We explain the spin segregation seen at Duke in a two-component gas of L6 i [X. Du, L. Luo, B. Clancy, and J. E. Thomas, Phys. Rev. Lett. 101, 150401 (2008)] as a mean-field effect describable via a collisionless Boltzmann equation. As seen in experiments, we find that slight differences in the trapping potentials in the two spin states drive small spin currents. The Hartree-Fock-type interactions convert these currents into a redistribution of populations in energy space, and consequently a long-lived spin texture develops. We explore the interaction strength dependence of these dynamics, finding nontrivial dependence on system parameters and close agreement with experiment. © 2009 The American Physical Society.