Two-spin relaxation in a silicon quantum dot*

We study spin relaxation for a two-electron silicon quantum dot. First we perform a configuration interaction calculation to obtain low-energy two-electron states, taking into account valley-orbit coupling, Coulomb interaction, and spin-orbit and using a singlet-triplet basis set. For spin-orbit matrix elements, we include both intrinsic terms (Rashba and Dresselhaus) and extrinsic factors (magnetic field gradients resulting from a micromagnet). These matrix elements are analyzed with respect to their dependences on factors such as valley, spin, and orbital states, giving us insights into coupling between singlet and triplet states. We then calculate the spin-flip relaxation rates as a function of the external magnetic field. These transitions are enabled through electrical fluctuations within the system including contributions from phonon noise, Johnson noise, and 1/f noise.