pith. sign in

arxiv: 2606.24673 · v1 · pith:RD5M6J23new · submitted 2026-06-23 · ❄️ cond-mat.mtrl-sci

Fractional Magnonic Frequency Combs

Qian-Nan Huang , Zhiping Xue , Xudong Wang , Yanmeng Lei , Lihui Bai , Ke Xia , Gerrit E. W. Bauer , Tao Yu This is my paper

Pith reviewed 2026-06-25 22:46 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords magnonic frequency combsfractional combsthree-magnon scatteringmicrowave drivemagnetic spherenonlinear magnonicsfrequency metrology
0
0 comments X

The pith

Adding a low-power detuned microwave compresses magnonic comb spacings to rational fractions via three-magnon scattering.

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

The paper establishes that fractional magnonic frequency combs emerge in a high-quality magnetic sphere when a secondary low-power microwave is added with precise detuning to the main drive. This compresses the original comb spacings into rational fractions, producing dense spectral grids containing hundreds of lines. The dominant mechanism is identified as parametric three-magnon scattering, which operates at lower power than the nonlinearities governing combs in optomechanical systems. A sympathetic reader would care because the setup functions as a frequency vernier caliper with higher sensitivity for potential use in precision metrology.

Core claim

In a high-quality magnetic sphere, microwave driving produces integer magnonic frequency combs with equal spacing. Adding a low-power, precisely detuned secondary microwave compresses these spacings to a rational fraction of the original, generating high-density spectral grids with hundreds of lines. Theoretical analysis shows that parametric three-magnon scattering is the dominant nonlinear process reproducing the observations, a mechanism unique to magnets that does not exist in optomechanical systems where Kerr and optical nonlinearities require much higher power.

What carries the argument

Parametric three-magnon scattering: the nonlinear magnon interaction process that dominates at low power and enables the rational compression of frequency spacings when the detuned drive is present.

If this is right

  • The platform operates as a frequency vernier caliper with much higher sensitivity than integer MFCs.
  • High-density spectral grids with hundreds of lines become accessible at low input power.
  • The mechanism remains unique to magnetic systems and does not appear in optomechanical combs.
  • The approach enables precision metrology applications through the compressed fractional spacings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar detuning techniques could be tested in other spin-wave or magnon systems to produce even denser fractional grids.
  • The low-power operation might allow integration with existing microwave measurement setups for routine frequency calibration.
  • Exploring different sphere sizes or materials could reveal how the fractional ratio depends on material parameters.

Load-bearing premise

The high-quality magnetic sphere and precise detuning of the secondary microwave allow three-magnon scattering to dominate the nonlinear dynamics at low power without interference from other processes.

What would settle it

Varying the detuning or power of the secondary microwave in the same sphere and observing that the resulting spectrum either fails to form lines at rational fractional spacings or requires higher power for the effect to appear.

Figures

Figures reproduced from arXiv: 2606.24673 by Gerrit E. W. Bauer, Ke Xia, Lihui Bai, Qian-Nan Huang, Tao Yu, Xudong Wang, Yanmeng Lei, Zhiping Xue.

Figure 1
Figure 1. Figure 1: FIG. 1. Principle of fractional MFC via parametric three [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Experimental realization of fractional MFC. (a) A [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Alternating parity cascade for generating frac [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Amplification of frequency shift using the frac [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison between measured and calculated spectra of fractional MFC for different fraction control parameters [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

Magnonic frequency combs (MFCs) are spectacular phenomena in microwave-driven high-quality magnets. Like the equally spaced prongs in a comb, conventional \textit{integer} MFCs are sharp resonances with an equal and constant frequency difference. Here we report \textit{fractional} MFCs in a high-quality magnetic sphere that emerges when adding a low-power, precisely detuned microwave to the main drive that compresses the frequency spacings to a rational fraction of the original comb, generating high-density spectral grids with hundreds of lines. The theoretical analysis finds that parametric three-magnon scattering is the dominant non-linear process that reproduces the observation well. This mechanism is unique to magnets: it does not exist in an optomechanical system, where the Kerr and optical nonlinearities govern comb formation at a much higher power input. Since our platform operates as a frequency ``vernier caliper" with much higher sensitivity than integer MFCs, it has application potential in precision metrology.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper reports the observation of fractional magnonic frequency combs in a high-quality magnetic sphere. Adding a low-power, precisely detuned secondary microwave to the main drive compresses the comb spacings to a rational fraction of the original, producing high-density grids with hundreds of lines. Parametric three-magnon scattering is identified as the dominant nonlinear process that reproduces the observations, a mechanism absent in optomechanical systems.

