This book emerged from a close collaboration of the authors which started in the fall of 2000.Early that year one of us（J.S.）had joined the Stanford faculty after spending nearly 15 years at the IBM Almaden Research Center and theother（H.C.S.）had just retired from a chair at the ETH Ziirich and come toStanford as a visiting professor.

 Introduction

1.1 Magnetism Magical yet Practical

1.2 History of Magnetism

1.3 Magnetism, Neutrons, Polarized Electrons, and X-rays

 1.3.1 Spin Polarized Electrons and Magnetism

 1.3.2 Polarized X-rays and Magnetism

1.4 Developments in the Second Half of the 20th Century

1.5 Some Thoughts about the Future

1.6 About the Present Book

Part Ⅰ Fields and Moments

 2 Electric Fields, Currents, and Magnetic Fields

2.1 Signs and Units in Magnetism

2.2 The Electric Field

2.3 The Electric Current and its Magnetic Field

2.4 High Current Densities

2.5 Magnetic and Electric Fields inside Materials

2.6 The Relation of the Three Magnetic Vectors in Magnetic Materials

 2.6.1 Stray and Demagnetizing Fields of Thin Films

 2.6.2 Applications of Stray and Demagnetizing Fields

2.7 Symmetry Properties of Electric and Magnetic Fields

 2.7.1 Parity

 2.7.2 Time Reversal

 3 Magnetic Moments and their Interactions with Magnetic Fields

3.1 The Classical Definition of the Magnetic Moment

3.2 From Classical to Quantum Mechanical Magnetic Moments

 3.2.1 The Bohr Magneton

 3.2.2 Spin and Orbital Magnetic Moments

3.3 Magnetic Dipole Moments in an External Magnetic Field

3.4 The Energy of a Magnetic Dipole in a Magnetic Field

3.5 The Force on a Magnetic Dipole in an Inhomogeneous Field

 3.5.1 The Stern-Gerlach Experiment

 3.5.2 The Mott Detector

 3.5.3 Magnetic Force Microscopy

3.6 The Torque on a Magnetic Moment in a Magnetic Field

 3.6.1 Precession of Moments

 3.6.2 Damping of the Precession

 3.6.3 Magnetic Resonance

3.7 Time-Energy Correlation

 3.7.1 The Heisenberg Uncertainty Principle

 3.7.2 Classical Spin Precession

 3.7.3 Quantum Mechanical Spin Precession

 4 Time Dependent Fields

4.1 Overview

4.2 Basic Concepts of Relativistic Motion

 4.2.1 Length and Time Transformations Between Inertial Systems

 4.2.2 Electric and Magnetic Field Transformations between Inertial Systems

4.3 Fields of a Charge in Uniform Motion Velocity Fields

 4.3.1 Characteristics of Velocity Fields

 4.3.2 Creation of Large Currents and Magnetic Fields

 4.3.3 Creation of Ultrashort Electron Pulses and Fields

 4.3.4 The Temporal Nature of Velocity Fields

4.4 Acceleration Fields Creation of EM Radiation

 4.4.1 Polarized X-rays Synchrotron Radiation

 4.4.2 Brighter and Shorter X-ray Pulses rom Undulators to Free Electron Lasers

 5 Polarized Electromagnetic Waves

5.1 Maxwell's Equations and their Symmetries

5.2 The Electromagnetic Wave Equation

5.3 Intensity, Flux, Energy, and Momentum of EM Waves

5.4 The Basis States of Polarized EM Waves

 5.4.1 Photon Angular Momentum

 5.4.2 Linearly Polarized Basis States

 5.4.3 Circularly Polarized Basis States

 5.4.4 Chirality and Angular Momentum of Circular EM Waves

 5.4.5 Summary of Unit Polarization Vectors

5.5 Natural and Elliptical Polarization

 5.5.1 Natural Polarization

 5.5.2 Elliptical Polarization

 5.5.3 The Degree of Photon Polarization

5.6 Transmission of EM Waves through Chiral and Magnetic Media

Part Ⅱ History and Concepts of Magnetic Interactions

 6  Exchange, Spin-Orbit and Zeeman Interactions

6.1 Overview

6.2 The Spin Dependent Atomic Hamiltonian or Pauli Equation

 6.2.1 Independent Electrons in a Central Field

 6.2.2 Interactions between two Particles - Symmetrization Postulate and Exclusion Principle

6.3 The Exchange Interaction

 6.3.1 Electron Exchange in Atoms

