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REVIEW 2 major objections 5 minor 78 references

G-type Antiferromagnetic BiFeO$_3$ is a Multiferroic $g$-wave Altermagnet

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read G-type antiferromagnetic BiFeO3 is a bulk g-wave altermagnet, with spin-split bands up to about 0.2 eV and four nodal surfaces crossing the Brillouin zone center.

desk verdict Solid classification paper: the g-wave claim itself is group-theoretically clean, but the new continuity-enforced nodal-surface concept is argued rather than proven, and the symmetry input is load-bearing though almost certainly correct. read the letter →

arxiv 2505.18965 v1 pith:FWRBFK2U submitted 2025-05-25 cond-mat.mtrl-sci

Andrea Urru , Daniel Seleznev , Yujia Teng , Se Young Park , Sebastian E. Reyes-Lillo , Karin M. Rabe This is my paper
classification cond-mat.mtrl-sci
keywords altermagnetismBiFeO3multiferroicsspinsplittingLauegroupg-wavenodalsurfacesferroelectricswitching
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that G-type antiferromagnetic BiFeO3, a well-known multiferroic, is also a g-wave altermagnet. Altermagnets have zero net magnetization yet their electronic bands split by spin in the absence of spin-orbit coupling, and here the computed splitting reaches roughly 0.2 eV on general wavevectors. The paper makes the case visible with a band-structure plotting scheme that samples general reciprocal-space lines instead of only high-symmetry lines, and it explains why the splitting was missed before. It also works out the symmetry of the spin-splitting function, classifies its nodal surfaces, and provides a complete group-theory table assigning d-, g-, or i-wave character to all crystallographic Laue groups. Because BFO is ferroelectric, the authors conclude that the altermagnetic spin splitting should be controllable by an electric field.

What carries the argument

The argument is carried by the spin-splitting function $\Delta(\mathbf{k})$, the average energy difference between spin-up and spin-down bands at each wavevector, together with the symmetry of the magnetic space group. For G-type BFO without SOC, the relevant group is R3c' (type III, No. 161.71), whose spin space group contains neither PT nor Ut; the spin point group 132m belongs to spin Laue group $1\bar{3}2m$, so $\Delta(\mathbf{k})$ must transform as the $\Gamma_2^+$ irrep of the crystallographic Laue group $\bar{3}m$. The classification machinery decomposes the rotation-group representations $D^{(l)}$ into irreps of the Laue group: the lowest l that contains the spin-splitting irrep is $l=4$, i.e., g-wave. Nodal surfaces are classified as symmetry-enforced (three mirror planes plus two-fold axis lines forced by combinations of symmetries) or continuity-enforced (connected surfaces whose existence follows from the sign alternation and continuity of $\Delta(\mathbf{k})$); counting them correctly gives four nodal surfaces through $\Gamma$. A symmetry-adapted plane-wave expansion $W_s(\mathbf{k})$ parametrizes $\Delta(\mathbf{k})$ and shows how the splitting is controlled by oxygen-octahedron rotations that distinguish the two Fe sublattices.

What would settle it

A decisive test would be a spin-resolved photoemission measurement or a zero-SOC DFT calculation on a G-type BiFeO3 sample (thin film where the cycloid is suppressed) along a general reciprocal-space line: if the two spin channels remain degenerate beyond numerical noise, the altermagnetic claim collapses. Alternatively, a structural refinement showing the oxygen octahedra around the two iron sites rotate in the same sense, so that a pure translation connects the sublattices, would invalidate the R3c' assignment that the argument relies on.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that G-type antiferromagnetic BiFeO3 is a bulk g-wave altermagnet. In the limit of zero spin-orbit coupling, the magnetic space group R3c' lacks both PT symmetry and the combined spin-rotation-plus-translation symmetry Ut, so nothing forbids spin-split bands; the computed bands show a splitting of up to about 0.2 eV that alternates sign across the Brillouin zone and vanishes exactly on the high-symmetry lines. The spin-splitting function $\Delta(\mathbf{k})$ transforms as the $\Gamma_2^+$ irreducible representation of the crystallographic Laue group $\bar{3}m$, and decomposing the O(3) representations $D^{(l)}$ shows the lowest l containing this irrep is $l=4$, the g-wave channel, with four nodal surfaces crossing $\Gamma$ once the continuity-enforced surface is counted correctly. The same analysis yields a complete (d,g,i)-wave classification table for the three-dimensional case.

