Spin Hall Effect in the Presence of Spin Diffusion

Hirsch Phys. Rev. Lett. 83, 1834 (1999) recently proposed a spin Hall effect based on the anomalous scattering mechanism in the absence of spin-flip scattering. Since the anomalous scattering causes both anomalous currents and a finite spin-diffusion length, we derive the spin Hall effect in the presence of spin diffusion from a semiclassical Boltzmann equation. When the formulation is applied to certain metals and semiconductors, the magnitude of the spin Hall voltage due to the spin accumulation is found to be much larger than that of magnetic multilayers. An experiment is proposed to measure this spin Hall effect.