Spin relaxation and antisymmetric exchange in n-doped III-V semiconductor

Recently K. Kavokin [Phys. Rev. B 64, 075305 (2001)] suggested that the Dzyaloshinskii-Moriya interaction between localized electrons governs slow spin relaxation in $n$-doped GaAs in the regime close to the metal-insulator transition. We derive the correct spin Hamiltonian and apply it to the determination of spin dephasing time using the method of moments expansion. We argue that the proposed mechanism is insufficient to explain the observed values of the spin relaxation time.