline anisotropy in complex oxides like Pr0.5Sr0.5CoO3,
which undergoes a PM-FM phase transition at TC ~235 K followed by a structurally
coupled magnetocrystalline anisotropy transition at TA ~120 K. Our findings point to the
existence of a distinct class of phenomena in correlated materials due to the unique
interplay between structure and magnetic anisotropy. Since the structural change at the TA
in Pr0.5Sr0.5CoO3 is not associated with any magnetic transition, Pr0.5Sr0.5CoO3 provides
an excellent system for determining the structural entropy change and its contribution to
the MCE in magnetocaloric materials. Having systematically studied the influence of the
structurally coupled magnetocrystalline anisotropy transition on the MCE in Pr1-xSrxCoO3
(x = 0.3, 0.35, 0.4, and 0.5) compounds, we have demonstrated, for the first time, that the
structural entropy contributes significantly to the total entropy change and the structurally
coupled magnetocrystalline anisotropy plays a crucial role in tailoring the magnetocaloric
properties for active magnetic refrigeration technology [1]. Our study has shed light on
one of the most challenging issues in the research field of magnetocaloric materials.
117
8.1 Introduction
Although relatively less studied than the manganites, cobaltites of the formula R1-
xMxCoO3 (R= Lanthanide, M = Alkaline-Earth) present interesting characteristics,
perhaps the most well-known example being the spin-state transition in LaCoO3 [2-4].
The presence of Co on the perovskite B-site leads to an additional spin-state degree of
freedom due to similar magnitudes of the crystal field and Hund’s rule exchange
energies. This, along with the significantly larger magnetocrystalline anisotropy, makes
the study of cobaltites intriguing, both for fundamental understanding as well as device
applications, for which manipulation of the anisotropy is desirable.
Half-doped Pr1-xSrxCoO3 (x=0.5) is known to exhibit particularly unusual
magnetic behavior that is not consistent with the phase behavior often seen in manganites
and other complex oxide systems [5-9]. This system undergoes a PM-FM phase transition
at TC ~235 K and a magnetic anomaly in the field-cooled magnetization versus
temperature profiles is observed at TA ~120 K. In order to understand this anomaly,
systematic studies were recently undertaken to rule out the phase transitions that are most
routinely associated with perovskites such as charge ordering, antiferromagnetic
ordering, ferrimagnetism, or spin-flip transitions [10].
It was conclusively shown that all of the observed behavior can be explained by a
ferromagnetic to ferromagnetic (FM-FM) transition resulting from a structural change
that drives a transition in the magnetocrystalline anisotropy. Because this FM-FM
transition is not seen in transport measurements, and traditional magnetometry
measurements provided minimal information on the nature of the magnetocrystalline
anisotropy, we show below that the TS measurement technique is extremely well-suited
118
to explore this particular structure-driven magnetocrystalline anisotropy transition.
Furthermore, it has been noted that the largest MCEs are observed in materials exhibiting
a FOMT coupled with a crystal structure change [9].
Since the magnetic and structural changes are often coupled with each other, it is
challenging to decouple the structural entropy contribution from the magnetic entropy
contribution to the total MCE. Since the structural change at the TA in Pr0.5Sr0.5CoO3 is
not associated with any magnetic transition, Pr0.5Sr0.5CoO3 provides an excellent system
for determining the structural entropy change and its contribution to the MCE in
magnetocaloric materials. Our systematic study of the influence of the structurally
coupled magnetocrystalline anisotropy transition on the MCE in Pr1-xSrxCoO3 (x = 0.3,
0.35, 0.4, and 0.5) compounds has addressed this outstanding issue. The polycrystalline
samples were supplied by Professor Christopher Leighton from the University of
Minnesota.
8.2 Results and Discussion
8.2.1 Anomalous magnetism and Magnetocaloric effect in Pr1-xSrxCoO3 (0.3 ≤ x ≤
0.5)
Figure 8.1 shows the M(T) curves for PSCO with various substitution values
recorded while cooling under a high field (0H=5T). While cooling, there exists a sharp
increase in M signifying a second order PM to FM transition at TC ~190K, 200K, 220K,
230K or x=0.3, 0.35, 0.4, 0.5 respectively. However, for smaller cooling fields, (inset of
Fig. 8.1), there is an appearance of a second transition. While cooling we see first a large
increase in the magnetization at the TC, followed by a decrease (increase) in
magnetization at lower temperature (TA~120K) under cooling fields of less than (greater
119
than) 750 Oe [3]. At cooling fields in which the magnetization is saturated, no anomaly is
observed in the M(T). Note that the decrease (increase) in magnetization upon cooling in
low (high) field is manifest as a gradual change in curvature starting at around TA and
persists well into the low temperature regime.
0 50 100 150 200 250 3000.0
0.5
1.0
1.5
M
(
B/a
t.C
o)
T (K)
x=0.3
x=0.35
x=0.4
x=0.35
0H=5 T
0 50 100 150 200 2500.00
0.05
0.10
0.15
0H=1 mT
TA=120 K
0.0
0.5
1.0
0H=0.1 T
x=0.5
Figure 8.1: Temperature dependence of the magnetization of Pr1−xSrxCoO3 (x=0.3, 0.35,
0.4, and 0.5) compounds when a magnetic field 0H=5 T is applied. Inset: Temperature
dependence of the magnetization at low field (0H=1 mT) and intermediate field
(0H=0.1T) in the x=0.5 sample.
The ~120 K transition has been attributed to a strong coupling between
structural/magnetocrystalline anisotropy [11]. Because of the structural transition that
occurs at TA there is a large change in the direction of the easy axis of magnetization. It
has been shown from previous work [11] that the sample exhibits no change in overall
crystal symmetry, or even any non-negligible change in unit cell volume, however, there
is a drastic change in the lattice parameters (a~+1.15% and b~-1.10%) [4, 12] near the
transition at TA. The structural transition is believed to be due to Pr-O hybridization [13].
When Lopez-Morales et.al. examined PrBa2Cu3O7-, the only rare-earth 1:2:3 system that
120
is insulating rather than metallic or superconducting, they found that the unusual
tendency of Pr 4f–O 2p hybridization is the cause of the nonsuperconducting state. The
lack of change in crystal symmetry in PSCO is drastically different from what is observed
in materials with similar properties [14-16]. Also, since the two transitions are well
separated in T, PSCO provides a rare opportunity to study the effect of a structural
transition on the MCE.
0 1 2 3 4 5
0.0
0.5
1.0
1.5
2.0
T=
32
0 K
TC=
23
0 K
M (
B/a
t.C
o)
0H (T)
T=
5 Kx=0.5
Figure 8.2: Field dependence, from 5 K to 320 K in 5 K increments, of the magnetization
of the polycrystalline Pr0.5Sr0.5CoO3 compounds. The magnetization curve is marked
(open symbol) at the Curie temperature of the sample TC (x = 0.5) =230 K.
Figure 8.2 shows the isothermal magnetization versus applied field (M(H)) as a
function of temperature for half-doped PSCO, used for calculating the SM. Since, the
equations used integrate between successive M(H) curves, the large gaps between
successive curve are associated with peaks in SM. The open symbols represent M(H) at
TC, interestingly, above TC, there appears to be a minor ferromagnetic signal attributed to
ferromagnetic clusters.
Figure 8.3, shows the calculated change in magnetic entropy for x = 0.3-0.5. The
first peak at high temperature at Tpk~190K, 200K, 220K, 230K for x = 0.30, x = 0.35, x =
121
0.40, x = 0.50, respectively, is associated with the PM to FM transition. However, for x =
0.4 and 0.5, we see a rather large change in entropy at lower temperatures TA~70K and
120K for x = 0.4 and 0.5 respectively, which is associated with the
structural/magnetocrystalline anisotropy transition. Interestingly, the samples that exhibit
the second peak also show an enhanced and broadened MCE at TC, suggesting that there
is a clear advantage to coupling between a magnetic and structural transition from the
perspective of achieving the maximum RC.
