  We investigate the influence of the Hartree-Fock self-energy, acting as an
effective magnetic field, on the anomalous D'yakonov-Perel' spin relaxation in
InAs (110) quantum wells when the magnetic field in the Voigt configuration is
much stronger than the spin-orbit-coupled field. The transverse and
longitudinal spin relaxations are discussed both analytically and numerically.
For the transverse configuration, it is found that the spin relaxation is very
sensitive to the Hartree-Fock effective magnetic field, which is very different
from the conventional D'yakonov-Perel' spin relaxation. Even an extremely small
spin polarization ($P=0.1\%$) can significantly influence the behavior of the
spin relaxation. It is further revealed that this comes from the {\em unique}
form of the effective inhomogeneous broadening, originated from the mutually
perpendicular spin-orbit-coupled field and strong magnetic field. It is shown
that this effective inhomogeneous broadening is very small and hence very
sensitive to the Hartree-Fock field. Moreover, we further find that in the spin
polarization dependence, the transverse spin relaxation time decreases with the
increase of the spin polarization in the intermediate spin polarization regime,
which is also very different from the conventional situation, where the spin
relaxation is always suppressed by the Hartree-Fock field. It is revealed that
this {\em opposite} trends come from the additional spin relaxation channel
induced by the HF field. For the longitudinal configuration, we find that the
spin relaxation can be either suppressed or enhanced by the Hartree-Fock field
if the spin polarization is parallel or antiparallel to the magnetic field.
