Breakdown of the drift-diffusion model for transverse spin transport in a disordered Pt film

Spin accumulation and spin current profiles are calculated for a disordered Pt film subjected to an in-plane electric current within the nonequilibrium Green function approach. In the bulklike region of the sample, this approach captures the intrinsic spin Hall effect found in other calculations. Near the surfaces, the results reveal qualitative differences with the results of the widely used spin-diffusion model, even when the boundary conditions are modified to try to account for them. One difference is that the effective spin-diffusion length for transverse spin transport is significantly different from its longitudinal counterpart and is instead similar to the mean-free path. This feature may be generic for spin currents generated via the intrinsic spin-Hall mechanism because of the differences in transport mechanisms compared to longitudinal spin transport. Orbital accumulation in the Pt film is only significant in the immediate vicinity of the surfaces and has a small component penetrating into the bulk only in the presence of spin-orbit coupling, as a secondary effect induced by the spin accumulation.