Load-bearing premise

The load-bearing premise is that the magnetic space group of G-type BiFeO3 without spin-orbit coupling is R3c' (type III, No. 161.71), meaning the two iron sublattices are related by a mirror glide rather than by a pure translation; if that assignment is wrong and a pure translation connects the sublattices, the symmetry-enforced spin splitting vanishes.

Editorial extensions

If this is right

  • G-type BiFeO3 provides a room-temperature multiferroic altermagnet: zero net magnetization, insulating nature, and spin splitting comparable to ferromagnets, which is usable in spintronic devices without stray fields.
  • On the paper's analysis, the oxygen-octahedron rotation mode R4+ is what breaks the Ut symmetry, so switching the octahedral rotation pattern reverses the sign of the spin splitting; since those rotations are locked to the ferroelectric polarization, the altermagnetic spin splitting should be electric-field switchable.
  • The generalized band-structure plotting path, which pairs general k with its mirror image, is a direct way to expose altermagnetism: along the high-symmetry lines the bands stay degenerate, but on general lines the splitting appears and alternates.
  • The complete classification table assigns d-, g-, or i-wave character to every one-dimensional, inversion-even, non-identical irrep of the 11 crystallographic Laue groups, and shows that three Laue groups ($\bar{1}$, $\bar{3}$, and $m\bar{3}$) cannot support altermagnetism.
  • The spin-splitting function can be efficiently parametrized by a few symmetry-adapted plane waves; the second star dominates, and coefficients from a 7×7×7 Monkhorst-Pack mesh match the full DFT fit, making the method cheap to apply to other materials.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial extension: any experiment that maps spin splitting on a single constant-kz plane would count six apparent nodal lines through $\Gamma$ and could misclassify BFO as i-wave; the correct g-wave identification requires tracing nodal-surface connectivity across planes.
  • Editorial extension: the same symmetry-adapted plane-wave expansion could be used to compare computed $\Delta(\mathbf{k})$ with angle-resolved photoemission maps, turning the wave-type classification into a directly testable momentum-space fingerprint.
  • Editorial extension: the classification recipe (find the Laue irrep of $\Delta(\mathbf{k})$, then the lowest l that contains it) could be automated against magnetic space group databases, making wave-type diagnosis a routine screening step for antiferromagnetic candidate materials.
  • Editorial extension: the ~0.2 eV splitting is a specific DFT prediction; if more accurate many-body calculations or surface and interface effects in films move the magnitude significantly, quantitative spintronics estimates would need revision, though the symmetry-based g-wave assignment would survive.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper argues that G-type antiferromagnetic BiFeO3 (BFO), in the absence of spin-orbit coupling, is a bulk g-wave altermagnet. The authors compute the non-SOC band structure along a newly introduced mixed high-symmetry/general reciprocal-space path and report spin splittings up to about 0.2 eV. They define a spin-splitting function Delta(k), map its nodal structure on constant-kz planes, and introduce symmetry-adapted plane-wave expansions W_s(k) fitted to the DFT data. They then give a group-theoretical classification based on irreducible representations of the crystallographic Laue group, assigning the altermagnetic pattern to the Gamma_2^+ irrep of the Laue group -3m and hence to the bulk g-wave class. A complete classification table for the 11 three-dimensional Laue groups is presented. Finally, the authors discuss the relation between ferroelectric distortion modes and the altermagnetic splitting, proposing that ferroelectric switching can control the spin splitting because octahedral rotations are locked to the polar mode.

Significance. If the results hold, this is a valuable and timely contribution: it identifies a widely studied multiferroic, BiFeO3, as a g-wave altermagnet, supplies a clean group-theoretic derivation of the d/g/i-wave classification that is independent of the DFT fitting, and provides a useful plotting scheme for exposing altermagnetic splitting that is invisible on conventional high-symmetry paths. The explicit plane-wave parametrization and the comparison between least-squares and Monkhorst-Pack coefficients in the Supplementary Material are also useful for future analyses. The main risk is not the central irrep-based classification, which is sound, but the paper's additional claim that certain nodal surfaces are 'continuity-enforced' for any system with the same spin Laue group, a claim that is used to reconcile an apparent i-wave counting with the g-wave assignment.

