pith. sign in

arxiv: 2505.01964 · v3 · submitted 2025-05-04 · ❄️ cond-mat.mtrl-sci

Altermagnetic type-II Multiferroics with N\'{e}el-order-locked Electric Polarization

Wen-Ti Guo , Junqi Xu , Yurong Yang , Haijun Zhang , Huaiqiang Wang This is my paper

Pith reviewed 2026-05-22 17:42 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords altermagnetismtype-II multiferroicsmagnetoelectric couplingNéel orderelectric polarizationtwo-dimensional materialslayer group symmetries
0
0 comments X

The pith

Altermagnetic Néel order generates spontaneous electric polarization locked to the magnetic structure.

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

The paper demonstrates that altermagnets with compensated collinear spins can produce electric polarization directly from their Néel order through symmetry breaking. This creates type-II multiferroics where the polarization is locked to the magnetic order in two-dimensional systems. A sympathetic reader would care because it offers a way to combine magnetism and ferroelectricity without net magnetization, opening routes to spintronic devices free of stray fields. The authors use layer group symmetry analysis to classify eight categories of magnetoelectric coupling and verify the mechanism with first-principles calculations on monolayer MgFe2N2.

Core claim

With the combination of symmetry analysis and microscopic theory, the generation of electric polarization by altermagnetic Néel order is explicitly demonstrated, establishing a microscopic mechanism of Néel-order-locked electric polarization in altermagnetic multiferroics. These pronounced magnetoelectric coupling behaviors are classified into eight distinct categories for two-dimensional altermagnets governed by layer group symmetries, and monolayer MgFe2N2 is identified as a prototypical example via first-principles calculations.

What carries the argument

The Néel-order-locked electric polarization arising from layer group symmetries that allow magnetoelectric coupling in compensated altermagnets.

If this is right

  • Magnetoelectric coupling behaviors in two-dimensional altermagnets fall into eight distinct categories set by layer group symmetries.
  • Monolayer MgFe2N2 serves as a concrete example of altermagnetic type-II multiferroicity.
  • The Néel order and locked polarization can be identified using magneto-optical microscopy.
  • Altermagnetic multiferroics connect type-II multiferroics with altermagnets for multifunctional spintronics applications.

Where Pith is reading between the lines

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

  • Electric switching of magnetism could become feasible in compensated systems that avoid external magnetic fields.
  • The symmetry classification may help screen additional 2D or layered candidates for similar locked polarization effects.
  • Bulk realizations of the same mechanism might exist if the appropriate layer or space group symmetries are preserved.

Load-bearing premise

The layer group symmetries and specific altermagnetic Néel order in the monolayer structure suffice to produce the polarization without dominant contributions from other interactions or defects.

What would settle it

First-principles calculations or direct measurements on monolayer MgFe2N2 showing no electric polarization that correlates with and reverses with the Néel order direction.

Figures

Figures reproduced from arXiv: 2505.01964 by Haijun Zhang, Huaiqiang Wang, Junqi Xu, Wen-Ti Guo, Yurong Yang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: a], the even-parity d orbitals of Fe ions mix up with the odd-parity p orbitals of the ligand N ions, inducing the non-zero electric dipole p ∝ ∑ i (S · eˆi) 2eˆi , where S represents the spin of Fe ion, while eˆi denotes the unit vector along the i-th Fe-N bond. As a result, the polar￾ization in MgFe2N2 directly originates from its magnetic structures, demonstrating robust intrinsic ME coupling. For in-pl… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Altermagnetism, an emergent magnetic phase featuring compensated collinear magnetic moments and momentum-dependent spin splittings, has recently garnered widespread interest. A critical issue concerns whether the unconventional spin structures can generate spontaneous electric polarization in altermagnets, thereby achieving type-II multiferroicity. Here, with the combination of symmetry analysis and microscopic theory, we explicitly demonstrate the generation of electric polarization by altermagnetic N\'eel order, and establish a microscopic mechanism of N\'eel-order-locked electric polarization in altermagnetic multiferroics.~We further reveal these pronounced magnetoelectric coupling behaviors and classify them into eight distinct categories for two-dimensional altermagnets governed by layer group symmetries. Then we take monolayer MgFe$_2$N$_2$ as a prototypical example of altermagnetic type-II multiferroics by first-principles calculations. We also propose to identify the N\'eel order and accompanying electric polarization in altermagnetic multiferroics by magneto-optical microscopy. Bridging type-II multiferroics and altermagnets, our work could pave the way for altermagnetic multifunctional spintronics.

