A spin projection scheme is presented which allows the decomposition of the
electric conductivity into two different spin channels within fully
relativistic abinitio transport calculations that account for the impact
of spin-orbit coupling. This is demonstrated by calculations of the
spin-resolved conductivity of Fe1−xCrx and Co1−xPtx 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