  We study theoretically phonon-induced spin dynamics of two electrons confined
in a self-assembled double quantum dot. We calculate the transition rates and
time evolution of occupations for the spin-triplet and spin-singlet states. We
characterize the relative importance of various relaxation channels as a
function of the electric and magnetic fields. The simulations are based on a
model combining the eight-band k.p method and configuration-interaction
approach. We show that the electron g-factor mismatch between the Zeeman
doublets localized on different dots opens a relatively fast triplet-singlet
relaxation channel. We also demonstrate, that the relaxation near the
triplet-singlet anticrossing is slowed down up to several orders of magnitude
due to vanishing of some relaxation channels.
