Spin injection in quantum wells with spatially dependent rashba interaction

We consider Rashba spin - orbit effects on spin transport driven by an electric field in semiconductor quantum wells. We derive spin diffusion equations that are valid when the mean free path and the Rashba spin - orbit interaction vary on length scales larger than the mean free path in the weak spin - orbit coupling limit. From these general diffusion equations, we derive boundary conditions between regions of different spin - orbit couplings. We show that spin injection is feasible when the electric field is perpendicular to the boundary between two regions. When the electric field is parallel to the boundary, spin injection only occurs when the mean free path changes within the boundary, in agreement with the recent work by Tserkovnyak et al ( Preprint cond- mat/ 0610190).