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Hidden altermagnetism

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read PT-symmetric bilayer Cr2SO hides altermagnetism in each layer and reveals it with an electric field.

desk verdict A clean symmetry-based idea with a plausible but numerically fragile material realization; the hidden altermagnetism concept is worth taking seriously. read the letter →

arxiv 2411.13795 v2 pith:IPA6ADB2 submitted 2024-11-21 cond-mat.mtrl-sci

San-Dong Guo This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords hiddenaltermagnetismspinpolarizationPTsymmetrybilayerCr2SOsplittingelectricfieldcontrolantiferromagneticspintronics
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

The paper proposes that a PT-symmetric antiferromagnet—a magnet with both space-inversion and time-reversal symmetry—can hide altermagnetism: its two inversion-partner layers each carry a d-wave spin-split band structure, yet the two split patterns cancel globally, leaving zero net spin polarization. The claim matters because it extends the idea of hidden spin polarization to an antiferromagnetic setting, creating a route to materials with no stray field but with layer-resolved spin texture that can be switched by an electric field. Using density-functional calculations, the paper identifies bilayer Cr2SO as a concrete candidate and shows that an out-of-plane electric field breaks the global inversion symmetry to expose a momentum-dependent spin splitting of about 203 meV at 0.03 V/A, close to the simple eEd estimate of 207 meV.

What carries the argument

The mechanism is the combination of global PT symmetry, which enforces zero net spin polarization, and local $[C_2\|O]$ symmetry, which enforces altermagnetic spin splitting within each sector. The paper also uses a construction rule: take an altermagnetic monolayer as sector B, mirror-reflect it to form the second layer, then rotate by $C_{2z}$ to make the bilayer inversion-symmetric with $P=C_{2z}M_h$. For bilayer Cr2SO, the altermagnetic splitting at the band edges is quantified, and its field dependence is captured by the linear estimate $eEd$, with $e$ the electron charge, $E$ the applied field, and $d=6.91$ Å the interlayer Cr-Cr distance.

What would settle it

A measurement that finds the ground state of bilayer Cr2SO to be AFM2 rather than AFM1, or a spin-resolved photoemission experiment under 0.03 V/A that fails to see a layer-projected spin splitting of about 203 meV at X/Y, would disprove the central claim.

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Extended reading notes

Core claim

The central claim is that a magnetic crystal with global PT symmetry can nevertheless be composed of two inversion-partner sectors that are each altermagnetic, a state the author calls hidden altermagnetism. In such a crystal, energy bands satisfy $E^{\uparrow}(\mathbf{k})=E^{\downarrow}(\mathbf{k})$ globally because $PT$ enforces degeneracy, while within each sector the combined spin-and-lattice symmetry denoted $[C_2\|O]$ (a two-fold spin rotation perpendicular to the spin axis paired with a lattice rotation or mirror) produces momentum-dependent spin splitting. For PT-symmetric bilayer Cr2SO in its AFM1 magnetic ground state, the paper demonstrates this hidden phase and shows that an out-of-plane electric field separates the two layers energetically; the resulting spin splitting between the first and second conduction bands at X/Y reaches 203 meV at 0.03 V/A, matching the eEd estimate of 207 meV within a few percent. With spin-orbit coupling, the in-plane magnetization gives a small valley splitting of about 4 meV in the conduction band and 2 meV in the valence band between the X and Y valleys.

Load-bearing premise

Everything rests on the bilayer choosing the intralayer/interlayer antiferromagnetic AFM1 order as its ground state, but that order wins by only 1.1 meV (S-terminal) and 3.0 meV (O-terminal) per unit cell, an energy difference smaller than typical density-functional error bars.

Editorial extensions

If this is right

  • If bilayer Cr2SO realizes hidden altermagnetism, then an out-of-plane electric field in either direction can expose a layer-resolved spin splitting of order 200 meV at achievable field strengths.
  • The hidden state has globally spin-degenerate bands and zero net magnetization, so it behaves like a conventional antiferromagnet until the field is applied.
  • Because the building block can be any two-dimensional altermagnet, the same stacking procedure could produce hidden altermagnetism in other Cr2O2-type, V2Se2O-type, V2SeTeO-type, and Fe2Se2O-type monolayers.
  • The approximately linear relation between spin splitting and field, captured by $eEd$, gives a simple design rule for estimating the required field in other bilayers.
  • Under spin-orbit coupling, the field-tuned bilayer shows valley polarization between X and Y valleys, with its sign controlled by the magnetization direction.

