• Letter
• Open Access

Khoa B. Le1, Ali Esquembre-Kučukalić2, Hsiao-Yi Chen3, Ivan Maliyov1, Yao Luo1, Jin-Jian Zhou4, Davide Sangalli5, Alejandro Molina-Sánchez2, and Marco Bernardi1

• 1Department of Applied Physics and Materials Science, and Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
• 2Institute of Materials Science (ICMUV), University of Valencia, Catedrático Beltrán 2, E-46980 Valencia, Spain
• 3Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
• 4School of Physics, Beijing Institute of Technology, Beijing 100081, China
• 5Istituto di Struttura della Materia-CNR (ISM-CNR), Area della Ricerca di Roma 1, Monterotondo Scalo, Italy

Abstract

Modeling spin-wave (magnon) dynamics in novel materials is important to advance spintronics and spin-based quantum technologies. The interactions between magnons and lattice vibrations (phonons) limit the length scale for magnon transport. However, quantifying these interactions remains challenging. Here, we show many-body calculations of magnon-phonon (mag-ph) coupling based on the ab initio Bethe-Salpeter equation. We derive expressions for mag-ph coupling matrices and compute them in two-dimensional ferromagnets, focusing on hydrogenated graphene and monolayer CrI3. Our analysis shows that electron-phonon (e−ph) and mag-ph interactions differ significantly, where modes with weak e−ph coupling can exhibit strong mag-ph coupling (and vice versa), and reveals which phonon modes couple more strongly with magnons. In both materials studied here, the inelastic magnon relaxation times decrease abruptly above the threshold for emission of strongly coupled phonons, revealing a low-energy window where magnons are long lived. Averaging over this window, we compute the temperature-dependent magnon mean free path, a key figure of merit for spintronics, entirely from first principles. The theory and computational tools shown in this Letter enable studies of magnon interactions, scattering, and dynamics in generic materials, advancing the design of magnetic systems and magnon- and spin-based devices.

• Magnons
• Phonons
• 2-dimensional systems
• Magnetic insulators
• Bethe-Salpeter equation
• Density functional calculations
• GW method
• Perturbation theory

See Also

Magnons in chromium trihalides calculated with the ab initio Bethe-Salpeter equation

Ali Esquembre-Kučukalić, Khoa B. Le, Alberto García-Cristóbal, Marco Bernardi, Davide Sangalli, and Alejandro Molina-Sánchez

Phys. Rev. B 112, 184412 (2025)

Article Text

Supplemental Material

References (70)

