Pith. sign in

REVIEW 3 major objections 4 minor 55 references

Magnonic chaotic comb

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read In a silicon-based synthetic antiferromagnet, ultrastrong magnon-magnon coupling is predicted to turn a microwave pump into magnonic frequency combs and then into chaotic combs via three bifurcation routes, with the chaos used to identify…

desk verdict A coherent simulation study that plausibly produces chaos from magnonic frequency combs in an ultrastrongly coupled SAF, but the 'comb' label is not supported by the paper's own chaotic spectra. read the letter →

arxiv 2505.23163 v1 pith:MMSZJLSK submitted 2025-05-29 cond-mat.str-el

Ruitong Sun , Guanqi Ye , Fusheng Ma This is my paper
classification cond-mat.str-el
keywords magnonicchaoticcombfrequencysyntheticantiferromagnetultrastrongmagnon-magnoncouplingthree-magnonprocessbifurcationroutestochaoslargestLyapunovexponentnoise-immunesignalidentification
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a magnonic counterpart to optical chaotic combs. Using two coupled Landau-Lifshitz-Gilbert equations for the macrospins of an uncompensated synthetic antiferromagnet on silicon, it shows that a microwave pump tuned near the upper hybrid mode drives three-magnon mixing that creates comb lines spaced by the lower hybrid mode frequency; increasing pump amplitude blurs the comb into chaos. The route to chaos depends on detuning: subcritical Hopf bifurcation for red detuning, torus-doubling bifurcation near resonance, and torus breakdown for blue detuning, each characterized by spectra, Poincaré maps, bifurcation diagrams, and the largest Lyapunov exponent. The authors argue that because the predicted pump thresholds are within experimental reach, silicon-compatible chaotic comb sources are feasible, and they demonstrate conceptually that intermittent chaos can recover a latent magnetic signal even when buried in Gaussian noise.

What carries the argument

The load-bearing object is the pair of coupled Landau-Lifshitz-Gilbert equations for the normalized magnetizations $m_1$ and $m_2$ of the two ferromagnetic layers, integrated by a fourth-order Runge-Kutta scheme with a 2 ps step. Ultrastrong coupling here means a coupling rate comparable to the mode frequencies and larger than all dissipation rates, realized in the model at $g/f_0 = 0.5$. The essential physical mechanism is three-magnon (three-wave) mixing between the hybridized modes $f_u$ and $f_d$: pumping at $f_p \approx f_u$ produces sum- and difference-frequency sidebands at $f_p \pm f_d$, and repeated mixing cascades into the comb $l f_p \pm n f_d$. The route analysis uses standard nonlinear-dynamics diagnostics—Poincaré maps of local maxima of $m_x$, bifurcation diagrams of $m_z$, and the largest Lyapunov exponent $\lambda_{LLE}$ from the divergence of nearby trajectories—to identify subcritical Hopf, torus-doubling, and torus-breakdown transitions.

What would settle it

Measure the frequency-field dispersion of a silicon-substrate uncompensated SAF at $H_x = 120$ mT: if the anticrossing does not put the hybrid modes near $f_u = 7.95$ GHz and $f_d = 0.52$ GHz with $g/f_0 \approx 0.5$, or if pumping near $f_p \approx 8$ GHz never produces the predicted MFC-to-MCC transition below roughly 12 mT, the central scenario would be falsified.

Watch

Extended reading notes

Core claim

The central discovery, on the paper's own terms, is that the same ultrastrong magnon-magnon coupling that hybridizes two spin-wave modes in a synthetic antiferromagnet can be used to generate a magnonic chaotic comb. For a two-macrospin SAF with $M_s = 6\times10^5$ A/m, $\alpha = 0.01$, anisotropy fields $H_{1a}=139$ mT and $H_{2a}=-500$ mT, interlayer coupling $H_{ex}=-200$ mT, and normalized coupling $g/f_0 = 0.5$, the lower and upper hybrid modes sit at $f_d = 0.52$ GHz and $f_u = 7.95$ GHz. A pumping field $h_p(t)$ tilted at $45^\circ$ in the $x$-$y$ plane excites a cascaded three-magnon process that produces comb lines at $l f_p \pm n f_d$; at pump amplitudes of roughly 6–12 mT, the teeth split through torus-doubling and eventually become randomly modulated. The paper identifies three distinct routes to this chaotic state—subcritical Hopf bifurcation, torus doubling, and torus breakdown—selected by the detuning $\Delta = f_p - f_u$, and supports the chaos claim with positive largest Lyapunov exponents. It further shows that pumping at the chaos edge creates intermittent comb bursts whose period $1/|f_s - f_p|$ encodes a latent magnetic signal, so the signal can be identified even when hidden under Gaussian noise.

