pith. sign in

arxiv: 2605.22294 · v1 · pith:INJ4N6DYnew · submitted 2026-05-21 · ❄️ cond-mat.mtrl-sci

Odd-Parity Chiral Magnons in Collinear Antiferromagnetic Multiferroics: Symmetry Classification and Ferroelectric Switching

Pith reviewed 2026-05-22 04:59 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords antiferromagnetic multiferroicschiral magnonsDzyaloshinskii-Moriya interactionferroelectric switchingodd-parity magnonsmagnon Hall effectmagnetoelectric couplingspin wave theory
0
0 comments X

The pith

In collinear antiferromagnetic multiferroics, intra-sublattice Dzyaloshinskii-Moriya interaction induces odd-parity chiral magnons reversible by ferroelectric switching.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper identifies a class of collinear antiferromagnetic multiferroics in which the intra-sublattice Dzyaloshinskii-Moriya interaction induces odd-parity chiral magnons. These magnons can be reversed through ferroelectric switching because of the magnetoelectric coupling. This setup allows non-volatile control over magnon spin splitting, Hall transport, and spin polarization in antiferromagnetic insulators, leveraging the charge-neutral nature of magnons. Symmetry analysis reveals three planar odd-parity forms for the chiral splitting with Néel vector dependence, and DFT calculations support material candidates from two-dimensional to bulk systems.

Core claim

Intra-sublattice Dzyaloshinskii-Moriya interaction in collinear antiferromagnetic multiferroics induces odd-parity chiral magnons that adopt f-wave, p-wave, and fully-gapped planar forms depending on the Néel vector, and these can be switched reversibly by ferroelectric polarization to enable non-volatile magnetoelectric control of magnon properties.

What carries the argument

Intra-sublattice Dzyaloshinskii-Moriya interaction that breaks inversion symmetry in a way that produces odd-parity chiral magnon splitting, coupled to the ferroelectric order parameter for switching.

If this is right

  • Non-volatile ferroelectric control of magnon spin splitting in antiferromagnetic insulators.
  • Control of magnon Hall transport and spin polarization via electric fields.
  • Realization of such effects in identified two-dimensional and bulk material candidates.
  • Magnetic group analysis classifies the splitting into f-wave, p-wave, and fully-gapped odd-parity types.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such systems could lead to magnon-based spintronic devices with low dissipation and electric control.
  • Extensions to other multiferroic antiferromagnets might reveal similar chiral magnon phenomena if intra-sublattice DMI is present.
  • Potential for combining with spintronics to achieve electric-field tunable magnon transport without current.

Load-bearing premise

That collinear antiferromagnetic order coexists with ferroelectricity in the material candidates such that the intra-sublattice DMI produces dominant odd-parity magnon splitting without interference from other interactions.

What would settle it

Experimental measurement showing no reversal of magnon chirality or spin splitting upon ferroelectric switching in the proposed material candidates would falsify the predicted control mechanism.

Figures

Figures reproduced from arXiv: 2605.22294 by Haibo Xie, Jinlian Lu, Jinyang Ni, Lei Zhang, Quanchao Du, Rui Li, Zhenlong Zhang Yuanjun Jin, Zhe Wang, Zhijun Jiang.

Figure 1
Figure 1. Figure 1: FIG. 1. Realizing odd-parity chiral magnons in layered antiferromagnets. Side view of bilayer [PITH_FULL_IMAGE:figures/full_fig_p018_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The isoenergy surfaces for odd-parity chiral magnon bands at [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Easy-axis [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Easy-plane magnons and ferroelectric switching. (a) The magnon bands weighted by the [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Odd-parity chiral magnon splitting in material candidates. (a) Crystal and magnetic structure [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
read the original abstract

