  Spin injection is a powerful experimental probe into a wealth of
nonequilibrium spin-dependent phenomena displayed by materials with spin-orbit
coupling (SOC). Here, we develop a theory of coupled spin-charge diffusive
transport in two-dimensional spin-valve devices. The theory describes a
realistic proximity-induced SOC with both spatially uniform and random
components of the SOC due to adatoms and imperfections, and applies to the two
dimensional electron gases found in two-dimensional materials and van der Walls
heterostructures. The various charge-to-spin conversion mechanisms known to be
present in diffusive metals, including the spin Hall effect and several
mechanisms contributing current-induced spin polarization are accounted for.
Our analysis shows that the dominant conversion mechanisms can be discerned by
analyzing the nonlocal resistance of the spin-valve for different polarizations
of the injected spins and as a function of the applied in-plane magnetic field.
