Simple Models of Magnetism

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For hundreds of years, models of magnetism have been pivotal in the understanding and advancement of science and technology, from the Earth's interpretation as a magnetic dipole to quantum mechanics, statistical physics, and modern nanotechnology. This book is the first to envision the field of magnetism in its entirety. It complements a rich literature on specific models of magnetism and provides an introduction to simple models, including some simple limits of complicated models. The book is written in an easily accessible style, with a limited amount of mathematics, and covers a wide range of quantum-mechanical, finite-temperature, micromagnetic, and dynamic models. It deals not only with basic magnetic quantities, such as moment, Curie temperature, anisotropy, and coercivity, but also with modern areas such as nanomagnetism and spintronics, and with 'exotic' themes, as exemplified by the polymer analogy of magnetic phase transitions. Throughout the book, a sharp line is drawn between simple and simplistic models, and much space is devoted to discuss the merits and failures of the individual model approaches.

About the Author:
Ralph Skomski is a Research Associate Professor at the Department of Physics and Astronomy and Nebraska Center for Materials and Nanoscience, University of Nebraska

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Product Details

  • ISBN-13: 9780198570752
  • Publisher: Oxford University Press
  • Publication date: 3/15/2008
  • Series: Oxford Graduate Texts Series
  • Pages: 336
  • Product dimensions: 9.80 (w) x 6.60 (h) x 0.90 (d)

Meet the Author

Ralph Skomski, Center for Materials Research and Analysis, University of Nebraska.

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Table of Contents

List of abbreviations     xii
List of panels and tables     xiv
Preface     xv
Introduction: The simplest models of magnetism     1
Field and magnetization     2
The circular-current model     4
Paramagnetic spins     6
Ising model and exchange     8
The viscoelastic model of magnetization dynamics     10
Exercises     13
Models of exchange     15
Atomic origin of exchange     17
One-electron wave functions     18
Two-electron wave functions     21
Hamiltonian and spin structure     22
Heisenberg model     25
Independent-electron approximation     27
Correlations     29
Hubbard model     32
Kondo model     34
Magnetic ions     36
Atomic orbitals     36
Angular-momentum algebra     39
Vector model and Hund's rules     41
Spin and orbital moment     41
Exchange between local moments     44
Exchange in oxides     44
Ruderman-Kittel exchange     46
Zero-temperature spin structure     48
Itinerant magnetism     51
Free electrons, Pauli susceptibility, and the Bloch model     54
Band structure     58
Stoner model and beyond     63
Itinerant antiferromagnets     66
Exercises     69
Models of magnetic anisotropy     73
Phenomenological models     74
Uniaxial anisotropy     75
Second-order anisotropy of general symmetry     76
Higher-order anisotropies of nonuniaxial symmetry     78
Cubic anisotropy     78
Anisotropy coefficients     79
Anisotropy fields     80
Models of pair anisotropy     80
Dipolar interactions and shape anisotropy     81
Demagnetizing factors     82
Applicability of the shape-anisotropy model     83
The Neel model     83
Spin-orbit coupling and crystal-field interaction     84
Relativistic origin of magnetism     85
Hydrogen-like atomic wave functions     87
Crystal-field interaction     87
Quenching     89
Spin-orbit coupling     90
The single-ion model of magnetic anisotropy     91
Rare-earth anisotropy      91
Point-charge model     95
The superposition model     97
Transition-metal anisotropy     98
Other anisotropies     100
Magnetoelasticity     100
Anisotropic exchange     101
Models of surface anisotropy     102
Exercises     104
Micromagnetic models     107
Stoner-Wohlfarth model     110
Aligned Stoner-Wohlfarth particles     111
Angular dependence     112
Spin reorientations and other first-order transitions     113
Limitations of the Stoner-Wohlfarth model     115
Hysteresis     116
Micromagnetic free energy     117
Magnetostatic self-interaction     118
Exchange stiffness     119
Linearized micromagnetic equations     120
Micromagnetic scaling     122
Domains and domain walls     123
Coercivity     128
Nucleation     130
Pinning     135
Phenomenological coercivity modeling     139
Grain-boundary models     141
Boundary conditions     141
Spin structure at grain boundaries     143
Models with atomic resolution      144
Nanojunctions     145
Exercises     146
Finite-temperature magnetism     149
Basic statistical mechanics     150
Probability and partition function     152
Fluctuations and response     153
Phase transitions     155
Landau theory     156
Spin-Space modeling     159
Heisenberg models     160
Ising, XY, and other n-vector models     161
Other discrete and continuum spin models     162
Ionic excitations     163
Spin fluctuations in itinerant magnets     164
Mean-field models     167
Mean-field Hamiltonians     168
Basic mean-field predictions     169
Ornstein-Zernike correlations     171
Magnetization and Curie temperature     172
Mean-field Curie temperature of n-vector models     173
Two-sublattice magnetism     174
Merits and limitations of mean-field models     178
Critical behavior     179
One-dimensional models     180
Superparamagnetic clusters     181
Ginzburg criterion     183
Fluctuations and criticality      184
Renormalization group     187
Temperature dependence of anisotropy     190
Callen and Callen model     191
Rare-earth anisotropy     193
Sublattice modeling     195
Exercises     196
Magnetization dynamics     199
Quantum dynamics and resonance     199
Spin precession     201
Uniform magnetic resonance     202
Spin waves     203
Spin dynamics in inhomogeneous magnets*     206
Relaxation     208
Damped precession     209
Physical origin of relaxation     210
A mechanical model     211
Coarse-grained models     213
Master equation     214
Fokker-Planck equations     216
Langevin models     218
Slow magnetization dynamics     220
Magnetic viscosity and sweep-rate dependence     223
Superposition model of magnetic viscosity     223
Asymptotic behavior*     225
Energy-barrier models     226
Linear and other laws     227
Superparamagnetism     228
Fluctuations     229
Exercises     233
Special topics and interdisciplinary models     237
Disordered magnets and spin glasses     237
Atomic disorder and electronic structure     238
Green Functions     239
Ferromagnetic order in inhomogeneous magnets     242
Spin glasses     244
Soft matter, transport, and magnetism     247
Random walks, polymers, and diffusion     248
The n = 0 vector-spin model     249
Polymers and critical dimensionality     250
Percolation     252
Diffusive transport     255
Gases in magnetic metals     256
Magnetoresistance     258
Other transport phenomena involving magnetism     261
Bruggeman model     263
Static and dynamic properties     263
Parameterization     265
Self-consistent materials equations     266
The response parameter g     267
Percolation in the Bruggeman model     267
Nanostructures, thin films, and surfaces     268
Length scales in nanomagnetism     270
Nanomagnetic effects of atomic origin     271
Random anisotropy     274
Cooperative magnetization processes     277
Two-phase nanostructures     279
Beyond magnetism     282
Metallurgy     283
Biology and medicine     285
Social sciences     286
Exercises     286
Appendix     289
Units and constants     289
Units systems and notation     289
Unit conversions     290
Physical constants     290
Mathematics     290
Linear equations     290
Eigenmode analysis     292
Real 2 x 2 matrices     293
Vector and functional calculus     295
Useful formulae     297
Basic quantum mechanics     297
Time dependence     298
Eigenvalues and eigenfunctions     298
Perturbation theory     299
Quantum statistics     300
Relativistic quantum mechanics     302
Electromagnetism     304
Maxwells equations     304
Simple magnetostatic solutions     306
Simple dynamic solutions     308
Magnetic materials     309
Transition-metal elements and alloys     310
Magnetic oxides     314
Rare-earth magnets      314
Forgotten and reinvented     315
References     319
Index     335
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