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Quantum Theory of Magnetism 2010 ed. [Kietas viršelis]

  • Formatas: Hardback, 752 pages, aukštis x plotis: 235x155 mm, weight: 2740 g, 148 Illustrations, black and white; XIII, 752 p. 148 illus., 1 Hardback
  • Išleidimo metai: 15-Oct-2009
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540854150
  • ISBN-13: 9783540854159
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 752 pages, aukštis x plotis: 235x155 mm, weight: 2740 g, 148 Illustrations, black and white; XIII, 752 p. 148 illus., 1 Hardback
  • Išleidimo metai: 15-Oct-2009
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540854150
  • ISBN-13: 9783540854159
Kitos knygos pagal šią temą:
Magnetism is one of the oldest and most fundamental problems of Solid State Physics although not being fully understood up to now. On the other hand it is one of the hottest topic of current research. Practically all branches of modern technological developments are based on ferromagnetism, especially what concerns information technology. The book, written in a tutorial style, starts from the fundamental features of atomic magnetism, discusses the essentially single-particle problems of dia- and paramagnetism, in order to provide the basis for the exclusively interesting collective magnetism (ferro, ferri, antiferro). Several types of exchange interactions, which take care under certain preconditions for a collective ordering of localized or itinerant permanent magnetic moments, are worked out. Under which conditions these exchange interactions are able to provoke a collective moment ordering for finite temperatures is investigated within a series of theoretical models, each of them considered for a very special class of magnetic materials. At the end some of the most interesting modern activities on collective magnetism are critically commented on.The book is written in a tutorial style appropriate for those who want to learn magnetism and eventually to do research work in this field. Numerous exercises with full solutions for testing own attempts will help to a deep understanding of the main aspects of collective ferromagnetism.
Basic Facts
1(24)
Macroscopic Maxwell Equations
1(6)
Magnetic Moment and Magnetization
7(6)
Susceptibility
13(2)
Classification of Magnetic Materials
15(4)
Diamagnetism
15(1)
Paramagnetism
15(2)
Collective Magnetism
17(2)
Elements of Thermodynamics
19(3)
Problems
22(3)
Atomic Magnetism
25(60)
Hund's Rules
25(3)
Russell-Saunders (LS-) Coupling
25(2)
Hund's Rules for LS Coupling
27(1)
Dirac Equation
28(6)
Electron Spin
34(6)
Spin-Orbit Coupling
40(5)
Wigner-Eckart Theorem
45(11)
Rotation
45(2)
Rotation Operator
47(1)
Angular Momentum
48(2)
Rotation Matrices
50(2)
Tensor Operators
52(1)
Wigner-Eckart Theorem
53(2)
Examples of Application
55(1)
Electron in an External Magnetic Field
56(6)
Nuclear Quadrupole Field
62(5)
Hyperfine Field
67(5)
Magnetic Hamiltonian of the Atomic Electron
72(2)
Many-Electron Systems
74(7)
Coulomb Interaction
74(1)
Spin-Orbit Coupling
75(1)
Further Couplings
76(5)
Problems
81(4)
Diamagnetism
85(52)
Bohr-van Leeuwen Theorem
85(2)
Larmor Diamagnetism (Insulators)
87(3)
The Sommerfeld Model of a Metal
90(14)
Properties of the Model
91(8)
Sommerfeld Expansion
99(5)
Landau Diamagnetism (Metals)
104(17)
Free Electrons in Magnetic Field (Landau Levels)
104(5)
Grand Canonical Potential of the Conduction Electrons
109(8)
Susceptibility of the Conduction Electrons
117(4)
The de Haas-Van Alphen Effect
121(13)
Oscillations in the Magnetic Susceptibility
121(3)
Electron Orbits in Magnetic Field
124(4)
Physical Origin of the Oscillations
128(3)
Onsager Argument
131(3)
Problems
134(3)
References
136(1)
Paramagnetism
137(38)
Pauli Spin Paramagnetism
138(17)
``Primitive'' Theory of the Pauli Spin Paramagnetism
138(3)
Temperature Corrections
141(1)
Exchange Corrections
142(13)
Paramagnetism of the Localized Electrons
155(16)
Weak Spin-Orbit Interaction
158(6)
Strong Spin-Orbit Coupling
164(2)
Van Vleck Paramagnetism
166(5)
Problems
171(4)
References
174(1)
Exchange Interaction
175(58)
Phenomenological Theories
178(6)
The Exchange Field
178(2)
