  Carrier density dependence of electron spin relaxation in an intrinsic GaAs
quantum well is investigated at room temperature using time-resolved circularly
polarized pump-probe spectroscopy. It is revealed that the spin relaxation time
first increases with density in the relatively low density regime where the
linear D'yakonov-Perel' spin-orbit coupling terms are dominant, and then tends
to decrease when the density is large and the cubic D'yakonov-Perel' spin-orbit
coupling terms become important. These features are in good agreement with
theoritical predictions by L\"u {\em et al.} [Phys. Rev. B {\bf 73}, 125314
(2006)]. A fully microscopic calculation based on numerically solving the
kinetic spin Bloch equations with both the D'yakonov-Perel' and the
Bir-Aronov-Pikus mechanisms included, reproduces the density dependence of spin
relaxation very well.
