Simple Models of Magnetism 1st Edition by Ralph Skomski ISBN 0198570759 978-0198570752
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ISBN 10: 0198570759
ISBN 13: 978-0198570752
Author: Ralph Skomski
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 dynamical 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.
Table of contents:
1 Introduction: The simplest models of magnetism
1.1 Field and magnetization
1.2 The circular-current model
1.3 Paramagnetic spins
1.4 Ising model and exchange
1.5 The viscoelastic model of magnetization dynamics Exercises
2 Models of exchange
2.1 Atomic origin of exchange
2.1.1 One-electron wave functions
2.1.2 Two-electron wave functions
2.1.3 Hamiltonian and spin structure
2.1.4 Heisenberg model
2.1.5 Independent-electron approximation
2.1.6 Correlations
2.1.7 *Hubbard model
2.1.8 *Condo model
2.2 Magnetic ions
2.2.1 Atomic orbitals
2.2.2 Angular-momentum algebra
2.2.3 Vector model and Hund’s rules
2.2.4 Spin and orbital moment
2.3 Exchange between local moments
2.3.1 Exchange in oxides
2.3.2 Ruderman-Kittel exchange
2.3.3 Zero-temperature spin structure
2.4 Itinerant magnetism
2.4.1 Free electrons, Pauli susceptibility, and the Bloch model
2.4.2 Band structure
2.4.3 Stoner model and beyond
2.4.4 Itinerant antiferromagnets
Exercises
3 Models of magnetic anisotropy
3.1 Phenomenological models
3.1.1 Uniaxial anisotropy
3.1.2 Second-order anisotropy of general symmetry
3.1.3 Higher-order anisotropies of nonuniaxial symmetry
3.1.4 Cubic anisotropy
3.1.5 Anisotropy coefficients
3.1.6 Anisotropy fields
3.2 Models of pair anisotropy
3.2.1 Dipolar interactions and shape anisotropy
3.2.2 Demagnetizing factors
3.2.3 Applicability of the shape-anisotropy model
3.2.4 The Néel model
3.3 Spin-orbit coupling and crystal-field interaction
3.3.1 Relativistic origin of magnetism
3.3.2 Hydrogen-like atomic wave functions
3.3.3 Crystal-field interaction
3.3.4 Quenching
3.3.5 Spin-orbit coupling
3.4 The single-ion model of magnetic anisotropy
3.4.1 Rare-earth anisotropy
3.4.2 Point-charge model
3.4.3 The superposition model
3.4.4 Transition-metal anisotropy
3.5 Other anisotropies
3.5.1 Magnetoelasticity
3.5.2 Anisotropic exchange
3.5.3 Models of surface anisotropy
Exercises
4 Micromagnetic models
4.1 Stoner-Wohlfarth model
4.1.1 Aligned Stoner-Wohlfarth particles
4.1.2 Angular dependence
4.1.3 Spin reorientations and other first-order transitions
4.1.4 Limitations of the Stoner-Wohlfarth model
4.2 Hysteresis
4.2.1 Micromagnetic free energy
4.2.2 *Magnetostatic self-interaction
4.2.3 *Exchange stiffness
4.2.4 Linearized micromagnetic equations
4.2.5 Micromagnetic scaling
4.2.6 Domains and domain walls
4.3 Coercivity
4.3.1 Nucleation
4.3.2 Pinning
4.3.3 Phenomenological coercivity modeling
4.4 Grain-boundary models
4.4.1 Boundary conditions
4.4.2 Spin structure at grain boundaries
4.4.3 Models with atomic resolution
4.4.4 Nanojunctions
Exercises
5 Finite-temperature magnetism
5.1 Basic statistical mechanics
5.1.1 Probability and partition function
5.1.2 Fluctuations and response
5.1.3 Phase transitions
5.1.4 Landau theory
5.2 Spin-Space modeling
5.2.1 Heisenberg models
5.2.2 Ising, XY, and other n-vector models
