Current and spin torque in a ferromagnet-quantum dot-ferromagnet tunneling system: quantum rate equations

We investigate the current and the spin torque in a system composed of a quantum dot (QD) connected to two ferromagnetic leads with arbitrary relative magnetization direction. An external magnetic field is applied to the QD, where the e–e Coulomb interaction is taken into account. Within the technique of quantum rate equations, the general expressions for the current and the spin torque are derived. It is found that when a weak longitudinal magnetic field (which is collinear with the magnetizations of the FM leads) is applied, the diode-like effect in the system still exists, but its working bias range is shifted or reduced, which depends on the direction of the magnetic field. When the voltage exceeds the working bias range, the device can work as a spin-current rectifier. If a transverse magnetic field is applied or if the system is asymmetrical, the current shows a nonmonotonous dependence on θ, and the torque shows a sin 2θ-like behavior. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008