0 50 100 150 200 250 3000.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100
0.5
1.0
1.5
2.0
2.5
TA=120 K
-S
M (
J K
-1 k
g-1)
T (K)
x=0.3
x=0.35
x=0.4
x=0.5
0H=5 T
TA=70 K
T-TC (K)
Figure 8.3: Temperature dependence of the magnetic entropy change for 0H=5 T of the
Pr1−xSrxCoO3 (x = 0.3, 0.35, 0.4, and 0.5) compounds. Solid arrows indicate the
temperatures (TA) of the second phase transition that occurs at low temperature Inset:
Reduced temperature dependence of the magnetic entropy change near TC.
From Fig. 8.3 we can also see that, depending on the doping concentration, the main peak
can be shifted to lower (higher) temperatures, which is quite useful for industrial
applications of magnetic refrigeration. For the peak at TC the ΔSM taken at 5T remains
almost unchanged for x = 0.3 and 0.35 (1.41 J/kg K) but increases for x = 0.4 (1.67 J/kg
K) and for x = 0.5 (2.2 J/kg K). For the peak at TA, it increases from 0.29 J/kg K for x =
0.4 to 0.79 J/kg K for x = 0.5.
122
According to the experimental results and theoretical validation [17-19], it can be
assumed that in a biphasic system the field dependence of ΔSM and RC follow power
laws of the field;
1( , )( , ) ( )M
T HnS T H a T H , (8.1)
( ) ( ) , (8.2)
where the exponent n1 depends, in general, on temperature and field, and its asymptotic
values are 1 and 2 when the values of temperature are quite far below and above TC,
respectively. The exponent n1 takes minimum values around the Curie temperatures of
the existing phases and an extreme value in the temperature range defined by the critical
temperatures of the constituent phases [20]. In a first approximation, this exponent can be
considered field independent at the temperature of TC and Tpk, and can be expressed in
terms of the critical exponents as [17] 1 1( ) ( ) 1 (1 ) / ( )C pkn T n T . On the
other hand, the exponent n2 that controls the field dependence of the RC is related to the
critical exponents by 2 1 / ( )n . Note that the exponents n1 and n2 are related
via the expression 2 1 1/ ( )n n .
Taking into in account that only two critical exponents are independent, all of
them can be calculated from n1 and n2. For instance, the critical exponents and can be
obtained according to
2 2
2 1 2 1
1 2;
n n
n n n n
. (8.3)
The field dependence of M
pkS and RC has been presented in Figs. 8.4a,c for the
whole studied compositional range, indicating two different, well-defined behaviors for
the x=0.3 and x=0.35 single phase systems (approximately the same M
pkS and RC
123
values), and for the x=0.4 and x=0.5 biphasic systems (for which those values are
different). As can be seen also in the inset of Fig. 8.3 for the single-phase systems
(approximately the same ΔSM(T) values) and for the biphasic systems (approximately the
same ΔSM(T-TC) values in the temperature range between the critical temperatures of the
two constituent phases).
0.0
0.5
1.0
1.5
2.0
2.50.00 0.25 0.50 0.75 1.00
0.25
0.50
0.75
1.00
0 1 2 3 4 5
0
25
50
75
100
0.00 0.25 0.50 0.75 1.000.00
0.25
0.50
0.75
1.00
-S
pk
M (
J K
-1 k
g-1)
x=0.3
x=0.35
x=0.4
x=0.5
a.
b.
s
h0.76
c.
RC
(J k
g-1)
0H (T)
d.rc
h1.33
Figure 8.4: Field dependence of the maximum magnetic entropy change (a) and the
refrigerant capacity (c) in the studied polycrystalline Pr1−xSrxCoO3 (x=0.3, 0.35, 0.4, and
0.5) compounds. Dimensionless field dependence of the dimensionless maximum
magnetic entropy change s (b), and dimensionless refrigerant capacity, rc (d). The non-
collapse into two master curves indicates that the exponents n1 and n2 are composition
dependent.
In order to compare the field evolution of the experimental data presented in Fig.
8.4a-c, it would be necessary to eliminate the factors of Eqs. (8.1) and (8.2) that depend
124
only on the composition and on the previously defined temperature span T (in this work
T=TFWHM for the whole composition range). By normalizing these expressions with the
values corresponding to the maximum applied field, dimensionless relationships can be
written for the different studied compositions [21].
1
1
1
2
2
2
max max
max max
( , ) ( )
( , ) ( )
( , , ) ( , )
( , , ) ( , )
pk
M
pk
M
AREA
AREA
nn
n
nn
n
S H x a x Hs h
S H x a x H
RC T H x b T x Hrc h
RC T H x b T x H
, (8.4)
where max/h H H . When the latter two power laws are plotted for the different
compositions (Figs. 8.4b,d), it can be seen that in general the exponents n1(x) and n2(x)
are composition dependent.
While Fig. 8.4(b) shows that the exponent n1 takes the values n1(x=0.3)=
n1(x=0.35)= n1(x=0.4)=0.76 and n1(x=0.5)=0.58, the Fig. 8.4(d) indicates that the
exponent n2 varies slightly in the full series taking the values n2(x=0.3)=1.33,
n2(x=0.35)=1.31, n2(x=0.4)=1.24 and n2(x=0.5)=1.23. According to Eq. (8.3), this means
that the critical exponent takes a value = 0.54 0.05 close to that in the mean field
theory (MFT=0.5) for x=0.3, 0.35 and 0.4, and a value = 0.358 0.001 close to that in
the Heisenberg model (H = 0.365 0.003) for x=0.5. These results reveal that the
magnetic interaction in the x=0.5 cobaltite is of short-range type. The smaller values of
the uncertainly for x=0.5 is due to the higher resolution of the field used for this
composition. On the other hand, the critical exponent takes increasing values when the
doping increases (x = 0.3) = 1.17 0.04, (x = 0.35) = 1.25 0.04, (x = 0.4) = 1.58
0.04, and decreasing value for the half doped cobaltite ( x = 0.5) = 1.178 0.003, very
similar to that of x=0.3.
125
8.2.2 Transverse susceptibility as a probe of the coupled
structural/magnetocrystalline anisotropy transition in Pr1-xSrxCoO3 (x = 0.5)
TS measurements were also performed on the Pr0.5Sr0.5CoO3 sample at a number
of temperatures to examine the temperature dependence of the anisotropic features across
TA. Figure 8.5 shows bipolar TS scans of Pr0.5Sr0.5CoO3 taken at four representative
temperatures: 20 K (8.5a), 95 K (8.5b), 110 K (8.5c), and 225 K (8.5d).
Figure 8.5: Bipolar transverse susceptibility scans of Pr0.5Sr0.5CoO3 as a function of
applied field for 20K (a), 95K (b), 110K (c), and 225K (d). On 8.5(a) the arrows indicate
the sequence of measurement; the anisotropy (Hk), crossover (Hcr), and switching (HS)
peaks are labeled [22].
The broader, high-field peaks seen on either side of μ0H=0, closest to saturation,
are the anisotropy peaks indicating the anisotropy fields, ±HK. The second peak observed
upon decreasing the field after positive saturation corresponds to the “crossover field”,
Hcr, which is defined as the field which separates the lower FC magnetization state from
the higher FC magnetization state for any given temperature occurring below TA, as
126
described above. The third peak observed is the prominent switching peak, HS.Figure
8.6a shows the temperature evolution of the TS curves for phase FM1 and Fig. 8.6b
shows the temperature evolution of the TS curves for FM2. Unlike in Fig. 8.5, the
magnitude of the TS signal appears in arbitrary units so that all of the curves could be fit
onto either graph in a manner that still clearly shows the important features. The degree
to which the two phases differ in appearance is remarkable. Whereas FM1 has a very
well-defined +HK peak for all temperatures up to the transition, and displays the
crossover field peak, the FM2 curve is largely dominated by the intense switching peak.
