A Combined Density Functional Theory and Monte Carlo Study of Manganites for Magnetic Refrigeration Romi Kaur Korotana Department of Chemistry Imperial College London A thesis submitted for the degree of Doctor of Philosophy Nov 2014 Declaration of Originality I hereby declare that this thesis is a presentation of my original research work and has not been submitted previously for a degree qualification or any other academic qualification at this University or any other institution of higher education. Wherever contributions of others are involved, every effort is made to indicate this, with due reference to literature and acknowledgements of collaborative research and discussions. The research work presented in this thesis was conducted under the guidance of Pro- fessor Nicholas M. Harrison at Imperial College London, London. Romi Kaur Korotana July 2014 3 Declaration of Copyright The copyright of this thesis rests with the author and is made available under a Creative Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work. 5 Abstract Perovskite oxides such as manganites are considered to be strong candidates for appli- cations in magnetic refrigeration technology, due to their remarkable magnetocaloric properties, in addition to low processing costs. Manganites with the general formula R1−xAxMnO3, particularly for A=Ca and 0.2 < x < 0.5, undergo a field driven tran- sition from a paramagnetic to ferromagnetic state, which is accompanied by changes in the lattice and electronic structure. Therefore, one may anticipate a large entropy change across the phase transition due to the first order nature. Despite many ex- perimental efforts to enhance the isothermal entropy change in manganites, the max- imum obtained value merely reaches a modest value in the field of a permanent mag- net. The present work aims to achieve an understanding of the relevant structural, magnetic, and electronic energy contributions to the stability of the doped compound La0.75Ca0.25MnO3. A combination of thermodynamics and first principles theory is applied to determine individual contributions to the total entropy change of the system by treating the electronic, lattice and magnetic components independently. For this purpose, hybrid-exchange density functional (B3LYP) calculations are performed for LaMnO3, CaMnO3 and La0.75Ca0.25MnO3. The most stable phases for the end-point compounds are described correctly. Computed results for the doped compound predict an anti-Jahn-Teller polaron in the localised hole state, which is influenced by long- range cooperative Jahn-Teller distortions. The analysis of the energy scales related to the magnetocaloric effect suggests that the charge, orbital, spin and lattice degrees of freedom are strongly coupled, since they are of a similar magnitude. Through the analysis of individual entropy contributions, it is identified that the electronic and lat- tice entropy changes oppose the magnetic entropy change. Therefore, the electronic and vibrational terms have a deleterious effect on the total entropy change. The results highlighted in the present work may provide a useful framework for the interpretation of experimental observations as well as valuable guidelines for tuning the magnetocaloric properties of oxides, such as manganites. 7 Acknowledgements This thesis would not be complete without acknowledging all the people who made it possible with their contributions. Foremost, I would like to express my deepest thanks to my supervisor, Professor Nicholas Harrison for giving me this opportunity and placing confidence in me. Nic’s guidance, encouragement, and extensive knowledge were key motivations throughout my PhD; for both, my personal and academic development. I wish to thank members of the Computational Material Sciences research group. Giuseppe has supported me at many critical stages of my research, he has been a valuable mentor throughout the PhD and I am grateful for all the help that was offered. Ruth and Ehsan, in particular, always made time and supported me through difficult periods. I’m also thankful to Leandro for his unwavering guidance during the initial stages of the PhD. A special acknowledgment goes to Monica and Leo, with whom I shared my office and an indefinate number of lunch and coffee breaks. Neither of them failed to make me smile. I would like to thank Frederico for being a wonderful desk buddy since the beginning of my PhD. In no particular order, I’d also like to acknowledge other colleagues: Ross, Jing, Bruno, Basma, Maryam, Hsiang-Han, Jassel, Joshua, Ariadna, Fatemeh, Vincent and David for memorable times. I owe a great debt of