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

TL;DR

This paper investigates how Rashba and Dresselhaus spin-orbit interactions influence spin accumulation in diffusive conductors, revealing conditions under which the magnetoelectric effect is suppressed or restored, especially near the symmetric point where their strengths are equal.

Contribution

It provides a detailed analysis of the conditions suppressing spin accumulation due to Rashba and Dresselhaus interactions, including finite size, cubic Dresselhaus terms, and finite frequency effects.

Findings

Spin accumulation vanishes when Rashba and Dresselhaus strengths are equal.

Finite size, cubic Dresselhaus interaction, and finite frequency can broaden the singularity.

Numerical simulations confirm the theoretical predictions.

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.