Reading between the lines

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

  • Editorially, the near-degeneracy of AFM1 and AFM2 (1.1 and 3.0 meV per cell) suggests the hidden phase may be switchable by strain or small magnetic fields, which would make the material more than a proof-of-principle.
  • Editorially, spin-resolved photoemission under an applied gate field is the most direct test; if the predicted 203 meV splitting at 0.03 V/A is observed with opposite spin character on the two layers, the concept is confirmed.
  • Editorially, the same reasoning could extend to twisted bilayer altermagnets, where the twist angle tunes interlayer coupling and therefore the field strength needed to reveal the hidden splitting.
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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

3 major / 4 minor

Summary. The paper introduces the concept of "hidden altermagnetism" for PT-symmetric antiferromagnets: the global PT symmetry forbids net spin splitting, but each of the two inversion-partner sectors is individually altermagnetic, producing nonzero local spin polarization. The authors propose a bilayer stacking construction, identify bilayer Cr2SO as a candidate, and use DFT+U to show that an out-of-plane electric field breaks global P, revealing momentum-dependent spin splitting with layer character. They report a field-induced splitting of about 203 meV at 0.03 V/Å, close to the eEd estimate of 207 meV, and discuss SOC-induced valley splitting.

Significance. If the material prediction holds, the concept of hidden altermagnetism is a valuable extension of hidden spin polarization to antiferromagnetic systems, and the bilayer stacking recipe provides a clear design principle. The paper explicitly separates the general symmetry construction from the material example, and the eEd consistency check for the field-induced splitting is a useful quantitative anchor. However, the central material prediction rests on a magnetic ground state whose energy margin is only 1–3 meV per cell, and the zero-field hidden local spin polarization is not explicitly demonstrated with layer-resolved data. The conceptual contribution is sound; the numerical material claim needs strengthening.

major comments (3)
  1. [Material realization] The AFM1 ground state, which carries the PT symmetry required for hidden altermagnetism, is reported to be lower than AFM2 by only 1.1 meV per cell (S-terminal) and 3.0 meV per cell (O-terminal). These margins are within typical GGA+U errors arising from the Hubbard U value, the exchange-correlation functional, and the vdW correction scheme. No U-dependence, functional-dependence, or vdW-scheme tests are reported, and no convergence data for k-points/cutoff are given for this energy difference. Since the entire hidden-altermagnetism prediction vanishes if AFM2 becomes the ground state, the material realization claim is not yet robust. Please compute ΔE(AFM2−AFM1) as a function of U (e.g., 2–5 eV), with alternative functionals (e.g., SCAN or HSE) and alternative vdW corrections, and report the magnetic moments and energy convergence.
  2. [Figure 2 and Section 'Material realization'] Hidden altermagnetism requires that, at zero electric field, each inversion-partner sector individually shows altermagnetic spin splitting while the global PT symmetry keeps the total bands spin-degenerate. The manuscript argues this from symmetry and shows only global band structures in Figure 2(e,f); no layer-resolved or sublattice-resolved spin projection is provided at E=0. To support the central claim for bilayer Cr2SO, please show layer- or sector-resolved spin-polarized bands (or real-space spin density integrated per sector) at E=0, demonstrating that the two sectors have opposite local spin polarization while the global spectrum remains degenerate.
  3. [Discussion and Conclusion] The interlayer exchange energy implied by the 1–3 meV/cell AFM1–AFM2 difference suggests a low magnetic ordering temperature for the bilayer. Since the paper states the hidden altermagnetism 'can be confirmed in experiment' and an electric field can be used to 'observe' it, the experimental feasibility depends on the magnetic order surviving at accessible temperatures. Please provide at least an estimate of the magnetic ordering temperature (e.g., via a simple mean-field estimate or Monte Carlo treatment of the interlayer exchange) or explicitly temper the experimental-observability claim until the magnetic ground state is better established.
minor comments (4)
  1. [Introduction] There are several typographical errors: 'takeing' should be 'taking', 'demonstrat' should be 'demonstrate', and 'Halll' should be 'Hall' in 'Anomalous Halll/Nernst effect'.
  2. [Figure 4] The axis label in Figure 4 appears garbled with font-encoding artifacts ('E/uni00000003/uni0000000b/...'); please replace with a properly typeset label such as 'E (V/Å)'.
  3. [References] Reference [41] to the Supplemental Material is given as 'at []' with an empty placeholder; please provide the correct link or DOI.
  4. [Figure 3] In the Figure 3 caption, 'E=+0.00' should simply be 'E=0.00' or 'E=0' for clarity.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central hidden-altermagnetism prediction rests on fresh DFT and a symmetry construction, not on fitted parameters or load-bearing self-citations.

