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  • Letter
  • Open Access

Current-control of chaos and effects of thermal fluctuations in magnetic tunnel junctions

Ryo Tatsumi1,2,*, Shinji Miwa3,4, Hiroaki Matsueda1,5, and Takahiro Chiba1,2,†

  • 1Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan
  • 2Department of Information Science and Technology, Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata 992-8510, Japan
  • 3The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
  • 4Trans-scale Quantum Science Institute, The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
  • 5Center for Science and Innovation in Spintronics, Tohoku University, Sendai 980-8577, Japan

  • *Contact author: tatsumi.ryo.p6@dc.tohoku.ac.jp
  • †Contact author: t.chiba@yz.yamagata-u.ac.jp
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Phys. Rev. Applied 26, L041005 – Published 21 October, 2026

DOI: https://doi.org/10.1103/nny3-5mnz

Abstract

We theoretically investigate the chaotic behavior of spin-torque ferromagnetic resonance in magnetic tunnel junctions (MTJs) with perpendicular magnetic anisotropy under thermal fluctuations. By calculating the Lyapunov exponent based on the Landau–Lifshitz–Gilbert equation, we demonstrate that an MTJ characterized by a double-well potential, composed of uniaxial magnetic anisotropy and an external dc magnetic field, exhibits chaotic magnetization dynamics that can be controlled by means of the dc bias via spin-transfer torque. Furthermore, we find that thermal fluctuations help to induce these chaotic magnetization dynamics, which can be regarded as noise-induced chaos. This research provides a basis for brain-inspired computing using spintronic devices and advances the understanding of the interplay between thermal fluctuations and chaos in magnetization dynamics.

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References (55)

