On boundary conditions for spin diffusion equations with Rashba spin-orbit interaction

We reexamine the boundary conditions of spin diffusion equations for dirty semiconductor heterostructures with weak linear Rashba spin-orbit interaction. Doing so, we focus on the influence of tangent derivatives of the particle density at the boundary on the magnetization. Such derivatives are associated with a spin accumulation in the presence of a density gradient. We show that the tangent derivatives enter the boundary conditions and argue that the spin-Hall effect is absent in such systems because of this fact.