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

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 𝐶2⁢𝑣 and 𝐶3⁢𝑣 symmetry groups, whereby the electron spectrum becomes anisotropic. We find that in the 𝐶2⁢𝑣 case, depending on the ratio between the Rashba SOC strengths along the principal axes, the nonequilibrium spin density deviates notably from the 90∘ rotation, with respect to the applied electric field, which is familiar in the isotropic case. In the 𝐶3⁢𝑣 case, when a warping cubic in momentum term is present, whereas the standard 90∘ 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, via both the diagrammatic implementation of the Kubo formula and 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.