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Propagation and localization of spin excitations at altermagnetic domain walls

Oksana Peschanska1, Jeroen van den Brink2,3,4, and Volodymyr P. Kravchuk1,2,3,*

  • *Contact author: v.kravchuk@ifw-dresden.de
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Phys. Rev. B 114, 194421 – Published 23 October, 2026

DOI: https://doi.org/10.1103/zgw5-99k2

Abstract

Altermagnets (AMs) are spin-compensated materials in which opposite-spin sublattices are connected by a symmetry that causes a spin splitting in their elementary excitations. As there is a strong effect of altermagnetism on domain wall properties, it is quite natural to also expect an enrichment of the physics of magnetic excitations at AM domain walls. Here, we consider the propagation of spin eigenexcitations along domain walls in easy-axial d-wave AMs. Investigating the presence of bound states localized on a domain wall, we find that the effect of the AM on the bound states strongly depends on the orientation of the domain wall relative to the crystallographic directions. If the domain wall is oriented along a nodal direction [100] or [010], AM does not change the number of bound states; however, it leads to a nonlinear dispersion and a tilt of the wavefront. The effect of AM is strongest when the domain wall is oriented along the directions [110] or [1¯10], i.e., along the directions of the strongest AM splitting in the magnon spectrum. In this case, (i) the additional gapped bound states appear, (ii) degeneracy of the eigenstates with respect to their polarization (right-hand or left-hand precession of the Néel vector) is removed, and (iii) the localization area of the bound states strongly depends on the eigenfrequency. The latter may lead to strong localization of the bound state at the domain wall. We further consider the influence of a static magnetic field that is applied along the easy axis and find that the magnetic field induces an asymmetry between the localization regions on opposite sides of the domain wall and sets an upper limit on the absolute value of the propagating eigenstate's wave vector.

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References (55)

