We investigate the influence of the Hartree-Fock self-energy, acting as an effective magnetic field, on the anomalous Dyakonov-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 Dyakonov-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 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 opposite trend comes 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.
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