Spin accumulation in diffusive conductors with Rashba and Dresselhaus spin-orbit interaction

We calculate the electrically induced spin accumulation in diffusive systems due to both Rashba (with strength α) and Dresselhaus (with strength β) spin-orbit interaction. Using a diffusion equation approach we find that magnetoelectric effects disappear and that there is thus no spin accumulation when both interactions have the same strength, α = ±β. In thermodynamically large systems, the finite spin accumulation predicted by Chaplik, Entin and Magarill, [Physica E 13, 744 (2002)] and by Trushin and Schliemann [Phys. Rev. B 75, 155323 (2007)] is recovered an infinitesimally small distance away from the singular point α = ±β. We show however that the singularity is broadened and that the suppression of spin accumulation becomes physically relevant (i) in finitesized systems of size L, (ii) in the presence of a cubic Dresselhaus interaction of strength γ, or (iii) for finite frequency measurements. We obtain the parametric range over which the magnetoelectric effect is suppressed in these three instances as (i) |α| − |β| ∼ 1/mL, (ii)|α| − |β| ∼ γp 2 F, and (iii) |α| − |β| ∼ p