# Quantum theory of magnetism

**Introduction**

Lecture 0. About the lecture course [slides]

Lecture 1. Introduction, Magnetic susceptibility; Dia-, para-, ferro- and antiferromagnetism [slides]

Lecture 2. Dia-, para-, ferro- and antiferromagnetism, dipole-dipole interaction, Bohr-van Leeuwen theorem [slides]

**Magnetism of free ions**

Lecture 3. Spin, orbital, and total moments. Hund's rules, spin-orbit coupling, atomic diamagnetism [slides]

Lecture 4. Atomic diamagnetism, Van Vleck paramagnetism [slides]

**Magnetism of ions in a crystal**

Lecture 4. Spherical and cubic harmonics, crystal-field splitting in a nut shell [slides]

Lecture 5. Application of the group theory for calculation of crystal-fields [slides]

Lecture 6. The Jahn-Teller effect [slides]

Lecture 7. Intra-atomic exchange interaction, spin-state transitions, orbital moment quenching [slides]

Lecture 8. Curie law [slides]

**Correlation effects **

Lecture 9. Second quantization. Tight-binding approximation [slides]

Lecture 10. Mott insulators. Hubbard model. Metal-insulator transitions [slides]

Lecture 11. Aproximate solutions of Hubbard model. Stoner model [slides]

Lecture 12. Mean-field approximation for Hubbard model. Different types of strongly correlated insulators. Doping of Mott insulators [slides]

**Heisenberg model**

Lecture 13. Derivation of the Heisenberg model, anisotropic part of exchange interaction. Other spin models [slides]

Lecture 14. Connection between Hubbard and Heisenberg models, interplay between spin and orbital degrees of freedom, Goodenough - Kanamori - Anderson rules [slides]