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An extremely fast spin relaxation of two-dimensional electrons has been observed in undoped CxaAs quantum wells. We present experimental evidence which shows that the fast intrinsic electron spin relaxation in GaAs quantum wells, at low temperatures and in the limit of weak scattering, is dominated by the conduction-band spin splitting in III-V compounds. We also show that in the limit of strong scattering, at high excitation intensity or in quantum wells with considerable imperfections, the electron spin relaxation is dominated by an exchange process. The spin exchange energy of the heavy-hole exciton of a 15-nm GaAs quantum well is estimated to be 35 (+15)peV.

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