A tunnel junction between a ferromagnet and a normal metal: Magnon-assisted contribution to thermopower and conductance

We develop a theoretical model of magnon-assisted transport in a mesoscopic tunnel junction between a ferromagnetic metal and a normal (nonmagnetic) 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(Π_↑(↓),Π_N), 0≤P≤1, depends on the relative sizes of the majority Π_↑ and minority Π _↓ band Fermi surface in the ferromagnet and of the Fermi surface of the normal metal Π_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 ∼ - (k_B/e)(k_BT/ω _D)^3/2P(Π_↑(↓),Π_N), where the temperature dependent factor (k_BT/ω_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 ω_D is the magnon Debye energy.