  1. A. Hubert and R. Schäfer, Magnetic Domains: The Analysis of Magnetic Microstructures (Springer–Verlag, Berlin, 1998).
  2. A. M. Kosevich, B. A. Ivanov, and A. S. Kovalev, Magnetic solitons, Phys. Rep. 194, 117 (1990).
  3. J. M. Winter, Bloch wall excitation. Application to nuclear resonance in a Bloch wall, Phys. Rev. 124, 452 (1961).
  4. A. A. Thiele, Excitation spectrum of magnetic domain walls, Phys. Rev. B 7, 391 (1973).
  5. H.-B. Braun, Fluctuations and instabilities of ferromagnetic domain-wall pairs in an external magnetic field, Phys. Rev. B 50, 16485 (1994).
  6. S. Zhang and O. Tchernyshyov, Ferromagnetic domain wall as a nonreciprocal string, Phys. Rev. B 98, 104411 (2018).
  7. D. I. Paul, Interaction of antiferromagnetic spin waves with a Bloch wall, Phys. Rev. 126, 78 (1962).
  8. L. F. Lemmens, I. Kimura, and W. J. M. d. Jonge, Sine-Gordon kink solitons and the magnetisation in one-dimensional antiferromagnetic chains, J. Phys. C 19, 139 (1986).
  9. B. A. Ivanov and A. K. Kolezhuk, Solitons in low-dimensional antiferromagnets, Low Temp. Phys. 21, 275 (1995).
  10. M. M. Bogdan and O. V. Charkina, Spin waves in easy-axis antiferromagnets with precessing domain walls, Low Temp. Phys. 40, 84 (2014).
  11. S. K. Kim, Y. Tserkovnyak, and O. Tchernyshyov, Propulsion of a domain wall in an antiferromagnet by magnons, Phys. Rev. B 90, 104406 (2014).
  12. P. Shen, Y. Tserkovnyak, and S. K. Kim, Driving a magnetized domain wall in an antiferromagnet by magnons, J. Appl. Phys. 127, 223905 (2020).
  13. H.-K. Park and S.-K. Kim, Channeling of spin waves in antiferromagnetic domain walls, Phys. Rev. B 103, 214420 (2021).
  14. F. Garcia-Sanchez, P. Borys, R. Soucaille, J.-P. Adam, R. L. Stamps, and J.-V. Kim, Narrow magnonic waveguides based on domain walls, Phys. Rev. Lett. 114, 247206 (2015).
  15. X. Xing and Y. Zhou, Fiber optics for spin waves, NPG Asia Mater. 8, e246 (2016).
  16. J. Lan, W. Yu, R. Wu, and J. Xiao, Spin-wave diode, Phys. Rev. X 5, 041049 (2015).
  17. Y. Henry, D. Stoeffler, J.-V. Kim, and M. Bailleul, Unidirectional spin-wave channeling along magnetic domain walls of Bloch type, Phys. Rev. B 100, 024416 (2019).
  18. L. Qiu and K. Shen, Tunable spin-wave nonreciprocity in synthetic antiferromagnetic domain walls, Phys. Rev. B 105, 094436 (2022).
  19. T. Wang, J. Ding, Q. Guan, J. Li, X. Zhou, C. Zhao, and Z. Dai, Spin-waves propagation along planar domain wall channels with perpendicular intersection, J. Appl. Phys. 137, 043906 (2025).
  20. K. Wagner, A. Kákay, K. Schultheiss, A. Henschke, T. Sebastian, and H. Schultheiss, Magnetic domain walls as reconfigurable spin-wave nanochannels, Nat. Nanotechnol. 11, 432 (2016).
  21. E. Albisetti, D. Petti, G. Sala, R. Silvani, S. Tacchi, S. Finizio, S. Wintz, A. Calò, X. Zheng, J. Raabe, E. Riedo, and R. Bertacco, Nanoscale spin-wave circuits based on engineered reconfigurable spin-textures, Commun. Phys. 1, 56 (2018).
  22. V. Sluka, T. Schneider, R. A. Gallardo, A. Kákay, M. Weigand, T. Warnatz, R. Mattheis, A. Roldán-Molina, P. Landeros, V. Tiberkevich, A. Slavin, G. Schütz, A. Erbe, A. Deac, J. Lindner, J. Raabe, J. Fassbender, and S. Wintz, Emission and propagation of 1D and 2D spin waves with nanoscale wavelengths in anisotropic spin textures, Nat. Nanotechnol. 14, 328 (2019).
  23. A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Magnon spintronics, Nat. Phys. 11, 453 (2015).
  24. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  25. 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).
  26. L. Šmejkal, R. González-Hernández, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci. Adv. 6, eaaz8809 (2020).
  27. L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022).
  28. O. Gomonay, V. P. Kravchuk, R. Jaeschke-Ubiergo, K. V. Yershov, T. Jungwirth, L. Šmejkal, J. van den Brink, and J. Sinova, Structure, control, and dynamics of altermagnetic textures, npj Spintron. 2, 35 (2024).
  29. V. P. Kravchuk, K. V. Yershov, J. I. Facio, Y. Guo, O. Janson, O. Gomonay, J. Sinova, and J. van den Brink, Chiral magnetic excitations and domain textures of g-wave altermagnets, Phys. Rev. B 112, 144421 (2025).
