Electrical and Heat Currents in Nanoscopic System with Ferromagnetic Electrodes of Non-Collinear Magnetic Moments

Thermoelectric properties of nanoscopic system composed of a single-level quantum dot attached to ferromagnetic electrodes are studied with the use of the non-equilibrium Green function formalism. Electrical and heat currents flowing through the system under temperature gradient and bias voltage are calculated in the non-linear regime. Both charge and heat currents strongly depend on configuration of magnetic moments in the leads. TMR ratio is mostly positive, but in a region of small bias voltages, where the electron flow is determined by the temperature gradient, electrical current in parallel and antiparallel configurations flows in opposite directions leading to considerable negative TMR.