  We present an extension of the relativistic electron transport theory for the
standard (charge) conductivity tensor of random alloys within the tight-binding
linear muffin-tin orbital method to the so-called spin-dependent conductivity
tensor, which describes the Kubo linear response of spin currents to external
electric fields. The approach is based on effective charge- and spin-current
operators, that correspond to intersite electron transport and that are
nonrandom, which simplifies the configuration averaging by means of the
coherent potential approximation. Special attention is paid to the Fermi sea
term of the spin-dependent conductivity tensor, which contains a nonzero
incoherent part, in contrast to the standard conductivity tensor. The developed
formalism is applied to the spin Hall effect in binary random nonmagnetic
alloys, both on a model level and for Pt-based alloys with an fcc structure. We
show that the spin Hall conductivity consists of three contributions (one
intrinsic and two extrinsic) which exhibit different concentration dependences
in the dilute limit of an alloy. Results for selected Pt alloys (Pt-Re, Pt-Ta)
lead to the spin Hall angles around 0.2; these sizable values are obtained for
compositions that belong to thermodynamically equilibrium phases. These alloys
can thus be considered as an alternative to other systems for efficient charge
to spin conversion, which are often metastable crystalline or amorphous alloys.

Materials Science;Mesoscale and Nanoscale Physics