 6.3.2 Electron Exchange in Molecules

 6.3.3 Magnetism and the Chemical Bond

 6.3.4 From Molecules to Solids

 6.3.5 The Heisenberg Hamiltonian

 6.3.6 The Hubbard Hamiltonian

 6.3.7 Heisenberg and Hubbard Models for H2

 6.3.8 Summary and Some General Rules for Electron Exchange

6.4 The Spin-Orbit Interaction

 6.4.1 Fine Structure in Atomic Spectra

 6.4.2 Semiclassical Model for the Spin-Orbit Interaction

 6.4.3 The Spin-Orbit Hamiltonian

 6.4.4 Importance of the Spin-Orbit Interaction

6.5 Hund's Rules

6.6 The Zeeman Interaction

 6.6.1 History and Theory of the Zeeman Effect

 6.6.2 Zeeman Versus Exchange Splitting of Electronic States

 6.6.3 Importance of the Zeeman Interaction

 7 Electronic and Magnetic Interactions in Solids

7.1 Chapter Overview

7.2 Localized versus Itinerant Magnetism The Role of the Centrifugal Potential

7.3 The Relative Size of Interactions in Solids

7.4 The Band Model of Ferromagnetism

 7.4.1 The Puzzle of the Broken Bohr Magneton Numbers

 7.4.2 The Stoner Model

 7.4.3 Origin of Band Structure

 7.4.4 Density Functional Theory

7.5 Ligand Field Theory

 7.5.1 Independent-Electron Ligand Field Theory

 7.5.2 Multiplet Ligand Field Theory

7.6 The Importance of Electron Correlation and Excited States

 7.6.1 Why are Oxides often Insulators?

 7.6.2 Correlation Effects in Rare Earths and Transition Metal Oxides

 7.6.3 From Delocalized to Localized Behavior Hubbard and LDA+U Models

7.7 Magnetism in Transition Metal Oxides

 7.7.1 Superexchange

 7.7.2 Double Exchange

 7.7.3 Colossal Magnetoresistance

 7.7.4 Magnetism of Magnetite

7.8 RKKY Exchange

 7.8.1 Point-like Spins in a Conduction Electron Sea

 7.8.2 Metallic Multilayers

7.9 Spin-Orbit Interaction Origin of the Magnetocrystalline Anisotropy

 7.9.1 The Bruno Model

 7.9.2 Description of Anisotropic Bonding

 7.9.3 Bonding, Orbital Moment, and Magnetocrystalline Anisotropy

Part Ⅲ Polarized Electron and X-Ray Techniques

 8 Polarized Electrons and Magnetism

8.1 Introduction

8.2 Generation of Spin-Polarized Electron Beams

 8.2.1 Separation of the Two Spin States

 8.2.2 The GaAs Spin-Polarized Electron Source

8.3 Spin-Polarized Electrons and Magnetic Materials Overview of Experiments

8.4 Formal Description of Spin-Polarized Electrons

 8.4.1 Quantum Behavior of the Spin

 8.4.2 Single Electron Polarization in the Pauli Spinor Formalism

 8.4.3 Description of a Spin-Polarized Electron Beam

8.5 Description of Spin Analyzers and Filters

 8.5.1 Incident Beam Polarization Spin Analyzer

 8.5.2 Transmitted Beam Polarization Spin Filter

 8.5.3 Determination of Analyzer Parameters

8.6 Interactions of Polarized Electrons with Materials

 8.6.1 Beam Transmission through a Spin Filter

 8.6.2 The Fundamental Interactions of a Spin-Polarized Beam with Matter

 8.6.3 Interaction of Polarized Electrons with Magnetic Materials Poincare's Sphere

8.7 Link Between Electron Polarization and Photon Polarization

 8.7.1 Photon Polarization in the Vector Field Representation

 8.7.2 Photon Polarization in the Spinor Representation

 8.7.3 Transmission of Polarized Photons through Magnetic Materials Poincare Formalism

 8.7.4 X-ray Faraday Effect and Poincare Formalism

 8.7.5 Poincare and Stokes Formalism

 9 Interactions of Polarized Photons with Matter

9.1 Overview

9.2 Terminology of Polarization Dependent Effects

9.3 SemiClassical Treatment of X-ray Scattering by Charges and Spins

 9.3.1 Scattering by a Single Electron

 9.3.2 Scattering by an Atom

9.4 SemiClassical Treatment of Resonant Interactions

 9.4.1 X-ray Absorption

 9.4.2 Resonant Scattering

 9.4.3 Correspondence between Resonant Scattering and Absorption

 9.4.4 The Kramers-Kronig Relations

9.5 Quantum-Theoretical Concepts