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 / 2 minor

Summary. The paper claims that symmetry analysis combined with microscopic theory demonstrates the generation of electric polarization by altermagnetic Néel order in type-II multiferroics. It classifies magnetoelectric coupling behaviors into eight categories for two-dimensional altermagnets under layer-group symmetries, presents monolayer MgFe₂N₂ as a prototypical example using first-principles calculations, and proposes magneto-optical microscopy to identify the Néel order and accompanying polarization.

Significance. If substantiated, the work establishes a microscopic mechanism linking altermagnetic order to locked electric polarization, bridging two active fields and providing a classification framework that could guide searches for altermagnetic multiferroics. The explicit use of layer-group symmetry and first-principles validation on a concrete material constitute concrete strengths.

major comments (1)
  1. [Abstract and first-principles calculations section] Abstract and first-principles calculations section: the central claim that the polarization is generated by and locked to the altermagnetic Néel order requires isolation from other contributions. The manuscript relaxes and computes polarization only for the target Néel configuration; no explicit comparison is reported to the non-magnetic state or to other collinear magnetic patterns allowed by the same layer group. Without these controls, residual ionic displacements or spin-orbit terms permitted independently of the altermagnetic order cannot be ruled out.
minor comments (2)
  1. [Abstract] The abstract refers to a 'microscopic theory' and 'first-principles calculations' but supplies no details on convergence criteria, k-point sampling, or how the electric polarization is extracted (Berry-phase vs. point-charge model).
  2. [Classification section] Notation for the eight classified categories is introduced without a compact table or explicit mapping to the layer groups; a summary table would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive major comment. We address the point below.

read point-by-point responses

  1. Referee: [Abstract and first-principles calculations section] Abstract and first-principles calculations section: the central claim that the polarization is generated by and locked to the altermagnetic Néel order requires isolation from other contributions. The manuscript relaxes and computes polarization only for the target Néel configuration; no explicit comparison is reported to the non-magnetic state or to other collinear magnetic patterns allowed by the same layer group. Without these controls, residual ionic displacements or spin-orbit terms permitted independently of the altermagnetic order cannot be ruled out.

    Authors: We agree that explicit comparisons in the first-principles section would strengthen the isolation of the altermagnetic Néel-order contribution. The symmetry analysis and microscopic theory in the manuscript already establish that electric polarization is symmetry-allowed exclusively by the target Néel order and is forbidden in the non-magnetic state or other collinear configurations permitted by the same layer group. To provide direct numerical confirmation and rule out residual contributions, we will add first-principles calculations of the polarization for the non-magnetic case and for alternative collinear magnetic patterns in the revised manuscript, including a new figure or table summarizing these results. revision: yes

Circularity Check

0 steps flagged

No circularity: symmetry analysis and first-principles results remain independent of each other

full rationale

The paper's central derivation proceeds from established layer-group symmetry constraints to a microscopic mechanism for Néel-order-induced polarization, then validates the mechanism numerically via DFT on the MgFe2N2 monolayer. Neither the symmetry classification nor the computed polarization reduces to a fitted parameter or self-citation by construction; the analytical steps supply independent constraints while the first-principles section supplies separate numerical evidence. No load-bearing step equates a prediction to its own input, and external layer-group theory is not replaced by an author-specific uniqueness theorem. This is the normal, self-contained case.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard symmetry principles of layer groups and the validity of density-functional theory for the chosen monolayer; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Layer group symmetries fully determine the allowed magnetoelectric couplings in 2D altermagnets
    Invoked to classify behaviors into eight distinct categories.

pith-pipeline@v0.9.0 · 5750 in / 1284 out tokens · 42904 ms · 2026-05-22T17:42:42.426870+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.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Classification and design of two-dimensional altermagnets

    cond-mat.mtrl-sci 2026-01 accept novelty 3.0

    A review that classifies two-dimensional altermagnets via spin-group theory, lists materials with large spin splitting, and outlines design strategies for experimental realization.

