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We calculate the spin relaxation rates in a parabolic InSb quantum dots dueto the spin interaction with acoustical phonons. We considered the deformationpotential mechanism as the dominant electron-phonon coupling in thePavlov-Firsov spin-phonon Hamiltonian. By studying suitable choices of magneticfield and lateral dot size, we determine regions where the spin relaxationrates can be practically suppressed. We analyze the behavior of the spinrelaxation rates as a function of an external magnetic field and mean quantumdot radius. Effects of the spin admixture due to Dresselhaus contribution tospin-orbit interaction are also discussed.

Phonon modulation of the spin-orbit interaction as a spin relaxation mechanism in InSb quantum dots