The Seebeck Effect in Double Tunnel Junctions with Ferromagnetic Electrodes and Central Layer Separated by Nonmagnetic Barriers

The Seebeck effect is analysed in the double planar tunnel junctions consisting of ferromagnetic electrodes and the central layer separated by nonmagnetic barriers with the arbitrary angle between magnetic moments in neighbouring ferromagnetic layers. The Seebeck coefficient is calculated as a function of the thickness of the central layer. The influence of temperature of the junction and the relative orientation of magnetic moments in ferromagnetic layers on this coefficient is also analysed. Calculations are performed in the linear response theory using the free-electron model. It has been found that the Seebeck coefficient oscillates with the thickness of the central layer and can be strongly enhanced in the junction with special central layer thickness due to electron tunnelling by resonant states. The form of the observed oscillations depends on the temperature of the junction. The magnitude of the Seebeck coefficient usually increases with the increase of the angle between magnetic moments in the neighbouring ferromagnetic layers as in the case of single junctions. However, in the junctions with the specially designated central layer the decrease of the magnitude of the Seebeck coefficient with the increase of this angle can be observed.