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arxiv: 2602.08790 · v2 · pith:JYMQQ2PUnew · submitted 2026-02-09 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall

d-wave Surface Altermagnetism in Centrosymmetric Collinear Antiferromagnets

Ersoy Sasioglu , Ingrid Mertig , Samir Lounis This is my paper

Pith reviewed 2026-05-21 13:20 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hall
keywords surface altermagnetismcentrosymmetric antiferromagnetsd-wave spin splittingcollinear antiferromagnetsantiunitary symmetrysublattice exchangenonrelativistic spin polarization
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The pith

Surface altermagnetism emerges without sublattice symmetry

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

Centrosymmetric collinear antiferromagnets have surfaces where inversion symmetry is broken, potentially allowing nonrelativistic d-wave spin splitting known as surface altermagnetism. This effect occurs only when no antiunitary symmetry survives at the surface that exchanges the two antiferromagnetically coupled sublattices and enforces spin degeneracy. The paper demonstrates this with symmetry analysis and first-principles calculations for V3Al and BaMn2Sb2, but shows that in MnPt a surviving translation-time-reversal symmetry keeps spins degenerate. The mechanism works across multiple classes of antiferromagnets and holds with spin-orbit coupling included, although heavier elements may see reduced spin polarization.

Core claim

Surface altermagnetism, a nonrelativistic d-wave spin splitting, appears at the surfaces of centrosymmetric collinear antiferromagnets only when broken inversion symmetry is not accompanied by a surviving antiunitary symmetry that exchanges the two antiferromagnetically coupled surface sublattices.

What carries the argument

Absence of an antiunitary symmetry at the surface that exchanges the two antiferromagnetically coupled sublattices and would otherwise enforce spin degeneracy.

Load-bearing premise

The chosen G-type antiferromagnets and their surface terminations represent the broader class, and first-principles calculations without spin-orbit coupling correctly capture the presence or absence of the sublattice-exchanging symmetry.

What would settle it

Detection of spin degeneracy at V3Al or BaMn2Sb2 surfaces, or spin splitting at the MnPt surface, would contradict the mechanism.

Figures

Figures reproduced from arXiv: 2602.08790 by Ersoy Sasioglu, Ingrid Mertig, Samir Lounis.

Figure 1
Figure 1. Figure 1: FIG. 1. Bulk and surface magnetic structures and symmetry conditions. (a) Bulk magnetic configurations of the centrosym [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Surface altermagnetic electronic structure of centrosymmetric AFMs. (a) Bulk and surface band structures of the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Layer-resolved surface altermagnetic states in V [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Broken inversion symmetry at the surfaces of centrosymmetric collinear antiferromagnets lifts combined inversion and time-reversal symmetry ($PT$) and can, in principle, enable nonrelativistic d-wave spin splitting, termed surface altermagnetism. Combining symmetry analysis with first-principles calculations, we show that surface inversion breaking, while necessary, is not sufficient for this effect. Surface altermagnetism emerges only when no antiunitary symmetry survives at the surface that exchanges the two antiferromagnetically coupled surface sublattices and enforces spin degeneracy. We demonstrate this mechanism explicitly for the centrosymmetric G-type antiferromagnets V$_3$Al and BaMn$_2$Sb$_2$, and contrast it with MnPt, where a sublattice-exchanging symmetry survives at the surface in the form of translation-time-reversal symmetry ($tT$), thereby preserving spin degeneracy despite broken inversion symmetry. The mechanism is shown to apply across multiple classes of centrosymmetric antiferromagnets and remains robust against spin-orbit coupling, although relativistic spin mixing in heavier-element compounds may reduce the observable spin polarization. These results establish a symmetry-based route toward realizing robust nonrelativistic momentum-dependent spin polarization at antiferromagnetic surfaces and interfaces.

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

0 major / 3 minor

Summary. The manuscript claims that d-wave surface altermagnetism emerges at the surfaces of centrosymmetric collinear antiferromagnets when inversion symmetry is broken but no antiunitary symmetry survives that exchanges the two antiferromagnetically coupled surface sublattices (thereby enforcing spin degeneracy). This is established via general symmetry analysis combined with first-principles DFT calculations (no SOC) on V3Al and BaMn2Sb2 surfaces, contrasted with MnPt where tT symmetry persists and preserves degeneracy. The mechanism is asserted to apply across multiple classes of such antiferromagnets and to remain robust against spin-orbit coupling, although relativistic effects may reduce observable polarization in heavier compounds.

