Tunable intrinsic phase of a spin torque oscillator

We show analytically why a spin torque oscillator (STO) locks to an alternating current (Iac), having the same frequency as the STO, at a nontrivial, intrinsic, phase value Δϕ0. We determine both the stability and the exact phase of the locked state and explain the recently observed phase jump by about 180° at the in-plane-to-out-of-plane precession boundary. Δϕ0 depends on the STO material parameters and is tunable through both the applied field and the dc current, which provides an additional control of the exact I-V phase in an STO driven radio frequency circuit.