major comments (2)
  1. [Sec. IV B and Fig. 6] The claim that the three two-fold nodal lines through Gamma are part of a single 'continuity-enforced' nodal surface is load-bearing for the discussion in Sec. V, where it resolves the apparent six-surface i-wave count into a four-surface g-wave count. The paper states that these surfaces are 'guaranteed by the continuity of the spin-splitting function' and 'will be present in the spin-splitting function of any system with a given spin Laue group,' but no proof is given. The cited codimension argument (Refs. 68-70) only shows that the generic zero set of a smooth function in three dimensions is codimension one; it does not by itself imply that a given symmetry-enforced nodal line must extend into an attached surface, nor that three distinct lines through a common point are connected in a single surface. Please either supply a rigorous topological/symmetry argument for this connectivity or explicitly state that the connectivity is a numerical observation for BFO and for the W_s(k) functions shown, not a theorem. This distinction matters because the final g-wave classification does not depend on the connectivity argument, but the paper's new 'continuity-enforced' concept and the intuitive l-counting resolution do.
  2. [Sec. II and Sec. III A] The entire altermagnetic classification rests on the assignment of the no-SOC magnetic space group of G-type BFO as R3c' (type III, No. 161.71), stated in Sec. II and used throughout. This assignment is almost certainly correct from the known R3c structure and G-type Fe order, but it is treated as an input rather than verified in the calculated state. Because the spin splitting vanishes identically if the actual magnetic space group contains [C2||E]t or PT, a direct symmetry check on the converged non-SOC DFT state (for example, by comparing the spin densities on the two Fe sublattices in a magnetic symmetry finder, or by checking that the two Fe sites are related by the c-glide rather than by a pure translation) would close the weakest link in the chain. This is a straightforward add-on to the existing calculation and would make the central claim self-contained.
minor comments (5)
  1. [Sec. IV C and SM Table SIII] The truncation of the plane-wave expansion at nine nontrivial stars is not discussed in the main text. Please state the convergence criterion used for the least-squares fit and, if possible, show that including additional stars does not change the nodal connectivity shown in Fig. 6.
  2. [Figs. 4 and 5] The heatmap captions do not specify the color scale or the range of Delta(k) in eV. Adding a color bar with numerical values would make the reported approximately 0.2 eV splitting and the faint nodal regions easier to assess.
  3. [Sec. III B] The statement that the bands in Fig. 3(b) 'have mostly spin-up and spin-down character along the x axis' would benefit from a quantitative measure of the spin polarization, since with SOC included the spin expectation value is not a good quantum number and the color scale is not defined.
  4. [Sec. V, Table I] The notation for spin Laue groups such as 24/1m and 1bar32m is used without a definition in the main text. A brief explanation or a pointer to the spin-group references would help readers not familiar with spin crystallographic notation.
  5. [SM Fig. S1] The caption mentions 'accidental nodes of the fitted function not discernible in the heatmap data.' Since Fig. 6 is generated from the same fitted function, please clarify which nodal features are properties of the fit and which are supported directly by the DFT data.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the g-wave classification follows from an externally grounded magnetic-space-group input through an independent group-theoretic derivation, and the plane-wave fit is descriptive rather than predictive.

full rationale

The derivation chain is: assumed no-SOC magnetic space group R3c' (type III, No. 161.71) for G-type BFO; spin point group 132m; spin Laue group 1bar32m; spin-splitting function Delta(k) transforming as Gamma2+ of the crystallographic Laue group 3bar m; decomposition of O(3) representations D(l) giving the lowest l=4 that contains Gamma2+; hence bulk g-wave. The only non-derived input is the R3c' assignment, which is an established crystallographic and magnetic input externally supported by experimental and prior first-principles work (Refs. [34]-[36], [55]) rather than a conclusion of this paper; starting a symmetry analysis from an externally grounded input is not circular. The plane-wave expansion in Eq. (10) is explicitly introduced as a parametrization, with the coefficients obtained by least-squares fitting to the DFT spin-splitting data, and the paper does not use those fitted coefficients as a prediction; the g-wave classification is obtained independently by irrep decomposition in Sec. V, not from the fit. The one self-citation, Ref. [34] for G-type ordering, is corroborated by external experiment [36] and other first-principles work [55], so it is not load-bearing. No equation in the paper reduces to its own input, no fitted parameter is renamed as a prediction, and no uniqueness theorem is imported from the authors' prior work. Therefore no significant circularity is present.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central g-wave classification rests on the standard group-theoretic relationship between the magnetic space group and the Laue-group irrep; the DFT data enter through the spin-splitting function whose symmetry properties are dictated by that irrep. The main non-standard input is the topological claim about continuity-enforced nodal surfaces, which is argued but not proved. The plane-wave coefficients are fitted parameters used only for visualization and parametrization.