Load-bearing premise

The load-bearing premise is that the two-macrospin Landau-Lifshitz-Gilbert model with the hand-set parameters ($M_s = 6\times10^5$ A/m, $\alpha = 0.01$, $H_{1a}=139$ mT, $H_{2a}=-500$ mT, $H_{ex}=-200$ mT) faithfully represents a real silicon-substrate synthetic antiferromagnet in the ultrastrong-coupling regime; if the negative anisotropy is not physically realizable, the damping is higher, or higher-order spin-wave modes matter, the predicted thresholds, comb spacings, and bifurcation routes could shift or disappear.

Editorial extensions

If this is right

  • A silicon-substrate synthetic antiferromagnet can serve as a microwave chaotic-comb source at pump amplitudes of roughly 6–12 mT, within the range of current experiments.
  • The comb tooth spacing is set by the lower hybrid mode $f_d \approx 0.52$ GHz, and the paper's supplementary results indicate the spacing and the chaos thresholds can be tuned through bias field and coupling strength.
  • The detuning of the pump selects which route to chaos the system takes, giving a control knob for switching between regular and chaotic comb operation.
  • The intermittency effect provides a generic scheme for weak-signal identification: any magnetic field component that amplitude-modulates the pump near the chaos threshold will imprint its beat frequency on the chaotic comb output.
  • Realizing magnonic chaotic combs would extend the known applications of optical chaotic combs—ranging, sensing, secure communication—to a CMOS-compatible, room-temperature magnonic platform.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the classical two-macrospin description remains valid at $g/f_0 = 0.5$, the same three-branch phase diagram could be used as a precision calibration tool: measuring the pump amplitude at which the comb first blurs gives a direct readout of the coupling strength and damping in a fabricated SAF.
  • The intermittency detection scheme is not limited to magnets: any environmental field that amplitude-modulates a pump driving a nonlinear oscillator near a chaos threshold should produce the same $1/\Delta f$ periodic switching, so the idea could transfer to other ultrastrongly coupled systems.
  • The paper does not test statistical randomness of the chaotic comb teeth; if the positive Lyapunov exponent translates into high-entropy amplitude and phase modulation, magnonic chaotic combs could be a candidate for physical random-number generation, but that remains an open step.
  • The predicted route sequences, such as period-1 to period-2 to period-4 to period-3 tori, are unusual and would provide a sharp quantitative fingerprint for experiments; reproducing them in a micromagnetic simulation would show whether the macrospin approximation adds or removes dynamical features.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a semiclassical mechanism for generating magnonic frequency combs (MFCs) and their chaotic counterparts ('magnonic chaotic combs', MCCs) in a silicon-compatible synthetic antiferromagnet (SAF) with ultra-strong magnon-magnon coupling. The authors integrate two coupled Landau-Lifshitz-Gilbert equations with a fixed-step RK4 scheme (Δt = 2 ps) and report, for the chosen parameter set (Ms = 6×10^5 A/m, α = 0.01, H1a = 139 mT, H2a = -500 mT, Hex = -200 mT), hybridized modes fu = 7.95 GHz and fd = 0.52 GHz with g/f0 = 0.5. Under resonant pumping near fu, they observe MFCs with tooth spacing fd; at higher pumping amplitudes the MFCs transition to chaos via three routes classified as subcritical Hopf bifurcation (red detuning), torus-doubling bifurcation (near resonance), and torus breakdown (blue detuning). The chaotic state is characterized by Poincaré maps, bifurcation diagrams, and largest Lyapunov exponents. The paper further proposes a noise-immune latent-signal identification scheme based on intermittency between MFCs and MCCs.

