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  • Letter
  • Open Access

Thermal Hall effect and gauge-field picture of magnons in antiferromagnetic skyrmion crystals

Masataka Kawano

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Phys. Rev. B 112, L060403 – Published 6 August, 2025

DOI: https://doi.org/10.1103/vqny-81z1

Abstract

Quasiparticle excitations in material solids often experience a fictitious gauge field, which can be a potential source of intriguing transport phenomena. Here, we show that low-energy excitations in insulating antiferromagnetic skyrmion crystals on the triangular lattice are effectively described by magnons with an SU(3) gauge field. The three-sublattice structure in the antiferromagnetic skyrmion crystals is inherited as three internal degrees of freedom for the magnons, which are coupled to their kinetic motion via the SU(3) gauge field that arises from the topologically nontrivial spin texture in real space. We show that the noncommutativity of the SU(3) gauge field breaks an effective time-reversal symmetry and contributes to a magnon thermal Hall effect. We further demonstrate the emergence of the finite thermal Hall conductivity in the antiferromagnetic skyrmion crystals by the linear spin-wave theory. The possible impact of different gauge structures on a thermal Hall conductivity is also discussed.

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References (63)

  1. X. G. Wen, F. Wilczek, and A. Zee, Chiral spin states and superconductivity, Phys. Rev. B 39, 11413 (1989).
  2. N. Nagaosa and P. A. Lee, Normal-state properties of the uniform resonating-valence-bond state, Phys. Rev. Lett. 64, 2450 (1990).
  3. P. A. Lee and N. Nagaosa, Gauge theory of the normal state of high-Tc superconductors, Phys. Rev. B 46, 5621 (1992).
  4. P. Matl, N. P. Ong, Y. F. Yan, Y. Q. Li, D. Studebaker, T. Baum, and G. Doubinina, Hall effect of the colossal magnetoresistance manganite La1−xCaxMnO3, Phys. Rev. B 57, 10248 (1998).
  5. J. Ye, Y. B. Kim, A. J. Millis, B. I. Shraiman, P. Majumdar, and Z. Tešanović, Berry phase theory of the anomalous Hall effect: Application to colossal magnetoresistance manganites, Phys. Rev. Lett. 83, 3737 (1999).
  6. K. Ohgushi, S. Murakami, and N. Nagaosa, Spin anisotropy and quantum Hall effect in the kagomé lattice: Chiral spin state based on a ferromagnet, Phys. Rev. B 62, R6065 (2000).
  7. S. H. Chun, M. B. Salamon, Y. Lyanda-Geller, P. M. Goldbart, and P. D. Han, Magnetotransport in manganites and the role of quantal phases: Theory and experiment, Phys. Rev. Lett. 84, 757 (2000).
  8. Y. Lyanda-Geller, S. H. Chun, M. B. Salamon, P. M. Goldbart, P. D. Han, Y. Tomioka, A. Asamitsu, and Y. Tokura, Charge transport in manganites: Hopping conduction, the anomalous Hall effect, and universal scaling, Phys. Rev. B 63, 184426 (2001).
  9. Y. Taguchi and Y. Tokura, Enhancement of anomalous Hall effect in a filling-changed pyrochlore-type molybdate, Europhys. Lett. 54, 401 (2001).
  10. Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa, and Y. Tokura, Spin chirality, Berry phase, and anomalous Hall effect in a frustrated ferromagnet, Science 291, 2573 (2001).
  11. S. Fujimoto, Hall effect of spin waves in frustrated magnets, Phys. Rev. Lett. 103, 047203 (2009).
  12. H. Katsura, N. Nagaosa, and P. A. Lee, Theory of the thermal Hall effect in quantum magnets, Phys. Rev. Lett. 104, 066403 (2010).
  13. Y. Onose, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, and Y. Tokura, Observation of the magnon Hall effect, Science 329, 297 (2010).
  14. S. A. Owerre, Topological thermal Hall effect in frustrated kagome antiferromagnets, Phys. Rev. B 95, 014422 (2017).
  15. P. Laurell and G. A. Fiete, Topological magnon bands and unconventional superconductivity in pyrochlore iridate thin films, Phys. Rev. Lett. 118, 177201 (2017).
  16. R. Matsumoto and S. Murakami, Theoretical prediction of a rotating magnon wave packet in ferromagnets, Phys. Rev. Lett. 106, 197202 (2011).