Significance. If the result holds, the work introduces a low-power route to dense spectral grids in magnonics with enhanced sensitivity compared to integer combs, offering a frequency vernier for precision metrology. The explicit distinction from Kerr/optical nonlinearities in other platforms is a useful conceptual contribution.

minor comments (2)
  1. [Theoretical analysis section] The abstract states that the three-magnon model reproduces the data well; the main text should include a dedicated subsection with the explicit model equations, fitting procedure, and quantitative error metrics to support this claim.
  2. Figure captions and axis labels should explicitly state the observed number of lines, the exact detuning values, and the power levels used in the fractional-comb experiments.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of the significance of fractional magnonic frequency combs, and the recommendation for minor revision. No specific major comments appear in the report provided.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper reports an experimental observation of fractional magnonic frequency combs under dual microwave drive and attributes the compressed spacings to parametric three-magnon scattering via standard nonlinear magnon dynamics. No derivation chain reduces a claimed prediction or uniqueness result to a fitted parameter or self-citation by construction; the theoretical reproduction is a physical model applied to measured spectra rather than a tautological renaming or ansatz smuggled through prior work. The distinction from optomechanics is presented as a material-specific property, not a load-bearing mathematical necessity. The derivation remains self-contained against external benchmarks of magnon scattering theory.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that three-magnon scattering dominates at the stated low powers; no free parameters or invented entities are specified in the abstract.

axioms (1)
  • domain assumption Parametric three-magnon scattering is the dominant nonlinear process
    Stated in the abstract as the mechanism that reproduces the fractional-comb observation.

pith-pipeline@v0.9.1-grok · 5721 in / 1238 out tokens · 46384 ms · 2026-06-25T22:46:13.865704+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

76 extracted references

  1. [1]

    T. Udem, R. Holzwarth, and T. W. H¨ ansch, Optical frequency metrology, Nature 416, 233 (2002)

    2002

  2. [2]

    S. T. Cundiff and J. Ye, Colloquium: Femtosecond opti- cal frequency combs, Rev. Mod. Phys. 75, 325 (2003)

    2003

  3. [3]

    T. W. H¨ ansch, Nobel lecture: Passion for precision, Rev. Mod. Phys. 78, 1297 (2006)

    2006

  4. [4]

    Del ´Haye, A

    P. Del ´Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Optical frequency comb generation from a monolithic microresonator, Na- ture 450, 1214 (2007)

    2007

  5. [5]

    Fortier and E

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

    2019

  6. [6]

    Hillbrand, D

    J. Hillbrand, D. Auth, M. Piccardo, N. Opaˇ cak, E. Gornik, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, In-phase and anti-phase synchronization in a laser frequency comb, Phys. Rev. Lett. 124, 023901 (2020)

    2020

  7. [7]

    S. B. Papp, K. Beha, P. Del ´Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, Microresonator fre- quency comb optical clock, Optica 1, 10 (2014)

    2014

  8. [8]

    A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Optical atomic clocks, Rev. Mod. Phys. 87, 637 (2015)

    2015

  9. [9]

    J. L. Hall, Nobel lecture: Defining and measuring optical frequencies, Rev. Mod. Phys. 78, 1279 (2006)

    2006

  10. [10]

    Trocha, M

    P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, and C. Koos, Ultrafast optical ranging us- ing microresonator soliton frequency combs, Science 359, 887 (2018)

    2018

  11. [11]

    J. Wang, Z. Lu, W. Wang, F. Zhang, J. Chen, Y. Wang, J. Zheng, S. T. Chu, W. Zhao, B. E. Little, X. Qu, and W. Zhang, Long-distance ranging with high precision us- ing a soliton microcomb, Photonics Res. 8, 1964 (2020)