Reference graph

Works this paper leans on

76 extracted references · 76 canonical work pages · cited by 1 Pith paper

  1. [1]

    H.-Y. Ma, M. Hu, N. Li, J. Liu, W. Yao, J.-F. Jia, and J. Liu, Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current, Nat. Commun. 12, 2846 (2021)

    work page 2021

  2. [2]

    I. I. Mazin, K. Koepernik, M. D. Johannes, R. González- Hernández, and L. Šmejkal, Prediction of unconventional magnetism in doped FeSb 2, Proc. Natl. Acad. Sci. 118, e2108924118 (2021)

    work page 2021

  3. [3]

    González-Hernández, L

    R. González-Hernández, L. Šmejkal, K. Vỳbornỳ, Y. Ya- hagi, J. Sinova, T. Jungwirth, and J. Železnỳ, Ef- ficient electrical spin splitter based on nonrelativis- tic collinear antiferromagnetism, Phys. Rev. Lett. 126, 127701 (2021)

    work page 2021

  4. [4]

    Šmejkal, Libor and Sinova, Jairo and Jungwirth, Tomas, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022)

    work page 2022

  5. [5]

    Šmejkal, J

    L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conven- tional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X 12, 031042 (2022)

    work page 2022

  6. [6]

    Turek, Altermagnetism and magnetic groups with pseudoscalar electron spin, Phys

    I. Turek, Altermagnetism and magnetic groups with pseudoscalar electron spin, Phys. Rev. B 106, 094432 (2022)

    work page 2022

  7. [7]

    Šmejkal, A

    L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakat- suji, and T. Jungwirth, Anomalous hall antiferromag- nets, Nat. Rev. Mater. 7, 482 (2022)

    work page 2022

  8. [8]

    P. Liu, J. Li, J. Han, X. Wan, and Q. Liu, Spin-group symmetry in magnetic materials with negligible spin- orbit coupling, Phys. Rev. X 12, 021016 (2022)

    work page 2022

  9. [9]

    and Šmejkal, L

    Krempaský, J. and Šmejkal, L. and D’Souza, S. W. and others, Altermagnetic lifting of Kramers spin degeneracy, Nature 626, 517 (2024)

    work page 2024

  10. [10]

    Reimers, L

    S. Reimers, L. Odenbreit, L. Šmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. Jaeschke Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty, et al., Direct observation of altermagnetic band splitting in CrSb thin films, Nat. Commun. 15, 2116 (2024)

    work page 2024

  11. [11]

    Tamang, S

    R. Tamang, S. Gurung, D. Rai, S. Brahimi, and S. Lou- nis, Newly discovered magnetic phase: A brief review on altermagnets, arXiv:2412.05377 (2024)

    work page arXiv 2024

  12. [12]

    J. Liu, J. Zhan, T. Li, J. Liu, S. Cheng, Y. Shi, L. Deng, M. Zhang, C. Li, J. Ding, et al., Absence of altermagnetic spin splitting character in rutile oxide RuO 2, Phys. Rev. Lett. 133, 176401 (2024)

    work page 2024

  13. [13]

    N. Wang, J. Chen, N. Ding, H. Zhang, S. Dong, and S.-S. Wang, Magneto-optical Kerr effect and magnetoelasticity in a weakly ferromagnetic RuF 4 monolayer, Phys. Rev. B 106, 064435 (2022)

    work page 2022

  14. [14]

    J. Ding, Z. Jiang, X. Chen, Z. Tao, Z. Liu, T. Li, J. Liu, J. Sun, J. Cheng, J. Liu, et al. , Large band splitting in g-wave altermagnet CrSb, Phys. Rev. Lett. 133, 206401 (2024)

    work page 2024

  15. [15]

    Chen, Z.-A

    H. Chen, Z.-A. Wang, P. Qin, Z. Meng, X. Zhou, X. Wang, L. Liu, G. Zhao, Z. Duan, T. Zhang, J. Liu, D.-F. Shao, C. Jiang, and Z. Liu, Spin-splitting magne- toresistance in altermagnetic ruo2 thin films, Advanced Materials 37, 2507764 (2025)

    work page 2025

  16. [16]

    X. Zhou, W. Feng, R.-W. Zhang, L. Šmejkal, J. Sinova, Y. Mokrousov, and Y. Yao, Crystal Thermal Transport in Altermagnetic RuO 2, Phys. Rev. Lett. 132, 056701 (2024)

    work page 2024

  17. [17]

