The research field "spintronic without magnetism" is based on the possibility to manipulate electric currents via spin-orbit coupling only. The spin Hall effect (SHE) is one of the most promising effects for the generation of spin polarized currents which is even present in non-magnetic materials. The SHE appears when an electric current flows through a medium with spin-orbit coupling present, leading to a spin-current perpendicular to the charge current.
In this work the SHE as well as the anomalous Hall effect (AHE) are investigated on a first principles level using the spin-polarized fully relativistic Korringa-Kohn-Rostoker Green's function method (SPR-KKR-GF) in conjunction with the linear response Kubo-Streda formalism. Intrinsic as well as extrinsic contributions to the SHE/AHE are treated on equal footing. This opened up for the first time the possibility to reliably decompose the SHE/AHE into skew and side-jump scattering as well as intrinsic contributions in a quantitative manner.