    1964

  12. [12]

    Marin-Palomo, J

    P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Microresonator-based solitons for massively parallel coherent optical communi- cations, Nature 546, 274 (2017)

    2017

  13. [13]

    J. Tan, Z. Zhao, Y. Wang, Z. Zhang, J. Liu, and N. Zhu, 12.5 gb/s multi-channel broadcasting transmission for free-space optical communication based on the optical frequency comb module, Opt. Express 26, 2099 (2018)

    2099

  14. [14]

    Corcoran, M

    B. Corcoran, M. Tan, X. Xu, A. Boes, J. Wu, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, Ultra-dense optical data transmission over standard fibre with a single chip source, Nat. Commun. 11, 2568 (2020)

    2020

  15. [15]

    A. A. Serga, A. V. Chumak, and B. Hillebrands, Yig magnonics, J. Phys. D 43, 264002 (2010)

    2010

  16. [16]

    B. Lenk, H. Ulrichs, F. Garbs, and M. Muenzenberg, The building blocks of magnonics, Phys. Rep. 507, 107 (2011)

    2011

  17. [17]

    G. E. W. Bauer, E. Saitoh, and B. J. van Wees, Spin caloritronics, Nat. Mater. 11, 391 (2012)

    2012

  18. [18]

    A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Magnon spintronics, Nat. Phys. 11, 453 (2015)

    2015

  19. [19]

    Grundler, Nanomagnonics around the corner, Nat

    D. Grundler, Nanomagnonics around the corner, Nat. Nanotechnol. 11, 407 (2016)

    2016

  20. [20]

    V. E. Demidov, S. Urazhdin, G. de Loubens, O. Klein, V. Cros, A. Anane, and S. O. Demokritov, Magnetiza- tion oscillations and waves driven by pure spin currents, 6 Phys. Rep. 673, 1 (2017)

    2017

  21. [21]

    Wang, G.-Q

    Y.-P. Wang, G.-Q. Zhang, D. Zhang, T.-F. Li, C.-M. Hu, and J. Q. You, Bistability of cavity magnon polaritons, Phys. Rev. Lett. 120, 057202 (2018)

    2018

  22. [22]

    Manchon, J

    A. Manchon, J. ˇZelezn´ y, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems, Rev. Mod. Phys. 91, 035004 (2019)

    2019

  23. [23]

    H. Wang, J. Chen, T. Liu, J. Zhang, K. Baumgaertl, C. Guo, Y. Li, C. Liu, P. Che, S. Tu, S. Liu, P. Gao, X. Han, D. Yu, M. Wu, D. Grundler, and H. Yu, Chiral spin-wave velocities induced by all-garnet inter- facial dzyaloshinskii-moriya interaction in ultrathin yt- trium iron garnet films, Phys. Rev. Lett. 124, 027203 (2020)

    2020

  24. [24]

    Shen, G.-T

    Z. Shen, G.-T. Xu, M. Zhang, Y.-L. Zhang, Y. Wang, C.- Z. Chai, C.-L. Zou, G.-C. Guo, and C.-H. Dong, Coher- ent coupling between phonons, magnons, and photons, Phys. Rev. Lett. 129, 243601 (2022)

    2022

  25. [25]

    T. Yu, J. Zou, B. Zeng, J. W. Rao, and K. Xia, Non- hermitian topological magnonics, Phys. Rep. 1062, 1 (2024)

    2024

  26. [26]

    N. J. Lambert, A. Schumer, J. J. Longdell, S. Rot- ter, and H. G. L. Schwefel, Coherent control of magnon–polaritons using an exceptional point, Nat. Phys. 21, 1570 (2025)

    2025

  27. [27]

    Z.-X. Liu, B. Wang, H. Xiong, and Y. Wu, Magnon- induced high-order sideband generation, Opt. Lett. 43, 3698 (2018)

    2018

  28. [28]

    Z. Wang, H. Y. Yuan, Y. Cao, Z.-X. Li, R. A. Duine, and P. Yan, Magnonic frequency comb through nonlin- ear magnon-skyrmion scattering, Phys. Rev. Lett. 127, 037202 (2021)

    2021

  29. [29]

