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We study Si:P donor electron spin decoherence due to anisotropic hyperfine(AHF) interaction with the surrounding nuclear spin bath. In particular, weclarify the electron spin echo envelope modulation (ESEEM) in the Si:P systemand the resonancelike contributions from nuclear spins in various shells awayfrom the P atoms. We suggest an approach to minimize AHF-induced decoherence byavoiding the resonances and orienting an applied magnetic field alongdirections that can periodically eliminate contributions from the dominantnearest neighbor atoms. Our remarkable agreement with experiment demonstratesnearly complete understanding of electron spin decoherence in Si:P whencombining ESEEM, spectral diffusion, instantaneous diffusion, and spin-latticerelaxation

Decoherence induced by anisotropic hyperfine interaction in Si spin qubits