Gauge theory approach for diffusive and precessional spin dynamics in a two-dimensional electron gas

We develop a gauge theory for diffusive and precessional spin dynamics in a two-dimensional electron gas. Our approach reveals a direct connection between the absence of the equilibrium spin current and a strong anisotropy in the spin relaxation: both effects arise if spin–orbit coupling is reduced to a pure gauge SU(2)SU(2) field. In this case, the spin–orbit coupling can be removed by a gauge transformation in the form of a local SU(2)SU(2) spin rotation. The resulting spin dynamics is exactly described in terms of two kinetic coefficients: the spin diffusion and electron mobility. After the inverse transformation, full diffusive and precessional spin density dynamics, including the anisotropic spin relaxation, formation of stable spin structures, and spin precession induced by a macroscopic current are restored. Explicit solutions of the spin evolution equations are found for the initially uniform spin density and for stable, nonuniform structures. Our analysis demonstrates a universal relation between the spin relaxation rate and spin-diffusion coefficient.