  We identify the Dresselhaus spin-orbit coupling as the source of the dominant
spin-relaxation mechanism in the impurity band of doped semiconductors. The
Dresselhaus-type (i.e. allowed by bulk-inversion asymmetry) hopping terms are
derived and incorporated into a tight-binding model of impurity sites, and they
are shown to unexpectedly dominate the spin relaxation, leading to
spin-relaxation times in good agreement with experimental values. This
conclusion is drawn from two complementary approaches employed to extract the
spin-relaxation time from the effective Hamiltonian: an analytical
diffusive-evolution calculation and a numerical finite-size scaling.
