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

TL;DR

This paper calculates the transverse spin-diffusion coefficient in a dilute Fermi gas at finite temperature, revealing three distinct regimes depending on temperature and magnetic field, and compares results with experimental data.

Contribution

It provides a detailed finite temperature analysis of the transverse spin diffusion in a spin-polarized Fermi gas, identifying three regimes and their dependence on temperature and magnetic field.

Findings

D⊥ ∼ H^{-2} for T ≪ H

D⊥ ∼ T^{-2} for T ≫ H with large spin-rotation parameter

D⊥ = D∥ ∝ T^{-2} for T ≫ H with small spin-rotation parameter

Abstract

We present a finite temperature calculation of the transverse spin-diffusion coefficient, $D_\bot$, 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 $D_\bot$ show three separate regimes: (a) $D_\bot \sim H^{-2}$ for $T \ll H$; (b) $D_\bot \sim T^{-2}$, $D_\bot /D_\parallel \neq 1$ for $T \gg H$ and large spin-rotation parameter $\xi \gg 1$, and (c) $D_\bot = D_\parallel \propto T^{-2}$ for $T \gg H$ and $\xi \ll 1$. Our results are qualitatively consistent with the available experimental data in weakly spin-polarized $^3{\rm He}$ and $^3{\rm He} - ^4{\rm He}$ mixtures.