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Boltzmann transport theory of magnon-exciton drag

Zakhar A. Iakovlev1, Akashdeep Kamra2, and Mikhail M. Glazov1

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Phys. Rev. B 113, 245424 – Published 23 June, 2026

DOI: https://doi.org/10.1103/s8bd-vb42

Abstract

We develop a microscopic theory of magnon-exciton drag effect in a bilayer van der Waals antiferromagnetic semiconductor CrSBr. Effective exciton-magnon coupling arises from an orbital mechanism: Magnons tilt the layer magnetizations, enabling charge carrier tunneling that mixes intralayer and interlayer excitons and thereby modulates the exciton energy. We derive the effective Hamiltonian of exciton-magnon coupling, based on our calculation of the magnon spectrum taking into account short-range exchange interaction between Cr-ion spins, single-ion anisotropy, and long-range dipole-dipole interactions. We show that despite rather small renormalization of exciton's energy and effective mass by the exciton-magnon interaction, the three key two-magnon processes, exciton-magnon scattering, two-magnon absorption by an exciton, and two-magnon emission, are highly efficient. By solving the Boltzmann kinetic equation, we evaluate a short exciton-magnon scattering time which is in the sub-ps range and strongly decreases with the increase in magnon population. Hence, exciton-magnon scattering is likely to be dominant over other scattering processes related to exciton-phonon and exciton-disorder interactions. We demonstrate that nonequilibrium magnons can efficiently drag excitons, resulting in a large and nearly isotropic exciton propagation that can significantly exceed the intrinsic anisotropic diffusion. Our results provide a theoretical basis for recent observations of anomalous exciton transport in CrSBr [F. Dirnberger et al., Nat. Nanotechnol. 21, 65 (2026)] and establish magnon-exciton drag as a powerful mechanism for controlling exciton propagation in magnetic systems.

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References (75)

  1. Q. H. Wang, A. Bedoya-Pinto, M. Blei, A. H. Dismukes, A. Hamo, S. Jenkins, M. Koperski, Y. Liu, Q.-C. Sun, E. J. Telford, H. H. Kim, M. Augustin, U. Vool, J.-X. Yin, L. H. Li, A. Falin, C. R. Dean, F. Casanova, R. F. L. Evans, M. Chshiev, et al., The magnetic genome of two-dimensional van der Waals materials, ACS Nano 16, 6960 (2022).
  2. K. S. Burch, D. Mandrus, and J.-G. Park, Magnetism in two-dimensional van der Waals materials, Nature (London) 563, 47 (2018).
  3. N. J. Brennan, C. A. Noble, J. Tang, M. E. Ziebel, and Y. J. Bae, Important elements of spin-exciton and magnon-exciton coupling, ACS Phys. Chem. Au 4, 322 (2024).
  4. F. Dirnberger, R. Bushati, B. Datta, A. Kumar, A. H. MacDonald, E. Baldini, and V. M. Menon, Spin-correlated exciton–polaritons in a van der Waals magnet, Nat. Nanotechnol. 17, 1060 (2022).
  5. N. P. Wilson, K. Lee, J. Cenker, K. Xie, A. H. Dismukes, E. J. Telford, J. Fonseca, S. Sivakumar, C. Dean, T. Cao, X. Roy, X. Xu, and X. Zhu, Interlayer electronic coupling on demand in a 2D magnetic semiconductor, Nat. Mater. 20, 1657 (2021).
  6. M.-C. Heißenbüttel, P.-M. Piel, J. Klein, T. Deilmann, U. Wurstbauer, and M. Rohlfing, Quadratic optical response to a magnetic field in the layered magnet CrSBr, Phys. Rev. B 111, 075107 (2025).
  7. M. A. Semina, F. Tabataba-Vakili, A. Rupp, A. S. Baimuratov, A. Högele, and M. M. Glazov, Excitons and trions in CrSBr bilayers, Phys. Rev. B 111, 205301 (2025).