  17. R. Matsumoto and S. Murakami, Rotational motion of magnons and the thermal Hall effect, Phys. Rev. B 84, 184406 (2011).
  18. T. Ideue, Y. Onose, H. Katsura, Y. Shiomi, S. Ishiwata, N. Nagaosa, and Y. Tokura, Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators, Phys. Rev. B 85, 134411 (2012).
  19. M. Hirschberger, R. Chisnell, Y. S. Lee, and N. P. Ong, Thermal Hall effect of spin excitations in a kagome magnet, Phys. Rev. Lett. 115, 106603 (2015).
  20. K. A. van Hoogdalem, Y. Tserkovnyak, and D. Loss, Magnetic texture-induced thermal Hall effects, Phys. Rev. B 87, 024402 (2013).
  21. L. Kong and J. Zang, Dynamics of an insulating skyrmion under a temperature gradient, Phys. Rev. Lett. 111, 067203 (2013).
  22. J. Iwasaki, A. J. Beekman, and N. Nagaosa, Theory of magnon-skyrmion scattering in chiral magnets, Phys. Rev. B 89, 064412 (2014).
  23. Y.-T. Oh, H. Lee, J.-H. Park, and J. H. Han, Dynamics of magnon fluid in Dzyaloshinskii-Moriya magnet and its manifestation in magnon-skyrmion scattering, Phys. Rev. B 91, 104435 (2015).
  24. A. Roldán-Molina, A. S. Nunez, and J. Fernández-Rossier, Topological spin waves in the atomic-scale magnetic skyrmion crystal, New J. Phys. 18, 045015 (2016).
  25. A. Mook, B. Göbel, J. Henk, and I. Mertig, Magnon transport in noncollinear spin textures: Anisotropies and topological magnon Hall effects, Phys. Rev. B 95, 020401(R) (2017).
  26. S. K. Kim, K. Nakata, D. Loss, and Y. Tserkovnyak, Tunable magnonic thermal Hall effect in skyrmion crystal phases of ferrimagnets, Phys. Rev. Lett. 122, 057204 (2019).
  27. P. Nikolić, Quantum field theory of topological spin dynamics, Phys. Rev. B 102, 075131 (2020).
  28. 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).
  29. M. Akazawa, H.-Y. Lee, H. Takeda, Y. Fujima, Y. Tokunaga, T.-h. Arima, J. H. Han, and M. Yamashita, Topological thermal Hall effect of magnons in magnetic skyrmion lattice, Phys. Rev. Res. 4, 043085 (2022).
  30. I. Kézsmárki, S. Bordács, P. Milde, E. Neuber, L. Eng, J. White, H. Rønnow, C. Dewhurst, M. Mochizuki, K. Yanai, H. Nakamura, D. Ehlers, V. Tsurkan, and A. Loidl, Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8, Nat. Mater. 14, 1116 (2015).
  31. E. Ruff, S. Widmann, P. Lunkenheimer, V. Tsurkan, S. Bordács, I. Kézsmárki, and A. Loidl, Multiferroicity and skyrmions carrying electric polarization in GaV4S8, Sci. Adv. 1, e1500916 (2015).
  32. Y. Fujima, N. Abe, Y. Tokunaga, and T. Arima, Thermodynamically stable skyrmion lattice at low temperatures in a bulk crystal of lacunar spinel GaV4Se8, Phys. Rev. B 95, 180410(R) (2017).
  33. S. Bordács, A. Butykai, B. G. Szigeti, J. S. White, R. Cubitt, A. O. Leonov, S. Widmann, D. Ehlers, H.-A. K. von Nidda, V. Tsurkan, A. Loidl, and I. Kézsmárki, Equilibrium skyrmion lattice ground state in a polar easy-plane magnet, Sci. Rep. 7, 7584 (2017).
  34. H. Takeda, M. Kawano, K. Tamura, M. Akazawa, J. Yan, T. Waki, H. Nakamura, K. Sato, Y. Narumi, M. Hagiwara, M. Yamashita, and C. Hotta, Magnon thermal Hall effect via emergent SU(3) flux on the antiferromagnetic skyrmion lattice, Nat. Commun. 15, 566 (2024).
  35. S. Reil, H.-J. Stork, and H. Haeuseler, Structural investigations of the compounds ASc2S4 (A = Mn, Fe, Cd), J. Alloy. Compd. 334, 92 (2002).
  36. V. Fritsch, J. Hemberger, N. Büttgen, E.-W. Scheidt, H.-A. Krug von Nidda, A. Loidl, and V. Tsurkan, Spin and orbital frustration in MnSc2S4 and FeSc2S4, Phys. Rev. Lett. 92, 116401 (2004).
  37. S. Gao, O. Zaharko, V. Tsurkan, Y. Su, J. White, G. Tucker, B. Roessli, F. Bourdarot, R. Sibille, D. Chernyshov, T. Fennell, A. Loidl, and C. Rüegg, Spiral spin-liquid and the emergence of a vortex-like state in MnSc2S4, Nat. Phys. 13, 157 (2017).
  38. S. Gao, H. D. Rosales, F. A. G. Albarracin, G. K. Tsurkan, T. Fennell, P. Steffens, M. Boehm, P. Cermak, A. Schneldewind, E. Ressouche, D. Cabra, C. Rüegg, and O. Zaharko, Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings, Nature (London) 586, 37 (2020).
  39. H. D. Rosales, D. C. Cabra, and P. Pujol, Three-sublattice skyrmion crystal in the antiferromagnetic triangular lattice, Phys. Rev. B 92, 214439 (2015).
