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Three-magnon scattering of spin wave on edge-localized mode in thin ferromagnetic film

Julia Kharlan*

Roman Verba

Krzysztof Sobucki†, Paweł Gruszecki, and Maciej Krawczyk‡

  • *Contact author: yulkha@amu.edu.pl
  • †Contact author: krzsob@amu.edu.pl
  • ‡Contact author: krawczyk@amu.edu.pl
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Phys. Rev. B 112, 214438 – Published 17 December, 2025

DOI: https://doi.org/10.1103/7rbt-2ywd

Abstract

Three-wave scattering is a fascinating phenomenon with many applications in various technologies. Reducing the system symmetry greatly affects three-wave scattering, which, in this case, goes beyond the simple momentum conservation law. In this study, we examine three-magnon scattering at the edge of a thin ferromagnetic film, when a bulk spin wave interacts with an edge-localized propagating spin wave upon the reflection. This creates new bulk spin waves at mixed frequencies by means of three-magnon confluence or stimulated splitting processes. Using our developed analytical theory, which has been confirmed by full micromagnetic simulations, we demonstrate that the amplitude of the wave generated in the stimulated splitting process is several times larger than that generated in the confluence process. This is primarily due to the lower group velocity of the wave formed in the splitting process than in confluence. Furthermore, the intensity of inelastically scattered waves exhibits a pronounced dependence on the incidence angle and frequency of the edge spin wave that goes beyond existing qualitative models. We show that the observed behaviors can only be explained by taking into account that the scattered waves are created by several elementary three-magnon processes involving the incident and reflected waves. The complex nature of the scattered wave creation results in a strong sensitivity of its amplitude to the phase accumulation of spin waves upon reflection.

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References (53)