  8. Y. J. Bae, J. Wang, A. Scheie, J. Xu, D. G. Chica, G. M. Diederich, J. Cenker, M. E. Ziebel, Y. Bai, H. Ren, C. R. Dean, M. Delor, X. Xu, X. Roy, A. D. Kent, and X. Zhu, Exciton-coupled coherent magnons in a 2D semiconductor, Nature (London) 609, 282 (2022).
  9. G. M. Diederich, J. Cenker, Y. Ren, J. Fonseca, D. G. Chica, Y. J. Bae, X. Zhu, X. Roy, T. Cao, D. Xiao, and X. Xu, Tunable interaction between excitons and hybridized magnons in a layered semiconductor, Nat. Nanotechnol. 18, 23 (2023).
  10. F. Dirnberger, J. Quan, R. Bushati, G. M. Diederich, M. Florian, J. Klein, K. Mosina, Z. Sofer, X. Xu, A. Kamra, F. J. García-Vidal, A. Alù, and V. M. Menon, Magneto-optics in a van der Waals magnet tuned by self-hybridized polaritons, Nature (London) 620, 533 (2023).
  11. O. Johansen, A. Kamra, C. Ulloa, A. Brataas, and R. A. Duine, Magnon-mediated indirect exciton condensation through antiferromagnetic insulators, Phys. Rev. Lett. 123, 167203 (2019).
  12. B. Datta, P. C. Adak, S. Yu, A. Valiyaparambil Dharmapalan, S. J. Hall, A. Vakulenko, F. Komissarenko, E. Kurganov, J. Quan, W. Wang, K. Mosina, Z. Sofer, D. Pashov, M. van Schilfgaarde, S. Acharya, A. Kamra, M. Y. Sfeir, A. Alù, A. B. Khanikaev, and V. M. Menon, Magnon-mediated exciton–exciton interaction in a van der Waals antiferromagnet, Nat. Mater. 24, 1027 (2025).
  13. B. Han, H. Shan, K. W. Song, M. Sun, A. Bulavin, I. G. Savenko, M. Esmann, M. Struve, V. Solovyeva, L. Lackner, F. Eilenberger, J. Regner, Z. Sofer, O. Kyriienko, and C. Schneider, Exciton-polariton condensate in the van der Waals magnet CrSBr, arXiv:2501.18233.
  14. N. Yazdani, M. I. Bodnarchuk, F. Bertolotti, N. Masciocchi, I. Fureraj, B. Guzelturk, B. L. Cotts, M. Zajac, G. Rainò, M. Jansen, S. C. Boehme, M. Yarema, M.-F. Lin, M. Kozina, A. Reid, X. Shen, S. Weathersby, X. Wang, E. Vauthey, A. Guagliardi, et al., Coupling to octahedral tilts in halide perovskite nanocrystals induces phonon-mediated attractive interactions between excitons, Nat. Phys. 20, 47 (2024).
  15. M. M. Glazov, Phonon wind and drag of excitons in monolayer semiconductors, Phys. Rev. B 100, 045426 (2019).
  16. F. Dirnberger, S. Terres, Z. A. Iakovlev, K. Mosina, Z. Sofer, A. Kamra, M. M. Glazov, and A. Chernikov, Exciton transport driven by spin excitations in an antiferromagnet, Nat. Nanotechnol. 21, 65 (2026).
  17. M. Bailyn, Maximum variational principle for conduction problems in a magnetic field, and the theory of magnon drag, Phys. Rev. 126, 2040 (1962).
  18. G. Zanmarchi and C. Haas, Magnon drag, Philips Res. Rept. 23, 389 (1968).
  19. K. Sugihara, Thermoelectric power of antiferromagnetic semiconductors near the Néel temperature, J. Phys. Chem. Solids 34, 1727 (1973).
  20. J. Klein, B. Pingault, M. Florian, M.-C. Heißenbüttel, A. Steinhoff, Z. Song, K. Torres, F. Dirnberger, J. B. Curtis, M. Weile, A. Penn, T. Deilmann, R. Dana, R. Bushati, J. Quan, J. Luxa, Z. Sofer, A. Alù, V. M. Menon, U. Wurstbauer, et al., The bulk van der Waals layered magnet CrSBr is a quasi-1D material, ACS Nano 17, 5316 (2023).
