Two-spin relaxation in a silicon quantum dot

We calculate two-spin relaxation in a silicon quantum dot. We first perform a partial configuration interaction calculation to obtain the low-energy singlet and triplet states taking into consideration valley-orbit coupling. We then consider spin-flip transitions due to spin-orbit coupling, both intrinsic (Rashba and Dresselhaus terms) and extrinsic (such as the magnetic field gradient due to a micromagnet), and calculate relaxation rates enabled by electrical fluctuations such as phonon noise, Johnson noise, and background charge fluctuations. We then explore the dependence of the relaxation rates on physical parameters such as the dot size, the spin-orbit coupling strength, and the external magnetic field.