Tilted spin torque-driven ferromagnetic resonance in a perpendicular-analyzer magnetic trilayer

A theoretical study is presented on the current-driven ferromagnetic resonance in the magnetic trilayers. On the basis of the Landau–Lifshitz–Gilbert–Slonczewski equation, we derive the output dc voltage for arbitrary anisotropy in the free and pinned layers by the linearization method. As an example, the resonance spectra of the tilted-polarizer and perpendicular-analyzer trilayer show that the equilibrium position, the resonant linewidth and the resonant location can be tuned by changing the magnitude and the direction of spin torque. The effective damping can be minimized through adjusting the current and the pinned-layer magnetization direction.