Parity Effect and Tunnel Magnetoresistance of Ferromagnet / Superconductor / Ferromagnet Single-Electron Tunneling Transistors

We theoretically study the tunnel magnetoresistance(TMR) of ferromagnet / superconductor / ferromagnet single-electron tunneling transistors with a special attention to the parity effect. It is shown that in the plateau region, there is no spin accumulation in the island even at finite bias voltage. However, the information of the injected spin is carried by the excess electron and thus the TMR exists. The spin relaxation rate of the excess electron can be estimated from the TMR. We also show that the TMR increases with decreasing the size of the superconducting island.