We observe that the diffusive spin current in a strongly interacting degenerate Fermi gas of $^{40}$K precesses about the local magnetization. As predicted by Leggett and Rice, precession is observed both in the Ramsey phase of a spin-echo sequence, and in the nonlinearity of the magnetization decay. At unitarity, we measure a Leggett-Rice parameter $gamma = 1.08(9)$ and a bare transverse spin diffusivity $D_0^perp = 2.3(4),hbar/m$ for a normal-state gas initialized with full polarization and at one fifth of the Fermi temperature, where $m$ is the atomic mass. One might expect $gamma = 0$ at unitarity, where two-body scattering is purely dissipative. We observe $gamma rightarrow 0$ as temperature is increased towards the Fermi temperature, consistent with calculations that show the degenerate Fermi sea restores a non-zero $gamma$. Tuning the scattering length $a$, we find that a sign change in $gamma$ occurs in the range $0 < (k_F a)^{-1} lesssim 1.3$, where $k_F$ is the Fermi momentum. We discuss how $gamma$ reveals the effective interaction strength of the gas, such that the sign change in $gamma$ indicates a switching of branch, between a repulsive and an attractive Fermi gas.
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