  We have studied the spin dynamics of a high-mobility two-dimensional electron
system in a GaAs/Al_{0.3}Ga_{0.7}As single quantum well by time-resolved
Faraday rotation and time-resolved Kerr rotation in dependence on the initial
degree of spin polarization, P, of the electrons. By increasing the initial
spin polarization from the low-P regime to a significant P of several percent,
we find that the spin dephasing time, $T_2^\ast$, increases from about 20 ps to
200 ps; Moreover, $T_2^\ast$ increases with temperature at small spin
polarization but decreases with temperature at large spin polarization. All
these features are in good agreement with theoretical predictions by Weng and
Wu [Phys. Rev. B {\bf 68}, 075312 (2003)]. Measurements as a function of spin
polarization at fixed electron density are performed to further confirm the
theory. A fully microscopic calculation is performed by setting up and
numerically solving the kinetic spin Bloch equations, including the
D'yakonov-Perel' and the Bir-Aronov-Pikus mechanisms, with {\em all} the
scattering explicitly included. We reproduce all principal features of the
experiments, i.e., a dramatic decrease of spin dephasing with increasing $P$
and the temperature dependences at different spin polarizations.
