Spin decoherence due to Ampere field fluctuation from acoustic phonons*

We compute the decoherence time of electron spin under the magnetic field produced by the phonon motion of the ions. By using the linear dispersion relation in elastic mediums, the magnetic field due to acoustic phonon motion and the time correlation function of the magnetic field are calculated numerically. We then solve the Redfield equation of motion for the reduced density matrix, which yields the decoherence time of electron spin from the time correlation function of the magnetic field. The calculations are carried out for both in NV center and in semiconductor quantum dots. The NV center result of SiC shows the onsite field dominates the decoherence time. The quantum dot calculation of GaAs, InSb, and InAs shows all atoms in dot contribute.