Extended pump-probe Faraday rotation spectroscopy of the submicrosecond electron spin dynamics in n-type GaAs

We develop an extended pump-probe Faraday rotation technique to study the submicrosecond electron spin dynamics with picosecond time resolution in a wide range of magnetic fields. The electron spin dephasing time $T_2^*$ and the longitudinal spin relaxation time $T_1$, both approaching $250$ ns in weak fields, are measured thereby in $n$-type bulk GaAs. By tailoring the pump pulse train through increasing the contained number of pulses, the buildup of resonant spin amplification is demonstrated for the electron spin polarization. The spin precession amplitude in high magnetic fields applied in the Voigt geometry shows a non-monotonic dynamics deviating strongly from a mono-exponential decay and revealing slow beatings. The beatings indicate a two spin component behavior with a $g$-factor difference of $\Delta g \sim 4\times10^{-4}$, much smaller than the $\Delta g$ expected for free and donor-bound electrons. This $g$-factor variation indicates efficient, but incomplete spin exchange averaging.