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Magnon superlattices around skyrmions in frustrated magnets

Adarsh Hullahalli1,2, Christos Panagopoulos1, and Christina Psaroudaki2,*

  • *Contact author: christina.psaroudaki@phys.ens.psl.fr
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Phys. Rev. Research 8, 043116 – Published 2 November, 2026

DOI: https://doi.org/10.1103/fhbj-ykvn

Abstract

Dynamic magnetic textures provide a versatile platform for controlling magnon states in spintronic systems. Here, we identify a class of crystal-like dynamical magnon patterns in centrosymmetric frustrated magnets. Their periodicity originates from the interference of symmetry-related finite-wave-vector magnons associated with the Mexican-hat dispersion of the uniformly magnetized state. In the presence of an atomic-scale skyrmion whose size is comparable to the low-energy magnon wavelength, these extended states hybridize with magnetically active skyrmion modes. The skyrmion breaks translational symmetry, selects a coherent finite-k superposition, and allows the resulting magnon superlattice to be efficiently excited by a spatially uniform ac field. A local Gaussian ac field generates the same pattern without a skyrmion, showing that the skyrmion selects and activates, rather than sets, the superlattice wavelength. In addition, helicity dynamics enables weak activation of otherwise magnetically inactive breathing modes, while skyrmion lattices support dispersive magnon bands with nontrivial Chern numbers inside the first magnon gap. These results establish frustrated magnets as a platform for controllable finite-wavelength magnon interference and texture-assisted spin-wave patterning.

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References (60)

