Spin projection and spin current density within relativistic electronic transport calculations

A spin projection scheme is presented which allows the decomposition of the electric conductivity into two different spin channels within fully relativistic \(ab\) \(initio\) transport calculations that account for the impact of spin-orbit coupling. This is demonstrated by calculations of the spin-resolved conductivity of Fe\(_{1-x}\)Cr\(_x\) and Co\(_{1-x}\)Pt\(_x\) disordered alloys on the basis of the corresponding Kubo-Greenwood equation implemented using the Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) band structure method. In addition, results for the residual resistivity of diluted Ni-based alloys are presented that are compared to theoretical and experimental ones that rely on Mott's two-current model for spin-polarized systems. The application of the scheme to deal with the spin-orbit induced spin Hall effect is discussed in addition.