# 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-like models**

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]

Lecture 15. Kugel-Khomskii model, superexchange interaction, double exchange [slides]

**Different approaches to ****Heisenberg model**

Lecture 16. Magnetic spirals, Luttinger-Tizsa method for classical Heisenberg model [slides]

Lecture 17. Mean-field approximation to Heisenberg model, Curie-Weiss law [slides]

Lecture 18. Spin-wave theory for ferromagnets, Bloch law, Mermin-Wagner theorem [slides]

Lecture 19. Spin-wave theory for antiferromagnets [slides]

**Low-dimensional magnetism **

Lecture 19. Dimers, the spin gaps, AFM chains in Ising model [slides]

Lecture 20. AFM chain in Heisenberg model, spinons, 2D Ising model [slides]

Lecture 21. Frustration, spin ice, order-by-disorder [slides]

**M****agnetism of itinerant (metallic) electrons**

Lecture 22. Fermi gas, Pauli susceptebility, Screening of Coloumb interavtion in metals [slides]

Lecture 23. Fermi liquid, Linear responce theory for non-interacting gas (random phase approximation) [slides]

Lecture 24. Susceptibility of interacting electronic gas, RKKY exchange, Fermi surface nesting [slides]

Lecture 25. Kondo effect, heavy-fermions [slides]