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Nonlinear spin diffusion and spin rotation in a trapped Fermi gas

Transverse spin diffusion in a polarized, interacting Fermi gas leads to the Leggett-Rice effect, where the spin current precesses around the local magnetization. With a spin-echo sequence both the transverse diffusivity and the spin-rotation parameter $γ$ are obtained; the sign of $γ$ reveals the repulsive or attractive character of the effective interaction. In a trapped Fermi gas the spin diffusion equations become nonlinear, and their numerical solution exhibits an inhomogeneous spin state even at the spin echo time. While the microscopic diffusivity and $γ$ increase at weak coupling, their apparent values inferred from the trap-averaged magnetization saturate in agreement with a recent experiment for a dilute ultracold Fermi gas.