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We study the effect of the Singwi-Tosi-Land-Sj\"{o}lander local fieldcorrection on spin relaxation/dephasing in $n$-type GaAs quantum wells at lowtemperature by constructing and numerically solving the kinetic spin Blochequations. We calculate the local field factor $G(q)$ in quantum wells bynumerically solving three equations which link the local field factor, thestructure factor, and the dielectric function, self-consistently. Such acorrection reduces both the electron-electron Coulomb scattering and theCoulomb Hartree-Fock term. We compare the spin relaxation times with andwithout this correction under different conditions such as temperature,electron density, well width and spin polarization. We find that thiscorrection leads to a decrease/increase of the spin relaxation time in thestrong/weak scattering limit. At high spin polarization, it reduces theHartree-Fock term and consequently tends to decrease the spin relaxation time.The modification of the spin relaxation time by the local field correction ismore or less moderate either due to the coexistence of scattering other thanthe Coulomb scattering at low spin polarization and/or due to the competingeffects from the Coulomb scattering and the Coulomb Hartree-Fock term at highpolarization.

Effect of Singwi-Tosi-Land-Sj\"{o}lander local field correction on spin relaxation in $n$-type GaAs quantum wells at low temperature