Microscopic theory of the inverse spin galvanic effect in anisotropic Rashba models

Abstract

The Rashba spin-orbit coupling (SOC) is a well-known mechanism for the spin-charge interconversion via the inverse and direct spin galvanic effects. The lack of a full inversion symmetry allows the coupling of the charge current and spin density. In this paper we investigate this phenomenon when the in-plane rotational symmetry is lowered to the $C_{2v}$ and $C_{3v}$ symmetry groups, whereby the electron spectrum becomes anisotropic. We find that in the $C_{2v}$ case, depending on the ratio between the Rashba SOC strengths along the principal axes, the non-equilibrium spin density deviates notably from the $90^o$ degrees rotation, with respect to the applied electric field, familiar in the isotropic case. In the $C_{3v}$ case, when a warping cubic-in-momentum term is present, whereas the standard $90^o$ degrees rotation of the spin density remains, the spin-charge interconversion depends on the intensity of the warping itself. The microscopic theory takes into account disorder including vertex corrections, both via the diagrammatic implementation of the Kubo formula and via the quantum kinetic theory. We show that vertex corrections are crucial to capture the details of the inverse spin galvanic effect in contrast to previous treatments based on the constant broadening approximation.