Magnetism I: from the atom to the solid state

Contents 

Preface ii

 1 Magnetism in Atoms 2

1.1 Magnetism in classical physics . . . . . . . . . . . . . . . . . . 2
1.2 Magnetism in quantum mechanics . . . . . . . . . . . . . . . . 5
 1.2.1 Free electrons in a magnetic field . . . . . . . . . . . . 5
1.2.2 Electron in a magnetic field and a central potential . . 7
 1.3 The formation of the magnetic moment in atoms . . . . . . . . 9
1.3.1 Paramagnetism in Atoms . . . . . . . . . . . . . . . . . 16
1.4 Exchange interaction and the Heisenberg-Dirac-Van Vleck Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

 2 Magnetism in solids 23

2.1 Stoner-Wohlfahrt model . . . . . . . . . . . . . . . . . . . . . 23
 2.2 Friedel-Oscillations . . . . . . . . . . . . . . . . . . . . . . . . 31
 2.2.1 The interatomic exchange interaction . . . . . . . . . . 31
 2.2.2 RKKY oscillations . . . . . . . . . . . . . . . . . . . . 32
2.2.3 Anhang: mathematical details of the model . . . . . . 34

3 Magnetic order at finite temperature 39

 3.1 Coupled effective spins: an N-body problem . . . . . . . . . . 40
3.2 Mean-field approximation (MFA) . . . . . . . . . . . . . . . . 42
 3.3 Mean-field universality class . . . . . . . . . . . . . . . . . . . 45
3.4 The Landau approach . . . . . . . . . . . . . . . . . . . . . . 48
 3.5 Classical spin models . . . . . . . . . . . . . . . . . . . . . . . 53
3.6 Correlation functions . . . . . . . . . . . . . . . . . . . . . . . 61
 3.7 Landau theory of correlations . . . . . . . . . . . . . . . . . . 66

 4 Magnetic domains and domain walls 71

4.1 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Domain walls in the classical Heisenberg model . . . . . . . . 74
4.3 Continuum formalism . . . . . . . . . . . . . . . . . . . . . . . 77
4.4 Beyond the Mean-Field Approximation . . . . . . . . . . . . . 80
4.5 Finite size and superparamagnetic limit . . . . . . . . . . . . . 88
4.6 Dipolar interaction . . . . . . . . . . . . . . . . . . . . . . . . 90
4.7 Dipolar interaction in extended systems . . . . . . . . . . . . . 94
4.8 Origin of magnetic domains . . . . . . . . . . . . . . . . . . . 100


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