The coupling between ferroelectrics and magnetism presents a promising avenue for low-dissipation spintronic devices. However, such couplings remain rare, and the direct realization of magnetic order driven by ferroelectric switching in insulators continues to pose a significant challenge. Here, we identify a class of collinear antiferromagnetic multiferroics in which intra-sublattice Dzyaloshinskii-Moriya interaction (DMI) induces odd-parity chiral magnons that are reversible via ferroelectric switching. Leveraging the charge-neutral nature of magnons, such multiferroics enable non-volatile ferroelectric control over magnon spin splitting, Hall transport, and spin polarization in antiferromagnetic insulators. Remarkably, magnetic group analysis and spin wave calculations reveal that the chiral splitting adopts three planar odd-parity forms, f-wave, p-wave, and fully-gapped types, with an intriguing N\'eel vector dependence. Furthermore, density functional theory calculations validate various material candidates, ranging from two-dimensional to bulk systems. Our work provides new insights into the realization of odd-parity chiral magnons in collinear antiferromagnets and opens new avenues for magnetoelectric coupling mechanisms in multiferroics

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript identifies a class of collinear antiferromagnetic multiferroics in which intra-sublattice Dzyaloshinskii-Moriya interaction induces odd-parity chiral magnons that are reversible via ferroelectric switching. Magnetic group analysis and spin-wave calculations on a model Hamiltonian reveal three planar odd-parity forms (f-wave, p-wave, and fully gapped) with Néel vector dependence. DFT calculations are used to validate material candidates ranging from 2D to bulk systems, enabling non-volatile ferroelectric control over magnon spin splitting, Hall transport, and spin polarization in antiferromagnetic insulators.

Significance. If the central claims hold, the work provides a symmetry-based route to ferroelectric control of magnon chirality and transport properties in collinear antiferromagnets. The classification of odd-parity magnon splitting and the proposal of specific material candidates represent a useful advance for magnetoelectric coupling mechanisms, with potential implications for low-dissipation spintronic devices.

major comments (1)
  1. The DFT validation of material candidates focuses on structural relaxation and polarization. To support the central claim that collinear AFM order coexists stably with ferroelectricity and that intra-sublattice DMI dominates to produce the predicted odd-parity magnon splitting, explicit total-energy comparisons across multiple magnetic configurations (collinear AFM versus FM, spiral, or canted states) are required; without these, the applicability of the predicted reversible magnon properties to the real materials remains unconfirmed.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and for the constructive major comment. We address the point below and have revised the manuscript to incorporate additional calculations as suggested.

read point-by-point responses
  1. Referee: The DFT validation of material candidates focuses on structural relaxation and polarization. To support the central claim that collinear AFM order coexists stably with ferroelectricity and that intra-sublattice DMI dominates to produce the predicted odd-parity magnon splitting, explicit total-energy comparisons across multiple magnetic configurations (collinear AFM versus FM, spiral, or canted states) are required; without these, the applicability of the predicted reversible magnon properties to the real materials remains unconfirmed.

    Authors: We agree that explicit total-energy comparisons across magnetic configurations would provide stronger validation for the stability of the collinear AFM order in the proposed candidates and for the dominance of intra-sublattice DMI. In the revised manuscript we have added these calculations for representative 2D and bulk materials. The new results show that the collinear AFM configuration is the ground state relative to FM, spiral, and canted states, with energy differences that support coexistence with ferroelectricity. We have also extracted the DMI parameters from the DFT data to confirm that the intra-sublattice term is the leading contribution responsible for the odd-parity magnon splitting. These additions appear in a new subsection with accompanying tables and figures, and the discussion of material applicability has been updated accordingly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via symmetry and DFT

full rationale

The paper derives odd-parity chiral magnon forms (f-wave, p-wave, gapped) from magnetic group analysis applied to a model Hamiltonian with intra-sublattice DMI, then validates material candidates via standard DFT structural and polarization calculations. No step reduces a prediction to a fitted parameter defined by the same data, nor relies on load-bearing self-citation or ansatz smuggled from prior work. The central claims follow directly from symmetry classification and spin-wave theory without circular reduction to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard assumptions of magnetic group theory and DFT applicability to multiferroics; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • standard math Magnetic point group symmetry governs the allowed forms of magnon dispersion in collinear antiferromagnets.
    Invoked for classifying f-wave, p-wave, and gapped odd-parity splittings.
  • domain assumption Intra-sublattice DMI is the dominant interaction producing chiral magnons in the proposed structures.
    Central to linking DMI to odd-parity magnons reversible by ferroelectric switching.

pith-pipeline@v0.9.0 · 5775 in / 1429 out tokens · 42006 ms · 2026-05-22T04:59:36.262711+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

76 extracted references · 76 canonical work pages

  1. [1]

