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Nonlinear magnon magnetic moment transport in triangular-lattice f-wave anti-altermagnets

Volodymyr P. Kravchuk1,2,3,*, Kostiantyn V. Yershov1,3, Bastián Pradenas1, Robin R. Neumann4,5, Rodrigo Jaeschke-Ubiergo6, Ricardo Zarzuela6, Jairo Sinova6,7, Jeroen van den Brink1,2, and Alexander Mook4

  • *Contact author: v.kravchuk@ifw-dresden.de
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Phys. Rev. B 114, 194410 – Published 13 October, 2026

DOI: https://doi.org/10.1103/zl26-y46s

Abstract

We study the spin excitations in the frustrated coplanar 120∘ ground state of the triangular-lattice Heisenberg antiferromagnet and demonstrate that they carry a magnetic moment perpendicular to the plane in which the spins order, despite the ground-state sublattice moments having no out-of-plane component. The symmetry of the momentum dependence of the magnetic moment and energy of the magnons renders the system an odd-parity f-wave magnet. Extending this model to a stack of antiferromagnetically coupled triangular layers provides a realization of magnons in a three-dimensional f-wave anti-altermagnet. We show that nonlinear thermal transport effects of magnons, such as Edelstein and spin-splitter effects, provide clear experimental signatures of magnons in f-wave anti-altermagnets.

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References (63)

