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Spin injection is a powerful experimental probe into a wealth ofnonequilibrium spin-dependent phenomena displayed by materials with spin-orbitcoupling (SOC). Here, we develop a theory of coupled spin-charge diffusivetransport in two-dimensional spin-valve devices. The theory describes arealistic proximity-induced SOC with both spatially uniform and randomcomponents of the SOC due to adatoms and imperfections, and applies to the twodimensional electron gases found in two-dimensional materials and van der Wallsheterostructures. The various charge-to-spin conversion mechanisms known to bepresent in diffusive metals, including the spin Hall effect and severalmechanisms contributing current-induced spin polarization are accounted for.Our analysis shows that the dominant conversion mechanisms can be discerned byanalyzing the nonlocal resistance of the spin-valve for different polarizationsof the injected spins and as a function of the applied in-plane magnetic field.

Theory of Spin Injection in Two-dimensional Metals with Proximity-Induced Spin-Orbit Coupling