Magnon-assisted transport and thermopower in ferromagnet–normal-metal tunnel junctions

Magnon-assisted transport across a tunnel junction between a ferromagnet and a normal (nonmagnetic) metal is studied theoretically. A finite temperature difference across the junction produces a nonequilibrium magnetization that drives a charge current, mediated by electrons via electron-magnon interactions, from the ferromagnet into the normal metal. The corresponding thermopower coefficient is large, $S\sim -{(k}_B{/e\left)\right(k}_{B}T/{\omega }_M{)}^{3/2}P({\Pi }_{+},{\Pi }_{-},{\Pi }_N)$ where $P({\Pi }_{+},{\Pi }_{-},{\Pi }_N),$ $0<~P<~1,$ represents the degree of spin polarization of the current response to a bias voltage, and depends on the relative sizes of the majority ${\Pi }_{+}$ and the minority ${\Pi }_{-}$ band Fermi surface in the ferromagnet and in the normal metal, ${\Pi }_N.$