https://doi.org/10.1140/epjb/s10051-024-00677-5
Regular Article - Solid State and Materials
Bifurcation analysis of strongly nonlinear injection locked spin torque oscillators
Univ. Grenoble Alpes, CEA, CNRS, Grenoble INP, IRIG-Spintec, 38000, Grenoble, France
Received:
20
November
2023
Accepted:
15
March
2024
Published online:
8
April
2024
We investigate analytically and numerically the dynamics of an injection locked in-plane uniform spin torque oscillator for several forcing configurations at large driving amplitudes. For the analysis, the spin wave amplitude equation is used to reduce the dynamics to a general auto oscillator equation in which the forcing is a complex valued function 
. Assuming that the oscillator is strongly non-isochronous and/or forced by a power forcing ( 
), we show that the parameters 
govern the main bifurcation features of the Arnold tongue diagram: (i) the locking range asymmetry is mainly controlled by the derivative 
, (ii) the loss of stability when the frequency mismatch between the generator and the oscillator increases occurs for a power threshold depending on and (iii) the frequency hysteretic range is related to the transient regime at zero mismatch frequency. Then, the model is compared with the macrospin simulation for driving amplitudes as large as 
for the magnetic field and 
for the current density. As predicted by the model, the forcing configuration (nature of the driving signal, applied stimuli direction, harmonic orders) affects substantially the oscillator dynamic. However, some discrepancies are observed. In particular, the prediction of the frequency and power locking range boundaries may be misestimated if the hysteretic boundaries are of same magnitude order. Moreover, the misestimation can be of two different types according to the bifurcation type. These effects are a further manifestation of the complexity of the dynamics in non-isochronous auto-oscillators.
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