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Calculation of electron spin relaxation time in germanium using the projection–reduction method

Using the electron spin resonance formula derived by the projection reduction method, the electron spin relaxation times in a system of electrons interacting with phonons through phonon-modulated spin–orbit coupling are calculated. The electron spin relaxation time (T1) in germanium decreases with increasing temperature (T) as at low temperatures and at high temperatures. This means that electrons are scattered mostly by acoustic phonon deformation at low temperatures and optical phonon deformation at high temperatures. The magnetic field (B) dependence of the relaxation time is at 70 K and at 120 K. These results nearly agree with the prediction of Yafet. It is also shown that the acoustic and optical deformation constants do not affect the temperature dependence of the relaxation time.