  1. E. Dagotto, Complexity in strongly correlated electronic systems, Science 309, 257 (2005).
  2. J. Chakhalian, J. W. Freeland, A. J. Millis, C. Panagopoulos, and J. M. Rondinelli, Colloquium: Emergent properties in plane view: Strong correlations at oxide interfaces, Rev. Mod. Phys. 86, 1189 (2014).
  3. Y. Tokura and N. Nagaosa, Nonreciprocal responses from non-centrosymmetric quantum materials, Nat. Commun. 9, 3740 (2018).
  4. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
  5. L. Balents, C. R. Dean, D. K. Efetov, and A. F. Young, Superconductivity and strong correlations in moiré flat bands, Nat. Phys. 16, 725 (2020).
  6. A. Fert, N. Reyren, and V. Cros, Magnetic skyrmions: Advances in physics and potential applications, Nat. Rev. Mater. 2, 17031 (2017).
  7. A. P. Petrović, C. Psaroudaki, P. Fischer, M. Garst, and C. Panagopoulos, Colloquium: Quantum properties and functionalities of magnetic skyrmions Rev. Mod. Phys. 97, 031001 (2025).
  8. A. O. Leonov and M. Mostovoy, Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet, Nat. Commun. 6, 8275 (2015).
  9. S.-Z. Lin and S. Hayami, Ginzburg-Landau theory for skyrmions in inversion-symmetric magnets with competing interactions, Phys. Rev. B 93, 064430 (2016).
  10. C. Psaroudaki and C. Panagopoulos, Skyrmion qubits: A new class of quantum logic elements based on nanoscale magnetization, Phys. Rev. Lett. 127, 067201 (2021).
  11. C. Psaroudaki and C. Panagopoulos, Skyrmion helicity: Quantization and quantum tunneling effects, Phys. Rev. B 106, 104422 (2022).
  12. M. Garst, J. Waizner, and D. Grundler, Collective spin excitations of helices and magnetic skyrmions: Review and perspectives of magnonics in non-centrosymmetric magnets, J. Phys. D 50, 293002 (2017).
  13. C. Schütte and M. Garst, Magnon-skyrmion scattering in chiral magnets, Phys. Rev. B 90, 094423 (2014).
  14. M. Mochizuki, X. Z. Yu, S. Seki, N. Kanazawa, W. Koshibae, J. Zang, M. Mostovoy, Y. Tokura, and N. Nagaosa, Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect, Nat. Mater. 13, 241 (2014).
  15. Z. Jin, C. Y. Meng, T. T. Liu, D. Y. Chen, Z. Fan, M. Zeng, X. B. Lu, X. S. Gao, M. H. Qin, and J.-M. Liu, Magnon-driven skyrmion dynamics in antiferromagnets: Effect of magnon polarization, Phys. Rev. B 104, 054419 (2021).
  16. S. A. Díaz, T. Hirosawa, J. Klinovaja, and D. Loss, Chiral magnonic edge states in ferromagnetic skyrmion crystals controlled by magnetic fields, Phys. Rev. Res. 2, 013231 (2020).
  17. T. Weber, D. M. Fobes, J. Waizner, P. Steffens, G. S. Tucker, M. Böhm, L. Beddrich, C. Franz, H. Gabold, R. Bewley, D. Voneshen, M. Skoulatos, R. Georgii, G. Ehlers, A. Bauer, C. Pfleiderer, P. Böni, M. Janoschek, and M. Garst, Topological magnon band structure of emergent Landau levels in a skyrmion lattice, Science 375, 1025 (2022).
  18. S. Seki, M. Garst, J. Waizner, R. Takagi, N. D. Khanh, Y. Okamura, K. Kondou, F. Kagawa, Y. Otani, and Y. Tokura, Propagation dynamics of spin excitations along skyrmion strings, Nat. Commun. 11, 256 (2020).
  19. P. Y. Portnichenko, J. Romhányi, Y. A. Onykiienko, A. Henschel, M. Schmidt, A. S. Cameron, M. A. Surmach, J. A. Lim, J. T. Park, A. Schneidewind, D. L. Abernathy, H. Rosner, J. van den Brink, and D. S. Inosov, Magnon spectrum of the helimagnetic insulator Cu2OSeO3, Nat. Commun. 7, 10725 (2016).
  20. P. Che, R. Ciola, M. Garst, V. Kravchuk, P. R. Baral, A. Magrez, H. Berger, T. Schönenberger, H. M. Rønnow, and D. Grundler, Multipole magnons in topological skyrmion lattices resolved by cryogenic Brillouin light scattering microscopy Commun. Mater. 6, 139 (2024).
