# Theory of current-induced spin polarizations in an electron gas

## TL;DR

This paper develops a theoretical framework for understanding current-induced spin polarization in a two-dimensional electron gas with spin-orbit coupling, revealing new spin-generation mechanisms and complex behaviors that align with recent experimental observations.

## Contribution

It introduces a new spin-generation torque from the Elliot-Yafet process and analyzes its impact on current-induced spin polarization in 2D electron gases with Rashba and Dresselhaus effects.

## Key findings

- Identification of a new spin-generation torque opposing the Dyakonov-Perel process
- Prediction of out-of-plane spin polarization components
- Complex dependence of spin polarization symmetry on internal fields

## Abstract

We derive the Bloch equations for the spin dynamics of a two-dimensional electron gas in the presence of spin-orbit coupling. For the latter we consider both the intrinsic mechanisms of structure inversion asymmetry (Rashba) and bulk inversion asymmetry (Dresselhaus), and the extrinsic ones arising from the scattering from impurities. The derivation is based on the SU(2) gauge-field formulation of the Rashba-Dresselhaus spin-orbit coupling. Our main result is the identification of a new spin-generation torque arising from the Elliot-Yafet process, which opposes a similar term arising from the Dyakonov-Perel process. The new spin-generation torque contributes to the current-induced spin polarization (CISP) -- also known as the Edelstein or inverse spin-galvanic effect. As a result, the behavior of the CISP turns out to be more complex than one would surmise from consideration of the internal Rashba-Dresselhaus fields alone. In particular, the symmetry of the current-induced spin polarization does not necessarily coincide with that of the internal Rashba-Dresselhaus field, and an out-of-plane component of the CISP is generally predicted, as observed in recent experiments. We also discuss the extension to the three-dimensional electron gas, which may be relevant for the interpretation of experiments in thin films.