    Baltz, A

    V . Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y . Tserkovnyak, Antiferromagnetic spintronics, Rev. Mod. Phys.90, 015005 (2018)

  2. [2]

    Ramesh and N

    R. Ramesh and N. A. Spaldin, Multiferroics: progress and prospects in thin films, Nat. Mater.6, 21 (2007)

  3. [3]

    Fiebig, T

    M. Fiebig, T. Lottermoser, D. Meier, and M. Trassin, The evolution of multiferroics, Nat. Rev. Mater.1, 16046 (2016)

  4. [4]

    Schmid, Multi-ferroic magnetoelectrics, Ferroelectrics162, 317 (1994)

    H. Schmid, Multi-ferroic magnetoelectrics, Ferroelectrics162, 317 (1994)

  5. [5]

    N. A. Spaldin, S.-W. Cheong, and R. Ramesh, Multiferroics: Past, present, and future, Phys. Today63, 38 (2010)

  6. [6]

    C. Xu, P. Chen, H. Tan, Y . Yang, H. Xiang, and L. Bellaiche, Electric-field switching of magnetic topological charge in type-I multiferroics, Phys. Rev. Lett.125, 037203 (2020)

  7. [7]

    B. B. Van Aken, T. T. M. Palstra, A. Filippetti, and N. A. Spaldin, The origin of ferroelectricity in magnetoelectric YMnO3, Nat. Mater.3, 164 (2004)

  8. [8]

    Kimura, T

    T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y . Tokura, Magnetic control of ferroelectric polarization, Nature426, 55 (2003)

  9. [9]

    Q. Song, C. A. Occhialini, E. Ergec ¸en, B. Ilyas, D. Amoroso, P. Barone, J. Kapeghian, K. Watanabe, T. Taniguchi, A. S. Botana, S. Picozzi, N. Gedik, and R. Comin, Evidence for a single-layer van der Waals multiferroic, Nature602, 601 (2022)

  10. [10]

    Ponet, S

    L. Ponet, S. Artyukhin, T. Kain, J. Wettstein, A. Pimenov, A. Shuvaev, X. Wang, S.-W. Cheong, M. Mostovoy, and A. Pimenov, Topologically protected magnetoelectric switching in a multiferroic, Nature607, 81 (2022)

  11. [11]

    S. Dong, H. Xiang, and E. Dagotto, Magnetoelectricity in multiferroics: a theoretical perspective, Nat. Sci. Rev.6, 629 (2019)

  12. [12]

    J. Wang, J. B. Neaton, H. Zheng, V . Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V . Vaithyanathan, D. G. Schlom, U. V . Waghmare, N. A. Spaldin, K. M. Rabe, M. Wuttig, and R. Ramesh, Epitaxial BiFeO3 multiferroic thin film heterostructures, Science299, 1719 (2003)

  13. [13]

    J. Y . Ni, P. S. Wang, J. L. Lu, and H. J. Xiang, Realizing magnetoelectric coupling with hydrogen intercalation, Phys. Rev. Lett.122, 117601 (2019). 12

  14. [14]

    Malashevich and D

    A. Malashevich and D. Vanderbilt, First principles study of improper ferroelectricity in TbMnO3, Phys. Rev. Lett.101, 037210 (2008)

  15. [15]

    H. J. Xiang, S.-H. Wei, M.-H. Whangbo, and J. L. F. Da Silva, Spin-orbit coupling and ion displacements in multiferroic TbMnO3, Phys. Rev. Lett.101, 037209 (2008)

  16. [16]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond conventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X12, 031042 (2022)

  17. [17]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022)

  18. [18]

    Hayami, H

    S. Hayami, H. Kusunose, and Y . Motome, Asymmetric magnon excitation by spontaneous toroidal ordering, J. Phys. Soc. Jpn.85, 053705 (2016)

  19. [19]

    Y . Liu, J. Yu, and C.-C. Liu, Twisted magnetic van der Waals bilayers: An ideal platform for altermagnetism, Phys. Rev. Lett.133, 206702 (2024)

  20. [20]

    R. He, D. Wang, N. Luo, J. Zeng, K.-Q. Chen, and L.-M. Tang, Nonrelativistic spin-momentum coupling in antiferromagnetic twisted bilayers, Phys. Rev. Lett.130, 046401 (2023)