The anisotropy peak appears much broader. We note here that while the TS experiments
reveal clear differences in anisotropy features between FM1 and FM2, this picture
remains slightly ambiguous in the M(T) and M(H) data.
Figure 8.6: Unipolar transverse susceptibility scans for several different temperatures
plotted on two plots depicting the two different ferromagnetic phases ((a) is FM1 and (b)
is FM2). The signal intensity appears in arbitrary units as some of the curves have been
shifted upward or downward for clarity [22].
127
To better illustrate the difference in anisotropy features between the ferromagnetic
states FM1 ( ) and FM2 ( ), we have superimposed the TS curves for
each phase onto two separate plots. The relative appearance of the curves for FM1 and
FM2 is akin to the comparison of two different materials entirely, rather than the
comparison of two structural phases of the same material. This, once again, indicates that
the TS technique is more suitable for studying anisotropy-driven transitions.
Figure 8.7 (a) shows the anisotropy field (+HK) as a function of temperature
where it is conclusively demonstrated that at higher temperatures, Pr0.5Sr0.5CoO3 has a
higher magnetocrystalline anisotropy phase (the FM2 phase) than at lower temperatures
(FM1 phase). For lower temperatures (T < TA,) the anisotropy field decreases with
increasing temperature, which is typical of most magnetic systems as the thermal energy
begins to compete with the anisotropy energy of the system. The structural transition at
120 K then appears as a dramatic increase in the HK to values even higher than those seen
at the lowest temperatures (μ0HK ≈ 184 mT at 120 K versus ≈125 mT at 10 K). The sharp
change in HK at TA is a direct consequence of the coupled structural/magnetocrystalline
anisotropy transition. After reaching this maximum, HK then slowly decreases again until
TC, where it goes to zero. The decrease of HK with temperature for T < TA and for TA < T
< TC is fully consistent with the perspective that the Pr0.5Sr0.5CoO3 system undergoes a
transition from one FM state to another.
The switching field is tracked as a function of temperature in Fig. 8.7 (b). Its
shape closely follows that reported in reference [10] for both the coercivity and fraction
of irreversible magnetization as measured by the first order reversal curve method [2].
This is not surprising, as all three properties are direct consequences of irreversible
128
hysteretic processes. At low temperatures, magnetization decreases rapidly until the
approach to TA where it experiences an uptick and a cusp at 120 K and then decreases
again until TC. While empirical data suggested this field should be around 75 mT, the
temperature dependence of this peak reveals that this crossover field is different for
different regions of the M(T) plots. Around the structural transition, the crossover field is
indeed measured by TS to be 75 mT.
Figure 8.7 (c) shows the evolution of the peak position associated with the
crossover field (Hcr) as a function of temperature. However, at lower temperatures, the
change in shape of the magnetization curves appears to occur at much lower fields,
around 20 mT, which then increases rapidly with temperature up to TA. It has already
been discussed that the presence of this peak lends insight to the crossover behavior
between the two types of anomalous M(T) curves.
Figure 8.7: Temperature dependence of the peaks positions in the transverse
susceptibility measurement. (a) Anisotropy field (+HK), (b) Switching field (HS), (c)
Crossover field (Hcr) [22].
129
It has been noted that due to poor magnetic coupling between the grains at low
temperatures (T << TA), the initial susceptibility is smaller in the FM1 region than in the
FM2 regions [16]. In addition, the magnetization has been found to increase with
increasing temperature in the FM1 region below the crossover field. Therefore, the
increase of Hcr with temperature at T < TA revealed in the TS profile is as expected,
consistently pointing to thermally activated improvement in intergranular coupling in this
temperature range.
8.3 Conclusions
We have used the transverse susceptibility and magnetocaloric measurement
techniques to examine the anisotropic magnetic properties of Pr0.5Sr0.5CoO3, specifically
the structure-driven magnetocrystalline anisotropy transition at 120 K. By using these
techniques, we were able to show that the FM-FM phase transition is clearly manifested
in the evolution of the anisotropy and switching peaks with temperature. The well-
documented unusual M(T) behavior, dependent upon cooling field, is present in the TS as
well in the form of a sharp peak at the crossover field which disappears above TA. We
showed (figure 8.6) that the rotation of the easy axis can also be deduced by comparing
the signal intensity from two different measurement orientations where a crossover
behavior is observed. We also observed a relatively rare structural transition, which is not
coupled with a magnetic transition, using the magnetocaloric effect. Collectively these
findings show that transverse susceptibility and the magnetocaloric effect are very useful
tools for lending insight into the unusual magnetic behavior of doped perovskites.
130
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tuning of magnetocaloric effect in Tb5Si2Ge2, Appl Phys Lett, 98 (2011).
[17] V. Franco, A. Conde, Scaling laws for the magnetocaloric effect in second order
phase transitions: From physics to applications for the characterization of materials, Int J
Refrig, 33 (2010) 465-473.
[18] V. Franco, A. Conde, M.D. Kuz'min, J.M. Romero-Enrique, The magnetocaloric
effect in materials with a second order phase transition: Are T-C and T-peak necessarily
coincident?, J Appl Phys, 105 (2009).
132
[19] V. Franco, A. Conde, J.M. Romero-Enrique, J.S. Blazquez, A universal curve for the
magnetocaloric effect: an analysis based on scaling relations, J Phys-Condens Mat, 20
(2008).
[20] R. Caballero-Flores, V. Franco, A. Conde, Q.Y. Dong, H.W. Zhang, Study of the
field dependence of the magnetocaloric effect in Nd1.25Fe11Ti: A multiphase magnetic
system, J Magn Magn Mater, 322 (2010) 804-807.
[21] R. Caballero-Flores, V. Franco, A. Conde, K.E. Knipling, M.A. Willard, Influence
of Co and Ni addition on the magnetocaloric effect in Fe88-2xCoxNixZr7B4Cu1 soft
magnetic amorphous alloys, Appl Phys Lett, 96 (2010).
[22] N. A. F. Huls, N. S. Bingham, M. H. Phan, H. Srikanth, D. D. Stauffer, and C.
Leighton, Transverse susceptibility as a probe of the magnetocrystalline anisotropy-
driven phase transition in Pr0.5Sr0.5CoO3. Physical Review B, 2011. 83(2).
133
CHAPTER 9.
A COMPLEX MAGNETIC PHASE DIAGRAM AND MAGNETOCALORIC
EFFECT IN Ca3Co2O6 SINGLE CRYSTALS
In the previous chapters we have shown the usefulness of MCE for probing the
magnetic ground states, phase coexistence, and field-induced kinetic arrest phenomena in
phase-separated manganites. In this chapter, we demonstrate that it is also very useful for
probing the complex ground state magnetism of Ca3Co2O6 (CCO), which exhibits spin
frustration and intrinsic low dimensionality due to the formation of 1D spin chains. Our
MCE experiments have provided new insights into the nature of switching between
multi-states and competing interactions within spin chains, and between them, leading to
a more comprehensive magnetic phase diagram.
9.1 Introduction
Ca3Co2O6 (CCO) has received considerable interest over the past decades due to the
complex interplay among the magnetic, electronic and structural properties. The refined
neutron and X-Ray powder diffraction data have shown that the material crystallizes in
the rhombohedral space group R c[1]. CCO consists of face sharing CoO6 trigonal
prisms and CoO6 octahedra chains running along the c-axis with six nearest neighbor
chains, forming a triangular lattice in the ab plane and all separated by Ca atoms.
Intrachain Co-Co separation is 2.59Ǻ, while interchain Co-Co separation is roughly twice
134
that, giving rise to large anisotropy and a quasi 1D structure. The Co ions in CCO are
found in the 3+ oxidation state, with alternating low-spin (LS) and high-spin (HS) states
for the octahedral and trigonal configurations, respectively [2]. Due to the nature of the
geometry, and the strong anisotropy of Co, CCO has long been considered to be an Ising-
like material, where each chain can be represented by a single spin in a 2-D lattice.
However, recent theoretical predictions [3] and experimental results [4] show that this is
an oversimplified description; therefore a full 3-D picture is needed.
