Magnetoresistance in single-electron transistors comprising a superconducting island with ferromagnetic leads

We report electric and magnetic field responses of single-electron transistors (SETs) comprising a superconducting island with ferromagnetic (FM) leads. We fabricated two SETs, one of which had relatively high resistance and the other had relatively low resistance. The SETs had two states for the gate charge: SET-ON or SET-OFF. They also had two states for the FM lead magnetization: parallel (P) or anti-parallel (AP) configuration. Current-voltage characteristics of four SET states ("P & SET-ON," "P & SET-OFF," "AP & SET-ON," and "AP & SET-OFF") were measured at approximately 0.1 K in a compact dilution refrigerator. Magnetoresistance ratio (MRR) values were obtained for the SET-ON and SET-OFF states, respectively. The higher-resistance SET1 exhibited positive MRR values for all measured bias voltages. The MRR enhancement was confirmed for the SET-OFF state, which agreed well with the co-tunneling model. The lower-resistance SET2, on the other hand, exhibited negative and positive MRR values for higher and lower bias voltage conditions, respectively. The bias voltage for the MRR polarity reversal was changed by the gate voltage. It was also confirmed that the co-tunneling model was partially valid for negative MRR values.