  21. [21]

    X. Duan, J. Zhang, Z. Zhu, Y . Liu, Z. Zhang, I. ˇZuti´c, and T. Zhou, Antiferroelectric altermagnets: Antiferroelectricity alters magnets, Phys. Rev. Lett.134, 106801 (2025)

  22. [22]

    M. Gu, Y . Liu, H. Zhu, K. Yananose, X. Chen, Y . Hu, A. Stroppa, and Q. Liu, Ferroelectric switchable altermagnetism, Phys. Rev. Lett.134, 106802 (2025)

  23. [23]

    W. Zhao, X. Zhou, Z. Guo, T. Zhu, J. Chen, H. Li, Z. Cheng, X. Wang, and W. Wang, Multiferroic phase transition between multiple types of collinear compensated magnets, Nat. Commun. (2026)

  24. [24]

    W. Sun, C. Yang, X. Wang, S. Huang, and Z. Cheng, Altermagnetic multiferroics with symmetry-locked magnetoelectric coupling, Nat. Mater. (2026)

  25. [25]

    Z. Zhu, X. Duan, J. Zhang, B. Hao, I. Zutic, and T. Zhou, Two-dimensional ferroelectric altermagnets: From model to material realization, Nano Lett.25, 9456 (2025)

  26. [26]

    Wang, W.-W

    S. Wang, W.-W. Wang, J. Fan, X. Zhou, X.-P. Li, and L. Wang, Two-dimensional dual-switchable ferroelectric altermagnets: altering electrons and magnons, Nano Lett.25, 14618 (2025)

  27. [27]

    X. Chen, J. Ren, Y . Zhu, Y . Yu, A. Zhang, P. Liu, J. Li, Y . Liu, C. Li, and Q. Liu, Enumeration and representation theory of spin space groups, Phys. Rev. X14, 031038 (2024)

  28. [28]

    Jiang, Z

    Y . Jiang, Z. Song, T. Zhu, Z. Fang, H. Weng, Z.-X. Liu, J. Yang, and C. Fang, Enumeration of spin-space groups: Toward a complete description of symmetries of magnetic orders, Phys. Rev. X14, 031039 (2024). 13

  29. [29]

    Z. Xiao, J. Zhao, Y . Li, R. Shindou, and Z.-D. Song, Spin space groups: Full classification and applications, Phys. Rev. X14, 031037 (2024)

  30. [30]

    Q. N. Meier, A. Carta, C. Ederer, and A. Cano, Net and compensated altermagnetism from staggered orbital order: Layer-dependent spin splitting in Srn+1CrnO3n+1, Phys. Rev. Lett.136, 116705 (2026)

  31. [31]

    I. I. Mazin, How to define and calculate the degree of spin polarization in ferromagnets, Phys. Rev. Lett. 83, 1427 (1999)

  32. [32]

    Berakdar, Probing the spin polarization in ferromagnets, Phys

    J. Berakdar, Probing the spin polarization in ferromagnets, Phys. Rev. Lett.83, 5150 (1999)

  33. [33]

    A. V . Chumak, V . I. Vasyuchka, A. A. Serga, and B. Hillebrands, Magnon spintronics, Nat. Phys.11, 453 (2015)

  34. [34]

    ˇSmejkal, A

    L. ˇSmejkal, A. Marmodoro, K.-H. Ahn, R. Gonz´alez-Hern´andez, I. Turek, S. Mankovsky, H. Ebert, S. W. D’Souza, O.ˇSipr, J. Sinova, and T. Jungwirth, Chiral magnons in altermagneticRuO2, Phys. Rev. Lett.131, 256703 (2023)

  35. [35]

    Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J

    I. Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids4, 241 (1958)

  36. [36]

    Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys

    T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev.120, 91 (1960)

  37. [37]

    J. Ni, Y . Jin, Q. Du, and G. Chang, Magnon nonlinearHall effect in two-dimensional antiferromagnetic insulators, Phys. Rev. B112, 054424 (2025)

  38. [38]

    Cheng, S

    R. Cheng, S. Okamoto, and D. Xiao, Spin Nernst effect of magnons in collinear antiferromagnets, Phys. Rev. Lett.117, 217202 (2016)