1. D. Basov, R. Averitt, and D. Hsieh, Towards properties on demand in quantum materials, Nat. Mater. 16, 1077 (2017).
2. L. Ye, M. Kang, J. Liu, F. Von Cube, C. R. Wicker, T. Suzuki, C. Jozwiak, A. Bostwick, E. Rotenberg, D. C. Bell et al., Massive Dirac fermions in a ferromagnetic kagome metal, Nature (London) 555, 638 (2018).
3. J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J.-G. Park, and H. Cheong, Ising-type magnetic ordering in atomically thin FePS3, Nano Lett. 16, 7433 (2016).
4. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals, Nature (London) 546, 265 (2017).
5. 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 et al., Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature (London) 546, 270 (2017).
6. K. Lee, A. H. Dismukes, E. J. Telford, R. A. Wiscons, J. Wang, X. Xu, C. Nuckolls, C. R. Dean, X. Roy, and X. Zhu, Magnetic order and symmetry in the 2D semiconductor CrSBr, Nano Lett. 21, 3511 (2021).
7. Y. Li, B. Yang, S. Xu, B. Huang, and W. Duan, Emergent phenomena in magnetic two-dimensional materials and van der Waals heterostructures, ACS Appl. Electron. Mater. 4, 3278 (2022).
8. S. Roche, B. van Wees, K. Garello, and S. O. Valenzuela, Spintronics with two-dimensional materials and van der Waals heterostructures, 2D Mater. 11, 043001 (2024).
9. S. S.-L. Zhang and S. Zhang, Magnon mediated electric current drag across a ferromagnetic insulator layer, Phys. Rev. Lett. 109, 096603 (2012).
10. S. A. Bender, R. A. Duine, and Y. Tserkovnyak, Electronic pumping of quasiequilibrium Bose-Einstein-condensed magnons, Phys. Rev. Lett. 108, 246601 (2012).
11. H. Yuan, Y. Cao, A. Kamra, R. Duine, and P. Yan, Quantum magnonics: When magnon spintronics meets quantum information science, Phys. Rep. 965, 1 (2022).
12. S. D. Bader and S. S. P. Parkin, Spintronics, Annu. Rev. Condens. Matter Phys. 1, 71 (2010).
13. V. V. Kruglyak, S. O. Demokritov, and D. Grundler, Magnonics, J. Phys. D: Appl. Phys. 43, 260301 (2010).
14. A. Chumak, V. Vasyuchka, A. Serga, and B. Hillebrands, Magnon spintronics, Nat. Phys. 11, 453 (2015).
15. B. Flebus, D. Grundler, B. Rana, Y. Otani, I. Barsukov, A. Barman, G. Gubbiotti, P. Landeros, J. Akerman, U. Ebels, P. Pirro, V. E. Demidov, K. Schultheiss, G. Csaba, Q. Wang, F. Ciubotaru, D. E. Nikonov, P. Che, R. Hertel, T. Ono et al., The 2024 magnonics roadmap, J. Phys.: Condens. Matter 36, 363501 (2024).
16. J. Lindner, K. Lenz, E. Kosubek, K. Baberschke, D. Spoddig, R. Meckenstock, J. Pelzl, Z. Frait, and D. L. Mills, Non-Gilbert-type damping of the magnetic relaxation in ultrathin ferromagnets: Importance of magnon-magnon scattering, Phys. Rev. B 68, 060102(R) (2003).
17. M. C. T. D. Müller, S. Blügel, and C. Friedrich, Electron-magnon scattering in elementary ferromagnets from first principles: Lifetime broadening and band anomalies, Phys. Rev. B 100, 045130 (2019).
18. U. Ritzmann, P. Baláž, P. Maldonado, K. Carva, and P. M. Oppeneer, High-frequency magnon excitation due to femtosecond spin-transfer torques, Phys. Rev. B 101, 174427 (2020).
19. D. Nabok, S. Blügel, and C. Friedrich, Electron-plasmon and electron-magnon scattering in ferromagnets from first principles by combining GW and GT self-energies, npj Comput. Mater. 7, 178 (2021).
20. M. Beens, R. A. Duine, and B. Koopmans, Modeling ultrafast demagnetization and spin transport: The interplay of spin-polarized electrons and thermal magnons, Phys. Rev. B 105, 144420 (2022).
21. S. F. Maehrlein, I. Radu, P. Maldonado, A. Paarmann, M. Gensch, A. M. Kalashnikova, R. V. Pisarev, M. Wolf, P. M. Oppeneer, J. Barker, and T. Kampfrath, Dissecting spin-phonon equilibration in ferrimagnetic insulators by ultrafast lattice excitation, Sci. Adv. 4, eaar5164 (2018).
22. T. Hioki, Y. Hashimoto, and E. Saitoh, Coherent oscillation between phonons and magnons, Commun. Phys. 5, 115 (2022).
23. F. Godejohann, A. V. Scherbakov, S. M. Kukhtaruk, A. N. Poddubny, D. D. Yaremkevich, M. Wang, A. Nadzeyka, D. R. Yakovlev, A. W. Rushforth, A. V. Akimov, and M. Bayer, Magnon polaron formed by selectively coupled coherent magnon and phonon modes of a surface patterned ferromagnet, Phys. Rev. B 102, 144438 (2020).
