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

We develop a theoretical model of magnon-assisted transport in a mesoscopic tunnel junction between a ferromagnetic metal and a normal (non-magnetic) metal. The current response to a bias voltage is dominated by the contribution of elastic processes rather than magnon-assisted processes and the degree of spin polarization of the current, parameterized by a function $P (\Pi_{\uparrow (\downarrow)},\Pi_{N})$, $0 \leq P \leq 1$, depends on the relative sizes of the majority $\Pi_{\uparrow}$ and minority $\Pi_{\downarrow}$ band Fermi surface in the ferromagnet and of the Fermi surface of the normal metal $\Pi_{N}$. On the other hand, magnon-assisted tunneling gives the dominant contribution to the current response to a temperature difference across the junction. The resulting thermopower is large, $S \sim - (k_B/e) (k_BT/\omega_{D})^{3/2} P (\Pi_{\uparrow (\downarrow)},\Pi_{N})$, where the temperature dependent factor $(k_{B}T/\omega_{D})^{3/2}$ reflects the fractional change in the net magnetization of the ferromagnet due to thermal magnons at temperature $T$ (Bloch's $T^{3/2}$ law) and $\omega_{D}$ is the magnon Debye energy.