 9.5.1 One-Electron and Configuration Pictures of X-ray Absorption

 9.5.2 Fermi's Golden Rule and Kramers-Heisenberg Relation

 9.5.3 Resonant Processes in the Electric'Dipole Approximation

 9.5.4 The Polarization Dependent Dipole Operator

 9.5.5 The Atomic Transition Matrix Element

 9.5.6 Transition Matrix Element for Atoms in Solids

9.6 The Orientation-Averaged Intensity Charge and Magnetic Moment Sum Rules

 9.6.1 The Orientation-Averaged Resonance Intensity

 9.6.2 Derivation of the Intensity Sum Rule for the Charge

 9.6.3 Origin of the XMCD Effect

 9.6.4 Two-Step Model for the XMCD Intensity

 9.6.5 The Orientation Averaged Sum Rules

9.7 The Orientation-Dependent Intensity Charge and Magnetic Moment Anisotropies

 9.7.1 Concepts of Linear Dichroism

 9.7.2 X-ray Natural Linear Dichroism

 9.7.3 Theory of X-ray Natural Linear Dichroism

 9.7.4 XNLD and Quadrupole Moment of the Charge

 9.7.5 X-ray Magnetic Linear Dichroism

 9.7.6 Simple Theory of X-ray Magnetic Linear Dichroism

 9.7.7 XMLD of the First and Second Kind

 9.7.8 Enhanced XMLD through Multiplet Effects

 9.7.9 The Orientation-Dependent Sum Rules

9.8 Magnetic Dichroism in X-ray Absorption and Scattering

 9.8.1 The Resonant Magnetic Scattering Intensity

 9.8.2 Link of Magnetic Resonant Scattering and Absorption

 10 X-rays and Magnetism Spectroscopy and Microscopy

10.1 Introduction

10.2 Overview of Different Types of X-ray Dichroism

10.3 Experimental Concepts of X-ray Absorption Spectroscopy

 10.3.1 General Concepts

 10.3.2 Experimental Arrangements

 10.3.3 Quantitative Analysis of Experimental Absorption Spectra

 10.3.4 Some Important Experimental Absorption Spectra

 10.3.5 XMCD Spectra of Magnetic Atoms From Thin Films to Isolated Atoms

 10.3.6 Sum Rule Analysis of XMCD Spectra Enhanced Orbital Moments in Small Clusters

 10.3.7 Measurement of Small Spin and Orbital Moments Pauli Paramagnetism

10.4 Magnetic Imaging with X-rays

 10.4.1 X-ray Microscopy Methods

 10.4.2 Lensless Imaging by Coherent Scattering

 10.4.3 Overview of Magnetic Imaging Results

Part Ⅳ Properties of and Phenomena in the Ferromagnetic Metals

 11 The Spontaneous Magnetization, Anisotropy, Domains

11.1 The Spontaneous Magnetization

 11.1.1 Temperature Dependence of the Magnetization in the Molecular Field Approximation

 11.1.2 Curie Temperature in the Weiss-Heisenberg Model

 11.1.3 Curie Temperature in the Stoner Model

 11.1.4 The Meaning of "Exchange" in the Weiss-Heisenberg and Stoner Models

 11.1.5 Thermal Excitations Spin Waves

 11.1.6 Critical- Fluctuations

11.2 The Magnetic Anisotropy

 11.2.1 The Shape Anisotropy

 11.2.2 The Magneto-Crystalline Anisotropy

 11.2.3 The Discovery of the Surface Induced Magnetic Anisotropy

11.3 The Magnetic Microstructure Magnetic Domains and Domain Walls

 11.3.1 Ferromagnetic Domains

 11.3.2 Antiferromagnetic Domains

11.4 Magnetization Curves and Hysteresis Loops

11.5 Magnetism in Small Particles

 11.5.1 Neel and Stoner-Wohlfarth Models

 11.5.2 Thermal Stability

 12 Magnetism of Metals

12.1 Overview

12.2 Band Theoretical Results for the Transition Metals

 12.2.1 Basic Results for the Density of States

 12.2.2 Prediction of Magnetic Properties

12.3 The Rare Earth Metals Band Theory versus Atomic Behavior

12.4 Spectroscopic Tests of the Band Model of Ferromagnetism

 12.4.1 Spin Resolved Inverse Photoemission

 12.4.2 Spin Resolved Photoemission

12.5 Resistivity of Transition Metals

 12.5.1 Conduction in Nonmagnetic Metals

 12.5.2 The Two Current Model

 12.5.3 Anisotropic Magnetoresistance of Metals

12.6 Spin Conserving Electron Transitions in Metals

 12.6.1 Spin Conserving Transitions and the Photoemission Mean Free Path

