We present a detailed study of the temperature-dependent electron spin relaxation rate in $n$-type bulk GaAs in the regime of the metal-to-insulator transition at vanishing magnetic fields. The high-accuracy measurements reveal the longest spin relaxation time for a doping concentration slightly below the metal-to-insulator transition at a finite temperature of $\sim 7\mathrm{K}$. This global minimum of the electron spin relaxation rate results from a delicate interplay of hyperfine interaction, variable range hopping, and the Dyakonov-Perel mechanism. At higher doping densities, the Dyakonov-Perel mechanism becomes dominant at all temperatures changing with temperature gradually from the degenerate to the nondegenerate regime. A theoretical model including temperature-dependent transport data yields not only quantitative agreement with the experimental data but reveals additionally the gradual change from percolation-based large angle momentum scattering to ionized impurity small angle scattering. A simple interpolation of all available data allows to extract a maximal-possible spin relaxation time in $n$-doped, bulk GaAs for negligible external magnetic fields of $\approx 1\mathrm{\mu }\mathrm{s}$.

• Received 25 April 2022
• Revised 27 July 2022
• Accepted 22 August 2022

DOI:https://doi.org/10.1103/PhysRevB.106.125202