  1. A. G. Gurevich and G. A. Melkov, Magnetization Oscillations and Waves (CRC Press, Boca Raton, 1996), p. 464.
  2. V. S. L'vov, Wave Turbulence under Parametric Excitation (Springer-Verlag, New York, 1994).
  3. S. Zheng, Z. Wang, Y. Wang, F. Sun, Q. He, P. Yan, and H. Y. Yuan, Tutorial: Nonlinear magnonics, J. Appl. Phys. 134, 151101 (2023).
  4. H. Suhl, The theory of ferromagnetic resonance at high signal powers, J. Phys. Chem. Solids 1, 209 (1957).
  5. C. E. Patton, Spin-wave instability theory in cubic single crystal magnetic insulators I. General theory, Phys. Status Solidi B 92, 211 (1979).
  6. H. Suhl, Foldover' effects caused by spin wave interactions in ferromagnetic resonance, J. Appl. Phys. 31, 935 (1960).
  7. P. Gottlieb and H. Suhl, Saturation of ferrimagnetic resonance with parallel pumping, J. Appl. Phys. 33, 1508 (1962).
  8. A. D. Boardman and S. A. Nikitov, Three- and four-magnon decay of nonlinear surface magnetostatic waves in thin ferromagnetic films, Phys. Rev. B 38, 11444 (1988).
  9. A. Y. Dobin and R. H. Victora, Intrinsic nonlinear ferromagnetic relaxation in thin metallic films, Phys. Rev. Lett. 90, 167203 (2003).
  10. G. Gibson and C. Jeffries, Observation of period doubling and chaos in spin-wave instabilities in yttrium iron garnet, Phys. Rev. A 29, 811 (1984).
  11. F. M. de Aguiar and S. M. Rezende, Observation of subharmonic routes to chaos in parallel-pumped spin waves in yttrium iron garnet, Phys. Rev. Lett. 56, 1070 (1986).
  12. S. N. Stitzer and P. R. Emtage, Nonlinear microwave signal-processing devices using thin ferrimagnetic films, Circuits Systems and Signal Process 4, 227 (1985).
  13. W. S. Ishak, Magnetostatic wave technology: A review, Proc. IEEE 76, 171 (1988).
  14. H. How, Magnetic microwave devices, in Encyclopedia of RF and Microwave Engineering (Wiley, New York, 2005).
  15. R. Verba, J. Kharlan, V. Borynskyi, D. Slobodianiuk, A. Etesamirad, and I. Barsukov, Controlling multimagnon interaction in magnetic nanodots and spintronic nanostructures, in Functional Magnetic and Spintronic Nanomaterials, edited by I. Vladymyrskyi, B. Hillebrands, A. Serha, D. Makarov, and O. Prokopenko (Springer Netherlands, Dordrecht, 2024), pp. 89–131.
  16. A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Magnon spintronics, Nat. Phys. 11, 453 (2015).
  17. P. Pirro, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Advances in coherent magnonics, Nat. Rev. Mater. 6, 1114 (2021).
  18. A. V. Chumak et al., Advances in magnetics roadmap on spin-wave computing, IEEE Trans. Magn. 58, 0800172 (2022).
  19. Q. Wang, M. Kewenig, M. Schneider, R. Verba, F. Kohl, B. Heinz, M. Geilen, M. Mohseni, B. Lägel, F. Ciubotaru, C. Adelmann, C. Dubs, S. D. Cotofana, O. V. Dobrovolskiy, T. Brächer, P. Pirro, and A. V. Chumak, A magnonic directional coupler for integrated magnonic half-adders, Nat. Electron. 3, 765 (2020).
  20. Q. Wang, G. Csaba, R. Verba, A. V. Chumak, and P. Pirro, Nanoscale magnonic networks, Phys. Rev. Appl. 21, 040503 (2024).
  21. A. Papp, W. Porod, and G. Csaba, Nanoscale neural network using non-linear spin-wave interference, Nat. Commun. 12, 6422 (2021).
  22. C. Koerner, R. Dreyer, M. Wagener, N. Liebing, H. G. Bauer, and G. Woltersdorf, Frequency multiplication by collective nanoscale spin-wave dynamics, Science 375, 1165 (2022).
  23. N. Kumar, P. Gruszecki, M. Gołębiewski, J. W. Kłos, and M. Krawczyk, Exciting high-frequency short-wavelength spin waves using high harmonics of a magnonic cavity mode-revision, Adv. Quantum Technol. 7, 2400015 (2024).
  24. V. E. Demidov, M. P. Kostylev, K. Rott, P. Krzysteczko, G. Reiss, and S. O. Demokritov, Generation of the second harmonic by spin waves propagating in microscopic stripes, Phys. Rev. B 83, 054408 (2011).
  25. I. Barsukov, H. K. Lee, A. A. Jara, Y.-J. Chen, A. M. Gonçalves, C. Sha, J. A. Katine, R. E. Arias, B. A. Ivanov, and I. N. Krivorotov, Giant nonlinear damping in nanoscale ferromagnets, Sci. Adv. 5, eaav6943 (2019).
  26. X. Ge, R. Verba, P. Pirro, A. V. Chumak, and Q. Wang, Nanoscaled magnon transistor based on stimulated three-magnon splitting, Appl. Phys. Lett. 124, 122413 (2024).
  27. P. E. Wigen, Nonlinear Phenomena and Chaos in Magnetic Materials (World Scientific, Singapore, 1994).
  28. C. L. Ordóñez-Romero, B. A. Kalinikos, P. Krivosik, W. Tong, P. Kabos, and C. E. Patton, Three-magnon splitting and confluence processes for spin-wave excitations in yttrium iron garnet films: Wave vector selective brillouin light scattering measurements and analysis, Phys. Rev. B 79, 144428 (2009).
