  The spin relaxation time of electrons in GaAs and GaN are determined with a
model that includes momentum scattering by phonons and ionized impurities, and
spin scattering by the Elliot-Yafet, D'yakonov-Perel, and Bir-Aronov-Pikus
mechanisms. Accurate bands generated using a long-range tight-binding
Hamiltonian obtained from empirical pseudopotentials are used. The inferred
temperature-dependence of the spin relaxation lifetime agrees well with
measured values in GaAs. We further show that the spin lifetimes decrease
rapidly with injected electrons energy and reach a local maximum at the
longitudinal optical phonon energy. Our calculation predicts that electron spin
lifetime in pure GaN is about 3 orders of magnitude longer than in GaAs at all
temperatures, primarily as a result of the lower spin-orbit interaction and
higher conduction band density of states.