5.2.3 Other discrete and continuum spin models
5.2.4 Ionic excitations
5.2.5 Spin fluctuations in itinerant magnets
5.3 Mesan-field models
5.3.1 Mean-field Hamiltonians
5.3.2 Basic mesan-field predictions
5.3.3 Ornstein-Zernike correlations
5.3.4 Magnetization and Curie temperature
5.3.5 *Mesan-field Curie temperature of n-vector models
5.3.6 Two-sublattice magnetism
5.3.7 Merits and limitations of mesan-field models
5.4 Critical behavior
5.4.1 One-dimensional models
5.4.2 Superparamagnetic clusters
5.4.3 *Ginzburg criterion
5.4.4 Fluctuations and criticality
5.4.5 Renormalization group
5.5 Temperature dependence of anisotropy
5.5.1 Callen and Callen model
5.5.2 Rare-earth anisotropy
5.5.3 Sublattice modeling
Exercises
6 Magnetization dynamics
6.1 Quantum dynamics and resonance
6.1.1 Spin precession
6.1.2 Uniform magnetic resonance
6.1.3 Spin waves
6.1.4 Spin dynamics in inhomogeneous magnets*
6.2 Relaxation
6.2.1 Damped precession
6.2.2 *Physical origin of relaxation
6.2.3 A mechanical model
6.3 Coarse-grained models
6.3.1 Master equation
6.3.2 Fokker-Planck equations
6.3.3 Langevin models
6.4 Slow magnetization dynamics
6.4.1 Magnetic viscosity and sweep-rate dependence
6.4.2 Superposition model of magnetic viscosity
6.4.3 Asymptotic behavior*
6.4.4 Energy-barrier models
6.4.5 Linear and other laws
6.4.6 Superparamagnetism
6.4.7 Fluctuations
Exercises
7 Special topics and interdisciplinary models
7.1 Disordered magnets and spin glassess
7.1.1 Atomic disorder and electronic structure
7.1.2 *Green Functions
7.1.3 Ferromagnetic order in inhomogeneous magnets
7.1.4 Spin glasses
7.2 Soft matter, transport, and magnetism
7.2.1 Random walks, polymers, and diffusion
7.2.2 *Then 0 vector-spin model
7.2.3 Polymers and critical dimensionality
7.2.4 Percolation
7.2.5 Diffusive transport
7.2.6 Gases in magnetic metals
7.2.7 Magnetoresistance
7.2.8 Other transport phenomena involving magnetism
7.3 Bruggeman model
7.3.1 Static and dynamic properties
7.3.2 Parameterization
7.3.3 Self-consistent materials equations
7.3.4 *The response parameter g
7.3.5 *Percolation in the Bruggeman model
7.4 Nanostructures, thin films, and surfaces
7.4.1 Length scales in nanomagnetism
7.4.2 Nanomagnetic effects of atomic origin
7.4.3 Random anisotropy
7.4.4 *Cooperative magnetization processes
7.4.5 Two-phase nanostructures
7.5 Beyond magnetism
7.5.1 Metallurgy
7.5.2 Biology and medicine
7.5.3 Social sciences
Exercises
Appendix
A.1 Units and constants
A.1.1 Units systems and notation
A.1.2 Unit conversions
A.1.3 Physical constants
A.2 Mathematics
A.2.1 Linear equations
A.2.2 Eigenmode analysis
A.2.3 Real 2 x 2 matrices
A.2.4 Vector and functional calculus
A.2.5 Useful formulae
A.3 Basic quantum mechanics
A.3.1 Time dependence
A.3.2 Eigenvalues and eigenfunctions
A.3.3 Perturbation theory
A.3.4 Quantum statistics
A.3.5 Relativistic quantum mechanics
A.4 Electromagnetism
A.4.1 Maxwells equations
A.4.2 Simple magnetostatic solutions
A.4.3 Simple dynamic solutions
A.5 Magnetic materials
A.5.1 Transition-metal elements and alloys
A.5.2 Magnetic oxides
A.5.3 Rare-earth magnets
A.6 Forgotten and reinvented
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