  We investigate the spin relaxation limited by the D'yakonov-Perel' mechanism
in $n$-type (111) GaAs quantum wells, by means of the kinetic spin Bloch
equation approach. In (111) GaAs quantum wells, the in-plane effective magnetic
field from the D'yakonov-Perel' term can be suppressed to zero on a special
momentum circle under the proper gate voltage, by the cancellation between the
Dresselhaus and Rashba spin-orbit coupling terms. When the spin-polarized
electrons mainly distribute around this special circle, the in-plane
inhomogeneous broadening is small and the spin relaxation can be suppressed,
especially for that along the growth direction of quantum well. This
cancellation effect may cause a peak (the cancellation peak) in the density or
temperature dependence of the spin relaxation time. In the density
(temperature) dependence, the interplay between the cancellation peak and the
ordinary density (Coulomb) peak leads to rich features of the density
(temperature) dependence of the spin relaxation time. The effect of impurities,
with its different weights on the cancellation peak and the Coulomb peak in the
temperature dependence of the spin relaxation, is revealed. We also show the
anisotropy of the spin relaxation with respect to the spin-polarization
direction.
