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Simple models of magnetism:

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1. Verfasser:	Skomski, Ralph 1961- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Oxford [u.a.] Oxford University Press 2008
Ausgabe:	1. publ.
Schriftenreihe:	Oxford graduate texts
Schlagworte:	Mathematisches Modell Magnetism > Mathematical models Magnetismus
Online-Zugang:	Table of contents only Inhaltsverzeichnis
Beschreibung:	Hier auch später erschienene, unveränd. Nachdrucke
Beschreibung:	XVI, 349 S. Ill., graph. Darst.
ISBN:	9780199655397 9780198570752

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adam_text	Contents List of abbreviations xii List of panels and tables xiv Preface xv 1 Introduction: The simplest models of magnetism 1 1.1 Field and magnetization 2 1.2 The circular-current model 4 1.3 Paramagnetic spins 6 1.4 Ising model and exchange 8 1.5 The viscoelastic model of magnetization dynamics 10 Exercises 13 2 Models of exchange 15 2.1 Atomic origin of exchange 17 2.1.1 One-electron wave functions 18 2.1.2 Two-electron wave functions 21 2.1.3 Hamiltonian and spin structure 22 2.1.4 Heisenberg model 25 2.1.5 Independent-electron approximation 27 2.1.6 Correlations 29 2.1.7 Hubbard model 32 2.1.8 Kondo model 34 2.2 Magnetic ions 36 2.2.1 Atomic orbitais 36 2.2.2 Angular-momentum algebra 39 2.2.3 Vector model and Hund s rules 41 2.2.4 Spin and orbital moment 41 2.3 Exchange between local moments 44 2.3.1 Exchange in oxides 44 2.3.2 Ruderman-Kittel exchange 46 2.3.3 Zero-temperature spin structure 48 2.4 Itinerant magnetism 51 2.4.1 Free electrons, Pauli susceptibility, and the Bloch model 54 2.4.2 Band structure 58 viii Contents 2.4.3 Stoner model and beyond 63 2.4.4 Itinerant antiferromagnets 66 Exercises 69 3 Models of magnetic anisotropy 73 3.1 Phenomenological models 74 3.1.1 Uniaxial anisotropy 75 3.1.2 Second-order anisotropy of general symmetry 76 3.1.3 Higher-order anisotropies of nonuniaxial symmetry 78 3.1.4 Cubic anisotropy 78 3.1.5 Anisotropy coefficients 79 3.1.6 Anisotropy fields 80 3.2 Models of pair anisotropy 80 3.2.1 Dipolar interactions and shape anisotropy 81 3.2.2 Demagnetizing factors 82 3.2.3 Applicability of the shape-anisotropy model 83 3.2.4 The Néel model 83 3.3 Spin-orbit coupling and crystal-field interaction 84 3.3.1 Relativistic origin of magnetism 85 3.3.2 Hydrogen-like atomic wave functions 87 3.3.3 Crystal-field interaction 87 3.3.4 Quenching 89 3.3.5 Spin-orbit coupling 90 3.4 The single-ion model of magnetic anisotropy 91 3.4.1 Rare-earth anisotropy 91 3.4.2 Point-charge model 95 3.4.3 The superposition model 97 3.4.4 Transition-metal anisotropy 98 3.5 Other anisotropies 100 3.5.1 Magnetoelasticity 100 3.5.2 Anisotropie exchange 101 3.5.3 Models of surface anisotropy 102 Exercises 104 4 Micromagnetic models 107 4.1 Stoner- Wohlfarth model 110 4.1.1 Aligned Stoner-Wohlfarth particles 111 4.1.2 Angular dependence 112 4.1.3 Spin reorientations and other first-order transitions 113 4.1.4 Limitations of the Stoner-Wohlfarth model 115 4.2 Hysteresis 116 4.2.1 Micromagnetic free energy 117 4.2.2 Magnetostatic self-interaction 118 4.2.3 Exchange stiffness 119 4.2.4 Linearized micromagnetic equations 120 4.2.5 Micromagnetic scaling 122 4.2.6 Domains and domain walls 123 Contents ix 4.3 Coercivity J28 4.3.1 Nucleation 130 4.3.2 Pinning 135 4.3.3 Phenomenological coercivity modeling 139 4.4 Grain-boundary models 141 АЛЛ Boundary conditions 141 4.4.2 Spin structure at grain boundaries 143 4.4.3 Models with atomic resolution I44 4.4.4 Nanojunctions I45 Exercises 145 Finite-temperature magnetism 149 5.1 Basic statistical mechanics 150 5.1.1 Probability and partition function 152 