Relaxation of shallow donor electron spin due to interaction with nuclear spin bath

We study the low-temperature dynamics of a shallow donor, e.g., P-31, impurity electron spin in silicon, interacting with the bath of nuclear spins of the Si-29 isotope. For small applied magnetic fields, the electron spin relaxation is controlled by the steady-state distribution of the nuclear spins. We calculate the relaxation times T-1 and T-2 as functions of the external magnetic field and conclude that nuclear spins play an important role in the donor electron spin decoherence in SI;P at low magnetic fields.