full rationale

The claimed derivation chain is a symmetry-based design principle (PT-symmetric stacking of two altermagnetic sectors) followed by fresh first-principles calculations for bilayer Cr2SO. The monolayer altermagnetism is not merely imported from Ref. [29]: the paper recomputes and plots the monolayer band structure (Fig. 2(d)) showing d-wave spin splitting. The PT-symmetric bilayer is constructed in the paper via mirror plus C2z operations, and the resulting global spin degeneracy follows from the PT symmetry of the AFM1 state, not from any fitted assumption. The only quantitative comparison, the field-induced spin splitting of about 203 meV versus the eEd estimate of about 207 meV, uses the interlayer Cr-Cr distance d=6.91 Å as a structural input and E=0.03 V/Å as the applied field; d is not a parameter tuned to match the DFT splitting, and the eEd formula is cited to independent work (Ref. [25]) and used only as a consistency check. Self-citations (Refs. [24], [27], [29]) appear in background statements about valley polarization, layer-dependent potentials, and monolayer Cr2SO, but none is load-bearing for the central hidden-altermagnetism claim. The small 1.1/3.0 meV energy difference between AFM1 and AFM2 is a numerical robustness concern (possibly within DFT error bars), not a circularity. No equation in the paper reduces to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particles, forces, or fields. The main free parameter is the Hubbard U, which is a standard DFT input. The assumptions are the reliability of PBE+U for this material, the stability of the AFM1 magnetic ground state, and the validity of the spin-group symmetry analysis. The magnetic ground-state energy difference is the most fragile assumption.

free parameters (1)
  • Hubbard U on Cr d-orbitals = 3.55 eV
    The Dudarev rotationally invariant U is chosen from prior literature, not derived or fitted within this paper. It directly affects the band gap, spin splitting magnitude, and magnetic ordering energies, so the quantitative predictions depend on this hand-set parameter.
assumptions (4)
  • domain assumption DFT with PBE+U and DFT-D3 provides a reliable description of the electronic structure and magnetic ground state of Cr2SO bilayers.
    All conclusions rely on VASP calculations with U=3.55 eV, a 500 eV cutoff, and a 15x15x1 k-mesh. No convergence tests or comparisons to experiment or higher-level theory are given, so the quantitative reliability rests on this assumption.
  • domain assumption The magnetic ground state is the collinear AFM1 ordering with PT symmetry.
    The paper reports that AFM1 is lower than AFM2 by only 1.1 and 3.0 meV per unit cell for the S- and O-terminal bilayers. Hidden altermagnetism depends on this specific magnetic ordering, and such small energy differences are within typical DFT error bars.
  • standard math The symmetry operators [C2||O] and [C2||P] can be applied independently to define altermagnetic sectors within the PT-symmetric bilayer.
    The derivation of local momentum-dependent spin splitting uses the combined spin rotation C2 and lattice operation O or P, following standard spin-group analysis for altermagnets. This is an accepted group-theoretic decomposition.
  • standard math The global P operator in the bilayer is realized as C2z*Mh, where Mh is a mirror operation and C2z is a two-fold rotation.
    The stacking construction in Figure 1 defines sector B, mirrors it to create an upper layer, and rotates the upper layer by 180 degrees to form a structure with inversion symmetry P=C2z*Mh. This is a geometric construction, not an empirical input.

