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

Interaction-Tuned Dynamical Transitions in a Rashba Spin-Orbit Coupled Fermi Gas