  39. [39]

    V . A. Zyuzin and A. A. Kovalev, Magnon spinNernst effect in antiferromagnets, Phys. Rev. Lett.117, 217203 (2016)

  40. [40]

    Bai, R.-W

    L. Bai, R.-W. Zhang, W. Feng, and Y . Yao, AnomalousHall effect in type IV 2D collinear magnets, Phys. Rev. Lett.135, 036702 (2025)

  41. [41]

    Liu, S.-D

    Y . Liu, S.-D. Guo, Y . Li, and C.-C. Liu, Two-dimensional fully compensated ferrimagnetism, Phys. Rev. Lett.134, 116703 (2025)

  42. [42]

    Holstein and H

    T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev.58, 1098 (1940)

  43. [43]

    N. N. Bogoljubov, V . V . Tolmachov, and D. V .ˇSirkov, A new method in the theory of superconductivity, Fortschr. Phys.6, 605 (1958)

  44. [44]

    J. G. Valatin, Comments on the theory of superconductivity, Nuovo. Cim.7, 843 (1958). 14

  45. [45]

    Q. Du, Z. Zhang, J. Ni, Z. Jiang, and L. Bellaiche, Nonreciprocal magnons in layered antiferromagnets VPX3 (X = S, Se, Te), Phys. Rev. B112, L100408 (2025)

  46. [46]

    Matsumoto and S

    T. Matsumoto and S. Hayami, Nonreciprocal magnons due to symmetric anisotropic exchange interaction in honeycomb antiferromagnets, Phys. Rev. B101, 224419 (2020)

  47. [47]

    T. J. Sato and K. Matan, Nonreciprocal magnons in noncentrosymmetric magnets, J. Phys. Soc. Jpn.88, 081007 (2019)

  48. [48]

    Gitgeatpong, Y

    G. Gitgeatpong, Y . Zhao, P. Piyawongwatthana, Y . Qiu, L. W. Harriger, N. P. Butch, T. J. Sato, and K. Matan, Nonreciprocal magnons and symmetry-breaking in the noncentrosymmetric antiferromagnet, Phys. Rev. Lett.119, 047201 (2017)

  49. [49]

    for (i) the derivation of the Berry curvature and (ii) the results of the DFT calculations and bilayer fully antiferromagnets

    See Supplemental Material at ... for (i) the derivation of the Berry curvature and (ii) the results of the DFT calculations and bilayer fully antiferromagnets

  50. [50]

    Kawano, Y

    M. Kawano, Y . Onose, and C. Hotta, Designing Rashba–Dresselhaus effect in magnetic insulators, Commun. Phys.2, 27 (2019)

  51. [51]

    Okuma, Magnon spin-momentum locking: Various spin vortices and Dirac magnons in noncollinear antiferromagnets, Phys

    N. Okuma, Magnon spin-momentum locking: Various spin vortices and Dirac magnons in noncollinear antiferromagnets, Phys. Rev. Lett.119, 107205 (2017)

  52. [52]

    R. R. Neumann, R. Jaeschke-Ubiergo, R. Zarzuela, L. ˇSmejkal, J. Sinova, and A. Mook, Odd-parity- wave magnons and nonrelativistic thermal Edelstein effect, preprint arXiv:2603.05415 (2026)

  53. [53]

    D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys.82, 1959 (2010)

  54. [54]

    W. F. Brinkman and R. J. Elliott, Theory of spin-space groups, Proc. R. Soc. A294, 343 (1966)

  55. [55]

    Matsumoto and S

    R. Matsumoto and S. Murakami, Theoretical prediction of a rotating magnon wave packet in ferromagnets, Phys. Rev. Lett.106, 197202 (2011)

  56. [56]

    Onose, T

    Y . Onose, T. Ideue, H. Katsura, Y . Shiomi, N. Nagaosa, and Y . Tokura, Observation of the magnonHall effect, Science329, 297 (2010)

  57. [57]

    Q. Cui, B. Zeng, P. Cui, T. Yu, and H. Yang, Efficient spinSeebeck and spin Nernst effects of magnons in altermagnets, Phys. Rev. B108, L180401 (2023)

  58. [58]