  29. H. J. Liu, G. A. Riley, C. L. Ordóñez-Romero, B. A. Kalinikos, and K. S. Buchanan, Time-resolved study of nonlinear three-magnon processes in yttrium iron garnet films, Phys. Rev. B 99, 024429 (2019).
  30. T. Qu, A. Hamill, R. H. Victora, and P. A. Crowell, Oscillations and confluence in three-magnon scattering of ferromagnetic resonance, Phys. Rev. B 107, L060401 (2023).
  31. K. Schultheiss, R. Verba, F. Wehrmann, K. Wagner, L. Körber, T. Hula, T. Hache, A. Kákay, A. A. Awad, V. Tiberkevich, A. N. Slavin, J. Fassbender, and H. Schultheiss, Excitation of whispering gallery magnons in a magnetic vortex, Phys. Rev. Lett. 122, 097202 (2019).
  32. R. E. Camley, Three-magnon processes in magnetic nanoelements: Quantization and localized mode effects, Phys. Rev. B 89, 214402 (2014).
  33. A. Etesamirad, J. Kharlan, R. Rodriguez, I. Barsukov, and R. Verba, Controlling selection rules for magnon scattering in nanomagnets by spatial symmetry breaking, Phys. Rev. Appl. 19, 044087 (2023).
  34. L. Körber, K. Schultheiss, T. Hula, R. Verba, J. Fassbender, A. Kákay, and H. Schultheiss, Nonlocal stimulation of three-magnon splitting in a magnetic vortex, Phys. Rev. Lett. 125, 207203 (2020).
  35. L. Körber, C. Heins, T. Hula, J.-V. Kim, S. Thlang, H. Schultheiss, J. Fassbender, and K. Schultheiss, Pattern recognition in reciprocal space with a magnon-scattering reservoir, Nat. Commun. 14, 3954 (2023).
  36. C. Heins, J.-V. Kim, L. Körber, J. Fassbender, H. Schultheiss, and K. Schultheiss, Benchmarking a magnon-scattering reservoir with modal and temporal multiplexing, Phys. Rev. Appl. 23, 054087 (2025).
  37. X. Yao, Z. Jin, Z. Wang, Z. Zeng, and P. Yan, Terahertz magnon frequency comb, Phys. Rev. B 108, 134427 (2023).
  38. Z. Wang, H. Y. Yuan, Y. Cao, Z.-X. Li, R. A. Duine, and P. Yan, Magnonic frequency comb through nonlinear magnon-skyrmion scattering, Phys. Rev. Lett. 127, 037202 (2021).
  39. Z.-W. Zhou, X.-G. Wang, Y.-Z. Nie, Q.-L. Xia, and G.-H. Guo, Spin wave frequency comb generated through interaction between propagating spin wave and oscillating domain wall, J. Magn. Magn. Mater. 534, 168046 (2021).
  40. Z. Wang, H. Y. Yuan, Y. Cao, and P. Yan, Twisted magnon frequency comb and Penrose superradiance, Phys. Rev. Lett. 129, 107203 (2022).
  41. P. Gruszecki, K. Y. Guslienko, I. L. Lyubchanskii, and M. Krawczyk, Inelastic spin-wave beam scattering by edge-localized spin waves in a ferromagnetic thin film, Phys. Rev. Appl. 17, 044038 (2022).
  42. K. Sobucki, I. Lyubchanskii, M. Krawczyk, and P. Gruszecki, Goos–Hänchen shift of inelastically scattered spin-wave beams and cascade nonlinear magnon processes, Sci. Rep. 15, 5538 (2025).
  43. H.-J. Chia, F. Guo, L. M. Belova, and R. D. McMichael, Two-dimensional spectroscopic imaging of individual ferromagnetic nanostripes, Phys. Rev. B 86, 184406 (2012).
  44. V. Tyberkevych, A. Slavin, P. Artemchuk, and G. Rowlands, Vector Hamiltonian formalism for nonlinear magnetization dynamics, arXiv:2011.13562.
  45. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  46. P. Krivosik and C. E. Patton, Hamiltonian formulation of nonlinear spin-wave dynamics: Theory and applications, Phys. Rev. B 82, 184428 (2010).
  47. K. Y. Guslienko and A. N. Slavin, Magnetostatic Green's functions for the description of spin waves in finite rectangular magnetic dots and stripes, J. Magn. Magn. Mater. 323, 2418 (2011).
  48. B. A. Kalinikos and A. N. Slavin, Theory of dipole-exchange spin wave spectrum for ferromagnetic films with mixed exchange boundary conditions, J. Phys. C: Solid State Phys. 19, 7013 (1986).
  49. J. Plemelj, Problems in the Sense of Riemann and Klein (Interscience Publishers, New York, 1964).
  50. A. Aharoni, Demagnetizing factors for rectangular ferromagnetic prisms, J. Appl. Phys. 83, 3432 (1998).
  51. K. Sobucki, Dataset for the article “Three-magnon scattering of spin wave on edge-localized mode in thin ferromagnetic film” [data set], Zenodo (2025), https://zenodo.org/records/16779052.
  52. A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. Van Waeyenberge, The design and verification of MuMax3, AIP Adv. 4, 107133 (2014).
  53. N. J. Whitehead, S. A. R. Horsley, T. G. Philbin, and V. V. Kruglyak, Graded index lenses for spin wave steering, Phys. Rev. B 100, 094404 (2019).

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Phys. Rev. B 112, 214438– Published 17 December, 2025
  • Received 8 August 2025
  • Revised 27 October 2025
  • Accepted 1 December 2025
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