free parameters (1)
  • Delta_s coefficients (s=1..9) of the symmetry-adapted plane-wave expansion = Table SIII: -0.00229, -0.03942, 0.014741, 0.02188, 0.02055, -0.00188, -0.00067, -0.01354, 0.00446 eV (least squares)
    Obtained by least-squares fit to the DFT spin-splitting data; they parametrize the nodal surfaces in Figs. 6 and S1-S3, but do not enter the symmetry-based g-wave classification.
assumptions (5)
  • domain assumption The magnetic space group without SOC of G-type BFO is R3c' (No. 161.71)
    Sec. II: based on the R3c crystal structure and G-type AFM order; it determines the spin point group 132m and all subsequent symmetry analysis.
  • domain assumption The spin-splitting function Delta(k) of Eq. (1) is real, continuous, periodic, and obeys the symmetry relations Eqs. (2)-(4)
    Sec. IV A: standard properties of band energies in collinear magnets without SOC.
  • standard math Delta(k) transforms as a one-dimensional, inversion-even, non-identical irrep of the crystallographic Laue group
    Sec. V: group-theoretic classification; the irrep decomposition method is standard representation theory.
  • ad hoc to paper Continuity alone guarantees that the three two-fold nodal lines through Gamma belong to one connected nodal surface for any system with the same spin Laue group
    Sec. IV B: asserted with a codimension argument and supported by DFT heatmaps; no rigorous proof is provided. Falsity would break the paper's nodal-counting resolution of the g/i paradox, though the irrep-based classification would remain.
  • domain assumption PBE without Hubbard U gives a sufficiently accurate electronic structure for the qualitative and semi-quantitative spin-splitting analysis
    SM computational details: a pragmatic DFT choice; BFO is a correlated oxide, so band energies and gap can be sensitive to the functional.

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Cite this review

Pith. "Pith review of G-type Antiferromagnetic BiFeO$_3$ is a Multiferroic $g$-wave Altermagnet." pith.science (2026). https://pith.science/paper/FWRBFK2U

@misc{pith2026250518965,
  author       = {Pith},
  title        = {Pith review of: G-type Antiferromagnetic BiFeO$_3$ is a Multiferroic $g$-wave Altermagnet},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FWRBFK2U}},
  note         = {Machine review of arXiv:2505.18965}
}
abstract

G-type antiferromagnetic BiFeO$_3$ is shown to be an altermagnet. We present the band structure using an unconventional scheme designed to highlight the distinctive spin splitting which is characteristic of altermagnets. We define and show plots of the spin-splitting function in reciprocal space. We show that the nodal surfaces of the spin-splitting function that follow from symmetry can be classified into two types, which we call symmetry-enforced and continuity-enforced. We describe the spin-splitting function with a simple parametrization in a basis of symmetry-adapted plane waves. Using group-theory analysis based on irreducible representations of the crystallographic Laue group, we confirm that the altermagnetism of G-type BiFeO$_3$ is $g$-wave and present a complete classification table for the general three-dimensional case. Finally, we discuss the effect of ferroelectric switching on the altermagnetic order, and identify three classes of ferroelectric altermagnets.

Figures

Figures reproduced from arXiv: 2505.18965 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Three-dimensional view of the rhombohedral R3 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Brillouin zone of the rhombohedral lattice. High [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Band structure of G-type BFO computed without SOC shown along a generalized path in reciprocal space, [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Heatmaps showing the spin-splitting function, as defined in the main text, on portions of the BZ at constant [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Heatmap of ∆( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Nodal surfaces of ∆( [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Heatmaps at constant [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. The top four valence bands in the band structure [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. (a) The top four valence bands in the band struc [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

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Reference graph

Works this paper leans on

78 extracted references · 45 canonical work pages

  1. [1]

    ˇSmejkal, J

    L. ˇSmejkal, 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)

    2022

  2. [2]

    ˇSmejkal, J

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

    2022

  3. [3]

    We further classify it as bulk since the character of the Γ + 2 irrep is −1 for the two-fold axes in the kz=0 plane

