We calculate the electrically induced spin accumulation in diffusive systems due to both Rashba (with strength $\alpha$) and Dresselhaus (with strength $\beta$) 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, $\alpha =\pm \beta$. 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 $\alpha =\pm \beta$. We show however that the singularity is broadened and that the suppression of spin accumulation becomes physically relevant (i) in finite-sized systems of size $L$, (ii) in the presence of a cubic Dresselhaus interaction of strength $\gamma$, or (iii) for finite-frequency measurements. We obtain the parametric range over which the magnetoelectric effect is suppressed in these three instances as (i) $\left|\alpha \right|-\left|\beta \right|\lesssim 1/mL$, (ii) $\left|\alpha \right|-\left|\beta \right|\lesssim \gamma p_{\text{F}}^2$, and (iii) $\left|\alpha \right|-\left|\beta \right|\lesssim \sqrt{\omega /m{p}_{\text{F}}\ell }$ with $\ell$ the elastic mean-free path and $p_{\text{F}}$ the Fermi momentum. We attribute the absence of spin accumulation close to $\alpha =\pm \beta$ to the underlying U(1) symmetry. We illustrate and confirm our predictions numerically.

• Received 23 September 2009

DOI:https://doi.org/10.1103/PhysRevB.81.085303