The challenging problem of skew scattering for Hall effects in dilute ferromagnetic alloys, with intertwined effects of spin-orbit coupling, magnetism and impurity scattering, is studied here from first principles. Our main aim is to identify chemica
l trends and work out simple rules for large skew scattering in terms of the impurity and host states at the Fermi surface, with particular emphasis on the interplay of the spin and anomalous Hall effects in one and the same system. The predicted trends are benchmarked by referring to three different emph{ab initio} methods based on different approximations with respect to the electronic structure and transport properties.
We present the rational design scheme intended to provide the stable high spin-polarization at the interfaces of the magneto-resistive junctions by fulfilling the criteria of structural and chemical compatibilities at the interface. This can be reali
zed by joining the semiconducting and half-metallic Heusler materials with similar structures. The present first-principal calculations verify that interface remains half-metallic if the nearest interface layers effectively form a stable Heusler material with the properties intermediate between the surrounding bulk parts. This leads to a simple rule for selecting the proper combinations.
