  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 which are not symmetric with respect to spatial
inversion, for instance in bulk zinc-blend 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 10^16cm-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.