    Attias, A

    L. Attias, A. Levchenko, and M. Khodas, Intrinsic anomalous Hall effect in altermagnets, Phys. Rev. B 110, 094425 (2024)

    work page 2024

  18. [18]

    L. Han, X. Fu, W. He, Y. Zhu, J. Dai, W. Yang, W. Zhu, H. Bai, C. Chen, C. Wan, et al. , Observation of non- volatile anomalous Nernst effect in altermagnet with collinear Néel vector, arXiv:2403.13427 (2024)

    work page arXiv 2024

  19. [19]

    Zeng and Y.-J

    S. Zeng and Y.-J. Zhao, Description of two-dimensional altermagnetism: Categorization using spin group theory, Phys. Rev. B 110, 054406 (2024)

    work page 2024

  20. [20]

    Z. Xiao, J. Zhao, Y. Li, R. Shindou, and Z.-D. Song, Spin space groups: Full classification and applications, Phys. Rev. X 14, 031037 (2024)

    work page 2024

  21. [21]

    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. X 14, 031039 (2024)

    work page 2024

  22. [22]

    R.-C. Xiao, H. Li, H. Han, W. Gan, M. Yang, D.- F. Shao, S.-H. Zhang, Y. Gao, M. Tian, and J. Zhou, Anomalous-hall néel textures in altermagnetic materi- als, Science China Physics, Mechanics & Astronomy 69, 217511 (2025)

    work page 2025

  23. [23]

    V. Leeb, A. Mook, L. Šmejkal, and J. Knolle, Sponta- neous formation of altermagnetism from orbital ordering, Phys. Rev. Lett. 132, 236701 (2024)

    work page 2024

  24. [24]

    Zhang, X

    F. Zhang, X. Cheng, Z. Yin, C. Liu, L. Deng, Y. Qiao, Z. Shi, S. Zhang, J. Lin, Z. Liu, M. Ye, Y. Huang, X. Meng, C. Zhang, T. Okuda, K. Shimada, S. Cui, Y. Zhao, G.-H. Cao, S. Qiao, J. Liu, and C. Chen, Crystal-symmetry-paired spin–valley locking in a layered room-temperature metallic altermagnet candidate, Nat. Phys. 21, 760 (2025)

    work page 2025

  25. [25]

    Z. Qian, Y. Yang, S. Liu, and C. Wu, Fragile uncon- ventional magnetism in ruo2 by proximity to landau- pomeranchuk instability, Phys. Rev. B 111, 174425 (2025)

    work page 2025

  26. [26]

    Q. Liu, X. Dai, and S. Blügel, Different facets of uncon- ventional magnetism, Nat. Phys. 21, 329 (2025)

    work page 2025

  27. [27]

    Liu and N

    Z. Liu and N. V. Medhekar, d-wave polarization-spin locking in two-dimensional altermagnets, Nano Letters 25, 13411 (2025)

    work page 2025

  28. [28]

    Z.-A. Wang, B. Li, S.-S. Zhang, W.-J. Lu, M. Tian, Y.-P. Sun, E. Y. Tsymbal, K. Wang, H. Du, and D.-F. Shao, Giant uncompensated magnon spin currents in x-type magnets, arXiv:2502.13511 (2025)

    work page arXiv 2025

  29. [29]

    Z.-F. Gao, S. Qu, B. Zeng, Y. Liu, J.-R. Wen, H. Sun, P.-J. Guo, and Z.-Y. Lu, AI-accelerated discovery of al- termagnetic materials, Nat. Sci. Rev. 12, nwaf066 (2025)

    work page 2025

  30. [30]

    J.-K. Yuan, Z. Pan, and C. Wu, Unconventional mag- netism in spin-orbit coupled systems, arXiv:2504.14577 (2025)

    work page arXiv 2025

  31. [31]

    M. Hu, X. Cheng, Z. Huang, and J. Liu, Catalog of C -Paired Spin-Momentum Locking in Antiferromagnetic Systems, Phys. Rev. X 15, 021083 (2025)

    work page 2025

  32. [32]

    Hayami, Y

    S. Hayami, Y. Yanagi, and H. Kusunose, Bottom-up de- sign of spin-split and reshaped electronic band structures 7 in antiferromagnets without spin-orbit coupling: Proce- dure on the basis of augmented multipoles, Phys. Rev. B 102, 144441 (2020)

    work page 2020

  33. [33]

