Low-Temperature Spin Diffusion in a Spin-Polarized Fermi Gas

Abstract

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 low-temperature Fermi-liquid behavior, $D_{\parallel }\propto T^{-2}$, the corresponding results for $D_{\perp }$ show three separate regimes: (a) $D_{\perp }\sim H^{-2}$ for $T\ll H$; (b) $D_{\perp }\sim T^{-2}$, $D_{\perp }/D_{\parallel }\ne 1$ for $T\gg H$ and large spin-rotation parameter $\xi \gg 1$, and (c) $D_{\perp }=D_{\parallel }\propto T^{-2}$ for $T\gg H$ and $\xi \ll 1$. Our results are qualitatively consistent with the available experimental data in weakly spin-polarized ${}^3\mathrm{He}$ and ${}^3\mathrm{He}{-}^4\mathrm{He}$ mixtures.

13 pages, REVTEX, 3 figures available upon request, RU-94-49

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