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Pith. "Pith review of Hidden altermagnetism." pith.science (2026). https://pith.science/paper/IPA6ADB2

@misc{pith2026241113795,
  author       = {Pith},
  title        = {Pith review of: Hidden altermagnetism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IPA6ADB2}},
  note         = {Machine review of arXiv:2411.13795}
}
abstract

Hidden spin polarization (HSP) with zero net spin polarization in total but non-zero local spin polarization has been proposed in certain nonmagnetic centrosymmetric compounds, where the individual sectors forming the inversion partners are all inversion asymmetry. Here, we extend this idea to antiferromagnetic materials with $PT$ symmetry (the joint symmetry of space inversion symmetry ($P$) and time-reversal symmetry ($T$)), producing zero net spin polarization in total, but either of the two inversion-partner sectors possesses altermagnetism, giving rise to non-zero local spin polarization in the real space, dubbed "hidden altermagnetism". By first-principle calculations, we predict that $PT$-symmetric bilayer $\mathrm{Cr_2SO}$ can serve as a possible candidate showing altermagnetic HSP. By applying an external electric field to break the global $P$ symmetry, the hidden altermagnetism can be separated and observed experimentally. Our works extend the hidden physics, and will also advance the theoretical and experimental search for new type of spin-polarized materials.

Figures

Figures reproduced from arXiv: 2411.13795 by the authors.

Figure 1
Figure 1. FIG. 1. (Color online)(a): For [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (d), showing altermagnetic spin splitting of d￾wave symmetry. The [C2∥Mxy] symmetry of Cr2SO leads to that:E↑(kx, ky)=[C2∥Mxy]E↑(kx, ky)=E↓(ky, kx), giv￾ing rise to spin degeneracy along Γ-M line in BZ. For other high symmetry paths, the spin-splitting can be ob￾served. It is clearly seen that two valleys at X and Y high￾symmetry points for both conduction and valence bands are related by [C2∥Mxy] symmetry, producin… view at source ↗
Figure 3
Figure 3. FIG. 3. (Color online)For O-terminal bilayer Cr [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (Color online) For O-terminal bilayer Cr [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (Color online) For O-terminal bilayer Cr [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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Works this paper leans on

43 extracted references · 3 canonical work pages

  1. [1]

    Dresselhaus, Spin-orbit coupling effects in zinc blende structures, Phys

    G. Dresselhaus, Spin-orbit coupling effects in zinc blende structures, Phys. Rev. 100, 580 (1955)

    1955

  2. [2]

    Y. A. Bychkov and E. I. Rashba, Oscillatory effects and the magnetic susceptibility of carriers in inversion layers, J. Phys. C Solid State Phys. 17, 6039 (1984)

    1984

  3. [3]

    Zhang, Q

    X. Zhang, Q. Liu, J. W. Luo, A. J. Freeman and A. Zunger, Hidden spin polarization in inversion-symmetric bulk crystals, Nat. Phys. 10, 387 (2014)

    2014

  4. [4]

    Cheng, J

    C. Cheng, J. T. Sun, X. R. Chen, and S. Meng, Hid- den spin polarization in the 1T-phase layered transition- metal dichalcogenides MX 2 (M= Zr, Hf; X= S, Se, Te), Sci. Bull. 63, 85 (2018)

    2018

  5. [5]

    Q. Liu, X. Zhang, H. Jin, K. Lam, J. Im, A. J. Free- man, and A. Zunger, Search and design of nonmagnetic centrosymmetric layered crystals with large local spin po- larization, Phys. Rev. B 91, 235204 (2015)

    2015

  6. [6]

    T. T. Debela, and H. S. Kang, Phase polymorphism and electronic structures of TeSe 2, J. Mater. Chem. C 6, 10218 (2018)

    2018

  7. [7]

