电子关联和磁性

Preface

1 Introduction

1.1 Magnetism and Other Effects of Electron-Electron Interaction

1.2 Sources of Magnetic Fields

1.3 Getting Acquainted: Magnetite

1.3.1 Charge States

1.3.2 Spin States

1.3.3 Charge Ordering

1.4 Variety of Correlated Systems: An Outline of the Course

2 Atoms, Ions, and Molecules

2.1 Hydrogen Atom in a Magnetic Field

2.1.1 Non-Relativistic Treatment

Motion in a Magnetic Field

Zeeman Effect (I)

2.1.2 Relativistic Effects

Spin-Orbit Coupling

Zeeman Effect (II)

Problem 2.1

2.2 Direct Exchange

Problem 2.2

2.3 Many-Electron Ions

Problem 2.3

2.3.1 Coupling to the Magnetic Field

Digression: The Bohr-Van Leeuwen Theorem

2.3.2 Hund's Rules

Problem 2.4

2.4 Paramagnetism and Diamagnetism

2.4.1 Paramagnetic Susceptibility

Magnetization Curve

Problems 2.5-2.8

2.4.2 Diamagnetism

Digression: Superstrong Fields

2.5 Hydrogen Molecule

2.5.1 Direct Exchange in Non-Orthogonal Orbitals

2.5.2 Kinetic Exchange

2.5.3 Molecular Orbitals versus Heitler-London

Solutions to the Problems

3 Crystal Field Theory

3.1 Incomplete Shells in an Anisotropic Environment: CrystaIFields

3.2 The Role of Symmetry Arguments in Quantum Mechanics

3.2.1 Irreducible Representations

3.3 The Octahedral Group

Problems 3.1-3.2

3.4 Symmetry Properties of Atomic States

3.5 Splitting of a d-Level in Cubic Field

3.5.1 Quenching the Orbital Angular Momentum

3.5.2 Partial Restoration ofOrbitalMomentum by Spin

Orbit Coupling

Problems 3.3-3.4

3.5.3 High-Spin versus Low-Spin States

3.6 Jahn-Teller Effect

3.7 Time Reversallnvariance

3.8 The f2 Configuration

3.8.1 Cubic Crystal Field

3.8.2 Tetragonal Crystal Field

3.8.3 Metamagnetic Transition

3.8.4 Exchange Induced Magnetism

Problems 3.5-3.6

3.9 DoubleGroups

……

4 Mott Transition and Hubbard Model

5 Mott Insulators

6 Heisenberg Magnets

7 Itinerant Electron Magnetism

8 Ferromagnetism in Hubbard Models

9 The Gutzwiller Variational Method

10 The Correlated Metallic State

11 Mixed Valence and Heavy Fermions

12 Quantum Hall Effect

A Hydrogen Atom

B Single-Spin-Flip Ansatz

C Gutzwiller Approximation

D Schrieffer-Wolff Transformation

Bibliography

Index

The one-term, 4-hours-a-week course on magnetism presented a chal-lenge known to all physicists in the field: research interests in the past half a century have been dominated by the effects of strong electron-electron interaction, while standard solid state physics textbooks re-main within the bounds of band theory which is a suitable language for weakly correlated systems, and then add a chapter on Heisenberg magnets whose very existence is in contradiction with the rest of the material, and gets never properly justified. The usual way of clarifying these matters is to go through a formal education in many-body theory, and to learn about strong correlation effects piecemeal from its applica-tions (and breakdowns). This, however, is usually the beginning of the professional career of a theoretician, and it may not be the most recom-mendable approach for others, One takes a long time to discover that there is a unified, non-formal way of thinking about strong correlation phenomena that has long been shared by experimentalists and theoreti-cians in the field; it can be called elementary and should be accessible to all - but it cannot be found in the well-known textbooks.