Current-induced torque in ferromagnetic single-electron devices in the limits of the fast and slow spin relaxation

Theoretical analysis of the spin-transfer torque acting on the magnetic moment of the central electrode (island) in a single-electron ferromagnetic transistor has been performed for the spin relaxation time in the island ranging from fast to slow spin relaxation limits. The magnetic configuration of die system can be generally arbitrary. Spin accumulation on the island, due to the spin asymmetry of tunnelling processes, is taken into account. Electric current flowing through the device is calculated in the regime of sequential transport, and the master equation is used to calculate probabilities of different charge and spin states in the island. The torque acting on the central electrode is then calculated from the spin current absorbed by magnetic moment of the island.