  30. K. V. Yershov, O. Gomonay, J. Sinova, J. van den Brink, and V. P. Kravchuk, Curvature-induced magnetization of altermagnetic films, Phys. Rev. Lett. 134, 116701 (2025).
  31. H. Vakili, E. Schwartz, and A. A. Kovalev, Spin-transfer torque in altermagnets with magnetic textures, Phys. Rev. Lett. 134, 176401 (2025).
  32. S. Sorn and Y. Mokrousov, Activation of anomalous Hall effect and orbital magnetization by domain walls in altermagnets, Phys. Rev. B 112, 245115 (2025).
  33. I. V. Bar'yakhtar and B. A. Ivanov, Nonlinear magnetization waves of an antiferromagnet, Sov. J. Low Temp. Phys. 5, 361 (1979).
  34. A. F. Andreev and V. I. Marchenko, Symmetry and macroscopical dynamics of a magnet, Sov. Phys. Usp. 23, 21 (1980).
  35. E. G. Tveten, A. Qaiumzadeh, O. A. Tretiakov, and A. Brataas, Staggered dynamics in antiferromagnets by collective coordinates, Phys. Rev. Lett. 110, 127208 (2013).
  36. Using the properties n0·e±=0, e±·e±=0, and e±·e∓=1/2, one can derive ψ=2(e−·n⊥)/1+n0·n and ψ*=2(e+·n⊥)/1+n0·n. Here n⊥=n−n0(n0·n) is projection of n on the plain perpendicular to n0.
  37. In the explicit form n0(x)=sechx(excosϕ0+eysinϕ0)−ptanhxez, and e±=−12[(ptanhxcosϕ0±isinϕ0)ex+(ptanhxsinϕ0∓icosϕ0)ey+sechxez].
  38. E. G. Tveten, A. Qaiumzadeh, and A. Brataas, Antiferromagnetic domain wall motion induced by spin waves, Phys. Rev. Lett. 112, 147204 (2014).
  39. G. L. Lamb, Elements of Soliton Theory, Pure & Applied Mathematics, A Wiley-Interscience Series of Text, Monographs & Tracts (John Wiley & Sons, New York, 1980).
  40. NIST Handbook of Mathematical Functions, edited by F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark (Cambridge University Press, New York, NY, 2010).
  41. Wavefront slope can be intuitively understood within the ray-optic model, in which a bound state propagating along a waveguide is represented as a plane wave that moves in a zigzag pattern between two parallel boundaries [54], where the law of reflection is violated.
  42. Note that the properties of the RH- and LH-polarized modes are interchanged if ɛ flips the sign.
  43. V. P. Kravchuk, O. Gomonay, D. D. Sheka, D. R. Rodrigues, K. Everschor-Sitte, J. Sinova, J. van den Brink, and Y. Gaididei, Spin eigenexcitations of an antiferromagnetic skyrmion, Phys. Rev. B 99, 184429 (2019).
  44. S. Lee, K. Nakata, O. Tchernyshyov, and S. K. Kim, Magnon dynamics in a skyrmion-textured domain wall of antiferromagnets, Phys. Rev. B 107, 184432 (2023).
  45. When ky→ky(cr) and ω→ω(cr)=ω(ky(cr)).
  46. With the proper choice of the coefficient C.
  47. P. Yan, X. S. Wang, and X. R. Wang, All-magnonic spin-transfer torque and domain wall propagation, Phys. Rev. Lett. 107, 177207 (2011).
  48. This is correct for ky=0 only.
  49. Levinson's theorem for 3D and 1D theories differs in the treatment of half-bound states, namely, the 1/2 term is present when there is no half-bound state, unlike in 3D [55].
  50. R. Eto, M. Gohlke, J. Sinova, M. Mochizuki, A. L. Chernyshev, and A. Mook, Spontaneous magnon decays from nonrelativistic time-reversal symmetry breaking in altermagnets, Phys. Rev. B 112, 094442 (2025).
  51. L. Garcia-Gassull, A. Razpopov, P. Peter Stavropoulos, I. I. Mazin, and R. Valentí, Microscopic origin of the magnetic interactions and their experimental signatures in altermagnetic La2O3Mn2Se2, npj Spintron. 4, 9 (2026).
  52. H. Bateman and A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. 1.
  53. Here we follow the procedure described in Ref. [39].
  54. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
  55. K. A. Kiers and W. van Dijk, Scattering in one dimensions: The coupled Schrödinger equation, threshold behaviour and Levinson's theorem, J. Mod. Phys. 37, 6033 (1996).

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Phys. Rev. B 114, 194421– Published 23 October, 2026
  • Received 30 June 2026
  • Revised 18 September 2026
  • Accepted 7 October 2026
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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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