  The bilayer heterostructures composed of an ultrathin ferromagnetic metal
(FM) and a material hosting strong spin-orbit (SO) coupling are principal
resource for SO torque and spin-to-charge conversion nonequilibrium effects in
spintronics. We demonstrate how hybridization of wavefunctions of Co layer and
a monolayer of transition metal dichalcogenides (TMDs)---such as semiconducting
MoSe$_2$ and WSe$_2$ or metallic TaSe$_2$---can lead to dramatic transmutation
of electronic and spin structure of Co within some distance away from its
interface with TMD, when compared to the bulk of Co or its surface in contact
with vacuum. This is due to proximity induced SO splitting of Co bands encoded
in the spectral functions and spin textures on its monolayers, which we obtain
using noncollinear density functional theory (ncDFT) combined with equilibrium
Green function (GF) calculations. In fact, SO splitting is present due to
structural inversion asymmetry of the bilayer even if SO coupling within TMD
monolayer is artificially switched off in ncDFT calculations, but switching it
on makes the effects associated with proximity SO coupling within Co layer
about five times larger. Injecting spin-unpolarized charge current through
SO-proximitized monolayers of Co generates nonequilibrium spin density over
them, so that its cross product with the magnetization of Co determines SO
torque. The SO torque computed via first-principles quantum transport
methodology, which combines ncDFT with nonequilibrium GF calculations, can be
used as the screening parameter to identify optimal combination of materials
and their interfaces for applications in spintronics. In particular, we
identify heterostructure two-monolayer-Co/monolayer-WSe$_2$ as the most
optimal.
