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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
E. Doedel, Auto: a program for the automatic bifurcation analysis of autonomous systems. Congr. Numer. 30, 265–284 (1981)
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)
M. Golubitsky, I. Stewart, D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, vol. 2 (Springer Science & Business Media, Berlin, 2012)
J. Grollier, V. Cros, A. Fert, Synchronization of spin-transfer oscillators driven by stimulated microwave currents. Phys. Rev. B 73, (2006)
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)
J. Katine, E.E. Fullerton, Device implications of spin-transfer torques. J. Magn. Magn. Mater. 320, 1217–1226 (2008)
Y.A. Kuznetsov, Elements of applied bifurcation theory, vol. 112 (Springer Science & Business Media, Berlin, 2013)
F. Mancoff, N. Rizzo, B. Engel, S. Tehrani, Phase-locking in double-point-contact spin-transfer devices. Nature 437, 393 (2005)
S. Murugesh, M. Lakshmanan, Spin-transfer torque induced reversal in magnetic domains. Chaos Solitons Fractals 41, 2773–2781 (2009)
J. Persson, Y. Zhou, J. Akerman, Phase-locked spin torque oscillators: impact of device variability and time delay. J. Appl. Phys. 101, 09A503 (2007)
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)
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)
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)
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)
J.A. Turtle, Synchronization in coupled spin-torque nano oscillators: nonlinear dynamics analysis. Ph.D. thesis, Diego State University, San, 2016
Acknowledgements
We recognize the support from the Office of Naval Research Grant N00014-16-1-2134.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply
About this paper
Cite this paper
Sturgis-Jensen, B., Palacios, A., Longhini, P., In, V. (2019). Bifurcation Analysis of Spin-Torque Nano Oscillators Parallel Array Configuration. In: In, V., Longhini, P., Palacios, A. (eds) Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-10892-2_31
Download citation
DOI: https://doi.org/10.1007/978-3-030-10892-2_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10891-5
Online ISBN: 978-3-030-10892-2
eBook Packages: EngineeringEngineering (R0)