Transverse spin transport in a disordered Pt film

Spin current and spin accumulation in a free-standing disordered Pt film carrying in-plane charge current are studied using the first-principles nonequilibrium Green's function approach. Disorder is treated within the Anderson model in a supercell embedded between the leads. The spin-Hall conductivity extracted from the data is insensitive to disorder strength, and its magnitude and energy dependence agree with the known intrinsic contribution. The effective spin-diffusion length extracted from the spin accumulation profile is about 1.3 nm (which is similar to or even shorter than the mean-free path), insensitive to disorder strength, and a few times shorter than the bulk spin-diffusion length for longitudinal transport extracted from separate Landauer-Buttiker calculations. These features suggest that spin relaxation near the Pt surface is dominated by the Dyakonov-Perel mechanism. With the Fermi level shifted 0.2 Ry lower, into the region of negative spin-Hall conductivity, the effective spin-diffusion length scales with the conductivity as expected for the Elliot-Yafet mechanism. The interpretation of the data within the spin-diffusion model at both energies requires the inclusion of a spin-relaxing boundary condition with a large spin-loss conductance that increases with disorder strength. These features show that the spin-diffusion model is pushed to its applicability limits in heavy metals with strong spin-orbit coupling such as Pt. We also find that orbital accumulation only penetrates into the bulk of Pt in the presence of spin-orbit coupling and is otherwise a purely surface effect.