Exact solution of the Boltzmann equation for low-temperature transport coefficients in metals II: Scattering by ferromagnons

TL;DR

This paper extends an exact solution technique for the Boltzmann equation to analyze magnon effects on transport in ferromagnetic metals at low temperatures, providing precise formulas for resistivity, heat conductivity, and thermopower.

Contribution

It introduces an exact method to compute magnon contributions to transport coefficients in ferromagnets, including precise prefactors and temperature dependencies.

Findings

Electrical resistivity $ ho o ext{exponentially small}$ at low T

Heat conductivity $\sigma_h o T^3 imes ext{exponential}$ at low T

Thermopower $S o T$ at low T

Abstract

In a previous paper (Paper I) we developed a technique for exactly solving the linearized Boltzmann equation for the electrical and thermal transport coefficients in metals in the low-temperature limit. Here we adapt this technique to determine the magnon contribution to the electrical and thermal conductivities, and to the thermopower, in metallic ferromagnets. For the electrical resistivity $\rho$ at asymptotically low temperatures we find $\rho \propto \exp{(-T_{\rm min}/T)}$, with $T_{\rm min}$ an energy scale that results from the exchange gap and a temperature independent prefactor of the exponential. The corresponding result for the heat conductivity is $\sigma_h \propto T^3\,\exp{(T_{\rm min}/T)}$, and thermopower is $S \propto T$. All of these results are exact, including the prefactors.