  1. Frustrated Spin Systems, 2nd ed., edited by H. T. Diep (World Scientific Publishing Company, Singapore, 2013).
  2. C. Lacroix, P. Mendels, and F. Mila, Introduction to Frustrated Magnetism: Materials, Experiments, Theory (Springer, Berlin, Heidelberg, 2011).
  3. H. Kawamura and S. Miyashita, Phase transition of the two-dimensional Heisenberg antiferromagnet on the triangular lattice, J. Phys. Soc. Jpn. 53, 9 (1984).
  4. S. Miyashita, The ground state and thermodynamic properties of generalized Heisenberg models on the triangular lattice, Prog. Theor. Phys. Suppl. 87, 112 (1986).
  5. A. V. Chubukov and D. I. Golosov, Quantum theory of an antiferromagnet on a triangular lattice in a magnetic field, J. Phys.: Condens. Matter 3, 69 (1991).
  6. L. Capriotti, A. E. Trumper, and S. Sorella, Long-range Néel order in the triangular Heisenberg model, Phys. Rev. Lett. 82, 3899 (1999).
  7. L. Seabra, T. Momoi, P. Sindzingre, and N. Shannon, Phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice in an applied magnetic field, Phys. Rev. B 84, 214418 (2011).
  8. T. Jolicoeur and J. C. Le Guillou, Spin-wave results for the triangular Heisenberg antiferromagnet, Phys. Rev. B 40, 2727 (1989).
  9. A. V. Chubukov, S. Sachdev, and T. Senthil, Large-S expansion for quantum antiferromagnets on a triangular lattice, J. Phys.: Condens. Matter 6, 8891 (1994).
  10. S. R. White and A. L. Chernyshev, Neél order in square and triangular lattice Heisenberg models, Phys. Rev. Lett. 99, 127004 (2007).
  11. A. L. Chernyshev and M. E. Zhitomirsky, Spin waves in a triangular lattice antiferromagnet: Decays, spectrum renormalization, and singularities, Phys. Rev. B 79, 144416 (2009).
  12. M. Mourigal, W. T. Fuhrman, A. L. Chernyshev, and M. E. Zhitomirsky, Dynamical structure factor of the triangular-lattice antiferromagnet, Phys. Rev. B 88, 094407 (2013).
  13. P. A. Maksimov, M. E. Zhitomirsky, and A. L. Chernyshev, Field-induced decays in XXZ triangular-lattice antiferromagnets, Phys. Rev. B 94, 140407(R) (2016).
  14. A. V. Syromyatnikov, Elementary excitations in spin-1/2 antiferromagnets on the triangular lattice, Phys. Rev. B 105, 144414 (2022).
  15. W. Zheng, J. O. Fjærestad, R. R. P. Singh, R. H. McKenzie, and R. Coldea, Anomalous excitation spectra of frustrated quantum antiferromagnets, Phys. Rev. Lett. 96, 057201 (2006).
  16. W. Zheng, J. O. Fjærestad, R. R. P. Singh, R. H. McKenzie, and R. Coldea, Excitation spectra of the spin-12 triangular-lattice Heisenberg antiferromagnet, Phys. Rev. B 74, 224420 (2006).
  17. B. D. Gaulin, M. F. Collins, and W. J. L. Buyers, Spin waves in the triangular antiferromagnet CsMnBr3, J. Appl. Phys. 61, 3409 (1987).
  18. M. M. Bordelon, C. Liu, L. Posthuma, P. M. Sarte, N. P. Butch, D. M. Pajerowski, A. Banerjee, L. Balents, and S. D. Wilson, Spin excitations in the frustrated triangular lattice antiferromagnet NaYbO2, Phys. Rev. B 101, 224427 (2020).
  19. J. Ma, Y. Kamiya, T. Hong, H. B. Cao, G. Ehlers, W. Tian, C. D. Batista, Z. L. Dun, H. D. Zhou, and M. Matsuda, Static and dynamical properties of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba3COSb2O9, Phys. Rev. Lett. 116, 087201 (2016).
  20. T. Dombre and N. Read, Nonlinear σ-models for triangular quantum antiferromagnets, Phys. Rev. B 39, 6797 (1989).
  21. S. Dasgupta and O. Tchernyshyov, Theory of spin waves in a hexagonal antiferromagnet, Phys. Rev. B 102, 144417 (2020).
  22. B. Pradenas and O. Tchernyshyov, Spin-frame field theory of a three-sublattice antiferromagnet, Phys. Rev. Lett. 132, 096703 (2024).
  23. B. Pradenas, G. Adamyan, and O. Tchernyshyov, Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice, Phys. Rev. B 112, 104402 (2025).
  24. R. Zarzuela and S. K. Kim, Non-Abelian gauge theory for magnons in topologically textured frustrated magnets, Phys. Rev. Lett. 134, 186701 (2025).
  25. 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).
  26. L. Šmejkal, A. Marmodoro, K.-H. Ahn, R. González-Hernández, I. Turek, S. Mankovsky, H. Ebert, S. W. D'Souza, O. Šipr, J. Sinova, and T. Jungwirth, Chiral magnons in altermagnetic RuO2, Phys. Rev. Lett. 131, 256703 (2023).
  27. L. Wang, L. Shen, H. Bai, H.-A. Zhou, K. Shen, and W. Jiang, Electrical excitation and detection of chiral magnons in a compensated ferrimagnetic insulator, Phys. Rev. Lett. 133, 166705 (2024).
  28. N. W. Ashcroft and N. Mermin, Solid State Physics (Cengage Learning, Inc., Boston, 1976).
  29. A. Aharoni, Introduction to the Theory of Ferromagnetism (Oxford University Press, Oxford, 1996).
  30. R. R. Neumann, A. Mook, J. Henk, and I. Mertig, Orbital magnetic moment of magnons, Phys. Rev. Lett. 125, 117209 (2020).
  31. K. V. Yershov, V. P. Kravchuk, M. Daghofer, and J. van den Brink, Fluctuation-induced piezomagnetism in local moment altermagnets, Phys. Rev. B 110, 144421 (2024).
