Ab initio theory of temperature dependence of magnetic anisotropy in layered systems: Applications to thin Co films on Cu(100)

In this paper we present an extension of the relativistic disordered local moments (RDLM) scheme to layered systems in order to perform ab initio calculations of the temperature-dependent magnetic anisotropy energy of magnetic surfaces, interfaces, or films. As implemented within the relativistic spin-polarized screened Korringa-Kohn-Rostoker method, we apply this scheme to thin Co-n/Cu(100) films and observe a temperature dependence of the magnetic anisotropy energy (MAE) that significantly differs from that of the bulk systems studied so far. In addition to the overall agreement of our results with experiments in showing an in-plane magnetization for almost all layer thicknesses and temperatures under consideration, our calculations also systematically predict a temperature-induced reverse (in-plane to out-of-plane) spin reorientation. In order to explain this unexpected feature we fit the parameters of a classical Heisenberg model solved within the mean-field approach to the MAE obtained from the RDLM calculations, and conclude that the spin reorientation is driven by a competition of exchange and single-site anisotropies.