  We consider the time evolution of the magnetization in a Rashba
spin-orbit-coupled Fermi gas, starting from a fully-polarized initial state. We
model the dynamics using a Boltzmann equation, which we solve in the
Hartree-Fock approximation. The resulting non-linear system of equations gives
rise to three distinct dynamical regimes with qualitatively different
asymptotic behaviors of the magnetization at long times. The distinct regimes
and the transitions between them are controlled by the interaction strength:
for weakly interacting fermions, the magnetization decays to zero. For
intermediate interactions, it displays undamped oscillations about zero and for
strong interactions, a partially magnetized state is dynamically stabilized.
The dynamics we find is a spin analog of interaction induced self-trapping in
double-well Bose Einstein condensates. The predicted phenomena can be realized
in trapped Fermi gases with synthetic spin-orbit interactions.