  21. R. Damon and J. Eshbach, Magnetostatic modes of a ferromagnet slab, J. Phys. Chem. Solids 19, 308 (1961).
  22. B. A. Kalinikos and A. N. Slavin, Theory of dipole-exchange spin wave spectrum for ferromagnetic films with mixed exchange boundary conditions, J. Phys. C: Solid State Phys. 19, 7013 (1986).
  23. R. L. Stamps and R. E. Camley, Bulk and surface spin waves in thin‐film antiferromagnets, J. Appl. Phys. 56, 3497 (1984).
  24. A. Kamra, U. Agrawal, and W. Belzig, Noninteger-spin magnonic excitations in untextured magnets, Phys. Rev. B 96, 020411(R) (2017).
  25. A. E. Kanj, O. Gomonay, I. Boventer, P. Bortolotti, V. Cros, A. Anane, and R. Lebrun, Antiferromagnetic magnon spintronic based on nonreciprocal and nondegenerated ultra-fast spin-waves in the canted antiferromagnet α-Fe2O3, Sci. Adv. 9, eadh1601 (2023).
  26. Y. Sun, F. Meng, C. Lee, A. Soll, H. Zhang, R. Ramesh, J. Yao, Z. Sofer, and J. Orenstein, Dipolar spin wave packet transport in a van der Waals antiferromagnet, Nat. Phys. 20, 794 (2024).
  27. J. N. Ranhili, S. Khadka, J. Li, J. Cenker, A. M. Ruiz, A. Shumilin, J. J. Baldoví, K. Shen, M. Fedurin, M. Palmer, D. G. Chica, P. Byaruhanga, S. Chen, X. Xu, X. Roy, and B. Freelon, Ultrafast-induced coherent acoustic phonons in the two-dimensional magnet CrSBr, Struct. Dyn. 12, 024501 (2025).
  28. H. Liu and K. Shen, Spin wave dynamics excited by a focused laser pulse in antiferromagnet CrSBr, Phys. Rev. B 110, 024424 (2024).
  29. A. Scheie, M. Ziebel, D. G. Chica, Y. J. Bae, X. Wang, A. I. Kolesnikov, X. Zhu, and X. Roy, Spin waves and magnetic exchange Hamiltonian in CrSBr, Adv. Sci. 9, 2202467 (2022).
  30. A. Kamra, H. Keshtgar, P. Yan, and G. E. W. Bauer, Coherent elastic excitation of spin waves, Phys. Rev. B 91, 104409 (2015).
  31. 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).
  32. H. Fröhlich, Electrons in lattice fields, Adv. Phys. 3, 325 (1954).
  33. V. Eremenko, N. Kharchenko, Y. Litvinenko, and V. Naumenko, Magneto-optics and Spectroscopy of Antiferromagnets (Springer, New York, 2012).
  34. H. Yamamoto, D. S. McClure, C. Marzzacco, and M. Waldman, Energy migration in a nearly one-dimensional compound, tetramethyl ammonium manganese chloride (TMMC), Chem. Phys. 22, 79 (1977).
  35. G. L. McPherson and A. H. Francis, Extensive energy transfer in a nearly one-dimensional crystal: The emisson spectrum of CsMnBr3 doped with Nd3+, Phys. Rev. Lett. 41, 1681 (1978).
  36. K. Ueda and Y. Tanabe, Exciton motion in antiferromagnets, J. Phys. Soc. Jpn. 48, 1137 (1980).
  37. X. Bo, F. Li, X. Xu, X. Wan, and Y. Pu, Calculated magnetic exchange interactions in the van der Waals layered magnet CrSBr, New J. Phys. 25, 013026 (2023).
  38. R. den Teuling, R. Das, A. V. Bondarenko, E. V. Tartakovskaya, G. E. W. Bauer, and Y. M. Blanter, Spin waves in the bilayer van der Waals magnet CrSBr, Phys. Rev. B 112, 144442 (2025).
  39. F. Tabataba-Vakili, H. P. G. Nguyen, A. Rupp, K. Mosina, A. Papavasileiou, K. Watanabe, T. Taniguchi, P. Maletinsky, M. M. Glazov, Z. Sofer, A. S. Baimuratov, and A. Högele, Doping-control of excitons and magnetism in few-layer CrSBr, Nat. Commun. 15, 4735 (2024).
