The spin Hall effect (SHE) is the generation in a paramagnetic system of a spin current perpendicular to an applied electric field, leading to spin accumulation with opposite magnetization at the edges. Spin accumulation can be measured directly through optical techniques in semiconductor quantum wells of GaAs and InAs. The possibility of an intrinsic SHE has been put forward in the two dimensional electron gas with spin orbit coupling. This case has attracted most attention due its simplicity and a big amount of theoretical work has been developed on this subject in the last two years. In this talk I will discuss the state of art of SHE and its generalization to the case of a perpendicular applied magnetic field.
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