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We study the electron spin relaxation in intrinsic and $p$-type (001) GaAsquantum wells by constructing and numerically solving the kinetic spin Blochequations. All the relevant scatterings are explicitly included, especially thespin-flip electron-heavy hole exchange scattering which leads to theBir-Aronov-Pikus spin relaxation. We show that, due to the neglection of thenonlinear terms in the electron-heavy hole exchange scattering in theFermi-golden-rule approach, the spin relaxation due to the Bir-Aronov-Pikusmechanism is greatly exaggerated at moderately high electron density and lowtemperature in the literature. We compare the spin relaxation time due to theBir-Aronov-Pikus mechanism with that due to the D'yakonov-Perel' mechanismwhich is also calculated from the kinetic spin Bloch equations with all thescatterings, especially the spin-conserving electron-electron andelectron-heavy hole scatterings, included. We find that, in intrinsic quantumwells, the effect from the Bir-Aronov-Pikus mechanism is much smaller than thatfrom the D'yakonov-Perel' mechanism at low temperature, and it is smaller by nomore than one order of magnitude at high temperature. In $p$-type quantumwells, the spin relaxation due to the Bir-Aronov-Pikus mechanism is also muchsmaller than the one due to the D'yakonov-Perel' mechanism at low temperatureand becomes comparable to each other at higher temperature when the holedensity and the width of the quantum well are large enough. We claim thatunlike in the bulk samples, the Bir-Aronov-Pikus mechanism hardly dominates thespin relaxation in two-dimensional samples.

Spin relaxation due to the Bir-Aronov-Pikus mechanism in intrinsic and $p$-type GaAs quantum wells from a fully microscopic approach