  Time resolved measurements of magnetization in n-GaAs have revealed a rich
array of spin decoherence processes, and have shown that fairly long lifetimes
(\sim 100 ns) can be achieved under certain circumstances. In time-resolved
Faraday rotation and time-resolved Kerr rotation the evolution of the
magnetization can be followed as a function of temperature, applied field,
doping level and excitation level. We present a theory for the spin relaxation
in n-GaAs based on a set of rate equations for two interacting thermalized
subsystems of spins: localized states on donor sites and itinerant states in
the conduction band. The conduction band spins relax by scattering from defects
or phonons through the D'yakonov-Perel' mechanism, while the localized spins
relax by interacting with phonons (when in an applied field) or through the
Dzyaloshinskii-Moriya interaction. In this model, numerous features of the
data, including puzzling temperature and doping dependences of the relaxation
time, find an explanation.
