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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 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.
K. V. Kavokin (Fri,) studied this question.