Random walk approach to spin dynamics in a two-dimensional electron gas with spin-orbit coupling

TL;DR

This paper develops a semi-classical random walk model to describe spin polarization wave dynamics in two-dimensional electron gases with spin-orbit coupling, predicting dispersion relations and effects of electric fields consistent with quantum calculations.

Contribution

It introduces a novel semi-classical random walk approach to spin dynamics, capturing effects of spin-orbit interactions and electric fields in quantum wells, aligning with quantum mechanical results.

Findings

Spin waves acquire a field-induced phase velocity crossing zero at a nonzero wavevector.

Spin-wave decay rate is field-independent at this wavevector but increases quadratically away from it.

Predictions are testable via transient spin grating experiments.

Abstract

We introduce and solve a semi-classical random walk (RW) model that describes the dynamics of spin polarization waves in zinc-blende semiconductor quantum wells. We derive the dispersion relations for these waves, including the Rashba, linear and cubic Dresselhaus spin-orbit interactions, as well as the effects of an electric field applied parallel to the spin polarization wavevector. In agreement with fully quantum mechanical calculations [Kleinert and Bryksin, Phys. Rev. B \textbf{76}, 205326 (2007)], the RW approach predicts that spin waves acquire a phase velocity in the presence of the field that crosses zero at a nonzero wavevector, $q_0$. In addition, we show that the spin-wave decay rate is independent of field at $q_0$ but increases as $(q-q_0)^2$ for $q\neq q_0$. These predictions can be tested experimentally by suitable transient spin grating experiments.