Significance. If the central 'chaotic comb' claim holds, this would be a notable theoretical addition to the emerging field of nonlinear magnonics, connecting ultrastrong magnon-magnon coupling in CMOS-compatible SAFs with chaotic dynamics and comb generation. The paper has clear strengths: the comb-teeth spacings and the bifurcation routes are outputs of direct numerical integration rather than fitted targets; the diagnostics (temporal evolution, Poincaré maps, bifurcation diagrams, LLEs) are internally consistent; and the integration scheme is explicitly stated. The proposed signal-identification scheme is a concrete, falsifiable application. However, the central new object—the magnonic chaotic comb—is not actually demonstrated to be a frequency comb in the chaotic regime; the manuscript's own spectral descriptions indicate continuous broadband spectra rather than discrete, equally spaced lines. This is a load-bearing issue for the title, abstract, and proposed applications, and it must be resolved before the central claim can be accepted.

major comments (3)
  1. [Results, Figs. 2f and 3a–c] The paper's own spectral evidence does not establish that the chaotic state is a frequency comb. In Fig. 2f the transition to the claimed MCC is described as 'comb teeth blur, expand into a disordered continuous distribution'; Fig. 3a describes a 'disordered continuous distribution', Fig. 3b a 'non-resolved tooth spacing', and Fig. 3c an 'elevated noise floor'. A frequency comb, including an optical chaotic comb, is defined by discrete equally spaced lines whose amplitudes or phases are chaotically modulated; a continuous broadband spectrum is not a comb. The title, abstract, and the proposed applications (ranging, communication, sensing) depend on the persistence of an underlying equally spaced grid of lines in the chaotic regime. Please provide high-resolution spectra and a quantitative line-extraction analysis showing equally spaced, chaotically modulated lines in the chaotic state, or alternatively revise the terminology and scope to 'magnonic chaos following MFC regimes' and temper the corresponding claims.
  2. [Methods, Eq. (3) and Eq. (11)] The computation of the largest Lyapunov exponent is not specified sufficiently to verify the chaos claim. Eq. (3) gives only the formal definition; there is no information on how the perturbation δm(t) is renormalized, how many drive periods are integrated, whether transients are discarded, or how convergence is assessed. In addition, no numerical convergence test is reported for the fixed time step Δt = 2 ps, even though the bifurcation diagrams and the sign of the LLE are central to classifying the three routes to chaos. Please provide the full LLE algorithm (e.g., Benettin-style reorthonormalization) and convergence checks with smaller time steps (e.g., 1 ps and 0.5 ps) and longer integration windows.
  3. [Methods and Discussion, parameter set] The parameter set used for the SAF (Ms = 6×10^5 A/m, α1 = α2 = 0.01, H1a = 139 mT, H2a = -500 mT, Hex = -200 mT) is introduced without an experimental reference, a material-stack specification, or a sensitivity analysis. The negative anisotropy field of -500 mT is unusually large, and the statement in the Discussion that 'experimental demonstration of our findings is fully feasible' depends on the realizability and robustness of this set. Since the pumping thresholds, the comb tooth spacing, and the bifurcation routes could shift with these parameters, please either cite a concrete SAF stack that realizes this regime or provide a parameter-sensitivity study showing that the reported phenomena persist over a plausible range of material parameters.
minor comments (4)
  1. [Throughout] There are several typographical errors and inconsistent terms: 'peroid' for 'period' (Figs. 2e and 2f), 'tours-doubling' for 'torus-doubling' (Fig. 4b), 'peroid-3 torus-doubling' in the Fig. 1 caption, and 'three-wave mixing' in the abstract versus 'three-magnon process' in the Results. Please unify the terminology.
  2. [Results, Eqs. (4)–(6) and Fig. 5] The signal-identification scheme assumes hp >> S0 so that the phase φ in Eq. (5) is negligible, but the quantitative condition for this approximation is not given. For the example with hp around 8.6 mT and S0 = 0.5 mT the assumption is plausible, but a bound such as S0/hp < 0.1 would make the validity explicit.
  3. [Methods, Eq. (3)] The notation λLLE is used for a scalar but the text refers to 'Lyapunov exponents' in the plural; only the largest exponent is computed. Please state this explicitly and consistently.
  4. [Data availability] The data-availability statement says data are available on request but no mention is made of code availability. Providing the integration and LLE code would strengthen reproducibility and is now standard for numerical manuscripts.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the comb spectra, bifurcation routes, and Lyapunov exponents are numerical outputs of an un-fitted LLG model, and the only self-citation is background support.

