Optical pump-probe measurements of spin-dynamics at temperatures down to 1.5K are described for a series of (001)-oriented GaAs/AlGaAs quantum well samples containing high mobility two-dimensional electron gases (2DEGs). For well widths ranging from 5 nm to 20 nm and 2DEG sheet densities from 1.75x1011cm-2 to 3.5x1011cm-2 the evolution of a small injected spin population is found to be a damped oscillation rather than exponential relaxation, consistent with the quasi-collision-free regime of Dyakonov-Perel spin dynamics. A Monte Carlo simulation method is used to extract the spin-orbit-induced electron spin precession frequency |W(kF)| and electron momentum scattering time tp* at the Fermi wavevector. The spin decay time passes through a minimum at a temperature corresponding to the transition from collision-free to collision-dominated regimes and tp* is found to be close to the ensemble momentum scattering time tp obtained from Hall measurements of electron mobility. The values of |W(kF)| give the Dresselhaus (BIA) coefficient of spin-orbit interaction as a function of electron confinement energy in the quantum show, qualitatively, the behaviour expected from k.p theory.
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