Magnetoresistance and exchange coupling in a ferromagnetic tunnel junction with ferromagnetic layers of finite thickness

Based on a two-band model, we investigate the tunnel magnetoresistance (TMR) and interlayer exchange coupling (IEC) in a ferromagnet/insulator (semiconductor)/ferromagnet [FM/I(S)/FM] tunnel junction covered on both sides by nonmagnetic metal layers. Our results show that (1) the TMR oscillates with the thickness of ferromagnetic layers and can reach very large values under suitable conditions, which may in general not be reached in a FM/I(S)/FM tunnel junction with an infinitely thick ferromagnetic layer. This suggests an alternative way to obtain large TMR; (2) the bilinear coupling (Formula presented) and biquadratic coupling (Formula presented) decrease exponentially with the increase of barrier thickness, whereas they oscillate with the thickness of the FM layer, and (Formula presented) can reach considerably large values under some conditions; (3) the oscillations of the IEC and the TMR with the FM layer thickness are correlated owing to the quantum-size effect, namely, the oscillation period and phase of the TMR are exactly the same as that of the IEC. Furthermore, the quantum-size effect can also give rise to a positive TMR (inverse spin-valve effect).