    Razzoli, T

    E. Razzoli, T. Jaouen, M. L. Mottas, B. Hildebrand, G. Monney, A. Pisoni, S. Muff, M. Fanciulli, N. C. Plumb, V. A. Rogalev, V. N. Strocov, J. Mesot, M. Shi, J. H. Dil, H. Beck, and P. Aebi, Selective Probing of Hid- den Spin-Polarized States in Inversion-Symmetric Bulk MoS2, Phys. Rev. Lett. 118, 086402 (2017)

    2017

  8. [8]

    Zhang, S

    K. Zhang, S. Zhao, Z. Hao, S. Kumar, E. F. Schwier, Y. Zhang, H. Sun, Y. Wang, Y. Hao, X. Ma, C. Liu, L. Wang, X. Wang, K. Miyamoto, T. Okuda, C. Liu, J. Mei, K. Shimada, C. Chen, and Q. Liu, Observation of Spin-Momentum-Layer Locking in a Centrosymmetric Crystal, Phys. Rev. Lett. 127, 126402 (2021)

    2021

Show all 43 references
  1. [9]

    Gatti, D

    G. Gatti, D. Gosalbez-Mart ?nez, S. Roth, M. Fanciulli, M. Zacchigna, M. Kallane, K. Rossnagel, C. Jozwiak, A. Bostwick, E. Rotenberg, A. Magrez, H. Berger, I. Vobornik, J. Fujii, O. V. Yazyev, M. Grioni, and A. Crepaldi, Hidden bulk and surface effects in the spin po- larizat...

    2021

  2. [10]

    H. J. Qian, X. Zhang, C. M. Liu, Q. Jiang, W. J. Liu, H. M. Zha, D. Y. Wang, X. P. Shen, M. Ye, Y. F. Guo, and S. Qiao, Layer-locked spin states revealed in the cen- trosymmetric nodal-line semimetal HfSiS, Phys. Rev. B 104, 035145 (2021)

    2021

  3. [11]

    W. Yao, E. Wang, H. Huang, K. Deng, M. Yan, K. Zhang, K. Miyamoto, T. Okuda, L. Li, Y. Wang, H. Gao, C. Liu, W. Duan, and S. Zhou, Direct observation of spin-layer locking by local Rashba effect in monolayer semiconduct- ing PtSe2 film, Nat. Commun. 8, 14216 (2017)

    2017

  4. [12]

    S. Guan, J. X. Xiong, Z. Wang, and J. W. Luo, Progress of hidden spin polarization in inversion-symmetric crys- tals, Sci. China-Phys. Mech. Astron. 65, 237301 (2022)

    2022

  5. [13]

    J. H. Ryoo and C. H. Park, Hidden orbital polarization in diamond, silicon, germanium, gallium arsenide and lay- ered materials. NPG Asia Mater. 9, e382 (2017)

    2017

  6. [14]

    R. Chen, H. P. Sun, M. Gu, C. B. Hua, Q. Liu1, H. Z. Lu and X. C. Xie, Layer Hall effect induced by hidden Berry curvature in antiferromagnetic insulators, Natl Sci Rev, 11, nwac140 (2024)

    2024

  7. [15]

    ˘Smejkal, J

    L. ˘Smejkal, 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

  8. [16]

    Mazin, Altermagnetisma new punch line of fundamen- tal magnetism, Phys

    I. Mazin, Altermagnetisma new punch line of fundamen- tal magnetism, Phys. Rev. X 12, 040002 (2022)

    2022

  9. [17]

    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

  10. [18]

    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

  11. [19]

    Hayami and H

    S. Hayami and H. Kusunose, Essential role of the anisotropic magnetic dipole in the anomalous Hall effect, Phys. Rev. B 103, L180407 (2021)

    2021

  12. [20]

    Cheong and F.-T

    S.-W. Cheong and F.-T. Huang, Altermagnetism with non-collinear spins, npj Quantum Mater. 9, 13 (2024)

    2024

  13. [21]

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

    2024

  14. [22]

    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)

    2024

  15. [23]

