We present a finite temperature calculation of the transverse spin-diffusion coefficient $D_{\perp }$ in a dilute degenerate Fermi gas, in the presence of a small external magnetic field $H$. While the longitudinal diffusion coefficient displays the conventional Fermi-liquid dependence, $D_{\parallel }\propto T^{-2\mathrm{}}$, the behavior of $D_{\perp }$ shows three separate regimes: (a) $D_{\perp }\sim H^{-2\mathrm{}}$ for $T\ll H$, (b) $D_{\perp }\sim T^{-2\mathrm{}}$, $\frac{D_{\perp }}{D_{\parallel }}\ne 1$ for $T\gg H$ and large spin-rotation parameter $\xi \gg 1$, and (c) $D_{\perp }=D_{\parallel }\propto T^{-2\mathrm{}}$ for $T\gg H$ and $\xi \ll 1$. Our results are qualitatively consistent with the experimental data in weakly spin-polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$- ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures.

• Received 13 June 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.1613