# 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, Pascal constants, Van Vleck paramagnetism [slides]

Magnetism of ions in a crystal

Lecture 5. Spherical and cubic harmonics, crystal-field splitting in a nut shell, the Jahn-Teller effect [slides]

Lecture 6. Intra-atomic exchange interaction, spin-state transitions, orbital moment quenching [slides]

Lecture 7. Curie law, Brillouin function, imprtance of orbital moment quenching [slides]

Correlation effects

Lecture 8. Second quantization. Tight-binding approximation [slides]

Lecture 9. Mott insulators. Hubbard model. Metal-insulator transitions. Spectral function in Hubbard model. Phase diagram of non-degenerate Hubbard model on the square lattice. Different types of insulators (band, Mott, Slater, charge-transfer). [slides]

Heisenberg-like models

Lecture 10. Derivation of the Heisenberg model, symmtric and antisymmetric exchanges, Dzyaloshinskii-Moriya vector. Heisenberg's misperception. Different spin models. [slides]

Lecture 11. Exchange due to tunneling of electrons. Goodenough - Kanamori - Anderson rules. [slides]

Lecture 12. Kugel-Khomskii model. Superexchange interaction. Double exchange. [slides]

Different approaches to Heisenberg model

Lecture 13. Magnetic spirals, Luttinger-Tizsa method for classical Heisenberg model. [slides]

Lecture 14. Mean-field approximation to Heisenberg model. Curie-Weiss law. Critical indexes. [slides]

Lecture 15. Spin-wave theory for ferromagnets. [slides]

Lecture 16. Spin-wave theory for antiferromagnets. [slides]

Low-dimensional magnetism

Lecture 16. Dimers, spin gaps, Schottky anomaly. [slides]

Lecture 17. AFM chains in Ising model. AFM chain in Heisenberg model. Spinons, Haldane chains. 2D Ising. [slides]

Lecture 18. Berezinskii-Kosterlitz-Thauless transiton. Frustrations, spin liquids. Kitaev model. Single-ion anisotropy. Spin ice. Magnetic monopoles. Order-by-disorder. [slides]

Magnetism of itinerant (metallic) electrons

Lecture 19. Fermi gas. Pauli susceptebility. Screening of Coloumb interavtion in metals. Fermi-liquid. [slides]

Lecture 20. Linear response theory, Lindhard's formula. [slides]

Lecture 21. RKKY exchange. Nesting of the Fermi surface. Peierls transition, spin and charge density waves (SDW and CDW). [slides]

Lecture 22. Susceptibility of interacting electronic "gas". Generalized Stoner criterium. Mechanism of spin density waves (SDW) formation. [slides]

Lecture 23. Susceptibility of interacting electronic "gas". Generalized Stoner criterium. Mechanism of spin density waves (SDW) formation [slides]

Strong correlations in metallic systems

Lecture 26. Periodic and impurity Anderson models, Vonskovskii s-d and Kondo models [slides]

Lecture 27. Kondo problem, Abrikosov-Suhl resonance. Heavy fermions [slides]

Lecture 28. Mixed-valence compounds. Hybridization gap, Kondo insulators. Doniach phase diagram [slides]