gratitude to Lesley Cohen, Karl Sandeman, Zsolt Gercsi, Jo˜ao Amaral, Jeremy Turcaud and Jo˜ao Horta who have always inspired me with their deep insights for magnetocalorics. In particular, Zsolt and Jo˜ao Amaral always found the time to provide constructive feedback and guidance. My heartfelt appreciation and endless gratitude goes to my friends outside of academia, particularly Mithila, Chahat and Neelam. A special mention for members of the IC women’s cricket team: Taniya, Priya and Himani; who encouraged me to wind down at training sessions and provided invaluable support throughout my time at Imperial. I would also like to thank my ex-flatmates, Michael and Anita, with whom I shared some unforgettably fun times. My sincere thanks go to my siblings for their unreserved love. I am deeply grateful 9 to Ravi for his financial support, and Komal for believing that this journey would come to an end. Finally, I express my utmost gratitude to my mother and father, they raised me, supported me, taught me, and loved me unconditionally; this thesis would not have been possible without their guidance. The EPSRC is greatly acknowledged for funding the PhD. I would also like to mention that this work made use of the high performance computing facilities of Im- perial College London and - via membership of the UKs HPC Materials Chemistry Consortium funded by EPSRC (EP/F067496) - of HECToR, the UKs national high- performance computing service, which is provided by UoE HPCx Ltd at the University of Edinburgh, Cray Inc and NAG Ltd, and funded by the Office of Science and Tech- nology through EPSRC’s High End Computing Programme. 10 List of Publications R. Korotana, G. Mallia, Z. Gercsi, and N. M. Harrison, A hybrid density func- • tional study of Ca-doped LaMnO3, J. Appl. Phys. 113 17A910 2013. R. Korotana, G. Mallia, Z. Gercsi, L. Liborio and N. M. Harrison, A hybrid • density functional study of structural, bonding, and electronic properties of the manganite series: La1−xCaxMnO3 (at x=0, 1/4 and 1), Phys. Rev. B 89 205110 2014. R. Korotana, G. Mallia, and N. M. Harrison, A theoretical study of the • electronic, vibrational and magnetic contributions to the entropy change in La0.75Ca0.25MnO3 In preparation 11 List of Presentations Delft Days on Magnetocalorics, Delft, Holland, Oct 2013. (Poster) • Ab initio Modelling in Solid State Chemistry Workshop, Imperial College London, • UK, Sept 2013. (Poster) Chemistry Postgraduate Symposium, Imperial College London, UK, Jun 2013. • (Talk) 12th Joint MMM/Intermag Conference, Chicago, USA, Jan 2013. (Talk) • 5th IIR/IIF International Conference on Magnetic Refrigeration: THERMAG V, • Grenoble, France, Sept 2012. (Poster) Chemistry Postgraduate Symposium, Imperial College London, UK, Jun 2012. • (Poster) UK’s HPC Materials Chemistry Consortium, University College London, UK, • Mar 2012. (Talk) Ab initio Modelling in Solid State Chemistry Workshop, Imperial College London, • UK, Sept 2011. (Poster) 13 F or my parents Contents 1 Introduction 19 2 Magnetism and Phase Transitions 23 2.1 MacroscopicMagneticOrder . 23 2.2 MagneticInteractions . 25 2.3 ModelsofPhaseTransitions. 28 2.3.1 Landau Theory of Ferromagnetism . 28 2.3.2 TheBean-RodbellModel . 29 2.3.3 HeisenbergModel .......................... 30 2.3.4 IsingModel.............................. 31 2.3.5 HubbardModel............................ 31 3 The Magnetocaloric Effect 33 3.1 Thermodynamics............................... 33 3.2 Measuring the Magnetocaloric Effect . 35 3.3 MaterialsResearch .............................. 37 3.4 Manganites as Magnetocaloric Materials . 40 3.4.1 StructureandProperties . 40 3.4.2 Doped Perovskite Manganites . 42 3.5 Modelling of the Magnetocaloric Effect . 44 4 Theoretical Concepts and Techniques 47 4.1 ElectronicStructureMethods . 47 4.1.1 TheSchr¨odingerEquation. 48 4.1.2 Density Functional Theory (DFT) . 50 4.1.3 Exchange-Correlation Functionals . 52 4.2 TheBasisSetApproximation . 54 15 CONTENTS 4.2.1 Atomic Orbital (Gaussian) Basis Sets . 55 4.2.2 Plane-Wave (PW) Basis Sets . 56 4.3 PeriodicModel ................................ 56 4.4 TheCRYSTALCode............................. 57 4.4.1 Geometry Optimisation . 58 4.5 MonteCarloMethods ............................ 59 4.5.1 Metropolis Algorithm . 59 4.5.2 OutlineofMonteCarloCode . 60 5 The End-point Stoichiometric Compounds: LaMnO3 and CaMnO3 63 5.1 Orthorhombic LaMnO3 ........................... 64 5.1.1 ExperimentalStructure . 64 5.1.2 OptimizedStructure . 65 5.1.3 ElectronicStructure . 68 5.1.4 MagneticOrderingandPhases . 70 5.2 Orthorhombic CaMnO3 ........................... 73 5.2.1 OptimizedStructure