5.1.2 Fluctuations and response I53 5.1.3 Phase transitions I55 5.1.4 Landau theory 156 5.2 Spin-Space modeling I59 5.2.1 Heisenberg models 160 5.2.2 Ising, XY, and other n-vector models 161 5.2.3 Other discrete and continuum spin models 162 5.2.4 Ionic excitations 163 5.2.5 Spin fluctuations in itinerant magnets 164 5.3 Mean-field models 167 5.3.1 Mean-field Hamiltonians 168 5.3.2 Basic mean-field predictions 169 5.3.3 Ornstein-Zernike correlations 171 5.3.4 Magnetization and Curie temperature 172 5.3.5 Mean-field Curie temperature of n-vector models 173 5.3.6 Two-sublattice magnetism I74 5.3.7 Merits and limitations of mean-field models 178 5.4 Critical behavior 179 5.4.1 One-dimensional models 180 5.4.2 Superparamagnetic clusters 181 5.4.3 Ginzburg criterion 183 5.4.4 Fluctuations and criticality 184 5.4.5 Renormalization group 187 5.5 Temperature dependence of anisotropy 190 5.5.1 Callen and Callen model 191 5.5.2 Rare-earth anisotropy 193 5.5.3 Sublattice modeling 195 Exercises 196 Magnetization dynamics 199 6.1 Quantum dynamics and resonance I99 6.1.1 Spin precession 201 6.1.2 Uniform magnetic resonance 202 χ Contents 6.1.3 Spin waves 203 6.1.4 Spin dynamics in inhomogeneous magnets 206 6.2 Relaxation 208 6.2.1 Damped precession 209 6.2.2 ^Physical origin of relaxation 210 6.2.3 A mechanical model 211 6.3 Coarse-grained models 213 6.3.1 Master equation 214 6.3.2 Fokker-Planck equations 216 6.3.3 Langevin models 218 6.4 Slow magnetization dynamics 220 6.4.1 Magnetic viscosity and sweep-rate dependence 223 6.4.2 Superposition model of magnetic viscosity 223 6.4.3 Asymptotic behavior 225 6.4.4 Energy-barrier models 226 6.4.5 Linear and other laws 227 6.4.6 Superparamagnetism 228 6.4.7 Fluctuations 229 Exercises 233 7 Special topics and interdisciplinary models 237 7.1 Disordered magnets and spin glasses 237 7.1.1 Atomic disorder and electronic structure 238 7.1.2 Green Functions 239 7.1.3 Ferromagnetic order in inhomogeneous magnets 242 7.1.4 Spin glasses 244 7.2 Soft matter, transport, and magnetism 247 7.2.1 Random walks, polymers, and diffusion 248 7.2.2 The η = 0 vector-spin model 249 7.2.3 Polymers and critical dimensionality 250 7.2.4 Percolation 252 7.2.5 Diffusive transport 255 7.2.6 Gases in magnetic metals 256 7.2.7 Magnetoresistance 258 7.2.8 Other transport phenomena involving magnetism 261 7.3 Bruggeman model 263 7.3.1 Static and dynamic properties 263 7.3.2 Parameterization 265 7.3.3 Self-consisteut materials equations 266 7.3.4 The response parameter g 267 7.3.5 Percolation in the Bruggeman model 267 7.4 Nanostructures, thin films, and surfaces 268 7.4.1 Length scales in nanomagnetism 270 7.4.2 Nanomagnetic effects of atomic origin 271 7.4.3 Random anisotropy 274 Contents xi 7.4.4 *Cooperative magnetization processes 277 7.4.5 Two-phase nanostructures 279 7.5 Beyond magnetism 282 7.5.1 Metallurgy 283 7.5.2 Biology and medicine 285 7.5.3 Social sciences 286 Exercises 286 Appendix 289 A.I Units and constants 289 A. 1.1 Units systems and notation 289 A. 1.2 Unit conversions 290 A. 1.3 Physical constants 290 A.2 Mathematics 290 A. 2.1 Linear equations 290 A. 2.2 Eigenmode analysis 292 A.2.3 Real 2x2 matrices 293 A. 2.4 Vector and functional calculus 295 A.2. 5 Useful formulae 297 A.3 Basic quantum mechanics 297 A.3.1 Time dependence 298 A. 3.2 Eigenvalues and eigenfunctions 298 A.3.3 Perturbation theory 299 A. 3.4 Quantum statistics 300 A. 3.5 Relativistic quantum mechanics 302 A. 4 Electromagnetism 304 A. 4.1 Maxwells equations 304 A. 4.2 Simple magnetostatic solutions 306 A. 4.3 Simple dynamic solutions 308 A. 5 Magnetic materials 309 A. 5.1 Transition-metal elements and alloys 310 A. 5.2 Magnetic oxides 314 A. 5.3 Rare-earth magnets 314 A. 6 Forgotten and reinvented 315 References 319 Index 335
