Quantum theory of magnetism

General information on lecture course [pdf]

Part 1. Introduction [pdf]

§1.1 Basic thermodynamic notions and equations

§1.2 Magnetic susceptibility: types and units. Dynamical susceptibility.

§1.3 Dia-, Para-, Ferro- and antiferromagnets

§1.4 Magnetic spirals or a general way to set a magnetic (AFM) structure

§1.5 Dipole-dipole interaction

§1.6 Bohr - van Leeven theorem

Part 2. Magnetism of free ions [pdf]

§2.1 Spin and orbital momenta of an electron in quantum mechanics. Zeeman effect

§2.2 Hund’s rules. Spin-orbit coupling

§2.3 Diamagnetism of isolated atoms

§2.4 Van-Vleck paramagnetism

Part 3. Quasi independent ions [pdf]

§3.1 Properties of electronic orbitals. Cubic harmonics. sigma, pi, and delta bonding. Slater-Koster parameterization. LCAO

§3.2 Crystal-field splitting 

§3.3 Jahn-Teller effect 

§3.4 Breaking of Hund’s rules: Spin-state transitions 

§3.5 Breaking of Hund’s rules: Quenching of orbital momentum 

§3.6 Paramagnetism of magneto-active atoms 

§3.7 Paramagnetism in 3d transition metal compounds

Part 4. Correlation effects [pdf]

§4.1 Second quantization. Tight-binding method  

§4.2 General many-body description of a crystal. Hubbard model   

§4.3 Mott insulator. Mott-Hubbard transitions   

§4.4 Various types of insulators in condensed matter physics

Part 5. Heisenberg model [pdf1] [pdf2]

§5.1 Derivation of Heisenberg model   

§5.2 Spin models, describing exchange interaction   

§5.3 Tensor (matrix form) of Heisenberg model

§5.4 Connection between Hubbard and Heisenberg models

§5.5 Interplay between orbital and spin degrees of freedom. Goodenough-Kanamori-Anderson rules.

§5.6 Derivation of the Kugel-Khomskii model

§5.7 Superexchange interaction

§5.8 Double exchange interaction

Part 6. Different approaches for Heisenberg model

§6.1 Luttinger-Tisza method to solve classical Heisenberg model [pdf1]

§6.2 Mean-field theory for Heisenberg model [pdf2]

§6.3 Spin-wave theory for ferromagnets. Mermin-Wagner theorem [pdf3]

§6.4 Spin-wave theory for antiferromagnets. Zero-point fluctuations