    R. He, D. Wang, N. Luo, J. Zeng, K. Q. Chen and L. M. Tang, Nonrelativistic Spin-Momentum Coupling in An- tiferromagnetic Twisted Bilayers, Phys. Rev. Lett. 130, 046401 (2023)

    2023

  16. [24]

    S. D. Guo, Y. Liu, J. Yu and C. C. Liu, Valley polariza- tion in twisted altermagnetism, arXiv:2406.13950 (2024)

    2024 arXiv

  17. [25]

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

    2024

  18. [26]

    X. Duan, J. Zhang, Z. Zhang, I ˘Zuti´c and T. Zhou, An- tiferroelectric Altermagnets: Antiferroelectricity Alters Magnets, arXiv:2410.06071 (2024)

    2024 arXiv

  19. [27]

    S. D. Guo, X. S. Guo and G. Wang, Valley polarization in two-dimensional tetragonal altermagnetism, Phys. Rev. B 110, 184408 (2024)

    2024

  20. [28]

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

    2021

  21. [29]

    Guo, X.-S

    S.-D. Guo, X.-S. Guo, K. Cheng, K. Wang, and Y. S. Ang, Piezoelectric altermagnetism and spin-valley polar- ization in Janus monolayer Cr2SO, Appl. Phys. Lett 123, 082401 (2023)

    2023

  22. [30]

    X. Chen, D. Wang, L. Y. Li and B. Sanyal, Giant spin- 7 splitting and tunable spin-momentum locked transport in room temperature collinear antiferromagnetic semimetal- lic CrO monolayer, Appl. Phys. Lett.123, 022402 (2023)

    2023

  23. [31]

    Y. Zhu, T. Chen, Y. Li, L. Qiao, X. Ma, C. Liu, T. Hu, H. Gao and W. Ren, Multipiezo Effect in Altermagnetic V2SeTeO Monolayer, Nano Lett. 24, 472 (2024)

    2024

  24. [32]

    Y. Wu, L. Deng, X. Yin, J. Tong, F. Tian and X. Zhang, Valley-Related Multipiezo Effect and Noncollinear Spin Current in an Altermagnet Fe 2Se2O Monolayer, Nano Lett. 24, 10534 (2024)

    2024

  25. [33]

    C. Y. Tan, Z. F. Gao, H. C. Yang, K. Liu, P. J. Guo and Z. Y. Lu, Bipolarized Weyl semimetals and quan- tum crystal valley Hall effect in two-dimensional alter- magnetic materials, arXiv:2406.16603 (2024)

    2024 arXiv

  26. [34]

    Hohenberg and W

    P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140, A1133 (1965)

    1964

  27. [35]

    Kresse, Ab initio molecular dynamics for liquid met- als, J

    G. Kresse, Ab initio molecular dynamics for liquid met- als, J. Non-Cryst. Solids 193, 222 (1995)

    1995

  28. [36]

    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, Comput. Mater. Sci. 6, 15 (1996)

    1996

  29. [37]

    Kresse and D

    G. Kresse and D. Joubert, From ultrasoft pseudopoten- tials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999)

    1999

  30. [38]

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

    1996

  31. [39]

    S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spec- tra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57, 1505 (1998)

    1998

  32. [40]

    Grimme, S

    S. Grimme, S. Ehrlich and L. Goerigk, Effect of the damping function in dispersion corrected density func- tional theory, J. Comput. Chem. 32, 1456 (2011)

    2011

  33. [41]

    See Supplemental Material at [] for the magnetic configu- rations; the energy difference between AFM2 and AFM1 ordering vs E; the related energy band structures, the MAE vs E

  34. [42]

    Hu, Half-metallic antiferromagnet as a prospective material for spintronics, Adv

    X. Hu, Half-metallic antiferromagnet as a prospective material for spintronics, Adv. Mater. 24, 294 (2012)

    2012

  35. [43]

    Jungwirth, J

    T. Jungwirth, J. Sinova, A. Manchon, X. Marti, J. Wun- derlich and C. Felser, The multiple directions of antifer- romagnetic spintronics, Nat. Phys. 14, 200 (2018)

    2018

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