The origin of a broad feature above TN (centered around 100K) revealed by
calorimetric measurements [5] is currently under debate, and has been attributed to 1-D
magnetic ordering along the chains [6] or a spin-state transition, which is common for
this class of cobaltite materials [7]. Neutron diffraction studies have revealed long-range
magnetic ordering at TN ~ 25K; this is generally accepted as very strong FM intrachain
coupling, and a slightly weaker AFM interchain coupling. The 2-D Ising model discussed
above gives rise to a partially disordered antiferromagnet (PDA), where 2/3 of the chains
are coupled antiferromagnetically, and 1/3 are incoherent [8]. However, in the
intermediate temperature range (12K < T < 25K), resonant X-ray scattering [9]
discovered incommensuration in the magnetic order along the chain, implying a long
wavelength spin-density wave (SDW). Thermal conductivity measurements [10] have
shown an exchange-mediated heat transfer, which supports helical exchange pathways
rather than Ising-type behavior. Below T ~ 12K, there is an increase in the number of
“steps” in the field-driven magnetization process, as well as an increase in magnetic
hysteresis. These steps had led many to believe that the system exhibits quantum
tunneling of magnetization (QTM), similar to molecular magnets [11], however the idea
135
of QTM has been challenged, and the behavior is suggested to correspond more closely
to that of superparamagnetic clusters [12], or a host of metastable states. Below TFS ~ 8K,
CCO exhibits extremely slow spin dynamics, large magnetic hysteresis, and a very
pronounced frequency dependence in AC susceptibility measurements [13], which can all
be described as a frozen spin state.
Recent theoretical and experimental evidence suggests that below 25K, nearest
and next nearest neighbor AFM interactions stabilize the AFM state in the form of a
longitudinal amplitude-modulated SDW propagating along the chains [4]. As temperature
is decreased, the SDW becomes more unstable, leading to a large volume fraction of
short-range ordering giving rise to an overall highly disordered state [14].
It is clear that the complex magnetic behavior described above provides a unique
opportunity to study a variety of interactions with numerous probes. Much of the research
on CCO has been focused on probing the microstates either experimentally or
theoretically. This study focuses on the macroscopic details of the field- and temperature-
dependence of the change in magnetic entropy probed by the MCE. CCO single crystals
were grown by the floating zone method and provided by Prof. Sang-Wook Cheong’s
group at Rutgers University.
9.2 Results and Discussion
Figure 9.1 (a) shows the DC M(T) curve acquired under a field of H = 100 Oe.
The small deviation from M = 0 beginning below T ~ 70K is attributed to the onset of 1-
D magnetic ordering along the chains. Then at TC ~ 25K, there is a large jump in M
associated with FM intrachain coupling. At this ordering temperature, it is important to
note that the coupling between neighboring chains is AFM in nature, thus the large jump
136
in M(T) leads to the understanding that the intrachain FM coupling dominates in strength.
At even lower temperatures, the system enters a complex glassy regime.
Figure 9.1: Temperature dependence of (a) DC-magnetization at an applied field of 100
Oe (b) AC susceptibility with small AC magnetic field ~10 Oe at a variety of frequencies.
Also, magnetic field dependence of magnetization at (c) 25K and (d) 5K.
Magnetization dynamics were probed (Figure 9.1(b)) using AC magnetization
measurements in a small (HAC ~ 10 Oe) AC- magnetic field at various frequencies. The
strong frequency dependence can be described via an Arrehnius-like regime at higher
temperatures (T > 10K) and a quantum regime at lower temperatures (T <10 K) [15].
Figure 9.1 (c,d) shows M(H) curves at T = 25K and 5K; dM/dT is plotted in the inset. For
T < 10K, there is an increase in the number of steps in the M(H) curves, leading to strong
magnetization dynamics and coupling phenomena.
(a) (b)
(c) (d)
137
Figure 9.2 shows the isothermal M(H) curves used to calculate the MCE. Due to
the measurement process, H and T need to be stabilized in order to collect the data. For
CCO, this results in a smoother step in the magnetization due to the slow field sweep rate
[15]. For T > TN, there is a linear increase in M with increase in H, however, an approach
to saturation is evident in the curves.
0 2 4 6 8
0
20
40
60
80
100
T=5K
M (
em
u/g
)
0H (T)
T=120K
Figure 9.2: Isothermal magnetization vs. applied field for a temperature range of 120K-
5K with a temperature interval of 5K, and magnetic field from 0-7T.
This leads to the belief that the large bump in the heat capacity [5] at high
temperature is due to short-range FM order along the chains. Below TN, steps emerge in
the magnetization. A large plateau occurs at low field when M = MS/3 (MS is the
saturation magnetization), as the geometrically frustrated matrix enters the ferrimagnetic
(FIM) up-up-down (UUD) state in which 2/3 of the chains are aligned ferromagnetically
and 1/3 are aligned antiferromagnetically. There is another step 0H = 3.6T, above which
the system becomes fully ferromagnetically aligned. For T = 5K, more steps in M occur
138
at a regular interval [16] (0H = 0T, 1.2T, 2.4T and 3.6T). This is due to the stabilization
of micro-clusters of disorder within the chain [14].
Figure 9.3 shows the calculated temperature dependence of SM. The most
striking feature is the very large peak (–SMmax
~ 6.5 J/kgK) at 30K. This peak has the
signature of short-range FM ordering, which is believed to be correlated to the large
maximum seen in the heat capacity measurements [5].
0 20 40 60 80 100 120
-2
0
2
4
6
0H = 7 T
-S
M (
J / K
g K
)
T ( K )
0H = 0 T
Figure 9.3: Change in magnetic entropy as a function of temperature, calculated using
the thermodynamic Maxwell relation (Eqn. 3.9).
At TN, there is a small peak associated with FM intrachain alignment and AFM interchain
alignment. Due to the nature of the transition, –SM < 0 is expected, however, since –SM
> 0, this highlights the dominance of the intrachain FM coupling over the interchain
AFM coupling. For T ≤ 10K, –SM < 0, where the thermal fluctuations have stabilized the
AFM phase.
139
The MCE measurements become even more enlightening when looking into the
field dependence of SM. Figure 9.4 (a-d) shows –SM(H) for 30K, 20K, 15K and 10K
respectively. At T = 30K (Figure 9.4 (a)), –SM(H) shows a gradual increase with H,
similar to that of short-range FM ordering, leading to the belief that there are magnetic
interactions occurring above the long-range ordering temperature. These interactions are
believed to be the growth of FM clusters along the chains, and can extend up to
temperatures as high as 100K. The fact that the large peak is not observed until T = 30K
could be due to thermal fluctuations that cannot be overcome by the magnetic fields
available in our laboratory (up to ±7T). As the temperature is decreased below TN, a very
interesting feature emerges. Figure 9.4 (b), shows –SM(H) at 20K. As H is increased
there is an increase in –SM, as would be expected for FM ordering throughout CCO, i.e.
the UUD model discussed previously. Interestingly, –SM exhibits a maximum at 0H =
2T, then starts decreasing for fields in the range 2T < 0H < 3.6T. In this region, the FM
coupling has been stabilized, and the AFM coupling between nearest-neighbor (NN) and
next-nearest neighbor (NNN) chains is strong enough to slightly distort the FM ordering
present in each chain; this can be thought of as a disorder induced by order. A similar
feature has been observed in the helimagnet, Dy [17].
Finally, for large enough fields the disorder can be overcome and there is full FM
order throughout the sample. At T = 15K, (Figure 9.4 (c)) –SM(H) exhibits similar
features to those observed at higher temperatures, yet the dip in –SM at 0H = 2T
reaches negative values, in contrast to the T=20 K –SM(H) curve. The T = 15 K behavior
can be attributed to the system cooling below the “cross-over” temperature (T ~ 18K),
where the AFM coupling between NN and NNN chains increases, therefore further
140
stabilizing the AFM phase and increasing its negative contribution to –SM. At T = 10K
(Figure 9.4 (d)), the SDW is destabilized giving rise to a large volume fraction of short-
range order FM clusters, aligned either parallel or anti-parallel to the applied magnetic
field.