24. L. Liao, J. Liu, J. Puebla, Q. Shao, and Y. Otani, Hybrid magnon-phonon crystals, npj Spintronics 2, 47 (2024).
25. C. Berk, M. Jaris, W. Yang, S. Dhuey, S. Cabrini, and H. Schmidt, Strongly coupled magnon-phonon dynamics in a single nanomagnet, Nat. Commun. 10, 2652 (2019).
26. S. Boona, R. Myers, and J. Heremans, Spin caloritronics, Energy Environ. Sci. 7, 885 (2014).
27. T. Kikkawa, K. Shen, B. Flebus, R. A. Duine, K. I. Uchida, Z. Qiu, G. E. W. Bauer, and E. Saitoh, Magnon polarons in the spin seebeck effect, Phys. Rev. Lett. 117, 207203 (2016).
28. I. Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4, 241 (1958).
29. T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120, 91 (1960).
30. S. Toth and B. Lake, Linear spin wave theory for single-Q incommensurate magnetic structures, J. Phys.: Condens. Matter 27, 166002 (2015).
31. P. Delugas, O. Baseggio, I. Timrov, S. Baroni, and T. Gorni, Magnon-phonon interactions enhance the gap at the Dirac point in the spin-wave spectra of CrI3 two-dimensional magnets, Phys. Rev. B 107, 214452 (2023).
32. T. Gorni, O. Baseggio, P. Delugas, I. Timrov, and S. Baroni, First-principles study of the gap in the spin excitation spectrum of the CrI3 honeycomb ferromagnet, Phys. Rev. B 107, L220410 (2023).
33. H. Xiang, C. Lee, H.-J. Koo, X. Gong, and M.-H. Whangbo, Magnetic properties and energy-mapping analysis, Dalton Trans. 42, 823 (2013).
34. A. I. Liechtenstein, M. Katsnelson, V. Antropov, and V. Gubanov, Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys, J. Magn. Magn. Mater. 67, 65 (1987).
35. X. He, N. Helbig, M. J. Verstraete, and E. Bousquet, TB2J: A python package for computing magnetic interaction parameters, Comput. Phys. Commun. 264, 107938 (2021).
36. L.-W. Wang, L.-S. Xie, P.-X. Xu, and K. Xia, First-principles study of magnon-phonon interactions in gadolinium iron garnet, Phys. Rev. B 101, 165137 (2020).
37. A. Cong, J. Liu, W. Xue, H. Liu, Y. Liu, and K. Shen, Exchange-mediated magnon-phonon scattering in monolayer CrI3, Phys. Rev. B 106, 214424 (2022).
38. J. Cui, E. V. Boström, M. Ozerov, F. Wu, Q. Jiang, J.-H. Chu, C. Li, F. Liu, X. Xu, A. Rubio, and Q. Zhang, Chirality selective magnon-phonon hybridization and magnon-induced chiral phonons in a layered zigzag antiferromagnet, Nat. Commun. 14, 3396 (2023).
39. T. W. Metzger, K. A. Grishunin, C. Reinhoffer, R. M. Dubrovin, A. Arshad, I. Ilyakov, T. V. de Oliveira, A. Ponomaryov, J.-C. Deinert, S. Kovalev et al., Magnon-phonon Fermi resonance in antiferromagnetic CoF2, Nat. Commun. 15, 5472 (2024).
40. B. Flebus, K. Shen, T. Kikkawa, K. I. Uchida, Z. Qiu, E. Saitoh, R. A. Duine, and G. E. W. Bauer, Magnon-polaron transport in magnetic insulators, Phys. Rev. B 95, 144420 (2017).
41. G. Onida, L. Reining, and A. Rubio, Electronic excitations: Density-functional versus many-body Green’s-function approaches, Rev. Mod. Phys. 74, 601 (2002).
42. M. Rohlfing and S. G. Louie, Electron-hole excitations and optical spectra from first principles, Phys. Rev. B 62, 4927 (2000).
43. M. Palummo, M. Bernardi, and J. C. Grossman, Exciton radiative lifetimes in two-dimensional transition metal dichalcogenides, Nano Lett. 15, 2794 (2015).
44. H.-Y. Chen, D. Sangalli, and M. Bernardi, Exciton-phonon interaction and relaxation times from first principles, Phys. Rev. Lett. 125, 107401 (2020).
45. H.-Y. Chen, D. Sangalli, and M. Bernardi, First-principles ultrafast exciton dynamics and time-domain spectroscopies: Dark-exciton mediated valley depolarization in monolayer WSe2, Phys. Rev. Res. 4, 043203 (2022).
46. G. Antonius and S. G. Louie, Theory of exciton-phonon coupling, Phys. Rev. B 105, 085111 (2022).
47. Y.-H. Chan, J. B. Haber, M. H. Naik, J. B. Neaton, D. Y. Qiu, F. H. da Jornada, and S. G. Louie, Exciton lifetime and optical line width profile via exciton–phonon interactions: Theory and first-principles calculations for monolayer MoS2, Nano Lett. 23, 3971 (2023).