  40. M. A. Semina, M. M. Glazov, and E. Sherman, Interlayer exciton–polaron in atomically thin semiconductors, Ann. Phys. (NY) 532, 2000339 (2020).
  41. Z. A. Iakovlev, M. A. Semina, M. M. Glazov, and E. Y. Sherman, Flexural deformations and collapse of bilayer two-dimensional crystals by interlayer excitons, Phys. Rev. B 105, 205305 (2022).
  42. P. G. de Gennes, Effects of double exchange in magnetic crystals, Phys. Rev. 118, 141 (1960).
  43. E. L. Nagaev, Ground state and anomalous magnetic moment of conduction electrons in an antiferromagnetic semiconductor, Pis'ma ZhETF 6, 484 (1967) [JETP Lett. 6, 18 (1967)].
  44. A. Mauger and D. L. Mills, Role of conduction-electron–local-moment exchange in antiferromagnetic semiconductors: Ferrons and bound magnetic polarons, Phys. Rev. B 31, 8024 (1985).
  45. P. A. Wolff, Theory of bound magnetic polarons in semimagnetic semiconductors, in Semiconductors and Semimetals, edited by J. K. Furdyna and J. Kossut (Elsevier, Amsterdam, 1988), Vol. 25, pp. 413–454.
  46. E. L. Nagaev, Self-trapped states of charge carriers in magnetic semiconductors, J. Magn. Magn. Mater. 110, 39 (1992).
  47. I. A. Merkulov, D. R. Yakovlev, K. V. Kavokin, G. Mackh, W. Ossau, A. Waag, and G. Landwehr, Hierarchy of relaxation times in the formation of an excitonic magnetic polaron in (CdMn)Te, Pis'ma ZhETF 62, 313 (1995) [JETP Lett. 62, 335 (1995)].
  48. C. Benoit à la Guillaume, Y. G. Semenov, and M. Combescot, Free magnetic polaron: A nonlinear Hamiltonian approach, Phys. Rev. B 51, 14124 (1995).
  49. A. S. Alexandrov and J. T. Devreese, Advances in Polaron Physics (Springer, Berlin, 2010).
  50. M. M. Glazov, M. A. Semina, C. Robert, B. Urbaszek, T. Amand, and X. Marie, Intervalley polaron in atomically thin transition metal dichalcogenides, Phys. Rev. B 100, 041301(R) (2019).
  51. K. Kaasbjerg, K. S. Thygesen, and K. W. Jacobsen, Phonon-limited mobility in n-type single-layer MoS2 from first principles, Phys. Rev. B 85, 115317 (2012).
  52. S. Shree, M. Semina, C. Robert, B. Han, T. Amand, A. Balocchi, M. Manca, E. Courtade, X. Marie, T. Taniguchi, K. Watanabe, M. M. Glazov, and B. Urbaszek, Observation of exciton-phonon coupling in MoSe2 monolayers, Phys. Rev. B 98, 035302 (2018).
  53. M. M. Glazov, Z. A. Iakovlev, and S. Refaely-Abramson, Phonon-induced exciton weak localization in two-dimensional semiconductors, Appl. Phys. Lett. 121, 192106 (2022).
  54. B. Wang, Y. Wu, Y. Bai, P. Shi, G. Zhang, Y. Zhang, and C. Liu, Origin and regulation of triaxial magnetic anisotropy in the ferromagnetic semiconductor CrSBr monolayer, Nanoscale 15, 13402 (2023).
  55. A. Chernikov and M. M. Glazov, Chapter three: Exciton diffusion in 2D van der Waals semiconductors, in Semiconductors and Semimetals, edited by P. B. Deotare and Z. Mi (Elsevier, Amsterdam, 2023), Vol. 112, pp. 69–110.
  56. V. F. Gantmakher and Y. B. Levinson, Carrier Scattering in Metals and Semiconductors (North-Holland, Amsterdam, 1987).
  57. V. N. Mantsevich and M. M. Glazov, Viscous hydrodynamics of excitons in van der Waals heterostructures, Phys. Rev. B 110, 165305 (2024).
