  We report the anomalous Dyakonov-Perel' spin relaxation in ultracold
spin-orbit coupled $^{40}$K gas when the coupling between $|9/2,9/2\ >$ and
$|9/2,7/2\ >$ states (atcing as the effective Zeeman magnetic field) is much
stronger than the spin-orbit coupled field. Both the transverse and
longitudinal spin relaxations are investigated with small and large spin
polarizations. It is found that with small spin polarization, the transverse
(longitudinal) spin relaxation is divided into four (two) regimes: the normal
weak scattering regime, the anomalous Dyakonov-Perel'-like regime, the
anomalous Elliott-Yafet-like regime and the normal strong scattering regime
(the anomalous Elliott-Yafet-like regime and the normal strong scattering
regime), with only the normal weak scattering regime being in the weak
scattering limit. This is very different from the conventional situation under
the weak magnetic field, which is divided into the weak and strong scattering
regimes according to the weak/strong scattering limit. With large spin
polarization, we find that the Hartree-Fock self-energy, which acts as an
effective magnetic field, can markedly suppress the transverse spin relaxation
in both weak and strong scattering limits. Moreover, by noting that as both the
momentum relaxation time and the Hartree-Fock effective magnetic field vary
with the scattering length in cold atoms, the anomalous Dyakonov-Perel'-like
regime is suppressed and the transverse spin relaxation is hence divided into
three regimes in the scattering length dependence: the normal weak scattering
regime, the anomalous Elliott-Yafet-like regime and the strong scattering
regime. On the other hand, the longitudinal spin relaxation is again divided
into the anomalous EY-like and normal strong scattering regimes. ...
