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Results are given for spin relaxation in quantum dots due to acoustic phonon-assisted flips of single spins at low temperatures. The dominant spin relaxation processes for varying dot size, temperature, and magnetic field are identified. These processes are mediated by the spin-orbit interaction and are described within a generalized effective mass treatment. Particular attention is given to phonon coupling due to interface motion, which dominates the relaxation for dots with diameters 15nm, and also to a direct spin-phonon process that arises from valence-conduction band coupling and dominates the rates for increasing temperature. Low-temperature relaxation rates are found to be small and to depend strongly on size, on temperature, and on magnetic field. Results are illustrated with evaluations for GaAs/AlₗGa₁-ₗAs systems, and a minimum in the relaxation rate is found for dot diameters 20nm.
Woods et al. (Tue,) studied this question.