Thermopower, figure of merit and spin-transfer torque induced by the temperature gradient in planar tunnel junctions

The thermopower, charge and thermal conductance, and figure of merit as well as the spin-transfer torque generated by the temperature gradient in the planar tunnel junction consisting of ferromagnetic layers and the nonmagnetic tunnel barrier are investigated in the free-electron-like spin-polarized one-band model. In particular, the influence of the parameters of the junction as well as the influence of the relative orientation of magnetic moments on the studied phenomena are investigated. The thermopower can be related to the voltage drop generated by the temperature difference between electrodes under the condition that the charge current vanishes. It depends on the magnetic configuration of the junction. In junctions with high barriers the thermopower is maximal in the antiparallel configuration and it can be enhanced in junctions with strong spin-splitting of the electron bands. The component of the torque studied in the present paper is oriented in the plane formed by magnetic moments and it appears in the absence of the bias voltage. Its magnitude is insensitive to the sign of the temperature difference in contrast to the bias-induced in-plane torque which strongly depends on the polarization of the bias. The studied torque is usually smaller than the torque generated by the bias: however, it can be significant in junctions with low barriers.