  21. S. A. Montoya, S. Couture, J. J. Chess, J. C. T. Lee, N. Kent, M.-Y. Im, S. D. Kevan, P. Fischer, B. J. McMorran, S. Roy, V. Lomakin, and E. E. Fullerton, Resonant properties of dipole skyrmions in amorphous Fe/Gd multilayers, Phys. Rev. B 95, 224405 (2017).
  22. B. Satywali, V. P. Kravchuk, L. Pan, M. Raju, S. He, F. Ma, A. P. Petrović, M. Garst, and C. Panagopoulos, Microwave resonances of magnetic skyrmions in thin film multilayers, Nat. Commun. 12, 1909 (2021).
  23. G. Talmelli, T. Devolder, N. Träger, J. Förster, S. Wintz, M. Weigand, H. Stoll, M. Heyns, G. Schütz, I. P. Radu, J. Gräfe, F. Ciubotaru, and C. Adelmann, Reconfigurable submicrometer spin-wave majority gate with electrical transducers, Sci. Adv. 6, eabb4042 (2020).
  24. A. V. Chumak, A. A. Serga, and B. Hillebrands, Magnon transistor for all-magnon data processing, Nat. Commun. 5, 4700 (2014).
  25. Q. Wang, P. Pirro, R. Verba, A. Slavin, B. Hillebrands, and A. V. Chumak, Reconfigurable nanoscale spin-wave directional coupler, Sci. Adv. 4, e1701517 (2018).
  26. M. S. Sarker, L. Yao, H. Yamahara, K. Ma, Z. Liao, K. Terao, S. Tang, S. G. Ramaraj, M. Seki, and H. Tabata, Reconfigurable magnon interference by on-chip dynamic wavelength conversion, Sci. Rep. 13, 4872 (2023).
  27. S. Hayami, S.-Z. Lin, and C. D. Batista, Bubble and skyrmion crystals in frustrated magnets with easy-axis anisotropy, Phys. Rev. B 93, 184413 (2016).
  28. N. Metropolis and S. Ulam, The Monte Carlo method, J. Am. Stat. Assoc. 44, 335 (1949).
  29. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  30. J. Colpa, Diagonalization of the quadratic boson Hamiltonian, Physica A 93, 327 (1978).
  31. S. Toth and B. Lake, Linear spin wave theory for single-q incommensurate magnetic structures, J. Phys.: Condens. Matter 27, 166002 (2015).
  32. See Supplemental Material at http://link.aps.org/supplemental/10.1103/fhbj-ykvn for detailed derivations, theoretical analysis, and additional numerical simulations.
  33. G. Tatara, H. Kohno, and J. Shibata, Microscopic approach to current-driven domain wall dynamics, Phys. Rep. 468, 213 (2008).
  34. Y. V. Tymoshenko, Y. A. Onykiienko, T. Müller, R. Thomale, S. Rachel, A. S. Cameron, P. Y. Portnichenko, D. V. Efremov, V. Tsurkan, D. L. Abernathy, J. Ollivier, A. Schneidewind, A. Piovano, V. Felea, A. Loidl, and D. S. Inosov, Pseudo-Goldstone magnons in the frustrated S=3/2 Heisenberg helimagnet ZnCr2Se4 with a pyrochlore magnetic sublattice, Phys. Rev. X 7, 041049 (2017).
  35. M. Speight and T. Winyard, Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field, Phys. Rev. B 101, 134420 (2020).
  36. M. Kataoka, Spin waves in the helical spin density wave state due to the antisymmetric exchange interaction, J. Magn. Magn. Mater. 31–34, 341 (1983).
  37. G. M. Wysin and A. R. Völkel, Normal modes of vortices in easy-plane ferromagnets, Phys. Rev. B 52, 7412 (1995).
  38. S.-Z. Lin, C. D. Batista, and A. Saxena, Internal modes of a skyrmion in the ferromagnetic state of chiral magnets, Phys. Rev. B 89, 024415 (2014).
  39. T. Hirosawa, A. Mook, J. Klinovaja, and D. Loss, Magnetoelectric cavity magnonics in skyrmion crystals, PRX Quantum 3, 040321 (2022).
  40. M. Mochizuki, Spin-wave modes and their intense excitation effects in skyrmion crystals, Phys. Rev. Lett. 108, 017601 (2012).
  41. Y. Onose, Y. Okamura, S. Seki, S. Ishiwata, and Y. Tokura, Observation of magnetic excitations of skyrmion crystal in a helimagnetic insulator Cu2OSeO3, Phys. Rev. Lett. 109, 037603 (2012).
  42. S. A. Díaz, T. Hirosawa, D. Loss, and C. Psaroudaki, Spin wave radiation by a topological charge dipole, Nano Lett. 20, 6556 (2020).
  43. N. Zagury and S. M. Rezende, Theory of macroscopic excitations of magnons, Phys. Rev. B 4, 201 (1971).