  40. S. A. Díaz, J. Klinovaja, and D. Loss, Topological magnons and edge states in antiferromagnetic skyrmion crystals, Phys. Rev. Lett. 122, 187203 (2019).
  41. A. Mukherjee, D. S. Kathyat, and S. Kumar, Antiferromagnetic skyrmion crystals in the Rashba Hund's insulator on triangular lattice, Sci. Rep. 11, 9566 (2021).
  42. M. Mohylna, F. A. G. Albarracín, M. Žukovič, and H. D. Rosales, Spontaneous antiferromagnetic skyrmion/antiskyrmion lattice and spiral spin-liquid states in the frustrated triangular lattice, Phys. Rev. B 106, 224406 (2022).
  43. S. Hayami, Three-sublattice antiferro-type and ferri-type skyrmion crystals in centrosymmetric magnets, Phys. Rev. B 109, 014415 (2024).
  44. A. N. Bogdanov and D. A. Yablonskii, Contribution to the theory of inhomogeneous states of magnets in the region of magnetic-field-induced phase transitions. Mixed state of antiferromagnets, Sov. Phys. JETP 69, 142 (1989).
  45. A. N. Bogdanov, U. K. Rößler, M. Wolf, and K.-H. Müller, Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets, Phys. Rev. B 66, 214410 (2002).
  46. 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).
  47. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  48. M. E. Zhitomirsky and A. L. Chernyshev, Colloquium: Spontaneous magnon decays, Rev. Mod. Phys. 85, 219 (2013).
  49. A. Mook, J. Klinovaja, and D. Loss, Quantum damping of skyrmion crystal eigenmodes due to spontaneous quasiparticle decay, Phys. Rev. Res. 2, 033491 (2020).
  50. N. D. Mermin and T.-L. Ho, Circulation and angular momentum in the A phase of superfluid helium-3, Phys. Rev. Lett. 36, 594 (1976).
  51. See Supplemental Material at http://link.aps.org/supplemental/10.1103/vqny-81z1 for the details of the derivation of the equation of motion, the classical ground state, and the linear spin-wave theory, which also includes Ref. [62].
  52. T. Jolicoeur and J. C. Le Guillou, Spin-wave results for the triangular Heisenberg antiferromagnet, Phys. Rev. B 40, 2727 (1989).
  53. J. H. P. Colpa, Diagonalization of the quadratic boson Hamiltonian, Phys. A (Amsterdam) 93, 327 (1978).
  54. R. Matsumoto, R. Shindou, and S. Murakami, Thermal Hall effect of magnons in magnets with dipolar interaction, Phys. Rev. B 89, 054420 (2014).
  55. We chose different values of D/|J| for the FM-SkX and AFM-SkX so that the spin configurations would fit within a numerically tractable magnetic unit cell. See Supplemental Material for details [51].
  56. T. Dombre and N. Read, Nonlinear σ models for triangular quantum antiferromagnets, Phys. Rev. B 39, 6797 (1989).
  57. B. Pradenas and O. Tchernyshyov, Spin-frame field theory of a three-sublattice antiferromagnet, Phys. Rev. Lett. 132, 096703 (2024).
  58. B. Göbel, I. Mertig, and O. A. Tretiakov, Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles, Phys. Rep. 895, 1 (2021).
  59. X. Zhang, Y. Zhou, and M. Ezawa, Antiferromagnetic skyrmion: Stability, creation and manipulation, Sci. Rep. 6, 24795 (2016).
  60. B. Göbel, A. Mook, J. Henk, and I. Mertig, Antiferromagnetic skyrmion crystals: Generation, topological Hall, and topological spin Hall effect, Phys. Rev. B 96, 060406(R) (2017).
  61. S. Hayami, Antiferro skyrmion crystal phases in a synthetic bilayer antiferromagnet under an in-plane magnetic field, J. Phys. Soc. Jpn. 92, 084702 (2023).
  62. B. Berg and M. Lüscher, Definition and statistical distributions of a topological number in the lattice O(3) σ-model, Nucl. Phys. B 190, 412 (1981).
  63. M. Kawano, Thermal Hall effect and gauge-field picture of magnons in antiferromagnetic skyrmion crystals (2025), doi: 10.5281/zenodo.16732352.

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Phys. Rev. B 112, L060403– Published 6 August, 2025
  • Received 28 March 2024
  • Revised 19 June 2025
  • Accepted 23 July 2025
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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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