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 (ESR) 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 (QCs).