    L. Bai, W. Feng, S. Liu, L. Šmejkal, Y. Mokrousov, and Y. Yao, Altermagnetism: Exploring New Frontiers in Magnetism and Spintronics, Adv. Funct. Mater. 34, 2409327 (2024)

    work page 2024

  34. [34]

    C. Song, H. Bai, Z. Zhou, L. Han, H. Reichlova, J. H. Dil, J. Liu, X. Chen, and F. Pan, Altermagnets as a new class of functional materials, Nat. Rev. Mater. (2025)

    work page 2025

  35. [35]

    S. S. Fender, O. Gonzalez, and D. K. Bediako, Altermag- netism: A Chemical Perspective, J. Am. Chem. Soc. 147, 2257 (2025)

    work page 2025

  36. [36]

    R. Peng, J. Yang, L. Hu, W.-L. Ong, P. Ho, C. S. Lau, J. Liu, and Y. S. Ang, All-electrical layer-spintronics in altermagnetic bilayers, Mater. Horiz. 12, 2197 (2025)

    work page 2025

  37. [37]

    Santhosh, P

    S. Santhosh, P. Corbae, W. J. Yánez-Parreño, S. Ghosh, C. J. Jensen, A. V. Fedorov, M. Hashimoto, D. Lu, J. A. Borchers, A. J. Grutter, T. R. Charlton, S. Islam, D. Golovanova, Y. Zhao, A. Tauraso, A. Richardella, B. Yan, K. A. Mkhoyan, C. J. Palmstrøm, Y. Ou, and N. Samarth, Altermag- netic band splitting in 10 nm epitaxial crsb thin films, Advanced Mate...

    work page doi:10.1002/adma.202508977 2025

  38. [38]

    Samanta, M

    K. Samanta, M. Ležaić, M. Merte, F. Freimuth, S. Blügel, and Y. Mokrousov, Crystal Hall and crystal magneto- optical effect in thin films of SrRuO 3, J. Appl. Phys. 127, 213904 (2020)

    work page 2020

  39. [39]

    Zhang, H

    Y.-C. Zhang, H. Bai, D.-H. Zhang, C. Chen, L. Han, S.- X. Liang, R.-Y. Chu, J.-K. Dai, M. Sawicki, F. Pan, and C. Song, Probing the Néel Order in Altermagnetic RuO 2 Films via X-ray Magnetic Linear Dichroism, Chin. Phys. Lett. 42, 027301 (2025)

    work page 2025

  40. [40]

    Raboni Ferreira, Marina and Daurer, Benedikt J and Neethirajan, Jeffrey and Apseros, Andreas and Ruiz- Gómez, Sandra and Kaulich, Burkhard and Kazemian, Majid and Donnelly, Claire, Nanoscale Mapping of Mag- netic Orientations with Complex X-ray Magnetic Linear Dichroism, arXiv:2502.08617 (2025)

    work page arXiv 2025

  41. [41]

    Leiviskä, J

    M. Leiviskä, J. Rial, A. Bad’ura, R. L. Seeger, I. Kounta, S. Beckert, D. Kriegner, I. Joumard, E. Schmoranzerová, J. Sinova, O. Gomonay, A. Thomas, S. T. B. Goennen- wein, H. Reichlová, L. Šmejkal, L. Michez, T. Jungwirth, and V. Baltz, Anisotropy of the Anomalous Hall Effect in Thin Films of the Altermagnet Candidate Mn 5Si3, Phys. Rev. B 109, 224430 (2024)

    work page 2024

  42. [42]

    Z. Zhou, X. Cheng, M. Hu, R. Chu, H. Bai, L. Han, J. Liu, F. Pan, and C. Song, Manipulation of the alter- magnetic order in CrSb via crystal symmetry, Nature 638, 645 (2025)

    work page 2025

  43. [43]

    A. Wu, D. Cheng, X. Wang, M. Zeng, C. Liu, and X. Li, Optical signatures of noncentrosymmetric structural dis- tortion in altermagnetic MnTe, arXiv:2503.17742 (2025)

    work page arXiv 2025

  44. [44]

    L. Han, X. Fu, C. Song, Y. Zhu, X. Li, Z. Zhu, H. Bai, R. Chu, J. Dai, S. Liang, et al. , Discovery of a large magnetic nonlinear hall effect in an altermagnet, arXiv:2502.04920 (2025)

    work page arXiv 2025

  45. [45]