  32. A. B. Hellenes, T. Jungwirth, R. Jaeschke-Ubiergo, A. Chakraborty, J. Sinova, and L. Šmejkal, P-wave magnets, arXiv:2309.01607.
  33. J. Mitscherling, J. Priessnitz, C. K. Geschner, and L. Šmejkal, Microscopic origin of p-wave magnetism, arXiv:2603.09736.
  34. T. Jungwirth, R. M. Fernandes, E. Fradkin, A. H. MacDonald, J. Sinova, and L. Šmejkal, Altermagnetism: An unconventional spin-ordered phase of matter, Newton 1, 100162 (2025).
  35. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  36. 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).
  37. R. R. Neumann, R. Jaeschke-Ubiergo, R. Zarzuela, L. Šmejkal, J. Sinova, and A. Mook, Odd-parity-wave magnons and nonrelativistic thermal Edelstein effect, arXiv:2603.05415.
  38. Here T and t denote time reversal and translation, respectively.
  39. M. Weißenhofer and A. Marmodoro, Atomistic spin dynamics simulations of magnonic spin Seebeck and spin Nernst effects in altermagnets, Phys. Rev. B 110, 094427 (2024).
  40. Q. Cui, B. Zeng, P. Cui, T. Yu, and H. Yang, Efficient spin Seebeck and spin Nernst effects of magnons in altermagnets, Phys. Rev. B 108, L180401 (2023).
  41. Y. Yang, D. Wang, B. Yang, P. Wang, Y. Mu, Y. Tian, B. Zheng, W. Qin, K. Wang, B. Huang, B. Wang, X. Wan, and D. Wu, Altermagnet-driven magnon spin splitting Nernst effect, Phys. Rev. Lett. 136, 026701 (2026).
  42. H. Zhang and R. Cheng, Magnon thermal Edelstein effect detected by inverse spin Hall effect, Appl. Phys. Lett. 117, 222402 (2020).
  43. B. Li, A. Mook, A. Raeliarijaona, and A. A. Kovalev, Magnonic analog of the Edelstein effect in antiferromagnetic insulators, Phys. Rev. B 101, 024427 (2020).
  44. Q. Cui, X. Bai, Y. Ge, A. Edström, C. Li, Y. Sassa, C. Song, K. Wang, and A. Delin, Altermagnetic magnons in twisted van der Waals antiferromagnets, Nano Lett. 26, 5078 (2026).
  45. Note that, due to nonanalyticity of the dispersions ɛ±1,k in the Γ point, magnetic moments μ±1,kz are ill-defined in the Γ point.
  46. Here C3z denotes the threefold rotation in spin space and E is an identity operation.
  47. D. Litvin and W. Opechowski, Spin groups, Physica 76, 538 (1974).
  48. Note that this approximation is not valid if B=0.
  49. G. Adamyan, B. Pradenas, B. Ivanov, and O. Tchernyshyov, Geometric spin rotation in triangular antiferromagnets, Phys. Rev. Lett. 137, 026704 (2026).
  50. That is, it is assumed that ∂αβ2T=0 and the same for the higher derivatives.
  51. M. Ezawa, Third-order and fifth-order nonlinear spin-current generation in g-wave and i-wave altermagnets and perfectly nonreciprocal spin current in f-wave magnets, Phys. Rev. B 111, 125420 (2025).
  52. M. Ezawa, Nonlinear spin-Seebeck diode in f-wave magnets, third-order spin-Nernst effects in g-wave magnets, and spin-Nernst effects in i-wave altermagnets, Phys. Rev. B 113, L241301 (2026).
  53. N. Okuma, Magnon spin-momentum locking: Various spin vortices and Dirac magnons in noncollinear antiferromagnets, Phys. Rev. Lett. 119, 107205 (2017).
  54. S. M. Wu, W. Zhang, A. KC, P. Borisov, J. E. Pearson, J. S. Jiang, D. Lederman, A. Hoffmann, and A. Bhattacharya, Antiferromagnetic spin Seebeck effect, Phys. Rev. Lett. 116, 097204 (2016).
  55. P. Park, K. Park, T. Kim, Y. Kousaka, K. H. Lee, T. G. Perring, J. Jeong, U. Stuhr, J. Akimitsu, M. Kenzelmann, and J.-G. Park, Momentum-dependent magnon lifetime in the metallic noncollinear triangular antiferromagnet CrB2, Phys. Rev. Lett. 125, 027202 (2020).
  56. We used the fitting function Γk≈ck5, which corresponds to the 3D case [11].
  57. For ɛ0∼10meV [55], it corresponds to T<0.13ɛ0/kB≈15K. Note that TN=88K for CrB2 [55].
  58. A. Bose, S. Bhuktare, H. Singh, S. Dutta, V. G. Achanta, and A. A. Tulapurkar, Direct detection of spin Nernst effect in platinum, Appl. Phys. Lett. 112, 162401 (2018).
  59. A. Finco and V. Jacques, Single spin magnetometry and relaxometry applied to antiferromagnetic materials, APL Mater. 11, 100901 (2023).
  60. P. A. Maksimov, Z. Zhu, S. R. White, and A. L. Chernyshev, Anisotropic-exchange magnets on a triangular lattice: Spin waves, accidental degeneracies, and dual spin liquids, Phys. Rev. X 9, 021017 (2019).
  61. W. Fang, A. Raeliarijaona, P.-H. Chang, A. A. Kovalev, and K. D. Belashchenko, Spirals and skyrmions in antiferromagnetic triangular lattices, Phys. Rev. Mater. 5, 054401 (2021).
  62. C. A. Gallegos, S. Jiang, S. R. White, and A. L. Chernyshev, Phase diagram of the easy-axis triangular-lattice j1−j2 model, Phys. Rev. Lett. 134, 196702 (2025).
  63. C. Glittum and O. F. Syljuåsen, The finite-temperature behavior of a triangular Heisenberg antiferromagnet, J. Phys.: Condens. Matter 38, 135801 (2026).

Outline

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Phys. Rev. B 114, 194410– Published 13 October, 2026
  • Received 27 May 2026
  • Revised 13 August 2026
  • Accepted 24 September 2026
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