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Spin Accumulation in Diffusive Conductors with Rashba and Dresselhaus Spin-Orbit Interaction

Duckheim, Mathias and Loss, Daniel and Scheid, Matthias and Richter, Klaus and Adagideli, Inanc and Jacquod, Philippe (2010) Spin Accumulation in Diffusive Conductors with Rashba and Dresselhaus Spin-Orbit Interaction. Physical Review B (PRB) 81, 085303.

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Other URL: http://de.arxiv.org/abs/0909.4253, http://link.aps.org/doi/10.1103/PhysRevB.81.085303

Abstract

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 ${\bf 13}$ , 744 (2002)] and by Trushin and Schliemann [Phys. Rev. B ${\bf 75}$ , 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) $|\alpha|-|\beta| \lesssim 1/mL$ , (ii) $|\alpha|-|\beta| \lesssim \gamma p_{\rm F}^2$ , and (iii) $|\alpha|-|\beta| \lesssiM \sqrt{\omega/m p_{\rm F}\ell}$ with $\ell$ the elastic mean free path and $p_{\rm F}$ 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.