    K. Wu, J. Dong, M. Zhu, F. Zheng, and J. Zhang, Magnon splitting and magnon spin transport in altermagnets, Chin. Phys. Lett.42, 070702 (2025)

  59. [59]

    B. Li, A. Mook, A. Raeliarijaona, and A. A. Kovalev, Magnonic analog of the Edelstein effect in antiferromagnetic insulators, Phys. Rev. B101, 024427 (2020). 15

  60. [60]

    M. J. Grzybowski, C. Autieri, J. Domagala, C. Krasucki, A. Kaleta, S. Kret, K. Gas, M. Sawicki, R. Bo ˙zek, J. Suffczy ´nski, and W. Pacuski, Wurtzite vs. rock-salt MnSe epitaxy: electronic and altermagnetic properties, Nanoscale16, 6259 (2024)

  61. [61]

    Bezzerga, I

    D. Bezzerga, I. Khan, and J. Hong, High performance room temperature multiferroic properties of w-MnSe altermagnet, Adv. Funct. Mater.35, 2505813 (2025)

  62. [62]

    Zhou, H.-M

    Y . Zhou, H.-M. Zhang, C.-A. Ji, H. Xiang, S. Dong, J. M. Rondinelli, and X.-Z. Lu, Piezomagnetism- driven magnetoelectric coupling in altermagnetic multiferroic K3Cr2F7, Phys. Rev. B112, 094412 (2025)

  63. [63]

    Xu, X.-Z

    K. Xu, X.-Z. Lu, and H. Xiang, Designing new ferroelectrics with a general strategy, npj Quant. Mater. 2, 1 (2017)

  64. [64]

    H. Tan, M. Li, H. Liu, Z. Liu, Y . Li, and W. Duan, Two-dimensional ferromagnetic-ferroelectric multiferroics in violation of thed 0 rule, Phys. Rev. B99, 195434 (2019)

  65. [65]

    Q. Song, S. Stavri ´c, P. Barone, A. Droghetti, D. S. Antonenko, J. W. Venderbos, C. A. Occhialini, B. Ilyas, E. Ergec ¸en, N. Gedik, S.-W. Cheong, R. M. Fernandes, S. Picozzi, and R. Comin, Electrical switching of ap-wave magnet, Nature642, 64 (2025)

  66. [66]

    Priessnitz, A

    J. Priessnitz, A. B. Hellenes, R. Comin, and L. ˇSmejkal, Ferroelectric p-wave magnets, preprint arXiv:2603.19107 (2026)

  67. [67]

    Matsumoto, R

    R. Matsumoto, R. Shindou, and S. Murakami, Thermal Hall effect of magnons in magnets with dipolar interaction, Phys. Rev. B89, 054420 (2014)

  68. [68]

    Katsura, N

    H. Katsura, N. Nagaosa, and P. A. Lee, Theory of the thermal Hall effect in quantum magnets, Phys. Rev. Lett.104, 066403 (2010)

  69. [69]

    P. E. Bl ¨ochl, Projector augmented-wave method, Phys. Rev. B50, 17953 (1994)

  70. [70]

    Kresse and J

    G. Kresse and J. Furthm ¨uller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comp. Mater. Sci.6, 15 (1996)

  71. [71]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev, Lett.77, 3865 (1996)

  72. [72]

    A. I. Liechtenstein, V . I. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators, Phys. Rev. B52, R5467 (1995)

  73. [73]

    R. D. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Phys. Rev. B47, 1651(R) (1993). 16

  74. [74]

    H. J. Xiang, E. J. Kan, S.-H. Wei, M.-H. Whangbo, and X. G. Gong, Predicting the spin-lattice order of frustrated systems from first principles, Phys. Rev. B84, 224429 (2011)

  75. [75]

    Xiang, C

    H. Xiang, C. Lee, H.-J. Koo, X. Gong, and M.-H. Whangbo, Magnetic properties and energy-mapping analysis, Dalton Trans.42, 823 (2013)

  76. [76]

    Henkelman, B

    G. Henkelman, B. P. Uberuaga, and H. J´onsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys.113, 9901 (2000). 17 FIG. 1. Realizing odd-parity chiral magnons in layered antiferromagnets. Side view of bilayer antiferromagnets with P preserved (a) and P broken (d) , where blue balls refer to th...