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

Abstract

We calculate the electrically induced spin accumulation in diffusive systems\ndue to both Rashba (with strength $\\alpha)$ and Dresselhaus (with strength\n$\\beta)$ spin-orbit interaction. Using a diffusion equation approach we find\nthat magnetoelectric effects disappear and that there is thus no spin\naccumulation when both interactions have the same strength, $\\alpha=\\pm \\beta$.\nIn thermodynamically large systems, the finite spin accumulation predicted by\nChaplik, Entin and Magarill, [Physica E {\\bf 13}, 744 (2002)] and by Trushin\nand Schliemann [Phys. Rev. B {\\bf 75}, 155323 (2007)] is recovered an\ninfinitesimally small distance away from the singular point $\\alpha=\\pm \\beta$.\nWe show however that the singularity is broadened and that the suppression of\nspin accumulation becomes physically relevant (i) in finite-sized systems of\nsize $L$, (ii) in the presence of a cubic Dresselhaus interaction of strength\n$\\gamma$, or (iii) for finite frequency measurements. We obtain the parametric\nrange over which the magnetoelectric effect is suppressed in these three\ninstances as (i) $|\\alpha|-|\\beta| \\lesssim 1/mL$, (ii)$|\\alpha|-|\\beta|\n\\lesssim \\gamma p_{\\rm F}^2$, and (iii) $|\\alpha|-|\\beta| \\lesssiM\n\\sqrt{\\omega/m p_{\\rm F}\\ell}$ with $\\ell$ the elastic mean free path and\n$p_{\\rm F}$ the Fermi momentum. We attribute the absence of spin accumulation\nclose to $\\alpha=\\pm \\beta$ to the underlying U (1) symmetry. We illustrate and\nconfirm our predictions numerically.\n