D'yakonov-Perel' spin relaxation controlled by electron-electron scattering

The D'yakonov-Perel' mechanism of spin relaxation is connected with the spin splitting of the electron dispersion curve in crystals lacking a center of symmetry. In a two-dimensional noncentrosymmetric system, e.g. quantum well or heterojunction, the spin splitting is a linear function of k, at least for small values of k. We demonstrate that the spin relaxation time tau(s) due to the spin splitting is controlled not only by momentum relaxation processes as widely accepted but also by electron-electron collisions which have no effect on the electron mobility. In order to calculate the time tau(s) taking into account the electron-electron scattering, we have solved the two-dimensional kinetic equation for the electron spin density matrix. The result has been compared with that obtained assuming the momentum scattering to occur due to elastic scattering of electrons by ionized impurities. We have also extended the quasi-elastic approximation to describe the electron-electron collision integral for a spin-polarized three-dimensional electron gas.