Spin-wave-induced correction to the conductivity of ferromagnets

TL;DR

This paper calculates how spin waves in disordered ferromagnetic metals affect electrical conductivity, extending known corrections to include spin-wave interactions and analyzing different impurity scattering regimes.

Contribution

It generalizes the Altshuler-Aronov correction to account for spin-wave-mediated electron interactions in ferromagnets, providing explicit formulas for various impurity regimes.

Findings

In clean ferromagnets, correction scales as -T^{5/2} at high temperatures.

In dirty ferromagnets, the correction varies non-monotonically with temperature.

Derived a general expression for conductivity correction due to spin waves.

Abstract

We calculate the correction to the conductivity of a disordered ferromagnetic metal due to spin-wave-mediated electron--electron interactions. This correction is the generalization of the Altshuler-Aronov correction to spin-wave-mediated interactions. We derive a general expression for the conductivity correction to lowest order in the spin-wave-mediated interaction and for the limit that the exchange splitting $\Delta$ is much smaller than the Fermi energy. For a "clean" ferromagnet with $\Delta\tau_{\rm el}/\hbar \gg 1$, with $\tau_{\rm el}$ the mean time for impurity scattering, we find a correction $\delta \sigma \propto -T^{5/2}$ at temperatures $T$ above the spin wave gap. In the opposite, "dirty" limit, $\Delta\tau_{\rm el}/\hbar \ll 1$, the correction is a non-monotonous function of temperature.