Experimental extraction of donor-driven spin relaxation in n-type nondegenerate germanium

Using pure spin current transport measurements in lateral spin-valve devices, we study the spin relaxation in an n-type nondegenerate Ge layer, which is moderately doped Ge (P: similar to 10(18) cm(-3)). The obtained spin diffusion length (lambda(Ge)) of the nondegenerate Ge is two to three times greater than that of heavily doped degenerate Ge (P: similar to 10(19) cm(-3)) in the temperature range from 8 to 100 K. We find that the electron spin lifetime (tau) for the nondegenerate Ge is monotonically increased with decreasing temperature (T). The increase in t at temperatures less than 50 K can be interpreted in terms of the donor-driven spin relaxation mechanism including the 1/root T behavior in multivalley semiconductors, proposed by Song et al. [Y. Song, O. Chalaev, and H. Dery, Phys. Rev. Lett. 113, 167201 (2014)]. We note that it is important for the tau of the moderately doped nondegenerate Ge to partly consider the T-independent component of spin relaxation in addition to the 1/root T component.