A scheme suggested in the literature to determine the symmetry-imposed shape of linear response tensors is revised and extended to allow for the treatment of more complex situations. The extended scheme is applied to discuss the shape of the spin con
ductivity tensor for all magnetic space groups. This allows in particular investigating the character of longitudinal as well as transverse spin transport for arbitrary crystal structure and magnetic order that give rise e.g. to the spin Hall, Nernst and the spin-dependent Seebeck effects. In addition we draw attention to a new longitudinal spin transport phenomenon occurring in certain nonmagnetic solids.
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.
