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

TL;DR

This paper revisits the boundary conditions of spin diffusion equations in semiconductor heterostructures with Rashba spin-orbit interaction, highlighting the role of tangent derivatives and their impact on the spin-Hall effect.

Contribution

It demonstrates that tangent derivatives of particle density influence boundary conditions and argues that the spin-Hall effect is absent in these systems due to this.

Findings

Tangent derivatives affect boundary conditions in spin diffusion.

The spin-Hall effect is absent in systems with weak Rashba interaction.

Boundary conditions depend on density gradients and spin accumulation.

Abstract

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.