In this chapter we will describe the properties of magnetic thin films in the framework of a generalised Heisenberg model for localized magnetic moments with additional magnetostatic interactions and uniaxial anisotropy.

Here are the elements of the exchange tensor between the spins located at sites i and j, and represent the coordinates . is the anisotropy matrix, and is the spin vector at site i, ( ). First we determine the parameters appearing in the model from the first principle calculations and then study the thermodynamical macroscopic properties by means of the constrained Monte Carlo method [126], presented in chapter 4.

The self -consistent "ab-initio" calculations are performed in terms of the fully relativistic screened Khon-Korringa-Rostocker (SKKR) method [86]. Within this method , spin-polarization and relativistic effects (in particular, spin-orbit coupling) are treated on equal theoretical footing by solving the Kohn-Sham-Dirac equation. We employed the technique to map the electronic structure calculations into the Heisenberg model following L. Udvardi et. al [142]. The anisotropy energies have been extracted from the difference of the layer resolved band energies for the magnetization perpendicular and parallel to the surface. Since the spin-orbit coupling plays a key role in the magnetic anisotropy energy, the calculations were done by a fully relativistic spin polarized code, which was supplied by Dr. L. Szunyogh of the Budapest University of Technology and Economics, and henceforth we will call it the Budapest-Vienna Code.

Rocio Yanes