    (17) The lowest l for which Γ + 2 appears in the decomposition ofD(l) is l = 4, and thus the altermagnetic type is g- wave. We further classify it as bulk since the character of the Γ + 2 irrep is −1 for the two-fold axes in the kz=0 plane. The complete results for all the crystallographic Laue group irreps are presented in Table I. For each one- dimensio...

    work page

  4. [4]

    Hayami, Y

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

    2020

  5. [5]

    Hayami, Y

    S. Hayami, Y. Yanagi, and H. Kusunose, Momentum- dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019)

    2019

  6. [6]

    ˇSmejkal, R

    L. ˇSmejkal, R. Gonz´ alez-Hern´ andez, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci. Adv. 6, eaaz8809 (2020)

    2020

  7. [7]

    L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets, Phys. Rev. B 102, 014422 (2020)

    2020

  8. [8]

    L.-D. Yuan, Z. Wang, J.-W. Luo, and A. Zunger, Pre- diction of low- Z collinear and noncollinear antiferro- magnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling, Phys. Rev. Mater. 5, 014409 (2021)

    2021

Show all 78 references
  1. [9]

    I. I. Mazin, K. Koepernik, M. D. Johannes, R. Gonz´ alez- Hern´ andez, and L.ˇSmejkal, Prediction of unconventional magnetism in doped FeSb2, Proc. Natl. Acad. Sci. U.S.A. 118, e2108924118 (2021)

    2021

  2. [10]

    L.-D. Yuan, X. Zhang, C. M. Acosta, and A. Zunger, Uncovering spin-orbit coupling-independent hidden spin polarization of energy bands in antiferromagnets, Nat. Commun. 14, 5301 (2023)

    2023

  3. [11]

    Yuan and A

    L.-D. Yuan and A. Zunger, Degeneracy removal of spin bands in collinear antiferromagnets with non- interconvertible spin-structure motif pair, Adv. Mater. 35, 2211966 (2023)

    2023

  4. [12]

    Mazin (The PRX Editors), Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys

    I. Mazin (The PRX Editors), Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys. Rev. X 12, 040002 (2022)

    2022

  5. [13]

    Krempask´ y, L

    J. Krempask´ y, L. ˇSmejkal, S. W. D’Souza, M. Ha- jlaoui, G. Springholz, K. Uhl´ ıˇ rov´ a, F. Alarab, P. C. Constantinou, V. Strocov, D. Usanov, W. R. Pudelko, R. Gonz´ alez-Hern´ andez, A. Birk Hellenes, Z. Jansa, H. Reichlov´ a, Z. ˇSob´ aˇ n, R. D. Gonzalez Betancourt, P....

    2024

  6. [14]

    ˇSmejkal, A

    L. ˇSmejkal, A. B. Hellenes, R. Gonz´ alez-Hern´ andez, J. Sinova, and T. Jungwirth, Giant and tunneling mag- netoresistance in unconventional collinear antiferromag- nets with nonrelativistic spin-momentum coupling, Phys. Rev. X 12, 011028 (2022)

    2022

  7. [15]

    Gonz´ alez-Hern´ andez, L.ˇSmejkal, K

    R. Gonz´ alez-Hern´ andez, L.ˇSmejkal, K. V´ yborn´ y, Y. Ya- hagi, J. Sinova, T. Jungwirth, and J. ˇZelezn´ y, Ef- ficient electrical spin splitter based on nonrelativis- tic collinear antiferromagnetism, Phys. Rev. Lett. 126, 127701 (2021)

    2021

  8. [16]

    Watanabe, K

    H. Watanabe, K. Shinohara, T. Nomoto, A. Togo, and R. Arita, Symmetry analysis with spin crystallographic groups: Disentangling effects free of spin-orbit coupling in emergent electromagnetism, Phys. Rev. B 109, 094438 (2024)

    2024

  9. [17]

    F. Liu, Z. Zhang, X. Yuan, Y. Liu, S. Zhu, Z. Lu, and R. Xiong, Giant tunneling magnetoresistance in in- sulated altermagnet/ferromagnet junctions induced by spin-dependent tunneling effect, Phys. Rev. B 110, 134437 (2024)

    2024

  10. [18]

    Sharma and M

    L. Sharma and M. Thakurathi, Tunable Josephson diode effect in singlet superconductor-altermagnet-triplet su- perconductor junctions (2025), arXiv:2502.19371

