Electronic transport in a ferromagnetic single-electron transistor with non-collinear magnetizations in the co-tunnelling regime

Spin-dependent electronic transport in a ferromagnetic single-electron transistor (FM SET) is studied theoretically in the Coulomb blockade regime [1]. Two external electrodes and the central part (island) of the device are assumed to be ferromagnetic, with the corresponding magnetizations being non-collinear in a general case. First order (sequential) transport is suppressed in the Coulomb blockade regime, so the second order (co-tunnelling) processes give the dominant contribution to the current. The co-tunnelling processes take place via four intermediate (virtual) states of the island: two of them are with one extra electron on the central electrode of the device (in the spin-majority or spin-minority subbands), whereas the other two virtual states are with a hole (in the spin-majority or spin-minority subbands) in the central electrode. The co-tunnelling processes create electron-hole excitations of the central electrode, and in a general case they also can create spin excitations. However, we assume relatively fast spin relaxation in the island, hence the spin accumulation is neglected. Basic transport characteristics, like tunnelling current and tunnel magnetoresistance are calculated for an arbitrary magnetic configuration of the system.