    T. Hula, K. Schultheiss, F. J. T. Gon¸ calves, L. K¨ orber, M. Bejarano, M. Copus, L. Flacke, L. Liensberger, A. Buzdakov, A. K´ akay, M. Weiler, R. Camley, J. Fass- bender, and H. Schultheiss, Spin-wave frequency combs, Appl. Phys. Lett. 121, 112404 (2022)

    2022

  30. [30]

    J. Sun, S. Shi, and J. Wang, Strain modulation of magnonic frequency comb by magnon–skyrmion interac- tion in ferromagnetic materials, Adv. Eng. Mater. 24, 2101245 (2022)

    2022

  31. [31]

    Xiong, Magnonic frequency combs based on the reso- nantly enhanced magnetostrictive effect, Fundam Res 3, 8 (2023)

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

    2023

  32. [32]

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

    2023

  33. [33]

    G.-T. Xu, M. Zhang, Y. Wang, Z. Shen, G.-C. Guo, and C.-H. Dong, Magnonic frequency comb in the magnome- chanical resonator, Phys. Rev. Lett. 131, 243601 (2023)

    2023

  34. [34]

    J. W. Rao, B. Yao, C. Y. Wang, C. Zhang, T. Yu, and W. Lu, Unveiling a pump-induced magnon mode via its strong interaction with walker modes, Phys. Rev. Lett. 130, 046705 (2023)

    2023

  35. [35]

    Y. Liu, T. Liu, Q. Yang, G. Tian, Z. Hou, D. Chen, Z. Fan, M. Zeng, X. Lu, X. Gao, M. Qin, and J. Liu, Design of controllable magnon frequency comb in syn- thetic ferrimagnets, Phys. Rev. B 109, 174412 (2024)

    2024

  36. [36]

    Wu, H.-J

    Q. Wu, H.-J. Sun, Y.-D. Chen, and Z.-X. Liu, Microwave frequency combs through the rotational enhanced mag- netostrictive effect, Phys. Rev. A 110, 023507 (2024)

    2024

  37. [37]

    Liu, Dissipative coupling induced UWB magnonic frequency comb generation, Appl

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

    2024

  38. [38]

    C. Wang, J. Rao, Z. Chen, K. Zhao, L. Sun, B. Yao, T. Yu, Y.-P. Wang, and W. Lu, Enhancement of magnonic frequency combs by exceptional points, Nat. Phys. 20, 1139 (2024)

    2024

  39. [39]

    Liu, K.-K

    Y. Liu, K.-K. Zhang, R.-S. Zhao, X. Fei, X. Liu, Z. Jia, X. Liu, and X.-T. Xie, Nonreciprocal frequency combs by two-photon driving in cavity magnonics, Opt. Lett. 50, 4234 (2025)

    2025

  40. [40]

    Wang, X.-H

    B. Wang, X.-H. Lu, X. Jia, and H. Xiong, Mechanically induced magnonic frequency combs via the magnetostric- tive effect, Phys. Rev. A 111, 063703 (2025)

    2025

  41. [41]

    Lan, K.-Y

    G. Lan, K.-Y. Liu, Z. Wang, F. Xia, H. Xu, T. Guo, Y. Zhang, B. He, J. Li, C. Wan, G. E. W. Bauer, P. Yan, G.-Q. Liu, X.-Y. Pan, X. Han, and G. Yu, Coherent harmonic generation of magnons in spin textures, Nat. Commun. 16, 1178 (2025)

    2025

  42. [42]

    Heins, L

    C. Heins, L. K¨ orber, J.-V. Kim, T. Devolder, J. H. Mentink, A. K¨ akay, J. Fassbender, K. Schultheiss, and H. Schultheiss, Self-induced Floquet magnons in mag- netic vortices, Science 391, 190 (2026)

    2026

  43. [43]

    J.-H. Liu, G. He, Q. Wu, Y.-F. Yu, J.-D. Wang, and Z.-M. Zhang, Fraction-order sideband generation in an optomechanical system, Opt. Lett. 45, 5169 (2020)

    2020

  44. [44]

    Liu, Y.-F

    J.-H. Liu, Y.-F. Yu, Q. Wu, J.-D. Wang, and Z.-M. Zhang, Tunable high-order sideband generation in a cou- pled double-cavity optomechanical system, Opt. Express 29, 12266 (2021)

