Screening effect in spin Hall devices

The stationary state of the spin Hall bar is studied in the framework of a variational approach that includes nonequilibrium screening effects at the edges. The minimization of the power dissipated in the system is performed taking into account the spin-flip relaxation and the global constraints due to the electric generator and global charge conservation. The calculation is performed within the approximations of negligible spin-flip scattering and strong spin-flip scattering. In both cases, simple expressions of the spin accumulation and the longitudinal and transverse pure spin currents are derived analytically. In usual conditions, the maximum amplitude of the spin accumulation is expected to be of the order of 1% of the equilibrium density carriers.