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Emergent electric fields driven by phonon-coupled skyrmion resonances

Seno Aji*

  • Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia

  • *Contact author: senji77@sci.ui.ac.id

Phys. Rev. B 114, 074309 – Published 21 August, 2026

DOI: https://doi.org/10.1103/d751-kbdc

Abstract

We develop a coarse-grained theoretical description of the macroscopic emergent electric field generated by phonon-coupled lattice deformations in the breathing and rotational dynamics of a skyrmion lattice under microwave excitation. The analysis identifies the symmetry and dynamical conditions that yield rectified (dc) and oscillating (ac) electric fields, even in the absence of net translational motion of the skyrmion lattice, particularly in the dilute-lattice limit. Using experimentally measurable skyrmion profile parameters such as the equilibrium radius, domain-wall width, and dynamical resonance frequency of the skyrmion lattice, the model further enables identification of harmonic components contributing to the observed macroscopic electrodynamic response in the long-wavelength phonon limit (q0) and at finite phonon frequency, providing a unified framework for phonon-driven spin-charge-lattice coupling in topological magnets.

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References (56)

  1. N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8, 899 (2013).
  2. A. Fert, N. Reyren, and V. Cros, Magnetic skyrmions: Advances in physics and potential applications, Nat. Rev. Mater. 2, 17031 (2017).
  3. T. Schulz, R. Ritz, A. Bauer, M. Halder, M. Wagner, C. Franz, C. Pfleiderer, K. Everschor, M. Garst, and A. Rosch, Emergent electrodynamics of skyrmions in a chiral magnet, Nat. Phys. 8, 301 (2012).
  4. A. Rosch, Moving with the current, Nat. Nanotechnol. 8, 160 (2013).
  5. S. Li, X. Wang, and T. Rasing, Magnetic skyrmions: Basic properties and potential applications, Interdiscip. Mater. 2, 260 (2023).
  6. N. Verma, Z. Addison, and M. Randeria, Unified theory of the anomalous and topological Hall effects with phase-space Berry curvatures, Sci. Adv. 8, eabq2765 (2022).
  7. D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
  8. S.-S. Zhang, H. Ishizuka, H. Zhang, G. B. Halász, and C. D. Batista, Real-space Berry curvature of itinerant electron systems with spin-orbit interaction, Phys. Rev. B 101, 024420 (2020).
  9. T. Koide, A. Takeuchi, and M. Mochizuki, DC spinmotive force from microwave-active resonant dynamics of a skyrmion crystal under a tilted magnetic field, Phys. Rev. B 100, 014408 (2019).
  10. Y. Tokura and N. Kanazawa, Magnetic skyrmion materials, Chem. Rev. 121, 2857 (2021).
  11. S.-Z. Lin and A. Saxena, Dynamics of Dirac strings and monopolelike excitations in chiral magnets under a current drive, Phys. Rev. B 93, 060401(R) (2016).
  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. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. Böni, Topological Hall effect in the A phase of MnSi, Phys. Rev. Lett. 102, 186602 (2009).
  14. G. Tatara and H. Kohno, Theory of current-driven domain wall motion: Spin transfer versus momentum transfer, Phys. Rev. Lett. 92, 086601 (2004).
  15. M. E. Lucassen, G. C. F. L. Kruis, R. Lavrijsen, H. J. M. Swagten, B. Koopmans, and R. A. Duine, Spin motive forces due to magnetic vortices and domain walls, Phys. Rev. B 84, 014414 (2011).