0 2 4 6 8
0
2
4
6
-S
M (
J/k
g K
)
-S
M (
J/k
g K
)
0H (T)
0H (T)
0H (T)
-S
M (
J/k
g K
)
-S
M (
J/k
g K
)
0H (T)
(a) T = 30 K
0 2 4 6 8
0
2
4
(b) T = 20 K
0 2 4 6 8-0.5
0.0
0.5
1.0
1.5
2.0
2.5
HC3
HC2
HC1
(c) T = 15 K
0 2 4 6 8
-1.2
-0.8
-0.4
0.0
0.4
(d) T = 10 K
Figure 9.4: Change in magnetic entropy as a function of applied field at various constant
temperatures, (a) 30K, (b) 20K, (c) 15K and (d) 10K.
Therefore, on average CCO is in an AFM-like state leading to a purely negative –SM(H).
The slight upturn in –SM near oH = 3T is related to a small volume fraction of FM
correlations ordering with the field. However, by ordering these regions, there is, once
more, an increase in disorder brought about by distortion induced by neighboring chains.
Figure 9.5, represents a phase diagram constructed from the MCE data, where HC1
(shown in Figure 9.4 (c)) is related to the maximum (minimum) in –SM before the onset
141
of field-induced disorder. HC2 represents the field at which the maximum disorder is
induced in the chains.
0 2 4 6
(a)
dS
/dH
0H (T)
S
D
W
FIM
Disordered
FM
T = 20 K
6 8 10 12 14 16 18 20 22 240
1
2
3
4
5
6
7
8 (b)
SDW
Disorder Due to Order
AFM
FM
FIM
0H
(T
)
T (K)
HC3
HC2
HC1
HSDW
FIM
Figure 9.5: (a) First derivative of the field-dependent change in entropy. (b)
Magnetic phase diagram derived from the field- and temperature-dependent
change in magnetic entropy.
HC3 indicates the field at which the volume fraction of FM ordering starts to
become the dominant phase. From fig 9.5, as T is decreases below 25K it takes a
significantly larger value of H in order to achieve a large volume fraction of FM ordering
142
in CCO (in fact, for T = 5K –SM never crosses over zero, therefore we extrapolated
linearly), leading to the paradoxical conclusion that CCO becomes more disordered as T
decreases. HC2 remains almost constant for all T, and is associated with the large plateau
in M present at all T. For HC1, a crossover temperature exists; for T ≥ 15K a relatively
small field will globally align the material in the UUD FIM state described above.
However, for T < 15K, the system is in the short range order-SDW state which gives rise
to AFM-like behavior.
9.3 Conclusions
MCE data was taken for a wide range of temperatures and applied magnetic fields
for Ca3Co2O6. The MCE data seem to confirm the spin-density wave description that has
been proposed recently. The MCE data has also confirmed that CCO becomes more
disordered with a decrease in temperature and also exhibits field-driven and order-
induced disorder. These observations are consistent with previously studied helimagnets.
A new and comprehensive magnetic phase diagram is constructed for the first time from
MCE experiments.
References:
[1] H. Fjellvag, et. al., Crystal structure and possible charge ordering in one-dimensional
Ca3Co2O6, J Solid State Chem, 124 (1996) 190-194.
[2] S. Aasland, H. Fjellvag, B. Hauback, Magnetic properties of the one-dimensional
Ca3Co2O6, Solid State Commun, 101 (1997) 187-192.
[3] Y. Kamiya, C.D. Batista, Formation of Magnetic Microphases in Ca3Co2O6, Phys Rev
Lett, 109 (2012).
143
[4] S. Agrestini, C.L. Fleck, L.C. Chapon, C. Mazzoli, A. Bombardi, M.R. Lees, O.A.
Petrenko, Slow Magnetic Order-Order Transition in the Spin Chain Antiferromagnet
Ca3Co2O6, Phys Rev Lett, 106 (2011).
[5] V. Hardy, S. Lambert, M.R. Lees, D.M. Paul, Specific heat and magnetization study
on single crystals of the frustrated quasi-one-dimensional oxide Ca3Co2O6, Phys Rev B,
68 (2003).
[6] L.J. Dejongh, A.R. Miedema, Experiments on Simple Magnetic Model Systems, Adv
Phys, 23 (1974) 1-260.
[7] J.B. Goodenough, An Interpretation of the Magnetic Properties of the Perovskite-
Type Mixed Crystals La1-xSrxCoO3-Lambda, J Phys Chem Solids, 6 (1958) 287-297.
[8] H. Kageyama, K. Yoshimura, K. Kosuge, H. Mitamura, T. Goto, Field-induced
magnetic transitions in the one-dimensional compound Ca3Co2O6, J Phys Soc Jpn, 66
(1997) 1607-1610.
[9] S. Agrestini, C. Mazzoli, A. Bombardi, M.R. Lees, Incommensurate magnetic ground
state revealed by resonant x-ray scattering in the frustrated spin system Ca3Co2O6, Phys
Rev B, 77 (2008).
[10] J.G. Cheng, J.S. Zhou, J.B. Goodenough, Thermal conductivity, electron transport,
and magnetic properties of single-crystal Ca3Co2O6, Phys Rev B, 79 (2009).
[11] D. Gatteschi, R. Sessoli, Quantum tunneling of magnetization and related
phenomena in molecular materials, Angew Chem Int Edit, 42 (2003) 268-297.
[12] E.V. Sampathkumaran, N. Fujiwara, S. Rayaprol, P.K. Madhu, Y. Uwatoko,
Magnetic behavior of Co ions in the exotic spin-chain compound Ca3Co2O6 from Co-59
NMR studies, Phys Rev B, 70 (2004).
144
[13] A. Maignan, V. Hardy, S. Hebert, M. Drillon, M.R. Lees, O. Petrenko, D.M. Paul,
D. Khomskii, Quantum tunneling of the magnetization in the Ising chain compound
Ca3Co2O6, J Mater Chem, 14 (2004) 1231-1234.
[14] T. Moyoshi, K. Motoya, Incommensurate Magnetic Structure and Its Long-Time
Variation in a Geometrically Frustrated Magnet Ca3Co2O6, J Phys Soc Jpn, 80 (2011).
[15] V. Hardy, M.R. Lees, O.A. Petrenko, D.M. Paul, D. Flahaut, S. Hebert, A. Maignan,
Temperature and time dependence of the field-driven magnetization steps in Ca3Co2O6
single crystals, Phys Rev B, 70 (2004).
[16] Y.B. Kudasov, Magnetic structure and phase diagram in a spin-chain system:
Ca3Co2O6, Epl-Europhys Lett, 78 (2007).
[17] M. Foldeaki, R. Chahine, T.K. Bose, Magnetic Measurements - a Powerful Tool in
Magnetic Refrigerator Design, J Appl Phys, 77 (1995) 3528-3537.
145
CHAPTER 10.
CONCLUSIONS AND OUTLOOK
10.1 Conclusions
Throughout this dissertation I have demonstrated the effectiveness of the
magnetocaloric effect (MCE) and transverse susceptibility (TS) as probes used for
fundamental research rather than the standard application-based probes seen widely
throughout the community. First, the basic properties of manganite materials were
discussed, where the strongly coupled magnetic, electric and structural degrees of
freedom depend strongly on local strain caused by chemical doping. Manganites,
although very similar in structure, can be “tuned” drastically by varying the A-site radius
and applying external fields (i.e. pressure, magnetic and electric). This makes manganites
ideally suited for this kind of comprehensive study. Next, the magnetic and
magnetocaloric properties of bulk polycrystalline and thin-film samples of the Collosal
Magenetoresistive (CMR) manganite La0.7Ca0.3MnO3 were investigated to observe the
effects of reduced dimensionality in the system. Broadened transitions along with
reduced Curie temperature, magnetic moment, and magnetic entropy change were
observed in the thin-film sample. The film exhibited enhanced refrigerant capacity over
the polycrystalline sample, due to the change of the nature of the phase transition being
converted from a first-order to second-order paramagnetic to ferromagnetic transition.