full rationale

The paper's derivation chain is self-contained: it solves two coupled LLG equations (Eqs. 1-2, 7-11) with explicitly stated material parameters (Ms = 6 x 10^5 A/m, alpha = 0.01, H1a = 139 mT, H2a = -500 mT, Hex = -200 mT), obtains hybridized modes fu = 7.95 GHz and fd = 0.52 GHz, applies a sinusoidal pump, and then observes MFCs with tooth spacing fd and subsequent transitions to chaos. Nothing in the derivation is fitted to a pre-specified comb spectrum or to the claimed chaotic state; the spectra, Poincare maps, bifurcation diagrams, and LLEs are all generated from the same model without adjusting parameters to reproduce the output. The comb spacing fd is identified with the lower hybridized mode computed from the same model, but this is a dynamical consequence of the three-magnon coupling described in the Results, not a parameter fit disguised as a prediction. The paper cites the corresponding author's prior work (ref. 48) only as one example among several (refs. 46-49) that strong/ultrastrong magnon-magnon coupling has been achieved in SAFs; this is background support and is not load-bearing for the central claim. There is no imported uniqueness theorem, no ansatz smuggled in via self-citation, and no renamed known result. The skeptical concern that the chaotic spectra are described as 'disordered continuous distribution' and 'non-resolved tooth spacing' (Figs. 2f, 3a-c) is a possible correctness or labeling issue about whether the chaotic state is genuinely comb-like, not a circularity in the derivation. The paper also contains no explicit limitation passage that would change this assessment. Therefore, the appropriate circularity score is 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

All quantities in the ledger are input assumptions of the numerical demonstration. The paper introduces no new physical entity. The key cost is that the ultrastrong-coupling parameter regime, including a -500 mT anisotropy field and 0.01 damping, is asserted rather than experimentally anchored. The three-magnon comb mechanism is an assumed mechanism used to interpret the spectra.

free parameters (4)
  • Saturation magnetization Ms = 6 x 10^5 A/m
    Chosen for the SAF demonstration; sets the LLG timescale but is not anchored to a specific measured sample.
  • Gilbert damping alpha_i = 0.01
    A typical low-damping value chosen for both layers; the onset of chaos and the comb thresholds are damping-sensitive.
  • Anisotropy fields H1a and H2a = 139 mT and -500 mT
    Hand-set asymmetry to break SAF symmetry and reach g/f0 = 0.5 ultrastrong coupling; the large negative value is not experimentally benchmarked.
  • Interlayer exchange field Hex = -200 mT
    Chosen antiferromagnetic coupling used with the anisotropy asymmetry to produce the hybrid modes at 7.95 GHz and 0.52 GHz.
assumptions (5)
  • standard math Landau-Lifshitz-Gilbert equations govern the coupled magnetization dynamics of the two SAF layers.
    Used in Eq. (1) and Eq. (7); a standard model but not a rigorous first-principles derivation.
  • domain assumption Each ferromagnetic layer is represented as one macrospin.
    The paper solves two coupled LLG equations for m1 and m2, neglecting spatial modes and exchange within layers.
  • domain assumption Classical LLG dynamics adequately capture the ultrastrong-coupling regime.
    The text invokes entangled or quantum ultrastrong coupling, yet all results come from classical integration of Eq. (11); no justification is given for this semiclassical limit.
  • ad hoc to paper The chosen parameter set realizes g/f0 = 0.5 ultrastrong coupling.
    The calculated spectrum in Fig. 2b and the coupling ratio follow from the hand-picked parameters, not from measured material data.
  • domain assumption Three-magnon processes produce the comb by cascaded sum and difference frequency generation.
    Stated in the first Results paragraph as the mechanism, but no analytic derivation of the cascaded process is provided.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Magnonic chaotic comb." pith.science (2026). https://pith.science/paper/MMSZJLSK

@misc{pith2026250523163,
  author       = {Pith},
  title        = {Pith review of: Magnonic chaotic comb},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MMSZJLSK}},
  note         = {Machine review of arXiv:2505.23163}
}
read the original abstract

