Role of relaxation in the spin Hall effect

The role of the relaxation due to the impurity scattering and/or the contacts to leads/electrodes are studied for the spin Hall effect (SHE). Relaxation is essential to attain the steady state and also the spin accumulation, but has been considered to be harmful for the intrinsic SHE (ISHE). These issues are examined quantitatively on two types of two-dimensional models, i.e., (a) Rashba model for n-type GaAs and (b) Luttinger model for p-type GaAs. It is found that ISHE is robust against the realistic strength of disorder producing the observable amount of spin accumulation. Especially in model (b) the spin current and the accumulation are an order of magnitude larger than those in model (a). Experimental observations are discussed quantitatively from these results.