    2021

  45. [45]

    S. Liu, Y. Li, Z. Song, S. Zhou, J. Wang, and B. Liu, Mul- tiple frequency combs via pump modulation in a three- mode optomechanical system, Opt. Express 33, 7016 (2025)

    2025

  46. [46]

    Wang, K.-W

    X. Wang, K.-W. Huang, Q.-Y. Qiu, and H. Xiong, Nonreciprocal double-carrier frequency combs in cav- ity magnonics, Chaos, Solitons & Fractals 176, 114137 (2023)

    2023

  47. [47]

    Wu, Y.-D

    Q. Wu, Y.-D. Chen, and Z.-X. Liu, Fraction-order side- band generation in a driven magnomechanical system, Chaos, Solitons & Fractals 200, 117072 (2025)

    2025

  48. [48]

    L. Zhou, H. Chen, S. Lei, C. Nie, and P. Luo, Magnon-squeezing-enhanced fractional magnonic fre- quency combs in cavity magnomechanics, Opt. Commun. 608, 132995 (2026)

    2026

  49. [49]

    T. Qu, Y. Xiong, X. Zhang, Y. Li, and W. Zhang, Pump- induced magnon anticrossing due to three-magnon split- ting and confluence, Phys. Rev. B 111, L180410 (2025)

    2025

  50. [50]

    Arfini, A

    M. Arfini, A. Bermejillo-Seco, A. Bondarenko, C. A. Potts, Y. M. Blanter, H. S. J. van der Zant, and G. A. Steele, Magnon-magnon interaction induced by nonlin- ear spin-wave dynamics, Phys. Rev. Lett. 135, 166703 (2025)

    2025

  51. [51]

    Huang, Z

    Q.-N. Huang, Z. Xue, and T. Yu, Observation of long- lifetime magnon pairs by Fano resonance of photons, APL Quantum 3, 026101 (2026)

    2026

  52. [52]

    B. Yao, T. Yu, Y. S. Gui, J. W. Rao, Y. T. Zhao, W. Lu, and C.-M. Hu, Coherent control of magnon radiative damping with local photon states, Commun. Phys.2, 161 (2019)

    2019

  53. [53]

    T. Yu, X. Zhang, S. Sharma, Y. M. Blanter, and G. E. W. Bauer, Chiral coupling of magnons in waveg- uides, Phys. Rev. B 101, 094414 (2020)

    2020

  54. [54]

    B. Z. Rameshti, S. V. Kusminskiy, J. A. Haigh, K. Usami, D. Lachance-Quirion, Y. Nakamura, C.-M. Hu, H. X. 7 Tang, G. E. W. Bauer, and Y. M. Blanter, Cavity magnonics, Phys. Rep. 979, 1 (2022)

    2022

  55. [55]

    L. R. Walker, Magnetostatic modes in ferromagnetic res- onance, Phys. Rev. 105, 390 (1957)

    1957

  56. [56]

    J. F. Dillon, Jr., Ferrimagnetic resonance in yttrium iron garnet, Phys. Rev. 105, 759 (1957)

    1957

  57. [57]

    Gloppe, R

    A. Gloppe, R. Hisatomi, Y. Nakata, Y. Nakamura, and K. Usami, Resonant magnetic induction tomography of a magnetized sphere, Phys. Rev. Appl. 12, 014061 (2019)

    2019

  58. [58]

    four-magnon process in frequency combs, and derivation of cascade process of fractional MFCs

    Refer to the Supplementary Material [...] for the observa- tion of integer MFCs at different pump powers, the mea- surement of operational upper limits of fractional MFC, the analysis of three-magnon vs. four-magnon process in frequency combs, and derivation of cascade process of fractional MFCs

  59. [59]

    P. W. Anderson and H. Suhl, Instability in the motion of ferromagnets at high microwave power levels, Phys. Rev. 100, 1788 (1955)

    1955

  60. [60]

    Suhl, The theory of ferromagnetic resonance at high signal powers, J

    H. Suhl, The theory of ferromagnetic resonance at high signal powers, J. Phys. Chem. Solids 1, 209 (1957)

    1957

  61. [61]

