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

We introduce and solve a semiclassical 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 wave vector. In agreement with calculations based on quantum kinetic theory (P. Kleinert and V. V. Bryksin, Phys. Rev. B 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 wave vector, q0. In addition, we show that the spin-wave decay rate is independent of field at q0 but increases as (q-q0)2 for q ≠ q0. These predictions can be tested experimentally by suitable transient spin grating experiments.