 12.6.2 Determination of the Spin-Dependent Mean Free Path using the Magnetic Tunnel Transistor

 12.6.3 Probability of Spin-Conserving relative to Spin-Non-Conserving Transitions

 12.6.4 The Complete Spin-Polarized Transmission Experiment

12.7 Transitions Between Opposite Spin States in Metals

 12.7.1 Classification of Transitions Between Opposite Spin States

 12.7.2 The Detection of Transitions between Opposite Spin States

12.8 Remaining Challenges

Part Ⅴ Topics in Contemporary Magnetism

 13 Surfaces and Interfaces of Ferromagnetic Metals

13.1 Overview

13.2 Spin-Polarized Electron Emission from Ferromagnetic Metals,

 13.2.1 Electron Emission into Vacuum

 13.2.2 Spin-Polarized Electron Tunneling between Solids

 13.2.3 Spin-Polarized Electron Tunneling Microscopy

13.3 Reflection of Electrons from a Ferromagnetic Surface

 13.3.1 Simple Reflection Experiments

 13.3.2 The Complete Reflection Experiment

13.4 Static Magnetic Coupling at Interfaces

 13.4.1 Magnetostatic Coupling

 13.4.2 Direct Coupling between Magnetic Layers

 13.4.3 Exchange Bias

 13.4.4 Induced Magnetism in Paramagnets and Diamagnets

 13.4.5 Coupling of Two Ferromagnets across a Nonmagnetic Spacer Layer

 14 Electron and Spin Transport

14.1 Currents Across Interfaces Between a Ferromagnet and a Noumagnet

 14.1.1 The Spin Accumulation Voltage in a Transparent Metallic Contact

 14.1.2 The Diffusion Equation for the Spins

 14.1.3 Spin Equilibration Processes, Distances and Times

 14.1.4 Giant Magneto-Resistance (GMR)

 14.1.5 Measurement of Spin Diffusion Lengths in Nonmagnet

 14.1.6 Typical Values for the Spin Accumulation Voltage,Boundary Resistance and GMR Effect

 14.1.7 The Important Role of Interfaces in GMR

14.2 Spin-Injection into a Ferromagnet

 14.2.1 Origin and Properties of Spin Injection Torques

 14.2.2 Switching of the Magnetization with Spin Currents Concepts

 14.2.3 Excitation and Switching of the Magnetization with Spin Currents Experiments

14.3 Spin Currents in Metals and Semiconductors

14.4 Spin-Based Transistors and Amplifiers

 15 Ultrafast Magnetization Dynamics

15.1 Introduction

15.2 Energy and Angular Momentum Exchange between Physical Reservoirs

 15.2.1 Thermodynamic Considerations

 15.2.2 Quantum Mechanical Considerations The Importance of Orbital Angular Momentum

15.3 Spin Relaxation and the Pauli Susceptibility

15.4 Probing the Magnetization after Laser Excitation

 15.4.1 Probing with Spin-Polarized Photoelectron Yield

 15.4.2 Probing with Energy Resolved Photoelectrons With or Without Spin Analysis

 15.4.3 Probing with the Magneto-Optic Kerr Effect

15.5 Dynamics Following Excitation with Magnetic Field Pulses

 15.5.1 Excitation with Weak Magnetic Field Pulses

 15.5.2 Excitation of a Magnetic Vortex

15.6 Switching of the Magnetization

 15.6.1 Precessional Switching of the In-Plane Magnetization

 15.6.2 Precessional Switching of the Magnetization for Perpendicular Recording Media

 15.6.3 Switching by Spin Injection and its Dynamics

 15.6.4 On the Possibility of All-Optical Switching

 15.6.5 The Hiibner Model of All-Optical Switching

 15.6.6 All-Optical Manipulation of the Magnetization

15.7 Dynamics of Antiferromagnetic Spins

Part Ⅵ Appendices

 Appendices

A.1 The International System of Units (SI)

A.2 The Cross Product

A.3 s, p, and d Orbitals

A.4 Spherical Tensors

A.5 Sum Rules for Spherical Tensor Matrix Elements

A.6 Polarization Dependent Dipole Operators

A.7 Spin-Orbit Basis Functions for p and d Orbitals

A.8 Quadrupole Moment and the X-ray Absorption Intensity

A.9 Lorentzian Line Shape and Integral

A.10 Ganssian Line Shape and Its Fourier Transform

A.11 Gaussian Pulses, Half-Cycle Pulses and Transforms

References

Index