  1. K. Aihara et al., Chaotic neural networks, Phys. Lett. A 144, 333 (1990).
  2. T. Yamada et al., Chaotic neural networks and the traveling salesman problem, in Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan, 1993), Vol. 2, pp. 1549–1552.
  3. C. Pan et al., A novel memristive chaotic neuron circuit and its application in chaotic neural networks for associative memory, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 40, 521 (2021).
  4. G. Tanaka et al., Recent advances in physical reservoir computing: A review, Neural Netw. 115, 100 (2019).
  5. Y. Paquot et al., Optoelectronic reservoir computing, Sci. Rep. 2, 287 (2012).
  6. J. Torrejon et al., Neuromorphic computing with nanoscale spintronic oscillators, Nature (London) 547, 428 (2017).
  7. S. Bhatti et al., Spintronics based random access memory: A review, Mater. Today 20, 530 (2017).
  8. K. Y. Camsari et al., p-bits for probabilistic spin logic, Appl. Phys. Rev. 6, 011305 (2019).
  9. W. Lee et al., Correlation free large-scale probabilistic computing using a true-random chaotic oscillator p-bit, Sci. Rep. 15, 8018 (2025).
  10. N. H. Packard, Adaptation toward the edge of chaos, in Dynamic Patterns in Complex Systems, J. A. S. Kelso,A. J. Mandell et al. (World Scientific, Singapore, 1988), pp. 293–301.
  11. R. Legenstein et al., Edge of chaos and prediction of computational performance for neural circuit models, Neural Netw. 20, 323 (2007).
  12. J. Boedecker et al., Information processing in echo state networks at the edge of chaos, Theory Biosci. 131, 205 (2012).
  13. N. Bertschinger et al., Real-time computation at the edge of chaos in recurrent neural networks, Neural Comput. 16, 1413 (2004).
  14. T. Furuta et al., Macromagnetic simulation for reservoir computing utilizing spin dynamics in magnetic tunnel junctions, Phys. Rev. Appl. 10, 034063 (2018).
  15. I. D. Mayergoyz et al., Nonlinear Magnetization Dynamics in Nanosystems (Elsevier, New York, 2009).
  16. R. Tatsumi et al., Chaotic magnetization dynamics in magnetic duffing oscillator, Phys. Rev. E 111, 064202 (2025).
  17. T. Chiba, Effects of magnonic Kerr nonlinearity on magnon-polaritons with a soft-mode, AIP Adv. 16, 025228 (2026).
  18. Z. Wang et al., Chaotic spin-wave solitons in magnetic film feedback rings, Phys. Rev. Lett. 107, 114102 (2011).
  19. A. B. Ustinov et al., Progressive development of spin wave chaos in active-ring oscillators, Phys. Rev. B 104, L140410 (2021).
  20. S. Petit-Watelot et al., Commensurability and chaos in magnetic vortex oscillations, Nat. Phys. 8, 682 (2012).
  21. K. Horizumi et al., Chaotic vortex dynamics in circular magnetic nanodisk with double disk structure induced by ac magnetic field, J. Magn. Soc. Jpn. 49, 42 (2025).
  22. Z. Li et al., Dynamic magnetization states of a spin valve in the presence of dc and ac currents: Synchronization, modification, and chaos, Phys. Rev. B 74, 054417 (2006).
  23. T. Yamaguchi et al., Synchronization and chaos in a spin-torque oscillator with a perpendicularly magnetized free layer, Phys. Rev. B 100, 224422 (2019).
  24. T. Taniguchi et al., Chaos in nanomagnet via feedback current, Phys. Rev. B 100, 174425 (2019).
  25. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer, New York, 2003).
  26. S. Yuasa et al., Giant room-temperature magnetoresistance in single-crystal Fe/MgO/Fe magnetic tunnel junctions, Nat. Mater. 3, 868 (2004).
  27. J.-G. J. Zhu et al., Magnetic tunnel junctions, Mater. Today 9, 36 (2006).
  28. A. A. Tulapurkar et al., Spin-torque diode effect in magnetic tunnel junctions, Nature (London) 438, 339 (2005).
  29. J. C. Sankey et al., Spin-transfer-driven ferromagnetic resonance of individual nanomagnets, Phys. Rev. Lett. 96, 227601 (2006).
  30. H. Kubota et al., Spin-torque oscillator based on magnetic tunnel junction with a perpendicularly magnetized free layer and in-plane magnetized polarizer, Appl. Phys. Express 6, 103003 (2013).
  31. M. Tsujikawa et al., Finite electric field effects in the large perpendicular magnetic anisotropy surface Pt/Fe/Pt(001): A first-principles study, Phys. Rev. Lett. 102, 247203 (2009).
  32. S. Iihama et al., Gilbert damping constants of Ta/CoFeB/MgO(Ta) thin films measured by optical detection of precessional magnetization dynamics, Phys. Rev. B 89, 174416 (2014).
  33. D. M. Lattery et al., Low gilbert damping constant in perpendicularly magnetized W/CoFeB/MgO films with high thermal stability, Sci. Rep. 8, 13395 (2018).
  34. E. A. Montoya et al., Magnetization reversal driven by low dimensional chaos in a nanoscale ferromagnet, Nat. Commun. 10, 543 (2019).
  35. R. Benzi et al., The mechanism of stochastic resonance, J. Phys. A 14, L453 (1981).
  36. L. Gammaitoni et al., Stochastic resonance, Rev. Mod. Phys. 70, 223 (1998).
  37. A. S. Pikovsky et al., Coherence resonance in a noise-driven excitable system, Phys. Rev. Lett. 78, 775 (1997).
  38. A. R. Bulsara et al., Homoclinic chaos in systems perturbed by weak langevin noise, Phys. Rev. A 41, 668 (1990).
  39. C. Gan, Noise-induced chaos in duffing oscillator with double wells, Nonlinear Dyn. 45, 305 (2006).
  40. Y. Lei et al., Onset of colored-noise-induced chaos in the generalized duffing system, Nonlinear Dyn. 89, 1371 (2017).
  41. F. Gassmann, Noise-induced chaos-order transitions, Phys. Rev. E 55, 2215 (1997).
  42. A. Pikovsky et al., Lyapunov Exponents: A Tool to Explore Complex Dynamics (Cambridge University Press, Cambridge, England, 2016).
  43. I. Shimada et al., A numerical approach to ergodic problem of dissipative dynamical systems, Prog. Theor. Phys. 61, 1605 (1979).
  44. R. H. Koch et al., Time-resolved reversal of spin-transfer switching in a nanomagnet, Phys. Rev. Lett. 92, 088302 (2004).
  45. T. Taniguchi et al., Thermal switching rate of a ferromagnetic material with uniaxial anisotropy, Phys. Rev. B 85, 184403 (2012).
  46. See Supplemental Material at http://link.aps.org/supplemental/10.1103/nny3-5mnz for supporting theory and numerical calculations of the Lyapunov exponent for various situations.
  47. S. H. Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering (Chapman and Hall/CRC Press, Boca Raton, 2024).
  48. W. Wernsdorfer et al., Experimental evidence of the Néel-brown model of magnetization reversal, Phys. Rev. Lett. 78, 1791 (1997).
  49. S. Kanai et al., Theory of relaxation time of stochastic nanomagnets, Phys. Rev. B 103, 094423 (2021).
  50. L. Soumah et al., Entropy-assisted nanosecond stochastic operation in perpendicular superparamagnetic tunnel junctions, Phys. Rev. Appl. 24, L011002 (2025).
  51. J. Namikawa, Chaotic itinerancy and power-law residence time distribution in stochastic dynamical systems, Phys. Rev. E 72, 026204 (2005).
  52. J. F. Heagy et al., Characterization of on-off intermittency, Phys. Rev. E 49, 1140 (1994).
  53. P. Bak et al., Self-organized criticality, Phys. Rev. A 38, 364 (1988).
  54. M. Aschwanden, Self-Organized Criticality in Astrophysics: The Statistics of Nonlinear Processes in the Universe (Springer Science & Business Media, Heidelberg, Germany, 2011).
  55. I. Kovacic et al., The Duffing Equation: Nonlinear Oscillators and Their Behaviour (John Wiley & Sons, New York, 2011).

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Phys. Rev. Applied 26, L041005– Published 21 October, 2026
  • Received 6 March 2026
  • Revised 29 June 2026
  • Accepted 18 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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