adam_txt	Contents List of abbreviations xii List of panels and tables xiv Preface xv 1 Introduction: The simplest models of magnetism 1 1.1 Field and magnetization 2 1.2 The circular-current model 4 1.3 Paramagnetic spins 6 1.4 Ising model and exchange 8 1.5 The viscoelastic model of magnetization dynamics 10 Exercises 13 2 Models of exchange 15 2.1 Atomic origin of exchange 17 2.1.1 One-electron wave functions 18 2.1.2 Two-electron wave functions 21 2.1.3 Hamiltonian and spin structure 22 2.1.4 Heisenberg model 25 2.1.5 Independent-electron approximation 27 2.1.6 Correlations 29 2.1.7 Hubbard model 32 2.1.8 Kondo model 34 2.2 Magnetic ions 36 2.2.1 Atomic orbitais 36 2.2.2 Angular-momentum algebra 39 2.2.3 Vector model and Hund's rules 41 2.2.4 Spin and orbital moment 41 2.3 Exchange between local moments 44 2.3.1 Exchange in oxides 44 2.3.2 Ruderman-Kittel exchange 46 2.3.3 Zero-temperature spin structure 48 2.4 Itinerant magnetism 51 2.4.1 Free electrons, Pauli susceptibility, and the Bloch model 54 2.4.2 Band structure 58 viii Contents 2.4.3 Stoner model and beyond 63 2.4.4 "Itinerant antiferromagnets 66 Exercises 69 3 Models of magnetic anisotropy 73 3.1 Phenomenological models 74 3.1.1 Uniaxial anisotropy 75 3.1.2 Second-order anisotropy of general symmetry 76 3.1.3 Higher-order anisotropies of nonuniaxial symmetry 78 3.1.4 Cubic anisotropy 78 3.1.5 Anisotropy coefficients 79 3.1.6 Anisotropy fields 80 3.2 Models of pair anisotropy 80 3.2.1 Dipolar interactions and shape anisotropy 81 3.2.2 Demagnetizing factors 82 3.2.3 Applicability of the shape-anisotropy model 83 3.2.4 The Néel model 83 3.3 Spin-orbit coupling and crystal-field interaction 84 3.3.1 Relativistic origin of magnetism 85 3.3.2 Hydrogen-like atomic wave functions 87 3.3.3 Crystal-field interaction 87 3.3.4 Quenching 89 3.3.5 Spin-orbit coupling 90 3.4 The single-ion model of magnetic anisotropy 91 3.4.1 Rare-earth anisotropy 91 3.4.2 Point-charge model 95 3.4.3 The superposition model 97 3.4.4 Transition-metal anisotropy 98 3.5 Other anisotropies 100 3.5.1 Magnetoelasticity 100 3.5.2 Anisotropie exchange 101 3.5.3 Models of surface anisotropy 102 Exercises 104 4 Micromagnetic models 107 4.1 Stoner- Wohlfarth model 110 4.1.1 Aligned Stoner-Wohlfarth particles 111 4.1.2 Angular dependence 112 4.1.3 Spin reorientations and other first-order transitions 113 4.1.4 Limitations of the Stoner-Wohlfarth model 115 4.2 Hysteresis 116 4.2.1 Micromagnetic free energy 117 4.2.2 Magnetostatic self-interaction 118 4.2.3 Exchange stiffness 119 4.2.4 Linearized micromagnetic equations 120 4.2.5 Micromagnetic scaling 122 4.2.6 Domains and domain walls 123 Contents ix 4.3 Coercivity J28 4.3.1 Nucleation 130 4.3.2 Pinning 135 4.3.3 Phenomenological coercivity modeling 139 4.4 Grain-boundary models 141 АЛЛ Boundary conditions 141 4.4.2 Spin structure at grain boundaries 143 4.4.3 Models with atomic resolution I44 4.4.4 Nanojunctions I45 Exercises 145 Finite-temperature magnetism 149 5.1 Basic statistical mechanics 150 5.1.1 Probability and partition function 152 5.1.2 Fluctuations and response I53 5.1.3 Phase transitions I55 5.1.4 Landau theory 156 5.2 Spin-Space modeling I59 5.2.1 Heisenberg models 160 5.2.2 Ising, XY, and other n-vector models 161 5.2.3 Other discrete and continuum spin models 162 5.2.4 Ionic excitations 163 5.2.5 Spin fluctuations in itinerant magnets 164 5.3 Mean-field models 167 5.3.1 Mean-field Hamiltonians 168 5.3.2 Basic mean-field predictions 169 5.3.3 Ornstein-Zernike correlations 171 5.3.4 Magnetization and Curie temperature 172 5.3.5 Mean-field Curie temperature of n-vector models 173 5.3.6 Two-sublattice magnetism I74 