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

We study the electron spin relaxation in intrinsic and p-type (001) GaAs quantum wells by constructing and numerically solving the kinetic spin Bloch equations. All the relevant scatterings are explicitly included, especially the spin-flip electron-heavy-hole exchange scattering which leads to the Bir-Aronov-Pikus spin relaxation. We show that, due to the neglection of the nonlinear terms in the electron-heavy-hole exchange scattering in the Fermi-golden-rule approach, the spin relaxation due to the Bir-Aronov-Pikus mechanism is greatly exaggerated at moderately high electron density and low temperature in the literature. We compare the spin relaxation time due to the Bir-Aronov-Pikus mechanism with that due to the D'yakonov-Perel' mechanism which is also calculated from the kinetic spin Bloch equations with all the scatterings, especially the spin-conserving electron-electron and electron-heavy-hole scatterings, included. We find that, in intrinsic quantum wells, the effect from the Bir-Aronov-Pikus mechanism is much smaller than that from the D'yakonov-Perel' mechanism at low temperature, and it is smaller by no more than 1 order of magnitude at high temperature. In p-type quantum wells, the spin relaxation due to the Bir-Aronov-Pikus mechanism is also much smaller than the one due to the D'yakonov-Perel' mechanism at low temperature and becomes comparable to each other at higher temperature when the hole density and the width of the quantum well are large enough. We claim that unlike in the bulk samples, which still require reexamination, the Bir-Aronov-Pikus mechanism hardly dominates the spin relaxation in two-dimensional samples.