Ab initio Theory of Magnetic Ordering: Electronic Origin of Pair- and Multi-Spin Interactions (Springer Theses)

Supervisor’s Foreword
Abstract
Publications Related to this ThesisThis thesis contains research carried out in the Theory Group of the Department of Physics between October 2014 and May 2018. The content of this thesis is my own work, unless stated otherwise, carried out under the supervision of Prof. J. B. Staunton.Parts of this thesis have been published in the following papers:Chapter 5: Pair- and four-spin interactions in the heavy rare earth elementsE. Mendive-Tapia and J. B. Staunton. Theory of magnetic ordering in the heavy rare earths: Ab initio electronic origin of pair- and four- spin interactions. Phys. Rev. Lett., 118:197202, 2017.Chapter 6: Frustrated magnetism in Mn-based antiperovskite Mn3GaNJ. Zemen, E. Mendive-Tapia, Z. Gercsi, R. Banerjee, J. B. Staunton, and K. G. Sandeman. Frustrated Magnetism and caloric effects in Mn-based antiperovskite nitrides: Ab initio theory. Phys. Rev. B, 95:184438, 2017.Chapter 7: The magnetism of Mn3A (A = Pt, Ir, Rh, Sn, Ga, Ge)E. Mendive-Tapia and J. B. Staunton. Ab initio theory of the Gibbs free energy and a hierarchy of local moment correlation functions in itinerant electron systems: The magnetism of the Mn3A materials class. Phys. Rev. B, 99:144424, 2019.The following publication has evolved from this doctoral dissertation:D. Boldrin, E. Mendive-Tapia, J. Zemen, J. B. Staunton, T. Hansen, A. Aznar, J. Ll. Tamarit, M. Barrio, P. Lloveras, J. Kim, X. Moya, and F. Cohen (2018). Multisite Exchange-Enhanced Barocaloric Response in Mn3NiN. Physical Review X, 8:041035, 2018.
Acknowledgements
Contents
Abbreviations
1 Introduction
	References
2 Ab initio Theory of Electronic Structure
	2.1 Density Functional Theory
		2.1.1 The Local Density Approximation
		2.1.2 Density Functional Theory Extended to Finite Temperatures
		2.1.3 Magnetism and Relativistic Effects in Density Functional Theory
	2.2 Multiple Scattering Theory
		2.2.1 Green\'s Functions and the Single-Center Scattering Problem
		2.2.2 Scattering Paths and the Multi-site Solution
		2.2.3 Density Calculation and the Lloyd Formula
	2.3 The Effective Medium Theory of Disorder:  The Coherent Potential Approximation
	References
3 Disordered Local Moment Theory  and Fast Electronic Responses
	3.1 Magnetism at Finite Temperatures and Conceptual Framework
	3.2 Mean-Field Theory and Statistical Mechanics  of Disordered Local Moments
	3.3 The Internal Local Field and Its Electronic Glue Origins
		3.3.1 The Coherent Potential Approximation of Disordered Local Moments
		3.3.2 Self-consistent Calculations
	3.4 Wave-Modulated Magnetic Structures from Fully Disordered Local Moments
		3.4.1 Calculation of the Direct Correlation Function
	References
4 Minimisation of the Gibbs Free Energy: Magnetic Phase Diagrams and Caloric Effects
	4.1 Multi-spin Interactions
	4.2 Magnetic Phase Diagrams
		4.2.1 The Equilibrium State: A Self-consistent Calculation
		4.2.2 Case Study: One Type of Magnetic Ordering
		4.2.3 Case Study: Ferromagnetism Versus Antiferromagnetism
	4.3 Application to bcc Iron
	4.4 Caloric Effects
	References
5 Pair- and Four-Spin Interactions  in the Heavy Rare Earth Elements
	5.1 The Magnetocaloric Effect in the Heavy Rare Earth Elements
	5.2 Summary and Conclusions
	References
6 Frustrated Magnetism in Mn-Based Antiperovskite Mn3GaN
	6.1 Unstrained Cubic System
	6.2 Biaxial Strain, the Elastocaloric Effect and Cooling Cycles
	6.3 Summary and Conclusions
	References
7 The Magnetism of Mn3A (A = Pt, Ir, Rh, Sn, Ga, Ge)
	7.1 First- and Second-Order Magnetic Phase Transitions in Cubic Mn3A (A = Pt, Ir, Rh)
		7.1.1 Experimental Properties
		7.1.2 High Temperature Regime and Magnetovolume Coupling
		7.1.3 Lower Temperature Regime and the Magnetic Phase Diagram of Mn3Pt
		7.1.4 On the Deficiencies of the Collinear AFM State
		7.1.5 The Barocaloric Effect of Mn3Pt
	7.2 Mn3A (A = Sn, Ga, Ge): Hexagonal and Tetragonal Structures
		7.2.1 Experimentally Observed Properties and Published Theoretical Calculations
		7.2.2 Application of DLM Theory to Hexagonal Mn3Sn, Mn3Ga and Mn3Ge
		7.2.3 Application of DLM Theory to Tetragonal Mn3Ga and Mn3Ge
	7.3 Summary and Conclusions
	References
8 Summary and Outlook
	References
Appendix  The CPA Equations in the Paramagnetic Limit