Theory of Transport Processes in Nearly Ferromagnetic Fermi Liquids

Abstract

A theory of the low-temperature transport processes of thermal conduction and spin diffusion in Fermi liquids near the ferromagnetic state is developed on the assumption that the predominant particle scattering at low temperatures occurs from persistent spin fluctuations, or "paramagnons," of the type discussed recently by Doniach and Engelsberg and by Berk and Schrieffer. A Boltzmann equation for this type of scattering is set up and solved by the usual variational procedure to obtain expressions for the coefficients of thermal conductivity K and spin-diffusion $D$. The latter are evaluated by using a simple model approximation for the paramagnon spectral density function ${A}_{\mathrm{q}}(\ensuremath{\omega})$, based on the correct RPA result at long wavelengths. It is found that in the limit $T\ensuremath{\rightarrow}0$, $K$ varies as ${T}^{\ensuremath{-}1}$ and $D$ as ${T}^{\ensuremath{-}2}$, in accordance with the predictions of the Landau theory. As $T$ increases from absolute zero, however, $K$ and $D$ fall off increasingly less rapidly than ${T}^{\ensuremath{-}1}$ and ${T}^{\ensuremath{-}2}$, respectively, and actually increase with increasing $T$ after passing through minima. The theory can therefore account for the observed temperature dependence of the thermal conductivity and spin diffuison of liquid ${\mathrm{He}}^{3}$. In particular, the theoretical predictions are in close agreement with the low-pressure thermal-conductivity and diffusion data obtained by the Illinois group.