    P.-J. Guo, Y. Gu, Z.-F. Gao, and Z.-Y. Lu, Altermagnetic ferroelectric LiFe 2F6 and spin-triplet excitonic insulator phase, arXiv:2312.13911 (2023)

    work page arXiv 2023

  46. [46]

    Zhang, C

    R.-W. Zhang, C. Cui, R. Li, J. Duan, L. Li, Z.-M. Yu, and Y. Yao, Predictable gate-field control of spin in alter- magnets with spin-layer coupling, Phys. Rev. Lett. 133, 056401 (2024)

    work page 2024

  47. [47]

    Matsuda, H

    J. Matsuda, H. Watanabe, and R. Arita, Multiferroic collinear antiferromagnets with hidden altermagnetic spin splitting, Phys. Rev. Lett. 134, 226703 (2025)

    work page 2025

  48. [48]

    Sheng, J

    Y. Sheng, J. Zhang, J. Liu, and M. Wu, Ubiquitous van der waals altermagnetism with sliding/moire ferroelec- tricity, Science China Physics, Mechanics & Astronomy 68, 297511 (2025)

    work page 2025

  49. [49]

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

    work page 2025

  50. [50]

    X. Duan, J. Zhang, Z. Zhu, Y. Liu, Z. Zhang, I. Žutić, and T. Zhou, Antiferroelectric Altermagnets: Antiferro- electricity Alters Magnets, Phys. Rev. Lett. 134, 106801 (2025)

    work page 2025

  51. [51]

    Camerano, A

    L. Camerano, A. O. Fumega, J. L. Lado, A. Stroppa, and G. Profeta, Multiferroic nematic d-wave altermagnetism driven by orbital-order on the honeycomb lattice, npj 2D Materials and Applications 9, 75 (2025)

    work page 2025

  52. [52]

    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 Letters 25, 14618 (2025)

    work page 2025

  53. [53]

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

    work page 2019

  54. [54]

    X. Li, C. Xu, B. Liu, X. Li, L. Bellaiche, and H. Xiang, Realistic Spin Model for Multiferroic NiI2, Phys. Rev. Lett. 131, 036701 (2023)

    work page 2023

  55. [55]

    C. Liu, W. Ren, and S. Picozzi, Spin-chirality-driven mul- tiferroicity in van der waals monolayers, Phys. Rev. Lett. 132, 086802 (2024)

    work page 2024

  56. [56]

    Stavrić, G

    S. Stavrić, G. Cuono, B. Yang, A. R. Puente-Uriona, J. Ibañez Azpiroz, P. Barone, A. Droghetti, and S. Pi- cozzi, Giant nonreciprocal band structure effect in a mul- tiferroic material, Phys. Rev. Lett. 135, 206401 (2025)

    work page 2025

  57. [57]

    Murakawa, Y

    H. Murakawa, Y. Onose, S. Miyahara, N. Furukawa, and Y. Tokura, Ferroelectricity induced by spin-dependent metal-ligand hybridization in Ba 2CoGe2O7, Phys. Rev. Lett. 105, 137202 (2010)

    work page 2010

  58. [58]

    Zhang, Y

    J. Zhang, Y. Zhou, F. Wang, X. Shen, J. Wang, and X. Lu, Coexistence and coupling of spin-induced ferro- electricity and ferromagnetism in perovskites, Phys. Rev. Lett. 129, 117603 (2022)

    work page 2022

  59. [59]

    Y. Zhou, H. Ye, J. Zhang, and S. Dong, Double-leaf Riemann surface topological converse magnetoelectricity, Phys. Rev. B 110, 054424 (2024)

    work page 2024

  60. [60]

    C. Jia, S. Onoda, N. Nagaosa, and J. H. Han, Bond elec- tronic polarization induced by spin, Phys. Rev. B 74, 224444 (2006)

    work page 2006

  61. [61]

    Matsumoto, K

    M. Matsumoto, K. Chimata, and M. Koga, Symmetry analysis of spin-dependent electric dipole and its appli- cation to magnetoelectric effects, J. Phys. Soc. Jpn. 86, 034704 (2017)

    work page 2017

  62. [62]

