Magnetism in Condensed Matter

Transcription

1 Magnetism in Condensed Matter STEPHEN BLUNDELL Department of Physics University of Oxford OXFORD 'UNIVERSITY PRESS

2 Contents 1 Introduction 1.1 Magnetic moments Magnetic moments and angular momentum Precession The Bohr magneton Magnetization and field Classical mechanics and magnetic moments Canonical momentum The Bohr van Leeuwen theorem Quantum mechanics of spin Orbital and spin angular momentum Pauli spin matrices and spinors Raising and lowering operators The coupling of two spins 13 2 Isolated magnetic moments An atom in a magnetic field Magnetic susceptibility Diamagnetism Paramagnetism Semiclassical treatment of paramagnetism Paramagnetism for J = The Brillouin function Van Vleck paramagnetism The ground state of an ion and Hund's rules Fine structure Hund's rules L S and j j coupling Adiabatic demagnetization Nuclear spins Hyperfine structure 40 3 Environments Crystal fields Origin of crystal fields Orbital quenching The Jahn Teller effect Magnetic resonance techniques Nuclear magnetic resonance 52

3 x Contents Electron spin resonance Mössbauer spectroscopy Muon-spin rotation 4 Interactions 4.1 Magnetic dipolar interaction 4.2 Exchange interaction Origin of exchange Direct exchange Indirect exchange in ionic solids: superexchange Indirect exchange in metals Double exchange Anisotropic exchange interaction Continuum approximation 5 Order and magnetic structures 5.1 Ferromagnetism The Weiss model of a ferromagnet Magnetic susceptibility The effect of a magnetic field Origin of the molecular field 5.2 Antiferromagnetism Weiss model of an antiferromagnet Magnetic susceptibility The effect of a strong magnetic field Types of antiferromagnetic order 5.3 Ferrimagnetism 5.4 Helical order 5.5 Spin glasses 5.6 Nuclear ordering 5.7 Measurement of magnetic order Magnetization and magnetic susceptibility Neutron scattering Other techniques 6 Order and broken symmetry 6.1 Broken symmetry 6.2 Models Landau theory of ferromagnetism Heisenberg and Ising models The one-dimensional Ising model (D 1, d = 1) The two-dimensional Ising model (D = 1, d = 2) 6.3 Consequences of broken symmetry 6.4 Phase transitions 6.5 Rigidity 6.6 Excitations Magnons The Bloch T 3/2 law The Mermin--Wagner Berezinskii theorem

4 Contents xi Measurement of spin waves Domains Domain walls Magnetocrystalline anisotropy Domain, wall width Domain formation Magnetization processes Domain wall observation Small magnetic particles The Stoner Wohlfarth model Soft and hard materials Magnetism in metals The free electron model Pauli paramagnetism Elementary derivation Crossover to localized behaviour Experimental techniques Spontaneously spin-split bands Spin-density functional theory 147 7,5 Landau levels Landau diamagnetism Magnetism of the electron gas Paramagnetic response of the electron gas Diamagnetic response of the electron gas The RKKY interaction Excitations in the electron gas Spin-density waves The Kondo effect The Hubbard model Neutron stars Competing interactions and low dimensionality Frustration Spin glasses Superparamägnetism One-dimensional magnets Spin chains Spinons Haldane chains Spin-Peierls transition Spin ladders Two-dimensional magnets Quantum phase transitions Thin films and multilayers Magneto-optics Magnetoresistance Magnetoresistance of ferromagnets Anisotropic magnetoresistance 1

5 xii Contents Giant magnetoresistance Exchange anisotropy Colossal magnetoresistance Hall effect 8.10 Organic and molecular magnets 8.11 Spin electronics A Units in electromagnetism B Electromagnetism B.1 Magnetic moments B.2 Maxwell's equations in free space B.3 Free and bound currents B.4 Maxwell's equations in matter B.5 Boundary conditions C Quantum and atomic physics 202 C.1 Quantum mechanics 202 C.2 Dirac bra and ket notation 203 C.3 The Bohr model 204 C.4 Orbital angular momentum 205 C.5 The hydrogen atom 206 C.6 The g-factor 207 C.7 d orbitals 209 C.8 The spin orbit interaction 210 C.9 Lande g-factor 210 C.10 Perturbation theory 211 D Energy in magnetism and demagnetizing fields 214 D.1 Energy 214 D.2 Demagnetizing factors 214 D.3 A ferromagnet of arbitrary shape 216 E Statisticat mechanics 219 E.1 The partition function and thermodynamic functions 219 E.2 The equipartition theorem 220 F Answers and hints to selected problems 222 G Symbols, constants and useful equations 230 Index 234