5.3.7 Merits and limitations of mean-field models 178 5.4 Critical behavior 179 5.4.1 One-dimensional models 180 5.4.2 Superparamagnetic clusters 181 5.4.3 Ginzburg criterion 183 5.4.4 Fluctuations and criticality 184 5.4.5 Renormalization group 187 5.5 Temperature dependence of anisotropy 190 5.5.1 Callen and Callen model 191 5.5.2 Rare-earth anisotropy 193 5.5.3 Sublattice modeling 195 Exercises 196 Magnetization dynamics 199 6.1 Quantum dynamics and resonance I99 6.1.1 Spin precession 201 6.1.2 Uniform magnetic resonance 202 χ Contents 6.1.3 Spin waves 203 6.1.4 Spin dynamics in inhomogeneous magnets 206 6.2 Relaxation 208 6.2.1 Damped precession 209 6.2.2 ^Physical origin of relaxation 210 6.2.3 A mechanical model 211 6.3 Coarse-grained models 213 6.3.1 Master equation 214 6.3.2 Fokker-Planck equations 216 6.3.3 Langevin models 218 6.4 Slow magnetization dynamics 220 6.4.1 Magnetic viscosity and sweep-rate dependence 223 6.4.2 Superposition model of magnetic viscosity 223 6.4.3 Asymptotic behavior 225 6.4.4 Energy-barrier models 226 6.4.5 Linear and other laws 227 6.4.6 Superparamagnetism 228 6.4.7 Fluctuations 229 Exercises 233 7 Special topics and interdisciplinary models 237 7.1 Disordered magnets and spin glasses 237 7.1.1 Atomic disorder and electronic structure 238 7.1.2 Green Functions 239 7.1.3 Ferromagnetic order in inhomogeneous magnets 242 7.1.4 Spin glasses 244 7.2 Soft matter, transport, and magnetism 247 7.2.1 Random walks, polymers, and diffusion 248 7.2.2 The η = 0 vector-spin model 249 7.2.3 Polymers and critical dimensionality 250 7.2.4 Percolation 252 7.2.5 Diffusive transport 255 7.2.6 Gases in magnetic metals 256 7.2.7 Magnetoresistance 258 7.2.8 Other transport phenomena involving magnetism 261 7.3 Bruggeman model 263 7.3.1 Static and dynamic properties 263 7.3.2 Parameterization 265 7.3.3 Self-consisteut materials equations 266 7.3.4 The response parameter g 267 7.3.5 Percolation in the Bruggeman model 267 7.4 Nanostructures, thin films, and surfaces 268 7.4.1 Length scales in nanomagnetism 270 7.4.2 Nanomagnetic effects of atomic origin 271 7.4.3 Random anisotropy 274 Contents xi 7.4.4 *Cooperative magnetization processes 277 7.4.5 Two-phase nanostructures 279 7.5 Beyond magnetism 282 7.5.1 Metallurgy 283 7.5.2 Biology and medicine 285 7.5.3 Social sciences 286 Exercises 286 Appendix 289 A.I Units and constants 289 A. 1.1 Units systems and notation 289 A. 1.2 Unit conversions 290 A. 1.3 Physical constants 290 A.2 Mathematics 290 A. 2.1 Linear equations 290 A. 2.2 Eigenmode analysis 292 A.2.3 Real 2x2 matrices 293 A. 2.4 Vector and functional calculus 295 A.2. 5 Useful formulae 297 A.3 Basic quantum mechanics 297 A.3.1 Time dependence 298 A. 3.2 Eigenvalues and eigenfunctions 298 A.3.3 Perturbation theory 299 A. 3.4 Quantum statistics 300 A. 3.5 Relativistic quantum mechanics 302 A. 4 Electromagnetism 304 A. 4.1 Maxwells equations 304 A. 4.2 Simple magnetostatic solutions 306 A. 4.3 Simple dynamic solutions 308 A. 5 Magnetic materials 309 A. 5.1 Transition-metal elements and alloys 310 A. 5.2 Magnetic oxides 314 A. 5.3 Rare-earth magnets 314 A. 6 Forgotten and reinvented 315 References 319 Index 335
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title	Simple models of magnetism
title_auth	Simple models of magnetism
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title_full	Simple models of magnetism Ralph Skomski
title_fullStr	Simple models of magnetism Ralph Skomski
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title_short	Simple models of magnetism
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work_keys_str_mv	AT skomskiralph simplemodelsofmagnetism

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