Interplay of intrinsic and extrinsic mechanisms to the spin Hall effect in a two-dimensional electron gas

In order to describe correctly the interplay of extrinsic and intrinsic spin–orbit mechanisms to the spin Hall effect, it is necessary to consider different sources of spin relaxation. We take into account the spin relaxation time τDPτDP due to the Dyakonov–Perel mechanism as well as the Elliott–Yafet spin-relaxation time τsτs due to the spin–orbit scattering from impurities. The total spin Hall conductivity depends crucially on the ratio τs/τDPτs/τDP.