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.