Spin-wave-induced correction to the conductivity of ferromagnets

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 $Δ$ is much smaller than the Fermi energy. For a "clean" ferromagnet with $Δτ_{\rm el}/\hbar \gg 1$, with $τ_{\rm el}$ the mean time for impurity scattering, we find a correction $δσ\propto -T^{5/2}$ at temperatures $T$ above the spin wave gap. In the opposite, "dirty" limit, $Δτ_{\rm el}/\hbar \ll 1$, the correction is a non-monotonous function of temperature.

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