  58. K. Wagner, J. Zipfel, R. Rosati, E. Wietek, J. D. Ziegler, S. Brem, R. Perea-Causín, T. Taniguchi, K. Watanabe, M. M. Glazov, E. Malic, and A. Chernikov, Nonclassical exciton diffusion in monolayer WSe2, Phys. Rev. Lett. 127, 076801 (2021).
  59. P. G. De Gennes and J. Friedel, Anomalies de résistivité dans certains métaux magníques, J. Phys. Chem. Solids 4, 71 (1958).
  60. M. E. Fisher and J. S. Langer, Resistive anomalies at magnetic critical points, Phys. Rev. Lett. 20, 665 (1968).
  61. Y. Suezaki and H. Mori, Dynamic critical phenomena in magnetic systems. II: Electrical resistivity near the Néel point, Prog. Theor. Phys. 41, 1177 (1969).
  62. T. Kasuya and A. Kondo, Anomalous resistivity near Curie temperature due to the critical scattering, Solid State Commun. 14, 253 (1974).
  63. M. Ausloos, On the Néel temperature and critical exponents determined from electronic transport coefficients in magnetic metals, Phys. B+C (Amsterdam) 86-88, 338 (1977).
  64. H. Adachi, K. Uchida, E. Saitoh, and S. Maekawa, Theory of the spin Seebeck effect, Rep. Prog. Phys. 76, 036501 (2013).
  65. Q. Cui, X. Bai, and A. Delin, Anisotropic magnon transport in van der Waals ferromagnetic insulators, Adv. Funct. Mater. 35, 2407469 (2024).
  66. B. Flebus, R. A. Duine, and Y. Tserkovnyak, Landau-Lifshitz theory of the magnon-drag thermopower, Europhys. Lett. 115, 57004 (2016).
  67. T. Yamaguchi, H. Kohno, and R. A. Duine, Microscopic theory of magnon-drag electron flow in ferromagnetic metals, Phys. Rev. B 99, 094425 (2019).
  68. J. Endo, H. Matsuura, and M. Ogata, Effect of paramagnon drag on thermoelectric transport properties: Linear response theory, Phys. Rev. B 105, 045101 (2022).
  69. L. E. Gurevich, Thermoelectric properties of conductors. I, J. Phys. (U.S.S.R.) 10, 67 (1946) [Zh. Eksp. Teor. Fiz. 16, 193 (1946)].
  70. Y. Gurevich and O. Mashkevich, The electron-phonon drag and transport phenomena in semiconductors, Phys. Rep. 181, 327 (1989).
  71. L. V. Keldysh, Phonon wind and dimensions of electron-hole drops in semiconductors, Pis'ma ZhETF 23, 100 (1967) [JETP Lett. 23, 86 (1976)].
  72. A. V. Kimel, A. M. Kalashnikova, A. Pogrebna, and A. K. Zvezdin, Fundamentals and perspectives of ultrafast photoferroic recording, Phys. Rep. 852, 1 (2020).
  73. A. M. Kalashnikova, N. E. Khokhlov, L. A. Shelukhin, and A. V. Scherbakov, Ultrafast laser-induced control of magnetic anisotropy in nanostructures, Tech. Phys. 67, 2335 (2022).
  74. J. Varela-Manjarres, Y. Ren, and B. K. Nikolic, Ultrafast optical excitation of magnons in two-dimensional antiferromagnetic semiconductors via spin torque mediated by unbound electron-hole pairs and excitons: Signatures in magnonic charge pumping, Phys. Rev. B 113, 134403 (2026).
  75. E. Wietek, M. Florian, J. Göser, T. Taniguchi, K. Watanabe, A. Högele, M. M. Glazov, A. Steinhoff, and A. Chernikov, Nonlinear and negative effective diffusivity of interlayer excitons in Moiré-free heterobilayers, Phys. Rev. Lett. 132, 016202 (2024).

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Phys. Rev. B 113, 245424– Published 23 June, 2026
  • Received 23 January 2026
  • Revised 14 April 2026
  • Accepted 8 June 2026
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