    2025

  11. [19]

    G. Z. X. Yang, Z.-T. Sun, Y.-M. Xie, and K. T. Law, Topological altermagnetic Josephson junctions (2025), arXiv:2502.20283

    2025 arXiv

  12. [20]

    P. M. Gunnink, J. Sinova, and A. Mook, Surface acoustic wave driven acoustic spin splitter ind-wave altermagnetic thin films (2025), arXiv:2502.18007

    2025

  13. [21]

    De Vita, C

    A. De Vita, C. Bigi, D. Romanin, M. D. Watson, V. Polewczyk, M. Zonno, F. Bertran, M. B. Petersen, F. Motti, G. Vinai, M. Tuniz, F. Cilento, M. Cuoco, B. M. Andersen, A. Kreisel, L. J. D’Onofrio, O. J. Clark, M. T. Edmonds, C. Candelora, M. Xu, S. Cheng, A. LaFleur, T. Antonel...

    2025

  14. [22]

    Noh, G.-H

    S. Noh, G.-H. Kim, J. Lee, H. Jung, U. Seo, G. So, J. Lee, S. Lee, M. Park, S. Yang, Y. S. Oh, H. Jin, C. Sohn, and J.-W. Yoo, Tunneling magnetoresistance in alter- magnetic RuO2-based magnetic tunnel junctions (2025), arXiv:2502.13599

    2025 arXiv

  15. [23]

    Sheng, A

    L. Sheng, A. Duvakina, H. Wang, K. Yamamoto, R. Yuan, J. Wang, P. Chen, W. He, K. Yu, Y. Zhang, J. Chen, J. Hu, W. Song, S. Liu, X. Han, D. Yu, J.-P. Ansermet, S. Maekawa, D. Grundler, and H. Yu, Con- trol of spin currents by magnon interference in a canted antiferromagnet, Na...

    2025

  16. [24]

    Samanta, D.-F

    K. Samanta, D.-F. Shao, and E. Y. Tsymbal, Spin fil- tering with insulating altermagnets, Nano Lett. 25, 3150 (2025)

    2025

  17. [25]

    Leivisk¨ a, R

    M. Leivisk¨ a, R. Firouzmandi, K.-H. Ahn, P. Kubaˇ sˇ cik, Z. Soban, S. P. Bommanaboyena, C. M¨ uller, D. Krieg- ner, S. Sailler, M. Lammel, K. K. Bestha, L. ˇSmejkal, J. Zelezny, A. U. B. Wolter, M. Scheufele, J. Fis- 14 cher, M. Opel, S. Gepr¨ ags, M. Althammer, B. B¨ uchner...

    2025

  18. [26]

    Feng, C.-Y

    P. Feng, C.-Y. Tan, M. Gao, X.-W. Yan, Z.-X. Liu, P.-J. Guo, F. Ma, and Z.-Y. Lu, Quantum crystal spin Hall effect in two-dimensional altermagnetic systems (2025), arXiv:2503.13397

    2025 arXiv

  19. [27]

    L. E. Golub and L. ˇSmejkal, Spin orientation by electric current in altermagnets (2025), arXiv:2503.12203

    2025 arXiv

  20. [28]

    Sourounis and A

    K. Sourounis and A. Manchon, Efficient generation of spin currents in altermagnets via magnon drag, Phys. Rev. B 111, 134448 (2025)

    2025

  21. [30]

    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)

    2022

  22. [31]

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

    2025

  23. [32]

    Hinuma, G

    Y. Hinuma, G. Pizzi, Y. Kumagai, F. Oba, and I. Tanaka, Band structure diagram paths based on crystallography, Comput. Mater. Sci. 128, 140 (2017)

    2017

  24. [33]

    L.-D. Yuan, A. B. Georgescu, and J. M. Rondinelli, Non- relativistic spin splitting at the Brillouin zone center in compensated magnets, Phys. Rev. Lett. 133, 216701 (2024)

    2024

  25. [34]

    J. B. Neaton, C. Ederer, U. V. Waghmare, N. A. Spaldin, and K. M. Rabe, First-principles study of spontaneous polarization in multiferroic BiFeO 3, Phys. Rev. B 71, 014113 (2005)

    2005

  26. [35]

    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 BiFeO 3 multifer- roic thin film heterostructures, Science 299, 1719 (2003)