Significance. If the central claim holds, the work supplies a symmetry-based route to nonrelativistic momentum-dependent spin polarization at antiferromagnetic surfaces and interfaces, with clear relevance to antiferromagnetic spintronics. Credit is due for the parameter-free symmetry derivation, the logical clarity of the analysis, and the explicit contrast between cases with and without the protecting symmetry; these elements avoid ad-hoc parameters and provide falsifiable predictions via the identified condition.

minor comments (3)
  1. The first use of the abbreviation tT (translation-time-reversal) should be accompanied by an explicit definition to aid readers.
  2. Figure captions for the surface band structures would benefit from a short statement of the surface termination and slab thickness used in the calculations.
  3. A small number of typographical inconsistencies appear in the reference list (e.g., journal abbreviations); these should be standardized.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their thorough and positive evaluation of our manuscript. The summary accurately captures our central claim and the supporting evidence from symmetry analysis and DFT calculations. We appreciate the recognition of the parameter-free nature of the symmetry derivation and the explicit contrast between protected and unprotected cases. Since the referee recommends minor revision but lists no specific major comments requiring substantive changes, we interpret this as a request for minor clarifications or editorial adjustments, which we will incorporate.

Circularity Check

0 steps flagged

No significant circularity; symmetry analysis is self-contained

full rationale

The paper derives its central claim via standard symmetry analysis: broken surface inversion lifts PT but spin degeneracy persists if an antiunitary symmetry (such as tT) survives that exchanges the two AF-coupled sublattices. This is applied to chosen G-type terminations and verified by DFT (no SOC) on V3Al, BaMn2Sb2 versus MnPt. No parameter is fitted and then relabeled as a prediction, no self-citation chain is load-bearing for the uniqueness of the symmetry condition, and the result does not reduce to a definition or ansatz imported from the authors' prior work. The derivation remains independent of the specific material examples chosen.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard group-theory symmetry constraints for magnetic crystals and conventional density-functional theory approximations; no new free parameters, ad-hoc axioms, or postulated entities are introduced.

axioms (1)
  • standard math Symmetry operations of the crystal and magnetic lattice determine whether spin degeneracy is enforced at the surface.
    Invoked throughout the symmetry analysis section of the abstract.

pith-pipeline@v0.9.0 · 5758 in / 1247 out tokens · 41049 ms · 2026-05-21T13:20:29.005813+00:00 · methodology

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Works this paper leans on

42 extracted references · 42 canonical work pages

  1. [1]

    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- ence Advances6, eaaz8809 (2020)

    work page 2020

  2. [2]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond conven- tional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Physical Review X12, 031042 (2022)

    work page 2022

  3. [3]

    ˇSmejkal, A

    L. ˇSmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous hall antiferromagnets, Na- ture Reviews Materials7, 482 (2022)

    work page 2022

  4. [4]

    Y. Guo, Y. Zhang, R. Gonz´ alez-Hern´ andez, L.ˇSmejkal, J. Sinova, and T. Jungwirth, Spin-split collinear antifer- romagnets: A large-scaleab initiostudy, Materials Today Physics32, 100991 (2023)

    work page 2023

  5. [5]

    I. I. Mazin, Altermagnetism in MnTe: Origin, predicted manifestations, and routes to detwinning, Physical Re- view B107, L100418 (2023)

    work page 2023

  6. [6]

    Jungwirth, L

    T. Jungwirth, L. ˇSmejkal, J. Sinova, R. Gonz´ alez- Hern´ andez,et al., Altermagnetic spintronics, arXiv preprint https://doi.org/10.48550/arXiv.2508.09748 (2025), arXiv:2508.09748, 2508.09748

    work page doi:10.48550/arxiv.2508.09748 2025

  7. [7]

    Giuli, N

    N. Giuli, N. Bittner, M. T. Mercaldo, M. Cuoco, P. Gen- tile, S. M. Winter, and R. Valent´ ı, Interaction-driven itinerant magnetism in altermagnets, Phys. Rev. B111, L020401 (2025)

    work page 2025

  8. [8]

    Fenget al., An anomalous hall effect in altermagnetic ruthenium dioxide, Nature Electronics5, 735 (2022)

    Z. Fenget al., An anomalous hall effect in altermagnetic ruthenium dioxide, Nature Electronics5, 735 (2022)

    work page 2022

  9. [9]

    Z. Lin, D. Chen, W. Lu, X. Liang, S. Feng, K. Yamagami, J. Osiecki, M. Leandersson, B. Thiagarajan, J. Liu,et al., Bulk band structure of RuO 2 measured with soft x-ray angle-resolved photoemission spectroscopy, Phys. Rev. B 111, 134450 (2025)

    work page 2025

  10. [10]

