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 $\mathrm{\Delta }$ is much smaller than the Fermi energy. For a “clean” ferromagnet with $\mathrm{\Delta }{\tau }_{\mathrm{e}\mathrm{l}}\mathrm{/}\mathrm{\hslash }\gg 1$, with ${\tau }_{\mathrm{e}\mathrm{l}}$ the mean time for impurity scattering, we find a correction $\delta \sigma \propto -T^{5\mathrm{/}2}$ at temperatures $T$ above the spin wave gap. In the opposite, “dirty” limit, $\mathrm{\Delta }{\tau }_{\mathrm{e}\mathrm{l}}\mathrm{/}\mathrm{\hslash }\ll 1$, the correction is a non-monotonous function of temperature.