Weiss Ferromagnet
180(4)
Direct Exchange Interaction
184(16)
Pauli's Principle
184(4)
The Heitler-London Method
188(7)
Dirac's Vector Model
195(5)
Indirect Exchange Interaction
200(26)
Rudermann-Kittel-Kasuya-Yosida (RKKY) Interaction
200(9)
Superexchange
209(8)
Double Exchange
217(9)
Problems
226(7)
References
231(2)
Ising Model
233(40)
The Model
234(2)
The One Dimensional Ising Model
236(9)
Spontaneous Magnetization
236(4)
One Dimensional Ising Model in External Field
240(5)
The Phase Transition of Two-Dimensional Ising Model
245(9)
The Method of Proof
245(2)
Finite Ising Lattice with Special Boundary Conditions
247(1)
Probabilities
247(2)
Realization Possibilities for the Polygons
249(3)
Magnetization of the Finite Lattice
252(1)
Thermodynamic Limit
252(2)
The Free Energy of the Two-Dimensional Ising Model
254(16)
High-Temperature Expansion
255(1)
Spin Products as Graphs
256(1)
Loops
257(4)
Directed Paths
261(3)
Matrix M1
264(2)
Free Energy per Spin
266(1)
Curie Temperature Tc
267(1)
Specific Heat
268(1)
Spontaneous Magnetization
269(1)
Problems
270(3)
References
271(2)
Heisenberg Model
273(114)
Model Hamiltonian
273(10)
Spin Operators
273(6)
Model Extensions
279(4)
Exact Statements
283(13)
Mermin-Wagner Theorem
283(8)
One-Magnon States of a Ferromagnet
291(5)
Molecular Field Approximations
296(26)
Ferromagnet
297(6)
Antiferromagnet
303(14)
Ferrimagnet
317(5)
Spin Waves
322(29)
Linear Spin Wave Theory for the Isotropic Ferromagnet
322(7)
``Renormalized'' Spin Waves
329(7)
Harmonic Approximation for Antiferromagnets
336(9)
Harmonic Approximation for a Ferromagnet with Dipolar Interaction
345(6)
Thermodynamics of S = 1/2 Ferromagnet
351(10)
Tyablikov Decoupling
351(3)
Spontaneous Magnetization
354(5)
Thermodynamic Potentials
359(2)
Thermodynamics of S ≥ 1/2 Ferromagnets
361(20)
Green's Functions
361(2)
Spontaneous Magnetization
363(8)
The Callen Method
371(10)
Problems
381(6)
References
386(1)
Hubbard Model
387(104)
Introduction
387(1)
Model for Band Magnets
388(7)
Solid as a Many-Body System
388(1)
Electrons in Narrow Energy Bands
389(4)
Hubbard Model
393(2)
Stoner Model
395(14)
Stoner Ansatz (Ferromagnet)
395(2)
Stoner Excitations
397(1)
Magnetic Phase Transition
398(7)
Static Susceptibility
405(4)
Exact Statements and General Properties
409(42)
Mermin-Wagner Theorem
410(5)
The Infinitely Narrow Band
415(5)
The Two-Site Model
420(7)
The Exactly Half-Filled Band
427(4)
Strong-Coupling Regime
431(6)
Spectral Moments
437(2)
High-Energy Expansions
439(2)
Weak-Coupling Regime
441(3)
Infinite Dimensions
444(4)
Effective ``impurity''-Problem
448(3)
Magnetism and Electronic Correlations
451(34)
Hubbard-I Approximation
451(3)
Interpolation Method
454(1)
Correlation Effects and Ferromagnetism
455(2)
Criterion for Ferromagnetism
457(4)
Static Susceptibility and Ferromagnetism
461(3)
Spin-Dependent Band Shift
464(6)
Quasiparticle Damping
470(5)
Dynamical Mean Field Theory
475(4)
Modified Perturbation Theory
479(3)
Curie Temperature, Magnetization and Static Susceptibility
482(3)
Problems
485(6)
References
490(1)
A Second Quantization
491(24)
Identical Particles
492(2)
Continuous Fock Representation
494(7)
Symmetrized Many-Particle States
494(1)
Construction Operators
495(2)
Many-Body Operators
497(4)
Discrete Fock Representation (Occupation Number Representation)
501(5)
Symmetrized Many-Particle States
501(2)
Construction Operators
503(3)
Examples
506(5)
Bloch Electrons
506(2)
Wannier Electrons
508(1)
Density Operator
509(1)
Coulomb Interaction
510(1)
Problems
511(4)
B The Method of Green's Functions
515(48)
Linear Response Theory
515(8)
Kubo Formula
515(3)
Magnetic Susceptibility
518(2)
Dielectric Function
520(3)
Spectroscopies and Spectral Densities
523(5)
Double-Time Green's Functions
528(17)
Definitions and Equations of Motion
528(3)
Spectral Representations
531(3)
Spectral Theorem
534(2)
Spectral Moments
536(1)
Kramer's-Kronig Relations
537(2)
Simple Applications
539(6)
The Quasiparticle Concept
545(14)
Interacting Electrons
545(3)
Electronic Self-energy
548(3)
Quasiparticles
551(4)
Quasiparticle Density of States
555(3)
Thermodynamics
558(1)
Problems
559(4)
C Solutions to Problems
563(180)
Index 743