The spin-orbit interaction in semiconductors is shown to result in an anisotropic contribution into the exchange Hamiltonian of a pair of localized conduction-band electrons. The anisotropic exchange interaction exists in semiconductor structures that are not symmetric with respect to spatial inversion, for instance in bulk zinc-blende semiconductors. The interaction has both symmetric and antisymmetric parts with respect to permutation of spin components. The antisymmetric (Dzyaloshinskii-Moriya) interaction is the strongest one. It contributes significantly into spin relaxation of localized electrons; in particular, it governs low-temperature spin relaxation in n-GaAs with the donor concentration near ${10}^{16}\hspace{0.5em}{\mathrm{cm}}^{-3}.$ The interaction must be allowed for in designing spintronic devices, especially spin-based quantum computers, where it may be a major source of decoherence and errors.

• Received 9 December 2000

DOI:https://doi.org/10.1103/PhysRevB.64.075305