Microscopic Theory of Magnon-Drag Thermoelectric Transport in Ferromagnetic Metals

A theoretical study of the magnon-drag Peltier and Seebeck effects in ferromagnetic metals is presented. A magnon heat current is described perturbatively from the microscopic viewpoint with respect to electron--magnon interactions and the electric field. Then, the magnon-drag Peltier coefficient $\Pi_\MAG$ is obtained as the ratio between the magnon heat current and the electric charge current. We show that $\Pi_\MAG=C_\MAG T^{5/2}$ at a low temperature $T$; that the coefficient $C_\MAG$ is proportional to the spin polarization $P$ of the electric conductivity; and that $P>0$ for $C_\MAG<0$, but $P<0$ for $C_\MAG>0$. From experimental results for magnon-drag Peltier effects, we estimate that the strength of the electron--magnon interaction is about 0.3 eV$\cdot\AA^{3/2}$ for permalloy.