Power and phase dynamics of injection-locked spin torque nano-oscillators under conservative and dissipative driving signals

Abstract

International audienceTo describe all possible injection locking configurations of spin torque nano-oscillators (STNO), previous analytical descriptions are extended by introducing the most general form of the driving force: ℱ ∝ +. We provide the expressions of the corresponding forcing functions ℱ for the six basic conservative and dissipative forcing torques (~ × and ~ × × with = , ,), and demonstrate at the example of a uniform in-plane magnetized STNO, that the general case (| | | |) as well as special cases, can occur depending on: (i) the nature of the forcing torque, (ii) the direction with respect to the equilibrium direction, (iii) the harmonic order and (iv) the operation point (dc current). These relations provide a straightforward means to analyze more complex forcing torques such as a rotating field or the superposition of damping-like and field-like spin transfer torques. Besides the phase properties we also address in detail the power properties of the injection locked state for which two new parameters are introduced: the locking power range and the power angle. They can provide important complementary information on the driving forces from experiment. The general description presented here is not limited to STNOs and is valid for any non-isochronous auto-oscillator driven by an elliptical forcing of conservative or dissipative nature