    S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee, B. Seok, J. Kim, B. G. Park, L. ˇSmejkal, C.-J. Kang, and C. Kim, Broken kramers degeneracy in altermagnetic MnTe, Phys. Rev. Lett.132, 036702 (2024)

    work page 2024

  11. [11]

    Reimers, L

    S. Reimers, L. Odenbreit, L. ˇSmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. Jaeschke Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty, T. Denneulin, W. Shi, R. E. Dunin-Borkowski, S. Das, M. Kl¨ aui, J. Sinova, and M. Jourdan, Direct observation of altermagnetic band splitting in CrSb thin films, Nat. Commun.15, 2116 (2024). 6

    work page 2024

  12. [12]

    Jiang, M

    B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei, Y. Sun, Y. Huang, X. Zheng, Y. Peng, L. He, S. Li, J. Luo, Z. Li, G. Chen, H. Li, H. Weng, and T. Qian, A metallic room-temperature d- wave altermagnet, Nat. Phys.21, 754 (2025)

    work page 2025

  13. [13]

    Biniskos, M

    N. Biniskos, M. dos Santos Dias, S. Agrestini, D. Svit´ ak, K.-J. Zhou, J. Posp´ ıˇ sil, and P.ˇCerm´ ak, Systematic map- ping of altermagnetic magnons by resonant inelastic x- ray circular dichroism, Nature Communications16, 9311 (2025)

    work page 2025

  14. [14]

    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)

    work page 2020

  15. [15]

    Sødequist and T

    J. Sødequist and T. Olsen, Two-dimensional al- termagnets from high throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects, Appl. Phys. Lett.124, https://doi.org/10.1063/5.0198285 (2024)

    work page doi:10.1063/5.0198285 2024

  16. [16]

    Brekke, A

    B. Brekke, A. Brataas, and A. Sudbø, Two-dimensional altermagnets: Superconductivity in a minimal micro- scopic model, Phys. Rev. B108, 224421 (2023)

    work page 2023

  17. [17]

    R. Xu, Y. Gao, and J. Liu, Chemical design of mono- layer altermagnets, National Science Review13, nwaf528 (2026)

    work page 2026

  18. [18]

    Jungwirth, J

    T. Jungwirth, J. Sinova, R. M. Fernandes, Q. Liu, H. Watanabe, S. Murakami, S. Nakatsuji, and L.ˇSmejkal, Symmetry, microscopy and spectroscopy signatures of al- termagnetism, Nature649, 837 (2026)

    work page 2026

  19. [19]

    X. Wan, S. Mandal, Y. Guo, and K. Haule, High- throughput search for metallic altermagnets by embed- ded dynamical mean field theory, Phys. Rev. Lett.135, 106501 (2025)

    work page 2025

  20. [20]

    Chang, I

    P.-H. Chang, I. I. Mazin, and K. D. Be- lashchenko, Inverse lieb materials: Altermag- netism and more, arXiv preprint arXiv:2508.04839 https://doi.org/10.48550/arXiv.2508.04839 (2025)

    work page doi:10.48550/arxiv.2508.04839 2025

  21. [21]

    Bhattarai, P

    R. Bhattarai, P. Minch, and T. D. Rhone, High- throughput screening of altermagnetic materials, Phys. Rev. Mater.9, 064403 (2025)

    work page 2025

  22. [22]

    Brahimi, D

    S. Brahimi, D. Prakash Rai, and S. Lounis, Confinement- induced altermagnetism in ruo2 ultrathin films, J. of Phys.: Condens. Matter37, 395801 (2025)

    work page 2025

  23. [23]

    L. Bai, W. Feng, S. Liu, L. ˇSmejkal, Y. Mokrousov, and Y. Yao, Altermagnetism: Exploring new frontiers in mag- netism and spintronics, Advanced Functional Materials 34, 2409327 (2024)

    work page 2024

  24. [24]

    Tamang, S

    R. Tamang, S. Gurung, D. P. Rai, S. Brahimi, and S. Lou- nis, Altermagnetism and altermagnets: A brief review, Magnetism5, 17 (2025)

    work page 2025

  25. [25]

    Matsuda, H

    J. Matsuda, H. Watanabe, and R. Arita, Multifer- roic collinear antiferromagnets with hidden altermag- netic spin splitting, Physical Review Letters134, 226703 (2025)

    work page 2025

  26. [26]

    P. A. McClarty and J. G. Rau, Landau theory of alter- magnetism, Physical review letters132, 176702 (2024)

    work page 2024

  27. [27]

