Spin accumulation in metallic thin films induced by electronic impurity scattering

To explore spin accumulation, evaluating the spin galvanic and spin Hall effects, we utilize the semiclassical Boltzmann equation based on input from the relativistic Korringa-Kohn-Rostoker Green's function method within the density functional theory. We calculate the spin accumulation including multiple contributions, especially skew-scattering (scattering-in term), and we compare this to three different approximations, which include the isotropic and anisotropic relaxation-time approximation. For heavy metals, with strong intrinsic spin-orbit coupling, we find that almost all the effects are captured within the anisotropic relaxation-time approximation. On the other hand, in light metals the contributions from the vertex corrections (scattering-in term) are comparable to the induced effect in the anisotropic relaxation-time approximation. We focus in particular on the influence of the atomic character of the substitutional impurities on the spin accumulation, as well as the dependence on the impurity position. As impurities will break the space inversion symmetry of the thin film, this will give rise to both symmetric and antisymmetric contributions to the spin accumulation. In general, we find that the impurities at the surface generate the largest efficiency of charge-to-spin conversion in the case of spin accumulation. Comparing our results to existing experimental findings for Pt, we find good agreement.