2 Temperature dependence of the effective surface anisotropy in thin films.

The total effective anisotropy in the presence of the surface effects is not an intrinsic parameter since it is strongly dependent on the thin film thickness. In this section we present two methods, "Scaling method" and "Separation of the surface torque method", suitable to separate the surface from the bulk anisotropy contributions as a function of the temperature in thin films. For simplicity, the thin films have parallel surface and bulk uniaxial anisotropy axes, both easy axes perpendicular to the thin film plane. We applied these two methods to extract the effective surface anisotropy constant of magnetic thin films with a simple cubic crystal structure and the Néel surface anisotropy constant $K_{s}=10\cdot K_{c}$. The size of the modeled system is increased from $Lz=3$ (4800 spins) to $Lz=10$ (16000 spins).