  16. S. Aji, T. Oda, Y. Fujishiro, N. Kanazawa, H. Saito, H. Endo, M. Hino, S. Itoh, T.-h. Arima, Y. Tokura, and T. Nakajima, Direct observations of spin fluctuations in hedgehog–anti-hedgehog spin lattice states in MnSi1xGex(x=0.6and0.8) at zero magnetic field, Phys. Rev. B 108, 054445 (2023).
  17. K. Everschor-Sitte, J. Masell, R. M. Reeve, and M. Kläui, Perspective: Magnetic skyrmions—overview of recent progress in an active research field, J. Appl. Phys. 124, 240901 (2018).
  18. Y. Okamura, F. Kagawa, M. Mochizuki, M. Kubota, S. Seki, S. Ishiwata, M. Kawasaki, Y. Onose, and Y. Tokura, Microwave magnetoelectric effect via skyrmion resonance modes in a helimagnetic multiferroic, Nat. Commun. 4, 2391 (2013).
  19. M. Mochizuki, Spin-wave modes and their intense excitation effects in skyrmion crystals, Phys. Rev. Lett. 108, 017601 (2012).
  20. J. Iwasaki, M. Mochizuki, and N. Nagaosa, Universal current-velocity relation of skyrmion motion in chiral magnets, Nat. Commun. 4, 1463 (2013).
  21. 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).
  22. 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).
  23. Y. Hu, X. Lan, and B. Wang, Nonlinear emergent elasticity and structural transitions of a skyrmion crystal under uniaxial distortion, Phys. Rev. B 99, 214412 (2019).
  24. S.-Z. Lin and A. Saxena, Noncircular skyrmion and its anisotropic response in thin films of chiral magnets under a tilted magnetic field, Phys. Rev. B 92, 180401(R) (2015).
  25. O. Petrova and O. Tchernyshyov, Spin waves in a skyrmion crystal, Phys. Rev. B 84, 214433 (2011).
  26. Y. Hu, Long-wavelength emergent phonons in Bloch skyrmion crystals distorted by exchange anisotropy and tilted magnetic fields, Phys. Rev. B 100, 144424 (2019).
  27. M. T. Birch, I. Belopolski, Y. Fujishiro, M. Kawamura, A. Kikkawa, Y. Taguchi, M. Hirschberger, N. Nagaosa, and Y. Tokura, Dynamic transition and Galilean relativity of current-driven skyrmions, Nature (London) 633, 554 (2024).
  28. S. Spachmann, A. Elghandour, M. Frontzek, W. Löser, and R. Klingeler, Magnetoelastic coupling and phases in the skyrmion lattice magnet Gd2PdSi3 discovered by high-resolution dilatometry, Phys. Rev. B 103, 184424 (2021).
  29. Y. Nii, T. Nakajima, A. Kikkawa, Y. Yamasaki, K. Ohishi, J. Suzuki, Y. Taguchi, T. Arima, Y. Tokura, and Y. Iwasa, Uniaxial stress control of skyrmion phase, Nat. Commun. 6, 8539 (2015).
  30. K. Adachi, H. Wilhelm, M. P. Schmidt, and M. A. Carpenter, Elastic and anelastic behavior associated with magnetic ordering in the skyrmion host Cu2OSeO3, Phys. Rev. B 109, 144413 (2024).
  31. J. Masell, D. R. Rodrigues, B. F. McKeever, and K. Everschor-Sitte, Spin-transfer torque driven motion, deformation, and instabilities of magnetic skyrmions at high currents, Phys. Rev. B 101, 214428 (2020).
  32. Y. Hu and B. Wang, Unified theory of magnetoelastic effects in B20 chiral magnets, New J. Phys. 19, 123002 (2017).
  33. T. Nomura, X.-X. Zhang, S. Zherlitsyn, J. Wosnitza, Y. Tokura, N. Nagaosa, and S. Seki, Phonon magnetochiral effect, Phys. Rev. Lett. 122, 145901 (2019).
  34. S. Zhang and S. S.-L. Zhang, Generalization of the Landau-Lifshitz-Gilbert equation for conducting ferromagnets, Phys. Rev. Lett. 102, 086601 (2009).
  35. K. Everschor-Sitte and M. Sitte, Real-space Berry phases: Skyrmion soccer (invited), J. Appl. Phys. 115, 172602 (2014).
  36. S. Meyer, M. Perini, S. von Malottki, A. Kubetzka, R. Wiesendanger, K. von Bergmann, and S. Heinze, Isolated zero field sub-10 nm skyrmions in ultrathin Co films, Nat. Commun. 10, 3823 (2019).
