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

Random walk approach to spin dynamics in a two-dimensional electron gas with spin-orbit coupling Luyi Yang, J. Orenstein, and Dung-Hai Lee Department of Physics, University of California, Berkeley, California 94720, USA. and Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA. (Dated: September 27, 2010) 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 calculations based on quantum kinetic theory [Kleinert and 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 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 = q 0 . These predictions can be tested experimentally by suitable transient spin grating experiments.