Spin transfer and critical current for magnetization reversal in ferromagnet-ferromagnet-ferromagnet double-barrier tunnel junctions

In terms of the Keldysh nonequilibrium Green's-function method and invoking the generalized Landau-Lifishiz- Gilbert equation in presence of the spin-transfer torque (STT), we have systematically investigated the spin-transfer effect as well as the critical current for magnetization reversal in the ferromagnet (FM)-ferromagnet-ferromagnet double-barrier magnetic tunnel junctions. It has been found that the tunnel magnetoresistance (TMR) increases dramatically with the increase in the molecular field of the middle FM, and the larger the molecular field, the greater the TMR. The STT is found to oscillate with the bias voltage for finite thickness of the middle FM, while the electrical current as a function of the bias is almost linear with slight oscillations. It has been shown that the molecular field and the polarization dependences of the critical voltage and critical electrical current show steplike behaviors for finite thicknesses of the middle FM. The order of magnitude of the critical current is estimated to be about 10(5)-10(6) A/cm(2). The present results are expected to be instructive for manufacturing the relevant spintronic devices.