The Theory of Magnetism I
Statics and Dynamics
Published on 1. August 1981
Book
Hardback
XV, 300 pages
978-3-540-10611-1 (ISBN)
Description
Starting with a historical introduction to the study of magnetism - one of the oldest sciences known to man - before considering the most modern theories and observations (magnetic bubbles and soap films, effects of magnetic impurities in metals and spin glasses), this book develops the concepts and the mathematical expertise necessary to understand contemporary research in this field. Magnetic systems are important in technology and applied science, but they are also prototypes of more complex mathematical structures of great importance to theoretical physics. These connections are made repeatedly in this volume. After development of the necessary quantum theory of angular momentum and of interacting electron systems, a number of models which have been successful in the interpretation of experimental results are introduced: the Ising model, the Heisenberg model, the Stoner theory, the Kondo phenomenon, and so on. In the second edition the thorough approach and the main features which made the first edition a popular text have been retained. All important theories are worked out in detail using methods and notation that are uniform throughout. Footnotes and an extensive bibliography provide a guide to the original literature. A number of problems test the reader's skill.
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Content
1. History of Magnetism.- 1.1 Physics and Metaphysics.- 1.2 Gilbert and Descartes.- 1.3 Rise of Modern Science.- 1.4 Electrodynamics.- 1.5 The Electron.- 1.6 The Demise of Classical Physics.- 1.7 Quantum Theory.- 1.8 Modern Foundations.- 1.9 Magnetic Bubbles.- 1.10 Ultimate Thin Films.- 1.11 Dilute Magnetic Alloys.- 1.12 New Directions.- 2. Exchange.- 2.1 Exchange Equals Overlap.- 2.2 Hydrogen Molecule.- 2.3 Three Hydrogen Atoms.- 2.4 Nonorthogonality Catastrophe.- 2.5 Method of Löwdin and Carr.- 3. Quantum Theory of Angular Momentum.- 3.1 Kinetic Angular Momentum.- 3.2 Spherical Harmonics.- 3.3 Reason for Integer l and m.- 3.4 Matrices of Angular Momentum.- 3.5 Pauli Spin Matrices.- 3.6 Compounding Angular Momentum.- 3.7 Equations of Motion of Interacting Angular Momenta.- 3.8 Coupled Boson Representation.- 3.9 Rotations.- 3.10 More on Compound Angular Momentum.- 3.11 Other Representations.- 3.12 Spins One-Half.- 3.13 Spins One.- 3.14 Quadratic Forms.- 4. Many-Electron Wavefunctions.- 4.1 Slater Determinants.- 4.2 Antisymmetrization.- 4.3 States of Three Electrons.- 4.4 Eigenfunctions of Total S2 and SZ.- 4.5 Ground State of Two Electrons: A Theorem.- 4.6 Hund's Rules.- 4.7 p3 Configuration.- 4.8 p2 and p4 Configurations.- 4.9 Independent Electrons.- 4.10 Electrons in One Dimension: A Theorem.- 4.11 The Wronskian.- 4.12 Theorem in Three Dimensions.- 4.13 Ordering Theorem Versus Hund's Rule.- 4.14 Second Quantization.- 5. From Magnons to Solitons: Spin Dynamics.- 5.1 Spin Waves as Harmonic Oscillators.- 5.2 One-Magnon Eigenstates in Ferromagnets.- 5.3 Two-Magnon States and Eigenstates in Ferromagnets.- 5.4 Bound States in One Dimension.- 5.5 Bound States in Two and Three Dimensions.- 5.6 One-Magnon Eigenstates in Heitler-London Solid.- 5.7 Nonlinear Spin Wave Theory.- 5.8 Perturbation-Theoretic Correction.- 5.9 Antiferromagnetic Magnons: The One-Dimensional XY Model.- 5.10 Bethe's Solution of One-Dimensional Heisenberg Antiferromagnet.- 5.11 Linearized Antiferromagnetic Magnons.- 5.12 Nonlinearities in Antiferromagnetism.- 5.13 Ferrimagnetism.- 5.14 Effects of Surfaces on Spin Wave Amplitudes.- 5.15 Vortices.- 5.16 Solitons: Introductory Material.- 5.17 Solitary Wave Solution.- 6. Magnetism in Metals.- 6.1 Bloch and Wannier States.- 6.2 Tight-Binding.- 6.3 Weak Magnetic Properties.- 6.4 Exchange in Solids: Construction of a Model Hamiltonian.- 6.5 Perturbation-Theoretic Derivation of Heisenberg Hamiltonian.- 6.6 Heisenberg Hamiltonian in Metals.- 6.7 Ordered Magnetic Metals: Deriving the Ground State.- 6.8 Kondo Effect.- 6.9 Spin Glasses.- 6.10 Magnetism Without Localized Spins: Preliminaries.- 6.11 Low-Density Electron Gas.- 6.12 Quasi-Particles.- 6.13 Nagaoka's Model.- 6.14 Degenerate Bands and Intra-Atomic Exchange Forces..- 6.15 Magnons in Metals.- 6.16 Marginal Magnetism of Impurities.- 6.17 Correlations and Equivalence to s-d Model.- References.