A relativistic RKKY interaction between two magnetic impurities-the origin of a magnetic anisotropic effect

We have developed a theoretical approach for examining magnetic anisotropic effects in metals. It is based upon a fully relativistic spin-polarised multiple scattering framework for describing the electrons. We apply the formalism to the situation of two magnetic impurities in a host material modelled by an electron gas with a uniform positively charged background and obtain an interaction between the two moments mediated by the relativistic electron gas. Apart from depending on the usual spatially isotropic ‘spin-spin’ term, the interaction is shown to be a polynomial function of anisotropic, Dzyaloshinsky- Moriya and pseudo-dipolar-type terms. These anisotropic terms are a direct consequence of the inclusion of relativistic (spin-orbit coupling) effects. We consider two impurities and examine how this interaction changes as the spin-polarisation effect grows with respect to the spin-orbit coupling. Finally, we study the interaction between two iron and then two cobalt impurities.