Two-spin relaxation of P dimers in silicon

We study two-electron singlet-triplet relaxation of donor-bound electrons in Silicon. Hyperfine interaction of the electrons with the phosphorus (P) nuclei, in combination with the electron-phonon interaction, lead to relaxation of the triplet states. Within the Heitler-London and effective-mass approximations, we calculate the triplet relaxation rates in the presence of an applied magnetic field. This relaxation mechanism affects the resonance peaks in current electron-spin-resonance experiments on P dimers. Moreover, the estimated time scales for the spin decay put an upper bound on the gate pulses needed to perform fault-tolerant two-qubit operations in donor-spin-based quantum computers. We have found the optimal regimes though, which mitigate this relaxation mechanism, yet permit sufficiently fast two-qubit operations.