Stationary states and screening equations in the spin-Hall effect

The characterization of the stationary states in the spin-Hall effect is discussed within the framework of the phenomenological two spin-channel model. It is shown that two different definitions of the stationary states can be applied in the spin-Hall effect, leading to two different types of state in the bulk: zero transverse spin-current or non-zero pure spin-current. This difference is due to the treatment of the region near the edges, in which electric charge accumulation occurs. The screening equations that describe the accumulation of electric charges due to spin-orbit coupling are derived. The spin-accumulation associated to spin-flip scattering and the spin-Hall accumulation due to spin-orbit coupling are two independent effects if we assume that the screening length is small with respect to the spin-diffusion length. The corresponding transport equations are discussed in terms of the Dyakonov-Perel equations.
Comment: The work is a pedological presentation of the problem of the stationary states in the spin-Hall effect, in complement to a previously submitted article arXiv :1609.03916v1 [cond-mat.mes-hall] 2016, entitled "Conditions for the generation of spin and charge currents in spin-Hall devices" (Europhys. Lett. 118, 67005 (2017))