    L. M. Pecora, Derivation and generalization of the Suhl spin-wave instability relations, Phys. Rev. B 37, 5473 (1988)

    1988

  62. [62]

    Schultheiss, K

    H. Schultheiss, K. Vogt, and B. Hillebrands, Direct ob- servation of nonlinear four-magnon scattering in spin- wave microconduits, Phys. Rev. B 86, 054414 (2012)

    2012

  63. [63]

    Pirro, T

    P. Pirro, T. Sebastian, T. Br¨ acher, A. A. Serga, T. Kub- ota, H. Naganuma, M. Oogane, Y. Ando, and B. Hille- brands, Non-Gilbert-damping mechanism in a ferromag- netic Heusler compound probed by nonlinear spin dy- namics, Phys. Rev. Lett. 113, 227601 (2014)

    2014

  64. [64]

    P. C. Fletcher and R. O. Bell, Ferrimagnetic resonance modes in spheres, J. Appl. Phys. 30, 687 (1959)

    1959

  65. [65]

    Balucani, F

    U. Balucani, F. Barocchi, and V. Tognetti, Three- magnon parametric processes: Damping-modified many- time green’s-function theory, Phys. Rev. B 6, 292 (1972)

    1972

  66. [66]

    C. B. de Araujo and S. M. Rezende, Saturation and co- herence properties of three-magnon nonlinear processes, Phys. Rev. B 9, 3074 (1974)

    1974

  67. [67]

    R.-C. Shen, J. Li, Z.-Y. Fan, Y.-P. Wang, and J. Q. You, Mechanical bistability in kerr-modified cavity magnome- chanics, Phys. Rev. Lett. 129, 123601 (2022)

    2022

  68. [68]

    Wang, G.-Q

    Y.-P. Wang, G.-Q. Zhang, D. Zhang, X.-Q. Luo, W. Xiong, S.-P. Wang, T.-F. Li, C.-M. Hu, and J. Q. You, Magnon kerr effect in a strongly coupled cavity- magnon system, Phys. Rev. B 94, 224410 (2016)

    2016

  69. [69]

    Zhang, Y

    G. Zhang, Y. Wang, and J. You, Theory of the magnon kerr effect in cavity magnonics, Science China Physics, Mechanics & Astronomy 62, 987511 (2019)

    2019

  70. [70]

    J. C. Slonczewski, Origin of magnetic anisotropy in cobalt-substituted magnetite, Phys. Rev. 110, 1341 (1958)

    1958

  71. [71]

    J. C. Slonczewski, Anisotropy and magnetostriction in magnetic oxides, J. Appl. Phys. 32, S253 (1961)

    1961

  72. [72]

    B. Yao, T. Yu, X. Zhang, W. Lu, Y. Gui, C.-M. Hu, and Y. M. Blanter, The microscopic origin of magnon- photon level attraction by traveling waves: Theory and experiment, Phys. Rev. B 100, 214426 (2019)

    2019

  73. [73]

    Peˇ rina,Quantum Statistics of Linear and Nonlinear Optical Phenomena (Springer Netherlands, Dordrecht, 1991)

    J. Peˇ rina,Quantum Statistics of Linear and Nonlinear Optical Phenomena (Springer Netherlands, Dordrecht, 1991)

    1991

  74. [74]

    Liu and Y.-Q

    Z.-X. Liu and Y.-Q. Li, Optomagnonic frequency combs, Photon. Res. 10, 2786 (2022)

    2022

  75. [75]

    Ghimire, A

    S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, Observation of high- order harmonic generation in a bulk crystal, Nature Physics 7, 138 (2011)

    2011

  76. [76]

    X. Mi, J. Rao, L. Yan, X. Wang, B. Lyu, B. Yao, S. Yan, and L. Bai, Ultrasensitive magnetometer based on cusp points of the photon-magnon synchronization mode, Phys. Rev. Lett. 136, 066701 (2026). END MA TTER Disregarding the negligible self-Kerr nonlinearity and accounting for the intrinsic dissipation γ0 for the Kit- tel magnon and γ±k for the magnon pa...

    2026