Optical chaotic comb, possessing the key metrics of intrinsic random amplitude, phase, and frequency modulation of comb lines, emerges as a novel chaotic source in information systems for coherence tomography, parallel ranging, and secure communications. Considering the analogies between magnons and photons, the magnonic analog of optical chaotic combs is expected but not yet explored. Here, we propose a scenario of generating magnonic chaotic combs based on mode coupling mechanism in magnonic systems. Especially, we theoretically demonstrate the realization of magnonic frequency combs through three-wave mixing between ultra-strongly coupled magnons in silicon based synthetic antiferromagnet platform. It is found that the realized magnonic frequency combs can transition to chaos via various routes, i.e., subcritical Hopf bifurcation, torus-doubling bifurcation, and torus breakdown. The robustness of magnonic chaotic combs is verified by characterizing the Poincare map, the bifurcation diagrams, and the largest Lyapunov exponents. Furthermore, the unique characters of chaotic combs, perturbation hypersensitivity and noise immunity, are conceptually validated by identifying latent magnetic signal contaminated by inherent noise. Our findings provide a magnonic paradigm of chaotic dynamics in complex systems for potential applications in CMOS-integrated metrology, sensing, and communication.

Figures

Figures reproduced from arXiv: 2505.23163 by the authors.

Figure 4
Figure 4. | Onset of instability by detuning Δ. Color plots of magnonic spectra as a function of Δ for three typical pumping amplitudes: a hp = 6 mT; b hp = 8 mT; and c hp = 12 mT, as marked by empty circles in Fig. 2c. First row presents overall views, and second row shows the zoom-in views for fp around fu. Noise-immune signal identification When a system is in the critical state, such as periodic oscillations but on the ve… view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    Nayfeh, A. H. & Balachandran, B. Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. (Wiley, New York, 1995)

    work page 1995

  2. [2]

    Chaos in Dynamical Systems

    Ott, E. Chaos in Dynamical Systems. (Cambridge University Press, Cambridge, 2002)

    work page 2002

  3. [3]

    Hayes, S., Grebogi, B. C. & Ott, E. Communicating with chaos. Phys. Rev. Lett. 70, 3031- 3034 (1993)

    work page 1993

  4. [4]

    Argyris, A. et al. Chaos-based communications at high bit rates using commercial fibre - optic links. Nature 438, 343-346 (2005)

    work page 2005

  5. [5]

    Uchida, A. et al. Fast physical random bit generation with chaotic semiconductor lasers. Nat. Photonics 2, 728-732 (2008)

    work page 2008

  6. [6]

    Cundiff, S. T. & Ye, J. Colloquium: Femtosecond optical frequency combs. Rev. Mod. Phys. 75, 325 (2003)

    work page 2003

  7. [7]

    Hänsch, T. W. Nobel lecture: Passion for precision. Rev. Mod. Phys. 78, 1297-1309 (2006)

    work page 2006

  8. [8]

    & Baumann, E

    Fortier, T. & Baumann, E. 20 years of developments in optical frequency comb technology and applications. Commun. Phys. 2, 153 (2019)

    work page 2019

Show all 55 references
  1. [9]

    Herr, T. et al. Universal formation dynamics and noise of Kerr -frequency combs in microresonators. Nat. Photonics 6, 480-487 (2012)

    2012

  2. [10]

    & Kippenberg, T

    Lukashchuk, A., Riemensberger, J., Tusnin, A., Liu, J . & Kippenberg, T. J. Chaotic microcomb-based parallel ranging. Nat. Photonics 17, 814-821 (2023)

    2023

  3. [11]

    Chen, R. et al. Breaking the temporal and frequency congestion of LiDAR by parallel chaos. Nat. Photonics 17, 306-314 (2023)

    2023

  4. [12]

    Shen, B. et al. Harnessing microcomb-based parallel chaos for random number generation and optical decision making. Nat. Commun. 14, 4590 (2023)

    2023

  5. [13]

    Wigen, P. E. Nonlinear Phenomena and Chaos in Magnetic Materials . (World Scientific, Singapore, 1994)

    1994

  6. [14]

    D., Bertotti, G

    Mayergoyz, I. D., Bertotti, G. & Serpico, C. Nonlinear Magnetization Dynamics in Nanosystems. (Elsevier, Amsterdam, 2009)

    2009

  7. [15]

    Li, Z., Li, Y . C. & Zhang, S. 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)

    2006

  8. [16]