  37. H. Wu, X. Hu, K. Jing, and X. R. Wang, Size and profile of skyrmions in skyrmion crystals, Commun. Phys. 4, 210 (2021).
  38. S. Rohart and A. Thiaville, Skyrmion confinement in ultrathin film nanostructures in the presence of Dzyaloshinskii-Moriya interaction, Phys. Rev. B 88, 184422 (2013).
  39. X. S. Wang, H. Y. Yuan, and X. R. Wang, A theory on skyrmion size, Commun. Phys. 1, 31 (2018).
  40. S. Aji, M. Anin Nabail Azhiim, N. Ika Puji Ayu, A. Badra Cahaya, K. Kusakabe, and M. Aziz Majidi, Spin current generation driven by skyrmion dynamics under magnetic anisotropy and polarized microwaves, J. Phys. D 58, 315003 (2025).
  41. X. Z. Lu, X. Wu, and H. J. Xiang, General microscopic model of magnetoelastic coupling from first principles, Phys. Rev. B 91, 100405(R) (2015).
  42. E. R. Callen and H. B. Callen, Static magnetoelastic coupling in cubic crystals, Phys. Rev. 129, 578 (1963).
  43. B. F. McKeever, D. R. Rodrigues, D. Pinna, A. Abanov, J. Sinova, and K. Everschor-Sitte, Characterizing breathing dynamics of magnetic skyrmions and antiskyrmions within the Hamiltonian formalism, Phys. Rev. B 99, 054430 (2019).
  44. S.-Z. Lin, Dynamics and inertia of a skyrmion in chiral magnets and interfaces: A linear response approach based on magnon excitations, Phys. Rev. B 96, 014407 (2017).
  45. F. Büttner, C. Moutafis, M. Schneider, B. Krüger, C. M. Günther, J. Geilhufe, C. v. K. Schmising, J. Mohanty, B. Pfau, S. Schaffert, A. Bisig, M. Foerster, T. Schulz, C. A. F. Vaz, J. H. Franken, H. J. M. Swagten, M. Kläui, and S. Eisebitt, Dynamics and inertia of skyrmionic spin structures, Nat. Phys. 11, 225 (2015).
  46. X. Li and C. S. Lynch, Strong electric field tuning of magnetism in self-biased multiferroic structures, Sci. Rep. 10, 21148 (2020).
  47. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd ed., Course of Theoretical Physics Vol. 7 (Butterworth-Heinemann, Oxford, 1986).
  48. E. Kuhl, Continuum mechanics, Lecture Notes for ME338 (Stanford University, 2003).
  49. S. L. Zhang, W. W. Wang, D. M. Burn, H. Peng, H. Berger, A. Bauer, C. Pfleiderer, G. van der Laan, and T. Hesjedal, Manipulation of skyrmion motion by magnetic field gradients, Nat. Commun. 9, 2115 (2018).
  50. Y. Yang, L. Zhao, D. Yi, T. Xu, Y. Chai, C. Zhang, D. Jiang, Y. Ji, D. Hou, W. Jiang, J. Tang, P. Yu, H. Wu, and T. Nan, Acoustic-driven magnetic skyrmion motion, Nat. Commun. 15, 1018 (2024).
  51. M. Foerster, F. Macià, N. Statuto, S. Finizio, A. Hernández-Mínguez, S. Lendínez, P. V. Santos, J. Fontcuberta, J. M. Hernàndez, M. Kläui, and L. Aballe, Direct imaging of delayed magneto-dynamic modes induced by surface acoustic waves, Nat. Commun. 8, 407 (2017).
  52. P. van Capel, E. Péronne, and J. Dijkhuis, Nonlinear ultrafast acoustics at the nano scale, Ultrasonics 56, 36 (2015).
  53. 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).
  54. X. Liu, Z. Jin, Z. Li, Z. Zeng, M. Li, Y. Yao, Y. Cao, Y. Zhang, and P. Yan, Low-lying magnon frequency comb in skyrmion crystals, Phys. Rev. B 110, 184413 (2024).
  55. 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).
  56. L. Dreher, M. Weiler, M. Pernpeintner, H. Huebl, R. Gross, M. S. Brandt, and S. T. B. Goennenwein, Surface acoustic wave driven ferromagnetic resonance in nickel thin films: Theory and experiment, Phys. Rev. B 86, 134415 (2012).

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