  We study Si:P donor electron spin decoherence due to anisotropic hyperfine
(AHF) interaction with the surrounding nuclear spin bath. In particular, we
clarify the electron spin echo envelope modulation (ESEEM) in the Si:P system
and the resonancelike contributions from nuclear spins in various shells away
from the P atoms. We suggest an approach to minimize AHF-induced decoherence by
avoiding the resonances and orienting an applied magnetic field along
directions that can periodically eliminate contributions from the dominant
nearest neighbor atoms. Our remarkable agreement with experiment demonstrates
nearly complete understanding of electron spin decoherence in Si:P when
combining ESEEM, spectral diffusion, instantaneous diffusion, and spin-lattice
relaxation.