    2003

  27. [36]

    S. R. Burns, O. Paull, J. Juraszek, V. Nagarajan, and D. Sando, The experimentalist’s guide to the cycloid, or noncollinear antiferromagnetism in epitaxial BiFeO 3, Adv. Mater. 32, 2003711 (2020)

    2020

  28. [37]

    Ederer and N

    C. Ederer and N. A. Spaldin, Weak ferromagnetism and magnetoelectric coupling in bismuth ferrite, Phys. Rev. B 71, 060401 (2005)

    2005

  29. [38]

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

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

    2024 arXiv

  30. [39]

    Bernardini, M

    F. Bernardini, M. Fiebig, and A. Cano, Ruddles- den–Popper and perovskite phases as a material platform for altermagnetism, J. Appl. Phys. 137, 103903 (2025)

    2025

  31. [40]

    J. Dong, K. Wu, M. Zhu, F. Zheng, X. Li, and J. Zhang, Nonrelativistic spin-splitting multiferroic antiferromag- net and compensated ferrimagnet with zero net magne- tization (2025), arXiv:2501.02914

    2025 arXiv

  32. [41]

    R. Dong, R. Cao, D. Tan, and R. Fei, Crystal symmetry selected pure spin photocurrent in altermagnetic insula- tors, Phys. Rev. B 111, 195210 (2025)

    2025

  33. [42]

    D. J. Chadi and M. L. Cohen, Special points in the Bril- louin zone, Phys. Rev. B 8, 5747 (1973)

    1973

  34. [43]

    D. J. Chadi and M. L. Cohen, Electronic structure of Hg1−xCdxTe alloys and charge-density calculations using representativek points, Phys. Rev. B 7, 692 (1973)

    1973

  35. [44]

    J. D. Joannopoulos and M. L. Cohen, Electronic charge densities for ZnS in the wurtzite and zincblende struc- tures, J. Phys. C: Solid State Phys. 6, 1572 (1973)

    1973

  36. [45]

    Baldereschi, Mean-Value Point in the Brillouin Zone, Phys

    A. Baldereschi, Mean-Value Point in the Brillouin Zone, Phys. Rev. B 7, 5212 (1973)

    1973

  37. [46]

    N. A. Hill, Why are there so few magnetic ferroelectrics?, J. Phys. Chem. B 104, 6694 (2000)

    2000

  38. [48]

    N. A. Spaldin and R. Ramesh, Advances in magnetoelec- tric multiferroics, Nature Mater. 18, 203 (2019)

    2019

  39. [49]

    Fiebig, T

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

    2016

  40. [50]

    H. Wang, H. Liu, M. Ye, and Y. Li, Are there type-III multiferroics? (2025), arXiv:2503.10681

    2025 arXiv

  41. [51]

    W. Sun, C. Yang, W. Wang, Y. Liu, X. Wang, S. Huang, and Z. Cheng, Proposing altermagnetic- ferroelectric type-III multiferroics with robust magneto- electric coupling, Adv. Mater. 2025, 2502575 (2025)

    2025

  42. [52]

    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)

    2025

  43. [53]

    N. A. Benedek and C. J. Fennie, Hybrid improper fer- roelectricity: A mechanism for controllable polarization- magnetization coupling, Phys. Rev. Lett. 106, 107204 (2011)

    2011

  44. [54]

    Z. Fu, Z. G. Yin, N. F. Chen, X. W. Zhang, Y. J. Zhao, Y. M. Bai, Y. Chen, H.-H. Wang, X. L. Zhang, and J. L. Wu, Tetragonal-tetragonal-monoclinic- rhombohedral transition: Strain relaxation of heavily compressed BiFeO3 epitaxial thin films, Appl. Phys. Lett. 104, 052908 (2014)

    2014

  45. [55]

    Sosnowska, T

    I. Sosnowska, T. P. Neumaier, and E. Steichele, Spiral magnetic ordering in bismuth ferrite, J. Phys. C: Solid State Phys. 15, 4835 (1982)

    1982

  46. [56]

    W. F. Brinkman and R. J. Elliott, Theory of spin-space groups, Proc. R. Soc. London, Ser. A. 294, 343 (1966)

    1966

  47. [57]

