TUnnel magnetoresistance in the ferromagnetic tunnel junction with ferromagnetic layers of finite thickness subjected to an electric field

Based on the two-band model, we investigate the tunnel magnetoresistance(TMR) in ferromagnet/insulator(semiconductor)/ferromagnet(FM/I(S)/FM) tunnel junction covered on both sides by nonmagnetic metal layers subjected to an electric field. Our results show that TMR oscillates with the thickness of ferromagnetic layers owing to the quantum-size effect and can reach very large value under suitable conditions, which may in general not be reached in FM/I(S)/FM with infinitely thick ferromagnetic layer. Although the electric field causes the change of the oscillation period, phase and amplitude of the TMR, a large TMR is still obtained in some situations with the electric field. Furthermore, the electric field does not change the feature that TMR varies monotonously with the change of magnetization angle of the middle ferromagnetic layer.