  We have theoretically studied phonon-mediated spin-flip processes of
electrons in a GaAs double quantum dot (DQD) holding two spins, under a phonon
temperature gradient over the DQD. Transition rates of inter-dot
phonon-assisted tunnel processes and intra-dot spin-flip processes involving
spin triplet states are formalized by the electron-phonon interaction
accompanied with the spin-orbit interaction. The calculations of the spin-flip
rates and the occupation probabilities of the spin-states in the two-electron
DQD with respect to the phonon temperature difference between the dots are
quantitatively consistent with our previous experiment. This theoretical study
on the temperature gradient effect onto spins in coupled QDs would be essential
for understanding spin-related thermodynamic physics.
