Temperature dependence of magnetic anisotropies in ultra-thin films

Anisotropies essentially affect magnetism in thin ferromagnetic films of few atomic layers. On the one hand they can stabilize long range order in these systems, on the other hand they strongly influence the orientation of magnetization. The intrinsic causes of anisotropies in these systems are the spin-orbit coupling of the electrons and the long-range magnetic dipole interaction. While the dipole interaction always favors an orientation of magnetization in the plane of the film, spin-orbit coupling can favor different orientations of magnetization on the surface and in the inner layers of the film. This can lead to a competition between anisotropies, which in turn leads to a spin reorientation transition with varying film thickness. This transition can be of varying order, i. e. be continuous or discontinuous. Experiments also find a spin reorientation transition with varying temperature, which until now was not well understood. In the framework of a classical Heisenberg model this transition is investigate d by means of different theoretical methods in the course of this thesis. At zero temperature the system can be dealt with analytically and criteria for the spin reorientation transition and its order are found. Furthermore it is investigated whether the long-range dipole interaction results in a domain ground state. These investigations are extended to finite temperatures by means of a molecular field theory and results are compared to Monte Carlo simulations. It is shown that in contrast to other works the temperature driven spin reorientation transition in the monolayer is discontinuous also in the simulations, whereas in general it is continuous for the bilayer. Consequently the molecular field theory and the Monte Carlo simulations agree qualitatively. Exemplary for thicker films the influence of an external magnetic field is investigated in the bilayer, furthermore the effective anisotropies Kn(T) of the phenomenological Landau theory are calculated numerically for the microscopic model. Analytic expres sions for the dependence of the anisotropies Kn(T) on the parameters of the model are obtained by the means of perturbation theory, which lead to a deeper understanding of the spin reorientation transition. Accordingly to this the origin for the spin reorientation transition lies in the differing temperature dependence of the dipolar and spin-orbit parts of the Kn(T). Additionally the magnetization in the surface of the film decreases more rapidly with increasing temperature. As a consequence the influence of the surface anisotropy decreases with increasing temperature. This effects a similar result as increasing the film thickness and leads to the transition. Finally the model is extended to continuous film thicknesses, since in experiment the spin reorientation transition depends crucially on film thickness. The results of this extended model are compared to experiment and give good agreement