  44. T. Kurumaji, T. Nakajima, M. Hirschberger, A. Kikkawa, Y. Yamasaki, H. Sagayama, H. Nakao, Y. Taguchi, T.-h. Arima, and Y. Tokura, Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet, Science 365, 914 (2019).
  45. M. Hirschberger, T. Nakajima, S. Gao, L. Peng, A. Kikkawa, T. Kurumaji, M. Kriener, Y. Yamasaki, H. Sagayama, H. Nakao, K. Ohishi, K. Kakurai, Y. Taguchi, X. Yu, T.-H. Arima, and Y. Tokura, Skyrmion phase and competing magnetic orders on a breathing kagomé lattice, Nat. Commun. 10, 5831 (2019).
  46. N. D. Khanh, T. Nakajima, X. Yu, S. Gao, K. Shibata, M. Hirschberger, Y. Yamasaki, H. Sagayama, H. Nakao, L. Peng, K. Nakajima, R. Takagi, T.-H. Arima, Y. Tokura, and S. Seki, Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet, Nat. Nanotechnol. 15, 444 (2020).
  47. Z. Hou, W. Ren, B. Ding, G. Xu, Y. Wang, B. Yang, Q. Zhang, Y. Zhang, E. Liu, F. Xu, W. Wang, G. Wu, X. Zhang, B. Shen, and Z. Zhang, Observation of various and spontaneous magnetic skyrmionic bubbles at room temperature in a frustrated kagome magnet with uniaxial magnetic anisotropy, Adv. Mater. 29, 1701144 (2017); Erratum 30, 1706306 (2018).
  48. A. Kubetzka, M. Bode, O. Pietzsch, and R. Wiesendanger, Spin-polarized scanning tunneling microscopy with antiferromagnetic probe tips, Phys. Rev. Lett. 88, 057201 (2002).
  49. R. Wiesendanger, Spin mapping at the nanoscale and atomic scale, Rev. Mod. Phys. 81, 1495 (2009).
  50. T. Mamyrbayev, K. Ikematsu, P. Meyer, A. Ershov, A. Momose, and J. Mohr, Super-resolution scanning transmission X-ray imaging using single biconcave parabolic refractive lens array, Sci. Rep. 9, 14366 (2019).
  51. Z. Xu, M. L. Palm, W. Huxter, K. Herb, J. M. Abendroth, K. Bouzehouane, O. Boulle, M. S. Gabor, J. Urrestarazu Larranaga, A. Morales, J. Rhensius, G. Puebla-Hellmann, and C. L. Degen, Minimizing sensor-sample distances in scanning nitrogen-vacancy magnetometry, ACS Nano 19, 8255 (2025).
  52. T. Sebastian, K. Schultheiss, B. Obry, B. Hillebrands, and H. Schultheiss, Micro-focused Brillouin light scattering: Imaging spin waves at the nanoscale, Front. Phys. 3 (2015).
  53. Y. Acremann, J. P. Strachan, V. Chembrolu, S. D. Andrews, T. Tyliszczak, J. A. Katine, M. J. Carey, B. M. Clemens, H. C. Siegmann, and J. Stöhr, Time-resolved imaging of spin transfer switching: Beyond the macrospin concept, Phys. Rev. Lett. 96, 217202 (2006).
  54. S. Bonetti, M. C. Hoffmann, M.-J. Sher, Z. Chen, S.-H. Yang, M. G. Samant, S. S. P. Parkin, and H. A. Dürr, THz-driven ultrafast spin-lattice scattering in amorphous metallic ferromagnets, Phys. Rev. Lett. 117, 087205 (2016).
  55. T. Nomoto, T. Koretsune, and R. Arita, Formation mechanism of the helical Q structure in Gd-based skyrmion materials, Phys. Rev. Lett. 125, 117204 (2020).
  56. R. Shindou, R. Matsumoto, S. Murakami, and J.-I. Ohe, Topological chiral magnonic edge mode in a magnonic crystal, Phys. Rev. B 87, 174427 (2013).
  57. S. A. Díaz, J. Klinovaja, and D. Loss, Topological magnons and edge states in antiferromagnetic skyrmion crystals, Phys. Rev. Lett. 122, 187203 (2019).
  58. J. Habel, A. Mook, J. Willsher, and J. Knolle, Breakdown of chiral edge modes in topological magnon insulators, Phys. Rev. B 109, 024441 (2024).
  59. E. Albisetti, D. Petti, G. Sala, R. Silvani, S. Tacchi, S. Finizio, S. Wintz, A. Calò, X. Zheng, J. Raabe, E. Riedo, and R. Bertacco, Nanoscale spin-wave circuits based on engineered reconfigurable spin-textures, Commun. Phys. 1, 56 (2018).
  60. H. Yu, J. Xiao, and H. Schultheiss, Magnetic texture based magnonics, Phys. Rep. 905, 1 (2021).

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Phys. Rev. Research 8, 043116– Published 2 November, 2026
  • Received 12 August 2025
  • Accepted 19 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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