    Dup´ e, I

    B. Dup´ e, I. C. Infante, G. Geneste, P.-E. Janolin, M. Bibes, A. Barth´ el´ emy, S. Lisenkov, L. Bellaiche, S. Ravy, and B. Dkhil, Competing phases in BiFeO3 thin films under compressive epitaxial strain, Phys. Rev. B 81, 144128 (2010)

    2010

  48. [58]

    A. F. Andreev and V. I. Marchenko, Macroscopic theory of spin waves, Sov. Phys. JETP 43, 794 (1976)

    1976

  49. [59]

    Litvin and W

    D. Litvin and W. Opechowski, Spin groups, Physica 76, 538 (1974)

    1974

  50. [60]

    A. F. Andreev and V. I. Marchenko, Symmetry and the macroscopic dynamics of magnetic materials, Sov. Phys. Usp. 23, 21 (1980)

    1980

  51. [61]

    D. B. Litvin, Spin point groups, Acta Cryst. A 33, 279 (1977)

    1977

  52. [62]

    M. I. Aroyo, A. Kirov, C. Capillas, J. M. Perez-Mato, and H. Wondratschek, Bilbao Crystallographic Server. 15 II. Representations of crystallographic point groups and space groups, Acta Cryst. A 62, 115 (2006)

    2006

  53. [63]

    Aroyo, J

    M. Aroyo, J. Perez-Mato, D. Orobengoa, E. Tasci, G. De La Flor, and A. Kirov, Crystallography online: Bil- bao crystallographic server, Bulg. Chem. Commun. 43, 183 (2011)

    2011

  54. [64]

    Y. Xu, L. Elcoro, Z.-D. Song, B. J. Wieder, M. G. Vergniory, N. Regnault, Y. Chen, C. Felser, and B. A. Bernevig, High-throughput calculations of mag- netic topological materials, Nature 586, 702 (2020)

    2020

  55. [65]

    M. I. Aroyo, J. M. Perez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov, and H. Won- dratschek, Bilbao crystallographic server: I. Databases and crystallographic computing programs, Z. Kristallogr. 221, 15 (2006)

    2006

  56. [66]

    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)

    2022

  57. [67]

    Elcoro, B

    L. Elcoro, B. J. Wieder, Z. Song, Y. Xu, B. Bradlyn, and B. A. Bernevig, Magnetic topological quantum chemistry, Nat. Commun. 12, 5965 (2021)

    2021

  58. [68]

    M. V. Berry, Aspects of degeneracy, in Chaotic Behavior in Quantum Systems (Springer US, 1985) p. 123–140

    1985

  59. [69]

    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)

    2024

  60. [70]

    N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018)

    2018

  61. [71]

    Vanderbilt, Berry Phases in Electronic Structure The- ory (Cambridge University Press, 2018)

    D. Vanderbilt, Berry Phases in Electronic Structure The- ory (Cambridge University Press, 2018)

    2018

  62. [72]

    G-type Antiferromagnetic BiFeO 3 is a Multiferroic g-wave Altermagnet

    J. T. Heron, J. L. Bosse, Q. He, Y. Gao, M. Trassin, L. Ye, J. D. Clarkson, C. Wang, J. Liu, S. Salahuddin, D. C. Ralph, D. G. Schlom, J. ´I˜ niguez, B. D. Huey, and R. Ramesh, Deterministic switching of ferromagnetism at room temperature using an electric field, Nature 516, 3...

    2014 arXiv

  63. [73]

    Bassani and G

    F. Bassani and G. Pastori Parravicini, Electronic states and optical transitions in solids (Pergamon Press, 1975)

    1975

  64. [75]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009)

    2009

  65. [76]

    Giannozzi, O

    P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, et al., Advanced capabilities for materials modelling with Quantum ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017)

    2017

  66. [77]

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

    1996

  67. [78]

    D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013)

    2013

  68. [79]

    H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976)

    1976

  69. [80]

    Kubel and H

    F. Kubel and H. Schmid, Structure of a ferroelectric and ferroelastic monodomain crystal of the perovskite BiFeO 3, Acta Cryst. B 46, 698 (1990)

    1990

  70. [111]

    MSG without SOC

    pseudo-cubic direction (Fig. 1(a)) and three c-glide planes (Fig. 1(b)) intersecting at the three-fold axis. The experimentally reported ground-state magnetic ordering of BFO is a spin cycloid with a period of ≈ 62 nm [53]. In thin films, this long-period cycloid is sup- press...

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