Spin relaxation of conduction electrons in highly-doped n-type germanium at low temperature

We present a theory of the spin relaxation time of the conduction electrons in highly-doped n-type germanium at liquid helium temperature. The theory is compared with some of our measurements and the experimental data available in the literature on As-doped germanium. The observed linewidth at T = 10 K is accounted for in the whole metallic concentration range (N_D > 3 × 10¹⁷cm^?3).In the lower concentration range (3 × 10¹⁷ < N_D < 10¹⁸cm^?3), the relevant mechanism is the random jumping of the g factor upon intervalley scattering. The agreement with experiment is good without any adjustable parameter.In the higher concentration range (N_D > 10¹⁸cm^?3), the dominant process for the linewidth is the spin-flip scattering by ionized donors (Elliott process); the usual theory is shown to be insufficient and the greater effectiveness of scattering by the localized part of the donor potentials is pointed out. The calculated linewidth is related to the intervalley scattering time T_iv. The agreement with experiment is good and predictions are given for the linewidth in the case of other shallow donors in the same concentration range.