146
Then, a systematic study on the effects of A-site cation doping on the
ferromagnetic phase transitions and critical behavior of La0.7Ca0.3−xSrxMnO3 (x = 0, 0.05,
0.1, 0.2 and 0.25) single crystals was presented. Using the Banerjee criterion and
Kouvel–Fisher method, it is shown that x∼0.1 is a tricritical point that separates the first-
order magnetic transition for x < 0.1 from a second-order magnetic transition for x > 0.1.
Above the tricritical point, the system exhibits a second-order magnetic transition with
the critical exponents belonging to the Heisenberg universality class with short-range
exchange interactions. This indicates that short-range magnetic interactions dominate in
these systems. It is shown that while the Double-Exchange (DE) mechanism and
formation of ferromagnetic clusters can account for the canonical MR and metal-like
conducting behavior in La0.7Ca0.3−xSrxMnO3 with x = 0.2 and 0.25. Other effects, such as
cooperative Jahn–Teller distortions and antiferromagnetic coupling are important
additions for understanding of the relationship between the PM–FM transition and the MI
transition, including CMR in La0.7Ca0.3−xSrxMnO3 with x = 0, 0.05 and 0.1. The change of
the PM–FM transition with chemical (internal) pressure introduced by substitution of
larger Sr ions for smaller Ca ions points to the strong coupling between the magnetic
order and structural parameters in these doped manganites.
The usefulness of MCE and TS for studying complex phase transitions and the
magnetic anisotropy along with its variation with temperature in half-doped manganites
such as Pr0.5Sr0.5MnO3 was demonstrated. The influence of first- and second-order
magnetic phase transitions on the MCE and RC of charge-ordered Pr0.5Sr0.5MnO3 was
displayed first. It is shown that the first-order magnetic transition at TCO induces a larger
MCE, but concentrates the MCE in a narrower temperature range, resulting in smaller
147
RC. However, the second-order magnetic transition at TC induces a smaller MCE, but
spreads the MCE over a broader temperature range, resulting in larger RC. Hysteretic
losses accompanying the first-order magnetic transition are very large below TCO and
therefore detrimental to the RC, whereas they are very small or negligible below TC, due
to the nature of the second-order magnetic transition. With TS, it is evidenced that there
is an abrupt change in magnetic anisotropy at the FM-AFM transition, which is
associated with the structural phase transition that occurs at the same temperature. This is
a clear indication of the strong correlations between magnetic and structural properties n
Pr0.5Sr0.5MnO3.
Systematic study of magnetocaloric measurements on La5/8−xPrxCa3/8MnO3 (x =
0.275) single crystals have revealed further insights into the complex multiple-phase
transitions. The system is FM at low temperature and becomes charge ordered at high
temperature. The dynamic strain-liquid phase is strongly affected by an applied magnetic
field, whereas the frozen strain-glass phase is nearly magnetic field independent. The
origin of the large MCE in the strain-liquid region arises from the suppression of dynamic
fluctuations in magnetic fields. The MCE data clarify that the sharp increase in the
magnetization below TC may not be due to the destabilization of the COI phase to the
FMM phase, but favors the idea of the growth of pre-existing FMM domain regions.
Overall, MCE and TS have proven to be excellent probes of the magnetic transitions and
ground-state magnetic properties of mixed-phase systems.
TS and MCE measurement techniques were used to examine the anisotropic
magnetic properties of Pr0.5Sr0.5CoO3, specifically the structure-driven magnetocrystalline
anisotropy transition at 120 K. By using these techniques, the FM-FM phase transition is
148
clearly manifested in the evolution of the anisotropy and switching peaks with
temperature. The well-documented unusual M(T) behavior, dependent upon cooling field,
is present in the TS, as well, in the form of a sharp peak at the crossover field which
disappears above TA. The rotation of the easy axis can also be deduced by comparing the
signal intensity from two different measurement orientations where a crossover behavior
is observed. Also observed was a relatively rare structural transition, which is not coupled
with a magnetic transition, using the MCE. Collectively these findings show that TS and
the MCE are very useful tools for lending insight into the unusual magnetic behavior of
doped perovskites.
Finally, magnetic and magnetocaloric data were taken for a wide range of
temperatures and applied magnetic fields for Ca3Co2O6 (CCO). The data seem to confirm
the spin-density wave description that has been proposed recently. MCE data has also
confirmed that CCO becomes more disordered with a decrease in temperature, and also
exhibits a field-driven, order-induced disorder. A new phase diagram was produced from
this data, further proving the usefulness of the MCE as a very powerful fundamental
probe.
10.2 Outlook
The CMR manganites are sensitive to all types of perturbations. In particular, it
has been shown in bulk that the internal (through the average size of the A-site cation) or
external pressure (via hydrostatic pressure) can strongly influence the magnetotransport
properties. Thus, strains affect the properties of manganite thin films, and, in
consequence, one needs to correctly understand the effects in order to obtain the desired
properties.
149
Van Tendeloo et al. [1] have studied the evolution of the microstructure as
function of the thickness in La0.7Sr0.3MnO3 films grown on LaAlO3. Close to the
interface, both the film and the substrate are elastically strained in opposite directions in
such a way that the interface is perfectly coherent. In the thicker films, the stress is partly
relieved after annealing by the formation of misfit dislocations. In general, a strain is
observed due to the epitaxial growth in very thin films i.e. lattice parameters adopt those
of the cubic lattice. However, when films reach a critical thickness (generally around
~100nm) the strain becomes relaxed and the film takes on the properties of its bulk
counterpart.
Another way to achieve exotic behavior in these materials is via the growth of
artificial superlattices and multilayer films. The interfaces of thin-film manganite
heterostructures are well documented sites for fundamentally altered magnetism.
Superlattices of FM and AFM layers can lead to an overall enhancement in magnetization
through an induced FM ordering extending into the AFM layer [2], while ferromagnetism
has also been observed at the interface of two AFM manganites [3]. Intriguingly, induced
magnetism can also occur in paramagnetic (PM) layers at FM/PM and AFM/PM
interfaces [4, 5].
La0.7Sr0.3MnO3 (La0.7Ca0.3MnO3) films grown on BaTiO3 (BTO) have recently [6]
been shown to exhibit large jumps in temperature-dependent magnetization due to strain
from first-order structural phase transitions, where BTO changes from rhombohedral to
orthorhombic at 200 K, from orthorhombic to tetragonal at 300 K and from tetragonal to
cubic at the ferroelectric Curie temperature TFEC ~ 400 K). However, since BTO is also a
piezoelectric material, the application of a relatively small electric field can also change
150
the substrate’s lattice parameters, allowing for the control of strain at temperatures below
TFEC.
Thus, by depositing complex oxide thin-films onto variable substrates, or in
composite multi-layered systems, the physical properties of the films will in turn be
“tunable,” thereby making these materials functional for a wide variety of applications,
and creating a vast playground for fundamental research.
References:
[1] F.S. Razavi, G. Gross, H.U. Habermeier, O. Lebedev, S. Amelinckx, G. Van
Tendeloo, A. Vigliante, Epitaxial strain induced metal insulator transition in
La0.9Sr0.1MnO3 and La0.88Sr0.1MnO3 thin films, Appl Phys Lett, 76 (2000) 155-157.
[2] A. Hoffmann, S.J. May, S.G.E. te Velthuis, S. Park, M.R. Fitzsimmons, G. Campillo,
M.E. Gomez, Magnetic depth profile of a modulation-doped La1-xCaxMnO3 exchange-
biased system, Phys Rev B, 80 (2009).
[3] T.S. Santos, B.J. Kirby, S. Kumar, S.J. May, J.A. Borchers, B.B. Maranville, J.
