Analytic expression for the giant fieldlike spin torque in spin-filter magnetic tunnel junctions

We propose analytic expressions for fieldlike, ${T}_{\ensuremath{\perp}}$, and spin-transfer, ${T}_{\ensuremath{\parallel}}$, spin torque components in the spin-filter-based magnetic tunnel junction (SFMTJ), by using the single-band tight-binding model with the nonequilibrium Keldysh formalism. In consideration of multireflection processes between noncollinear magnetization of the spin-filter (SF) barrier and the ferromagnetic (FM) electrode, the central spin-selective SF barrier plays an active role in the striking discovery ${T}_{\ensuremath{\perp}}\ensuremath{\gg}{T}_{\ensuremath{\parallel}}$, which can be further identified by the unusual barrier thickness dependence of giant ${T}_{\ensuremath{\perp}}$. Our general expressions reveal the sinusoidal angular dependence of both spin torque components, even in the presence of the SF barrier.