Invariant Tori in a Network of Two Spin-Torque Nano Oscillators

  • James TurtleEmail author
  • Antonio Palacios
  • Patrick Longhini
  • Visarath In
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 6)


Over the past few years it has been shown, through theory and experiments, that the AC current produced by spin torque nano-oscillators (STNO), coupled in an array, can lead to feedback between the STNOs causing them to synchronize and that, collectively, the microwave power output of the array is significantly larger than that of an individual oscillator. Other works have pointed, however, to the difficulty in achieving synchronization. In particular, Persson et al. [17] shows that the region of parameter space where the synchronization state exists for even a small array with two STNOs is rather small. In this work we explore in more detail the nature of the bifurcations that lead into and out of the synchronization state for the two-array case. The bifurcation analysis shows bistability between in-phase and out-of-phase oscillations. A more detailed analysis of the out-of-phase solutions reveals both limit-cycles and invariant tori that are responsible for anti-phase and quasi-periodic oscillations respectively. A continuation of unstable tori demonstrates a portion of the separatrix bounding the basins of attraction for the in- and out-of-phase limit-cycles.


Hopf Bifurcation Spin Valve Synchronization State Free Layer Saddle Node 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • James Turtle
    • 1
    Email author
  • Antonio Palacios
    • 2
  • Patrick Longhini
    • 3
  • Visarath In
    • 3
  1. 1.Predictive Science Inc.San DiegoUSA
  2. 2.San Diego State UniversitySan DiegoUSA
  3. 3.Space and Naval Warfare Systems Center PacificSan DiegoUSA

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