    Sivianes, F

    J. Sivianes, F. J. d. Santos, and J. Iba˜ nez-Azpiroz, Opti- cal signatures of spin symmetries in unconventional mag- nets, Physical Review Letters134, 196907 (2025)

    work page 2025

  28. [28]

    D. Jo, D. Go, Y. Mokrousov, P. M. Oppeneer, S.-W. Cheong, and H.-W. Lee, Weak ferromagnetism in alter- magnets from alternating g-tensor anisotropy, Physical review letters134, 196703 (2025)

    work page 2025

  29. [29]

    R. M. Sattigeri, G. Cuono, and C. Autieri, Altermagnetic surface states: towards the observation and utilization of altermagnetism in thin films, interfaces and topological materials, Nanoscale15, 16998 (2023)

    work page 2023

  30. [30]

    E. I. Rashba, Properties of semiconductors with an ex- tremum loop. i. cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop, Soviet Physics Solid State2, 1109 (1960)

    work page 1960

  31. [31]

    Dresselhaus, Spin-orbit coupling effects in zinc blende structures, Physical Review100, 580 (1955)

    G. Dresselhaus, Spin-orbit coupling effects in zinc blende structures, Physical Review100, 580 (1955)

    work page 1955

  32. [32]

    Supplemental material for ”d-wave surface alter- magnetism in centrosymmetric collinear antiferromag- nets”,https://link.aps.org/supplemental/10.1103/ PhysRevLett.XXX.YYYYY, contains computational de- tails, additional figures, and extended materials classi- fication

    work page

  33. [33]

    Smidstrup, T

    S. Smidstrup, T. Markussen, P. Vancraeyveld, J. Wellen- dorff, J. Schneider, T. Gunst, B. Verstichel, D. Stradi, P. A. Khomyakov, U. G. Vej-Hansen, M.-E. Lee, S. T. Chill, F. Rasmussen, G. Penazzi, F. Corsetti, A. Ojan- per¨ a, K. Jensen, M. L. N. Palsgaard, U. Martinez, A. Blom, M. Brandbyge, and K. Stokbro, QuantumATK: an integrated platform of electron...

    work page 2019

  34. [34]

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

    work page 1996

  35. [35]

    M. J. Van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G.-M. Rig- nanese, The PseudoDojo: Training and grading a 85 ele- ment optimized norm-conserving pseudopotential table, Comput. Phys. Commun.226, 39 (2018)

    work page 2018

  36. [36]

    Galanakis, S ¸

    I. Galanakis, S ¸. Tırpancı, K. ¨Ozdo˘ gan, and E. S ¸a¸ sıo˘ glu, Itinerant g-type antiferromagnetism in d 0 3-type v 3 z (z= al, ga, in) compounds: A first-principles study, Physical Review B94, 064401 (2016)

    work page 2016

  37. [37]

    Khmelevskyi, First-principles modeling of longitudinal spin fluctuations in itinerant electron antiferromagnets: High n´ eel temperature in the V3Al alloy, Phys

    S. Khmelevskyi, First-principles modeling of longitudinal spin fluctuations in itinerant electron antiferromagnets: High n´ eel temperature in the V3Al alloy, Phys. Rev. B 94, 024420 (2016)

    work page 2016

  38. [38]

    M. Tas, E. S ¸a¸ sıo˘ glu, C. Friedrich, S. Bl¨ ugel, and I. Galanakis, Design of L2 1-type antiferromag- netic semiconducting full-heusler compounds: A first principles DFT+GW study, J. Appl. Phys.121, https://doi.org/10.1063/1.4975351 (2017)

    work page doi:10.1063/1.4975351 2017

  39. [39]

    X. Chen, Y. Huang, J. Liu, H. Yuan, and H. Chen, Ef- fects of Ga substitution on electronic and thermoelectric properties of gapless semiconductor V3Al, RSC advances 9, 3847 (2019)

    work page 2019

  40. [40]

    J. An, A. S. Sefat, D. J. Singh, and M.-H. Du, Electronic structure and magnetism in BaMn 2As2 and BaMn 2Sb2, Phys. Rev. B79, 075120 (2009)

    work page 2009

  41. [41]

    N. S. Sangeetha, V. Smetana, A.-V. Mudring, and D. C. Johnston, Antiferromagnetism in semiconducting SrMn2Sb2 and BaMn 2Sb2 single crystals, Phys. Rev. B 97, 014402 (2017)

    work page 2017

  42. [42]

    Zhang, Z

    Q. Zhang, Z. Diao, H. Cao, A. Saleheen, R. Rishi, A. Sap- kota,et al., Structure-property relationship in layered BaMn2Sb2 and Ba 2Mn3Sb2O2, Physical Review B99, 184416 (2019)

    work page 2019