Zarestky, S.G.E.T. Velthuis, J. van den Brink, A. Bhattacharya, Delta Doping of
Ferromagnetism in Antiferromagnetic Manganite Superlattices, Phys Rev Lett, 107
(2011).
[4] D. Niebieskikwiat, et. al., Nanoscale magnetic structure of
ferromagnet/antiferromagnet manganite multilayers, Phys Rev Lett, 99 (2007).
[5] M. Gibert, P. Zubko, R. Scherwitzl, J. Iniguez, J.M. Triscone, Exchange bias in
LaNiO3-LaMnO3 superlattices, Nat Mater, 11 (2012) 195-198.
[6] X. Moya, et. al., Giant and reversible extrinsic magnetocaloric effects in
La0.7Ca0.3MnO3 films due to strain, Nat Mater, 12 (2013) 52-5
151
APPENDICES
152
APPENDIX A LIST OF PUBLICATIONS
1. N.S. Bingham, M.H. Phan, H. Srikanth, M.A. Torija, and C. Leighton,
Magnetocaloric effect and refrigerant capacity in charge-ordered manganites
Journal of Applied Physics 106, 023909 (2009)
2. N.S. Bingham, P. Lampen, M.H. Phan, T.D. Hoang, H.D. Chinh, C.L. Zhang,
S.W. Cheong, and H. Srikanth, Impact of nanostructuring on the magnetic and
magnetocaloric properties of microscale phase-separated La5/8-yPryCa3/8MnO3
manganites, Physical Review B 86, 064420 (2012)
3. N.S. Bingham, H. Wang, F. Qin, H.X. Peng, J. F. Sun, V. Franco, H. Srikanth,
and M.H. Phan, Excellent magnetocaloric properties of melt-extracted Gd-based
amorphous microwires, Applied Physics Letters 101, 102407 (2012)
4. N.S. Bingham, P. Lampen, T.L. Phan, M.H. Phan, S.C. Yu, and H. Srikanth,
Magnetocaloric effect and refrigerant capacity in Sm1-xSrxMnO3 manganites,
Journal of Applied Physics 111, 07D705 (2012)
5. M.H. Phan, M.B. Morales, N.S. Bingham, H. Srikanth, C.L. Zhang, and S.W.
Cheong, Phase Coexistence and Magnetocaloric Effect in La5/8-yPryCa3/8MnO3 (y
= 0.275), Physical Review B 81, 094413 (2010)
6. N.A. Frey, N.S. Bingham, M.H. Phan, H. Srikanth, D. D. Stauffer, and C.
Leighton, Transverse Susceptibility as a Probe of the Magnetocrystalline
Anisotropy – Driven Phase Transition in Pr0.5Sr0.5CoO3, Physical Review B 83,
024406 (2011).
153
7. M.H. Phan, S. Chandra, N.S. Bingham, H. Srikanth, C.L. Zhang, S.W. Cheong,
T. D. Hoang, and H. D. Chinh, Collapse of charge ordering and enhancement of
magnetocaloric effect in nanocrystalline La0.35Pr0.275Ca0.375MnO3, Applied
Physics Letters 97, 242506 (2010)
8. P. Lampen, N.S. Bingham, M.H. Phan, H. Kim, M. Osofsky, A. Piqué, T.L.
Phan, S.C. Yu, and H. Srikanth, Impact of reduced dimensionality on the
magnetic and magnetocaloric response of La0.7Ca0.3MnO3, Applied Physics
Letters 102, 062414 (2013)
9. M.H. Phan, V. Franco, N.S. Bingham, H. Srikanth, N.H Hur, and S.C. Yu,
Tricritical point and critical exponents of La0.7Ca0.3-xSrxMnO3 (x = 0, 0.05, 0.1,
0.2, 0.25) single crystals, Journal o Alloys and Compounds 2, 508 (2010).
10. F. Qin, H. Wang, H.X. Peng, N.S. Bingham, D.W. Xing, J. F. Sun, V. Franco, H.
Srikanth, and M.H. Phan, Mechanical and magnetocaloric properties of Gd-based
amorphous microwires fabricated by melt-extraction technique, Acta Materialia
61, 1284 (2013)
11. N.H. Hong, C.-K. Park, A. T. Raghavender, O. Ciftja, N.S. Bingham, M.H.
Phan, and H. Srikanth, Room temperature ferromagnetism in monoclinic Mn-
doped ZrO2 thin films, Journal of Applied Physics 111, 07C302 (2012)
12. D. Mukherjee, N.S. Bingham, M.H. Phan, H. Srikanth, P. Mukherjee, and S.
Witanachchi, Ziz-zag Interface and strain-influenced ferromagnetism in epitaxial
Mn3O4/La0.7Sr0.3MnO3 thin films grown on SrTiO3 (100) substrates, Journal of
Applied Physics 111, 07D730 (2012)
154
13. D. Mukherjee, N.S. Bingham, M. Hordagoda, M.H. Phan, H. Srikanth, P.
Mukherjee, and S. Witanachchi, Influence of microstructure and interfacial strain
on the magnetic properties of epitaxial Mn3O4/La0.7Sr0.3MnO3 layered-composite
thin films, Journal of Applied Physics 112, 083910 (2012)
14. D. Mukherjee, T. Dhakal, N.S. Bingham, M.H. Phan, H. Srikanth, P. Mukherjee,
and S. Witanachchi Role of crystal orientation on the magnetic properties of
CoFe2O4 thin films grown on Si (100) and Al2O3 (0001) substrates using pulsed
laser deposition, Physica B: Condensed Matter 406, 2663 (2011)
15. C. Miller, D. Williams, N.S. Bingham, and H. Srikanth, Magnetocaloric Effect
in Gd/W Thin Film Heterostructures, Journal of Applied Physics 107, 09A903
(2010)
16. D. Mukherjee, R. Hyde, M. Hordagoda, N.S. Bingham, H. Srikanth, S.
Witanachchi, and P. Mukherjee, Challenges in the stoichiometric growth of
polycrystalline and epitaxial PbZr0.52Ti0.48O3/La0.7Sr0.3MnO3 multiferroic
heterostructures using pulsed laser deposition, Journal of Applied Physics 112,
064101 (2012)
17. N.S. Bingham, M.H. Phan, H. Srikanth, M.A. Torija, and C. Leighton , Magnetic
anisotropy and spin-lattice coupling in Pr0.5Sr0.5MnO3, Physical Review B, 2013
(under consideration)
18. R. Caballero-Flores, N.S. Bingham, M.H. Phan, M.A. Torija, C. Leighton, V.
Franco, A. Conde, and H. Srikanth, Magnetocaloric effect and critical behavior in
Pr0.5Sr0.5MnO3: An analysis of the validity of the Maxwell relation and the nature
of phase transitions, Physical Review B, 2013 (under review)
155
19. N.S. Bingham, P. Lampen, M.H. Phan, S.W. Cheong, and H. Srikanth, A
complex magnetic diagram and magnetocaloric effect in Ca3Co2O6, Physical
Review B 2013 (rapid communication, under consideration)
20. N.S. Bingham, R. Caballero-Flores, M.H. Phan, M.A. Torija, C. Leighton, V.
Franco, A. Conde, and H. Srikanth, Magnetocaloric effect cross a coupled
structural/magnetocrystalline anisotropy transition in Pr1-xSrxMnO3 (x = 0.3, 0.35,
0.4, and 0.5) cobaltites, Applied Physics Letters, 2013 (under consideration)
21. A.R. Gorges, N.S. Bingham, M.K. DeAngelo, M.S. Hamilton, and J.L. Roberts,
Light Assisted Collisional Loss in 85/87 Rb Ultracold Optical Trap, Physical
Review A 78, 033420 (2008)
22. W.M. Tiernan, N.S. Bingham, J.C. Combs, Magnetization and Resistance of
Melt-Textured Growth YBCO Near TC and at Low magnetic Fields, AIP Conf.