48. T. Olsen, Unified treatment of magnons and excitons in monolayer CrI3 from many-body perturbation theory, Phys. Rev. Lett. 127, 166402 (2021).
49. M. Marsili, A. Molina-Sánchez, M. Palummo, D. Sangalli, and A. Marini, Spinorial formulation of the GW-BSE equations and spin properties of excitons in two-dimensional transition metal dichalcogenides, Phys. Rev. B 103, 155152 (2021).
50. M. Gatti and F. Sottile, Exciton dispersion from first principles, Phys. Rev. B 88, 155113 (2013).
51. A. E. Esquembre-Kučukalić, K. B. Le, A. García-Cristóbal, M. Bernardi, D. Sangalli, and A. Molina-Sánchez, companion paper, Magnons in chromium trihalides calculated with the ab initio Bethe-Salpeter equation, Phys. Rev. B 112, 184412 (2025).
52. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos et al., quantum espresso: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
53. D. Sangalli, A. Ferretti, H. Miranda, C. Attaccalite, I. Marri, E. Cannuccia, P. Melo, M. Marsili, F. Paleari, A. Marrazzo, G. Prandini, P. Bonfà, M. O. Atambo, F. Affinito, M. Palummo, A. Molina-Sánchez, C. Hogan, M. Grüning, D. Varsano, and A. Marini, Many-body perturbation theory calculations using the YAMBO code, J. Phys.: Condens. Matter 31, 325902 (2019).
54. A. Molina-Sánchez, G. Catarina, D. Sangalli, and J. Fernández-Rossier, Magneto-optical response of chromium trihalide monolayers: Chemical trends, J. Mater. Chem. C 8, 8856 (2020).
55. Our DFT calculations use the local spin-density approximation (LSDA) and a plane-wave basis set. We employ fully relativistic pseudopotentials [68] generated with the oncvpsp code [69]. The Brillouin zone sampling of electron k points, phonon q points, and magnon Q points are all performed on an 18×18×1 grid for semihydrogenated graphene, with a 70 Ry kinetic energy cutoff, and on a 12×12×1 with 90 Ry cutoff for monolayer CrI3. A truncation of the Coulomb interaction along the z axis is applied to simulate the phonon dispersion of an isolated layer. For mag-ph relaxation time calculations, the mag-ph coupling is obtained on dense momentum grids using linear interpolation.
56. 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).
57. See Supplemental Material at http://link.aps.org/supplemental/10.1103/489b-n5pd for derivations of magnon-phonon coupling and relaxation times, validation of our perturbative approach, and derivation and BSE calculations of magnon-phonon mixing, which includes Ref. [70].
58. M. Bernardi, First-principles dynamics of electrons and phonons, Eur. Phys. J. B 89, 239 (2016).
59. J.-J. Zhou, J. Park, I.-T. Lu, I. Maliyov, X. Tong, and M. Bernardi, perturbo: A software package for ab initio electron–phonon interactions, charge transport and ultrafast dynamics, Comput. Phys. Commun. 264, 107970 (2021).
60. S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001).
61. J. Park, J.-J. Zhou, Y. Luo, and M. Bernardi, Predicting phonon-induced spin decoherence from first principles: Colossal spin renormalization in condensed matter, Phys. Rev. Lett. 129, 197201 (2022).
62. S. Ren, J. Bonini, M. Stengel, C. E. Dreyer, and D. Vanderbilt, Adiabatic dynamics of coupled spins and phonons in magnetic insulators, Phys. Rev. X 14, 011041 (2024).
63. E. Mariani and F. von Oppen, Flexural phonons in free-standing graphene, Phys. Rev. Lett. 100, 076801 (2008).
64. L. Lindsay, D. A. Broido, and N. Mingo, Flexural phonons and thermal transport in graphene, Phys. Rev. B 82, 115427 (2010).
65. S. R. Boona and J. P. Heremans, Magnon thermal mean free path in yttrium iron garnet, Phys. Rev. B 90, 064421 (2014).
66. W. Fang, J. Simoni, and Y. Ping, Efficient method for calculating magnon-phonon coupling from first principles, Phys. Rev. B 111, 104431 (2025).
67. Data is available at: https://doi.org/10.24435/materialscloud:rg-mb
68. J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23, 5048 (1981).
69. D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013).
70. G. D. Mahan, Many-Particle Physics, 3rd ed. (Springer, New York, 2000).