Quantum Theory of Magnetism and its Application to Real Materials 1102-4`QTM

1. Magnetic properties of matter versus spin and orbital quantum numbers
of electrons. Magnetism in atoms, band magnetism, and magnetism with
localized moments.

2. Magnetism with localized magnetic moment on an example of La2CuO4 (a
compound from the high temperature superconductor family):

-- strong correlations and the Hubbard model,
-- from Hubbard to effective two-dimensional spin Heisenberg model.

3. Classical versus quantum magnetism on an example of La2CuO4:

-- neglecting quantum fluctuations (Ising model) and the classical Neel
state,
-- ground state and excitations of the two-dimensional Heisenberg model,
-- collective excitations ("magnons") of the two-dimensional Heisenberg
model using linear spin wave approximation,
-- comparing with the more classical ferromagnetic model.

4. Ordered ground state and collective magnetic excitations on an
example of La2CuO4:

-- principles of neutron and x-ray scattering (elastic and inelastic),
-- comparison with experiment.

5. Properties of other spin models -- ground state and collective
excitations with a short discussion on its origin, application to
materials, and experiments:

-- going even more quantum ("spinons" in the one-dimensional
antiferromagnetic Heisenberg model),
-- introducing frustrated interactions and spin liquids (Majumdar-Ghosh
/ bilinear-biquadratic models),
-- adding orbital degrees of freedom (Kugel-Khomskii models),
-- doping spins with holes (t-J and double exchange models).

6. Summary of open problems in the field.