    Y. Wu, Z. Zeng, H. Lu, X. Han, C. Yang, N. Liu, X. Zhao, L. Qiao, W. Ji, R. Che, et al. , Coexistence of ferroelec- tricity and antiferroelectricity in 2d van der waals multi- ferroic, Nat. Commun. 15, 8616 (2024)

    work page 2024

  63. [63]

    Matsukura, Y

    F. Matsukura, Y. Tokura, and H. Ohno, Control of magnetism by electric fields, Nat. Nanotechnol. 10, 209 (2015)

    work page 2015

  64. [64]

    Jiang, L

    S. Jiang, L. Li, Z. Wang, K. F. Mak, and J. Shan, Con- trolling Magnetism in 2D CrI 3 by Electrostatic Doping, Nat. Nanotechnol. 13, 549 (2018)

    work page 2018

  65. [65]

    Q. Song, C. A. Occhialini, E. Ergeçen, B. Ilyas, D. Amoroso, P. Barone, J. Kapeghian, K. Watanabe, 8 T. Taniguchi, A. S. Botana, S. Picozzi, N. Gedik, and R. Comin, Evidence for a single-layer van der Waals mul- tiferroic, Nature 602, 601 (2022)

    work page 2022

  66. [66]

    Murakawa, Y

    H. Murakawa, Y. Onose, S. Miyahara, N. Furukawa, and Y. Tokura, Comprehensive study of the ferroelectricity induced by the spin-dependent d-p hybridization mecha- nism in Ba 2XGe2O7 (X = Mn, Co, and Cu), Phys. Rev. B 85, 174106 (2012)

    work page 2012

  67. [67]

    C. Jia, S. Onoda, N. Nagaosa, and J. H. Han, Microscopic theory of spin-polarization coupling in multiferroic tran- sition metal oxides, Phys. Rev. B 76, 144424 (2007)

    work page 2007

  68. [68]

    Behovits, A

    Y. Behovits, A. L. Chekhov, S. Y. Bodnar, O. Gueck- stock, S. Reimers, Y. Lytvynenko, Y. Skourski, M. Wolf, T. S. Seifert, O. Gomonay, M. Kläui, M. Jourdan, and T. Kampfrath, Terahertz Néel spin-orbit torques drive nonlinear magnon dynamics in antiferromagnetic Mn2Au, Nat. Commun. 14, 6038 (2023)

    work page 2023

  69. [69]

    W. Sun, C. Yang, W. Wang, Y. Liu, X. Wang, S. Huang, and Z. Cheng, Proposing Altermagnetic-Ferroelectric Type-III Multiferroics with Robust Magnetoelectric Cou- pling, Adv. Mater. , 2502575 (2025)

    work page 2025

  70. [70]

    Šmejkal, Altermagnetic multiferroics and altermagne- toelectric effect, arXiv:2411.19928 (2024)

    L. Šmejkal, Altermagnetic multiferroics and altermagne- toelectric effect, arXiv:2411.19928 (2024)

    work page arXiv 2024

  71. [71]

    R. Cao, R. Dong, R. Fei, and Y. Yao, Designing spin- driven multiferroics in altermagnets, arXiv:2412.20347 (2024)

    work page arXiv 2024

  72. [72]

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

    work page 2025

  73. [73]

    Y. Zhu, M. Gu, Y. Liu, X. Chen, Y. Li, S. Du, and Q. Liu, Sliding ferroelectric control of unconventional magnetism in stacked bilayers, Phys. Rev. Lett. 135, 056801 (2025)

    work page 2025

  74. [74]

    Z. Zhu, Y. Liu, X. Duan, J. Zhang, B. Hao, S.-H. Wei, I. Žutić, and T. Zhou, Emergent multiferroic altermag- nets and spin control via noncollinear molecular polar- ization, Sci. China Phys. Mech. 68, 127562 (2025)

    work page 2025

  75. [75]

    D. Guo, J. Dai, R. Wang, C. Wang, and W. Ji, Mechani- cally and electrically switchable triferroic altermagnet in a pentagonal FeO2 monolayer, Phys. Rev. B 112, 195410 (2025)

    work page 2025

  76. [76]

    A. Urru, D. Seleznev, Y. Teng, S. Y. Park, S. E. Reyes- Lillo, and K. M. Rabe, G-type antiferromagnetic BiFeO3 is a multiferroic g-wave altermagnet, Phys. Rev. B 112, 104411 (2025)

    work page 2025