Advertisement

Bifurcation Analysis of Spin-Torque Nano Oscillators Parallel Array Configuration

  • Brian Sturgis-JensenEmail author
  • Antonio Palacios
  • Patrick Longhini
  • Visarath In
Conference paper
Part of the Understanding Complex Systems book series (UCS)

Abstract

The ability for a Spin Torque Nano Oscillator (STNO) to perform as a nano-scaled microwave voltage oscillator continues to be the focus of exten- sive research. Due to their small size (on the order of 10 nm), low power consumption, and ultrawide frequency range STNOs demonstrate significant potential for applications in microwave generation. To date, the ability for a STNO to produce microwave signals is achievable, however, the low power output produced by a single STNO currently renders them inoperable for applications. In response, various groups have proposed the synchronization of a network of STNOs such that the coherent signal produces a strong enough microwave signal at the nanoscale. Achieving synchronization, however, has proven to be a challenging task and raises complex problems related to the field of Nonlinear Dynamical Systems. In this work we analyze the problem of synchronization for networks of STNOs connected in parallel. Bifurcation diagrams for small networks of STNOs are computed which depicts bistability between in-phase and out-of- phase limit cycle oscillations for much of the phase space. In order to extend the analysis for large networks of STNOs, we exploit the \(S_{N}\) symmetry ex- hibited by the system all-to-all coupled STNOs. We develop implicit analytic expressions for Hopf bifurcations which yield synchronized limit cycle oscil- lations, allowing for the computation of the Hopf loci for an arbitrarily large network of oscillators. Through stability analysis we determine the parame- ter space for which the Hopf bifurcation is supercritical and exhibits a stable center-manifold. This analysis is completed for large arrays and used to nu- merically demonstrate synchronization in up to \(N =\) 1000 STNOs. These results should help guide future experiments and, eventually, lead to the design and fabrication of a nanoscale microwave signal generator.

Notes

Acknowledgements

We recognize the support from the Office of Naval Research Grant N00014-16-1-2134.

References

  1. 1.
    E. Doedel, Auto: a program for the automatic bifurcation analysis of autonomous systems. Congr. Numer. 30, 265–284 (1981)MathSciNetzbMATHGoogle Scholar
  2. 2.
    E.J. Doedel, A.R. Champneys, T.F. Fairgrieve, Y.A. Kuznetsov, B. Sandstede, X. Wang et al., Continuation and Bifurcation Software for Ordinary Differential Equations (with Homcont), (AUTO97, Concordia University, Canada, 1997)Google Scholar
  3. 3.
    M. Golubitsky, I. Stewart, D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, vol. 2 (Springer Science & Business Media, Berlin, 2012)Google Scholar
  4. 4.
    J. Grollier, V. Cros, A. Fert, Synchronization of spin-transfer oscillators driven by stimulated microwave currents. Phys. Rev. B 73, (2006)Google Scholar
  5. 5.
    S. Kaka, M.R. Pufall, W.H. Rippard, T.J. Silva, S.E. Russek, J.A. Katine, Mutual phase-locking of microwave spin torque nano-oscillators. Nature 437, 389–392 (2005)CrossRefGoogle Scholar
  6. 6.
    J. Katine, E.E. Fullerton, Device implications of spin-transfer torques. J. Magn. Magn. Mater. 320, 1217–1226 (2008)CrossRefGoogle Scholar
  7. 7.
    Y.A. Kuznetsov, Elements of applied bifurcation theory, vol. 112 (Springer Science & Business Media, Berlin, 2013)Google Scholar
  8. 8.
    F. Mancoff, N. Rizzo, B. Engel, S. Tehrani, Phase-locking in double-point-contact spin-transfer devices. Nature 437, 393 (2005)CrossRefGoogle Scholar
  9. 9.
    S. Murugesh, M. Lakshmanan, Spin-transfer torque induced reversal in magnetic domains. Chaos Solitons Fractals 41, 2773–2781 (2009)CrossRefGoogle Scholar
  10. 10.
    J. Persson, Y. Zhou, J. Akerman, Phase-locked spin torque oscillators: impact of device variability and time delay. J. Appl. Phys. 101, 09A503 (2007)CrossRefGoogle Scholar
  11. 11.
    W.H. Rippard, M.R. Pufall, S. Kaka, T.J. Silva, S.E. Russek, J.A. Katine, Injection locking and phase control of spin transfer nano-oscillators. Phys. Rev. Lett. 95, 067203 (2005)CrossRefGoogle Scholar
  12. 12.
    W.H. Rippard, M.R. Pufall, S.E. Russek, Comparison of frequency, linewidth, and output power in measurements of spin-transfer nanocontact oscillators. Phys. Rev. B 74, 224409 (2006)CrossRefGoogle Scholar
  13. 13.
    C. Serpico, R. Bonin, G. Bertotti, M. d’Aquino, I. Mayergoyz, Theory of injection locking for large magnetization motion in spin-transfer nano-oscillators. IEEE Trans. Magn. 45, 3441–3444 (2009)CrossRefGoogle Scholar
  14. 14.
    J. Turtle, P.-L. Buono, A. Palacios, C. Dabrowski, V. In, P. Longhini, Synchronization of spin torque nano-oscillators. Phys. Rev. B 95, 144412 (2017)CrossRefGoogle Scholar
  15. 15.
    J.A. Turtle, Synchronization in coupled spin-torque nano oscillators: nonlinear dynamics analysis. Ph.D. thesis, Diego State University, San, 2016Google Scholar

Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019

Authors and Affiliations

  • Brian Sturgis-Jensen
    • 1
    Email author
  • Antonio Palacios
    • 1
  • Patrick Longhini
    • 2
  • Visarath In
    • 2
  1. 1.San Diego State UniversitySan DiegoUSA
  2. 2.Space and Naval Warfare Systems Center PacificSan DiegoUSA

Personalised recommendations