    Yang, Z., Zhang, S. & Li, Y . C. Chaotic dynamics of spin-valve oscillators. Phys. Rev. Lett. 99, 134101 (2007)

    2007

  9. [17]

    Petit-Watelot, S. et al. Commensurability and chaos in magnetic vortex oscill ations. Nat. Phys. 8, 682-687 (2012)

    2012

  10. [18]

    Devolder, T. et al. Chaos in magnetic nanocontact vortex oscillators. Phys. Rev. Lett. 123, 147701 (2019)

    2019

  11. [19]

    Montoya, E. A. et al. Magnetization reversal driven by low dimensional chaos in a nanoscale ferromagnet. Nat. Commun. 10, 543 (2019)

    2019

  12. [20]

    Yoo, M. W. et al. Pattern generation and symbolic dynamics in a nanocontact vortex 17 oscillator. Nat. Commun. 11, 601 (2020)

    2020

  13. [21]

    & Shen, K

    Shen, L., Q iu, L. & Shen, K. Nonlinear dynamics of directly coupled skyrmions in ferrimagnetic spin torque nano-oscillators. npj Comput. Mater. 10, 48 (2024)

    2024

  14. [22]

    Wang, Z. et al. Magnonic frequency comb through nonlinear magnon-skyrmion scattering. Phys. Rev. Lett. 127, 037202 (2021)

    2021

  15. [23]

    Y ., Cao, Y

    Wang, Z., Y uan, H. Y ., Cao, Y . & Yan, P. Twisted magnon frequency comb and penrose superradiance. Phys. Rev. Lett. 129, 107203 (2022)

    2022

  16. [24]

    X., Peng, J

    Liu, Z. X., Peng, J. & Xiong, H. Generation of magnonic frequency combs via a two -tone microwave drive. Phys. Rev. A 107, 053708 (2023)

    2023

  17. [25]

    Magnonic frequency combs based on the resonantly enhanced magnetostrictive effect

    Xiong, H. Magnonic frequency combs based on the resonantly enhanced magnetostrictive effect. Fundam. Res. 3, 8-14 (2023)

    2023

  18. [26]

    & Zhou, Y

    Liang, X., Cao, Y ., Yan, P. & Zhou, Y . Asymmetric magnon frequency comb. Nano Lett. 24, 6730-6736 (2024)

    2024

  19. [27]

    Liu, Y . et al. Design of controllable magnon frequency comb in synthetic ferrimagnets. Phys. Rev. B 109, 174412 (2024)

    2024

  20. [28]

    Liu, Z. X. Dissipative coupling induced UWB magnonic frequency comb generation. Appl. Phys. Lett. 124, 032403 (2024)

    2024

  21. [29]

    Hula, T. et al. Spin-wave frequency combs. Appl. Phys. Lett. 121, 112404 (2022)

    2022

  22. [30]

    Xu, G. T. et al. Magnonic frequency comb in the magnomechanical resonator. Phys. Rev. Lett. 131, 243601 (2023)

    2023

  23. [31]

    Rao, J. W. et al. Unveiling a pump -induced magnon mode via its strong interaction with walker modes. Phys. Rev. Lett. 130, 046705 (2023)

    2023

  24. [32]

    Wang, C. et al. Enhancement of magnonic frequency combs by exceptional points. Nat. Phys. 20, 1139-1144 (2024)

    2024

  25. [33]

    & Nakamura, Y

    Lachance-Quirion, D., Tabuchi, Y ., Gloppe, A., Usami, K. & Nakamura, Y . Hybrid quantum systems based on magnonics. App. Phys. Express 12, 070101 (2019)

    2019

  26. [34]

    Awschalom, D. D. et al. Quantum engineering with hybrid magnonic systems and materials. IEEE Transactions on Quantum Engineering 2, 5500836 (2021)

    2021

  27. [35]

    Zare, R. B. et al. Cavity magnonics. Phys. Rep. 979, 1-61 (2022)

    2022

  28. [36]

    Klingler, S. et al. Spin-torque excitation of perpendicular standing spin waves in coupled YIG/Co Heterostructures. Phys. Rev. Lett. 120, 127201 (2018)

    2018

  29. [37]

    Chen, J. et al. Strong interlayer magnon -magnon coupling in magnetic metal -insulator hybrid nanostructures. Phys. Rev. Lett. 120, 217202 (2018)