Proc. Vol. 850, pp. 459-460 (2006)
156
APPENDIX B LIST OF CONFERENCE PRESENTATIONS
1. N.S. Bingham, M.H. Phan, H. Srikanth, and S.W. Cheong, Complex magnetism
in geometrically frustrated spin-chain Ca3Co2O6 probed by transverse
susceptibility and magnetocaloric effect, 12th INTERMAG/MMM Joint
conference, Chicago, January13th -18th
, 2013
2. D. Mukherjee, M. Hordagoda, R. Hyde, N.S. Bingham, H. Srikanth, P.
Mukherjee, S. Witanachchi, Epitaxial Growth of Multiferroic Heterostructures of
Magnetic and Ferroelectric Oxides using the Dual-laser Ablation Technique,
American Vacuum Society (AVS) 59, Tampa, FL, Oct. 28th
- Nov 2nd
, 2012
3. D. Mukherjee, M. Hordagoda, R. Hyde, N.S. Bingham, H. Srikanth, P.
Mukherjee, S. Witanachchi, Role of Dual-laser Ablation in Controlling Mn Oxide
Precipitation during the Epitaxial Growth of Mn Doped ZnO Thin Films with
Higher Doping Concentrations, American Vacuum Society (AVS) 59, Tampa,
FL, Oct. 28th
- Nov 2nd
, 2012
4. N.S. Bingham, R. Caballeo-Flores, M.H. Phan, M.A. Torija, C. Leighton, and H.
Srikanth, Magnetocaloric effect and critical behavior in Pr0.5Sr0.5MnO3: An
analysis on the validity of Maxwell relation and nature of phase transitions.
INTERMAG 2012, Vancouver B.C., May 7 – 11, 2012.
5. N.S. Bingham, T.L. Phan, M.H. Phan, S.C. Yu and H. Srikanth, Phase
coexistence and magnetocaloric effect in Sm1-xSrxMnO3 (x = 0.42, 0.44, 0.46)
manganites, 56th
annual Magnetism and Magnetic Materials (MMM) conference,
Scottsdale, Az., Oct. 30 - Nov 4, 2011
157
6. N.S. Bingham, M.H. Phan, H. Srikanth, C.L. Zhang, and S.W. Cheong,
Multiphase transitions and complex phase diagram in mixed phase
(La,Pr,Ca)MnO3 manganites, 56th
annual Magnetism and Magnetic Materials
(MMM) conference, Scottsdale, Az., Oct. 30 - Nov 4, 2011
7. P. Lampen, N.S. Bingham, M.H. Phan, H. Srikanth, C.L. Zhang, S. W. Cheong,
T.D. Hoang, and H.D. Chinh, Impact of nanostructuring on the magnetic and
magnetocaloric properties of La0.25Pr0.375Ca0.375MnO3, 56th
annual Magnetism and
Magnetic Materials (MMM) conference, Scottsdale, Az., Oct. 30 - Nov 4, 2011
8. D. Mukherjee, N.S. Bingham, M.H. Phan, H. Srikanth, P. Mukherjee and S.
Witanachchi, Ziz-zag interface and strain-influenced ferromagnetism in epitaxial
Mn3O4/La0.7Sr0.3MnO3 thin films grown on MgO (100) and SrTiO3 (100)
substrates , 56th
annual Magnetism and Magnetic Materials (MMM) conference,
Scottsdale, Az., Oct. 30 - Nov 4, 2011
9. N.S. Bingham, P. Lampen1 M.H. Phan, H. Srikanth, C.L. Zhang, S.W. Cheong,
T. H. Hoang, and H. D. Chinh, Impact of nanostructuring on the magnetic and
magnetocaloric properties of phase separated LaPrCaMnO3 manganites, Presented
at 1st Centennial of Superconductivity: Trends on Nanoscale Superconductivity
and Magnetism International Workshop, Cali, Colombia, June 29th
- July 1st, 2011
10. N.S. Bingham, M.H. Phan, H. Srikanth, M.A. Torija and C. Leighton,
Magnetocaloric effect across the coupled structural magnetocrystalline anisotropy
transition in Pr1-xSrxCoO3 (x = 0.3-0.5), Presented at APS March Meeting, Dallas,
Texas, March 21 - 25, 2011
158
11. M.H. Phan, N.S. Bingham, H. Srikanth, C.L. Zhang, and S.W. Cheong, Probing
multiple magnetic transitions and phase coexistence in mixed phase manganites,
Presented at APS March Meeting, Dallas, Texas, March 21 - 25, 2011
12. P. Lampen, N.S. Bingham, M.H. Phan, H. Srikanth, T.D. Hoang, and H.D.
Chinh, Influence of particle size on the magnetic and magnetocaloric properties of
nanocrystalline La2/8Pr3/8Ca3/8MnO3, Presented at APS March Meeting, Dallas,
Texas, March 21 - 25, 2011
13. D.V. Williams, C. Bauer, N.S. Bingham, H. Srikanth and C.W. Miller, Impact of
post-deposition annealing on the magnetic entropy change in Gd thin films. 55th
annual Magnetism and Magnetic Materials (MMM) conference, Nov. 14-18, 2010
Atlanta GA. (Winner of the best poster award)
14. N. S. Bingham, M.H. Phan, M. A. Torija, C. Leighton, and H. Srikanth,
Influence of the coupled structural/magnetocrystalline anisotropy transition on
magnetic entropy change in Pr1-xSrxCoO3, 55th
annual Magnetism and Magnetic
Materials (MMM) conference, Atlanta, GA, Nov. 14-18, 2010
15. N.S. Bingham, M.H. Phan, H. Srikanth, M. A. Torija, C. Leighton,
Magnetocaloric Effect and Refrigerant Capacity in Charge-Ordered
Pr0.5Sr0.5MnO3, APS March Meeting, Portland Oregon, March 15—19, 2010
16. N. Laurita, S. Chandra, N.S. Bingham, M.H. Phan, H. Srikanth, T. H. Hoang, H.
D. Chinh, T.Z. Ward, J. Shen, Phase coexistence and collapse of charge ordering
in low-dimensional (La,Pr)CaMnO3, APS March Meeting, Portland Oregon,
March 15-19, 2010
159
17. M.H. Phan, N.S. Bingham, H. Srikanth, M. Torija and C. Leighton,
Magnetocaloric effect and transverse susceptibility in Pr-Sr-Mn-O, 2009
INTERMAG Conference, Sacramento CA, May 4-8, 2009
18. M.H. Phan, N.S. Bingham, N. A. Frey, M. A. Torija, C. Leighton and H.
Srikanth, Probing magnetic anisotropy and phase transitions in PSMO using RF
transverse susceptibility, 11th
joint MMM-INTERMAG conference, Washington
DC, January 18-22, 2010
19. M.H. Phan, M. B. Morales, N.S. Bingham, S. Chandra, C.L. Zhang, S.-W.
Cheong, T.D. Hoang, H. D. Chinh, and H. Srikanth, Collapse of charge-order and
enhanced magnetocaloric effect in nanostructured (La,Pr,Sr)CaMnO3, 11th
joint
MMM-INTERMAG conference, Washington DC, January 18-22, 2010
20. N.S. Bingham, M.H. Phan, H. Srikanth, M.A. Torija, and C. Leighton, A
Comparative Study of the Influence of First and Second Order Transitions on the
Magnetocaloric Effect and Refrigerant Capacity in Half-doped Manganites, 2nd
Annual IEEE Summer school, Nanjing, China, Sept. 2009, Poster
21. W.M. Tiernan, N.S. Bingham, J.C. Combs, Magnetization and Resistance of
Melt-Textured Growth YBCO Near TC and at Low magnetic Fields, 24th
International Conference on Low Temperature Physics, Orlando, FL, Aug. 2005
22. W.M. Tiernan, N.S. Bingham, J.C. Combs, Magnetization and Resistance of
Melt-Textured Growth YBCO Near TC and at Low magnetic Fields, Colorado
Research Symposium, Grand Junction, Colorado, Aug. 2003
