Surface-Induced Magnetic Anisotropy of Impurities

We present theoretical and numerical studies of the magnetic anisotropy energy of an atomic-like impurity near the surface of a metallic host (Au). The valence band of the host metal is described in terms of a realistic tight-binding surface Green´s function technique. We compare two models: (i) when spin-orbit coupling is taken into account in the d-band of the host and (ii) when the impurity´s d-level experiences strong spin-orbit splitting. The level splitting of the impurity´s spin-states is calculated in leading (first or second) order of the exchange interaction between the impurity and the host atoms. It is shown that the magnetic anisotropy constant is an oscillating function of the distance d of the impurity from the surface. For large distances, an asymptotic analysis implies that the period of these oscillations is determined by the extremal vectors of the host´s Fermi Surface and the amplitude decays as 1/d². Our numerical results clearly suggest that the host-induced magnetic anisotropy energy is by several orders smaller in magnitude than the one originating from a strong local spin-orbit coupling.