    2018

  30. [38]

    Liensberger, L. et al. Exchange-enhanced ultrastrong magnon -magnon coupling in a compensated ferrimagnet. Phys. Rev. Lett. 123, 117204 (2019)

    2019

  31. [39]

    Macneill, D. et al. Gigahertz frequency antiferromagnetic resonance and strong magnon - magnon coupling in the layered crystal CrCl3. Phys. Rev. Lett. 123, 047204 (2019)

    2019

  32. [40]

    Li, Y . et al. Coherent spin pumping in a strongly coupled magnon -magnon hybrid system. Phys. Rev. Lett. 124, 117202 (2020)

    2020

  33. [41]

    Makihara, T. et al. Ultrastrong magnon -magnon coupling dominated by antiresonant interactions. Nat. Commun. 12, 3115 (2021)

    2021

  34. [42]

    Li, W. et al. Ultrastrong magnon-magnon coupling and chirality switching in antiferromagnet CrPS4. Adv. Funct. Mater. 33, 2303781 (2023)

    2023

  35. [43]

    Dieny, B. et al. Opportunities and challenges for spintronics in the microelectronics industry. 18 Nat. Electron. 3, 446-459 (2020)

    2020

  36. [44]

    Grunberg, P., Schreiber, R., Pang, Y ., Brodsky, M. B. & Sowers, H. Layered magnetic structures: evidence for antiferromagnetic coupling of Fe layers across Cr interlayers. Phys. Rev. Lett. 57, 2442 (1986)

    1986

  37. [45]

    A., Lee, K

    Duine, R. A., Lee, K. J., Parkin, S. S. P. & Stiles, M. D. Synthetic antiferromagnetic spintronics. Nat. Phys. 14, 217-219 (2018)

    2018

  38. [46]

    & Ono, T

    Shiota, Y ., Taniguchi, T., Ishibashi, M., Moriyama, T. & Ono, T. Tunable magnon-magnon coupling mediated by dynamic dipolar interaction in synthetic antiferromagnets. Phys. Rev. Lett. 125, 017203 (2020)

    2020

  39. [47]

    Li, M., Lu, J. & He, W. Symmetry breaking induced magnon-magnon coupling in synthetic antiferromagnets. Phys. Rev. B 103, 064429 (2021)

    2021

  40. [48]

    Dai, C. & Ma, F. Strong magnon-magnon coupling in synthetic antiferromagnets. Appl. Phys. Lett. 118, 112405 (2021)

    2021

  41. [49]

    Wang, Y . et al. Ultrastrong to nearly deep -strong magnon-magnon coupling with a high degree of freedom in synthetic antiferromagnets. Nat. Commun. 15, 2077 (2024)

    2024

  42. [50]

    & Nori, F

    Frisk Kockum A., Miranowicz, A., De Liberato, S., Savasta, S. & Nori, F. Ultrastrong coupling between light and matter. Nat. Rev. Phys. 1, 19-40 (2019)

    2019

  43. [51]

    & Solano, E

    Forn-Díaz, P., Lamata, L., Rico, E., Kono, J. & Solano, E. Ultrastrong coupling regimes of light-matter interaction. Rev. Mod. Phys. 91, 025005 (2019)

    2019

  44. [52]

    Das, S. R. et al. Instabilities near ultrastrong coupling in a microwave optomechanical cavity. Phys. Rev. Lett. 131, 067001 (2023)

    2023

  45. [53]

    Rezende, S. M. & De Aguiar, F. M. Nonlinear dynamics in microwave driven coupled magnetic multilayer systems. J. Appl. Phys. 79, 6309-6311 (1996)

    1996

  46. [54]

    See Supplementary Materials for details about theoretical calculation, coupling properties of SAF, chirality of hybridized modes, parametric instability, routes to MCCs, effect of bias magnetic field and coupling strength, which includes Refs. 1, 14

  47. [55]

    Numerical calculation of Lyapunov exponents

    Marco, S. Numerical calculation of Lyapunov exponents. Math. J. 6, 78-84 (1996). Acknowledgements The authors thank Peiqing Tong for helpful discussions on chaos theory; Yu Zhang for suggestions on Poincaré map; and Junwen Sun for advice on Runge-Kutta integration scheme. This...

    1996

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.