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We unravel theoretically a key intrinsic relaxation mechanism among thelow-lying singlet and triplet donor-pair states in silicon, an importantelement in the fast-developing field of spintronics and quantum computation.Despite the perceived weak spin-orbit coupling (SOC) in Si, we find that ourdiscovered relaxation mechanism, combined with the electron-phonon andinter-donor interactions, dominantly drives the transitions in the two-electronstates over a large range of donor coupling regime. The scaling of therelaxation rate with inter-donor exchange interaction $J$ goes from $J^5$ to$J^4$ at the low to high temperature limits. Our analytical study draws on thesymmetry analysis over combined band, donor envelope and valley configurations.It uncovers naturally the dependence on the donor-alignment direction andtriplet spin orientation, and especially on the dominant SOC source from donorimpurities. While a magnetic field is not necessary for this relaxation, unlikein the single-donor spin relaxation, we discuss the crossover behavior withincreasing Zeeman energy in order to facilitate comparison with experiments.

Spin-orbit coupling induced two-electron relaxation in silicon donor pairs