  Decoherence of a shallow donor electron spin in silicon caused by
electron-lattice interaction is studied. We find that there are two time scales
associated with the evolution of the electron spin density matrix: the fast but
incomplete decay due to the interaction with non-resonant phonons followed by
slow relaxation resulting from spin flips accompanied by resonant phonon
emission. We estimate both time scales as well as the magnitude of the initial
drop of coherence for P donor in Si and argue that the approach used is
suitable for evaluation of phonon induced decoherence for a general class of
localized spin states in semiconductors.
