Stability analysis of perpendicular magnetic trilayers with a field-like spin torque

We have analytically studied the magnetization dynamics in magnetic trilayers with perpendicular anisotropy for both free and pinned layers. By linear stability analysis, we obtain the phase diagram parameterized by the current, magnetic field and relative strength of the field-like spin torque to Slonczewski torque. Under the control of the current and external magnetic field, several magnetic states, such as quasi-parallel and quasi-antiparallel stable states, out-of-plane precession, and bistable states can be realized. The precession frequency can be expressed as a function of the current and external magnetic field. In addition, the presence of field-like spin torque can change the switching current and precession frequency.