The electron density dependence of the electron spin relaxation time in a system of electrons interacting with phonons through phonon-modulated spin-orbit coupling was calculated using the formula for electron spin resonance derived by the projection-reduction method. The electron spin relaxation time in GaAs increased with increasing electron density, and the electron density was found to affect the electron spin relaxation differently according to temperature. The electron spin in GaAs was relaxed mainly by optical phonon scattering at high electron densities and piezoelectric phonon scattering at relatively low electron densities.
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