  We address the possible occurrence of ultracold atom ferromagnetism by
evaluating the free energy of a spin polarized Fermi gas to second order in its
interaction parameter. We find that Hartree-Fock theory underestimates the
tendency toward ferromagnetism, predict that the ferromagnetic transition is
first order at low temperatures, and point out that the spin coherence time of
gases prepared in a ferromagnetic state is strongly enhanced as the transition
is approached. We relate our results to recent experiments.
