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Coupled Spin-Density-Wave and Bond-Order Driven Metal-Insulator Transition in Altermagnetic CsCr$_2$S$_2$O

T0 review · 2 major / 5 minor · reviewed 2026-07-31 · grok-4.5

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Pith's one-line read In CsCr2S2O a pre-existing altermagnetic order activates a coupled secondary spin-density wave and Cr–S bond order that together drive the metal-insulator transition.

desk verdict Solid orbital-selective DFT case for a magnetism-activated sSDW–BO MIT in CsCr2S2O; the free-energy g is phenomenological, but the constrained calculations still make the mechanism worth engaging. read the letter →

arxiv 2607.28329 v1 pith:MBN7FCF5 submitted 2026-07-30 cond-mat.str-el

Chenchao Xu , Wansheng Bai , Guo-Xiang Zhi , Yi Liu , Xiaoqun Wang , Jianhui Dai , Chao Cao This is my paper · ORCID
classification cond-mat.str-el
keywords altermagnetismmetal-insulatortransitionspin-densitywavebondorderorbital-selectivephysicsCsCr2S2OC-typeantiferromagnetism
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 argues that the near-room-temperature metal-insulator transition in layered CsCr2S2O is not a conventional Mott or charge-density-wave transition. Localized Cr dyz orbitals first form the C-type antiferromagnetic (altermagnetic) background that breaks time-reversal symmetry. On that background, on-site correlations enhance a secondary spin-density-wave instability of the still-metallic Cr dxz electrons; the secondary wave couples to a Cr–S bond order and forces the sulfur atoms to displace. One coupled instability simultaneously opens the gap, disproportionates charge, and modulates Cr moments, matching the experimental order in which magnetism appears a few tens of kelvin before the structural and insulating transition. The same orbital partition explains why the isostructural vanadium compounds lack this transition.

What carries the argument

The phenomenological free-energy coupling g M0 δM Φbond, allowed only once the C-AFM order M0 is present. It linearly mixes the secondary SDW amplitude δM with the Cr–S bond-order parameter Φbond, softens the bond stiffness, and drives the lattice unstable when rbond ramp equals g squared times M0 squared.

What would settle it

If scattering between the magnetic and insulating transitions showed no M-point phonon softening or diffuse intensity, or if a calculation that freezes the secondary moment modulation still produced a double-well sulfur potential, the claimed coupling would be ruled out.

Watch

Extended reading notes

Core claim

The metal-insulator transition in CsCr2S2O is a single coupled secondary spin-density-wave and bond-order instability of the itinerant Cr-dxz–S-pz channel. Pre-existing C-type antiferromagnetic order, carried mainly by localized Cr-dyz moments, breaks time-reversal symmetry and thereby permits a linear coupling between the secondary moment modulation and the Cr–S bond order; the resulting composite order produces the observed sulfur displacement, charge disproportionation, Cr-moment modulation, and gap opening while preserving altermagnetic spin splitting.

Load-bearing premise

The double-well lattice instability and the enhanced susceptibilities appear only inside a static density-functional treatment once an on-site repulsion U is chosen by hand and set large enough; without that choice the coupling does not emerge.

Editorial extensions

If this is right

  • The structural transition must lock Cr-moment amplitude modulation in phase with the sulfur displacement.
  • Enhanced M-point precursor fluctuations (phonon softening or diffuse scattering) should appear between the magnetic and insulating transitions.
  • The same transition is absent in vanadium analogues because the fluctuating orbital does not couple to the metal–ligand bonding channel.
  • Altermagnetic spin splitting survives the distortion under residual glide-mirror protection.

Reading between the lines

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

  • Orbital-selective partitioning of local-moment versus itinerant channels may activate similar coupled bond-order transitions in other multiorbital altermagnets.
  • Pressure or ligand substitution that detunes Cr–S hybridization could separate or suppress the two transition temperatures.
  • The free-energy form supplies a design rule: any pre-existing time-reversal-odd order can linearly unlock otherwise forbidden bond-order instabilities.
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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 manuscript argues that the near-room-temperature metal–insulator transition in altermagnetic CsCr2S2O is a single coupled secondary spin-density-wave (sSDW) and Cr-dxz–S-pz bond-order (BO) instability of the itinerant channel, activated by the pre-existing C-type AFM order that breaks time-reversal symmetry. DFT(+U) total energies show a double-well sulfur-displacement potential only in the C-AFM state at finite U; the same distortion produces charge disproportionation, Cr-moment amplitude modulation, and gap opening while preserving altermagnetic spin splitting. Orbital-resolved DOS and Wannier analysis assign local-moment C-AFM primarily to Cr-dyz and the low-energy metallic channel to hybridized Cr-dxz–S-pz. Bare and RPA susceptibilities for both sSDW amplitude and Cr–S bonding peak at the structural ordering vector M; a minimal free-energy functional with a bilinear term g M0 δM Φbond is introduced to encode the magnetism-enabled coupling. The same orbital logic is used to explain the absence of an analogous MIT in isostructural V-based compounds.

Significance. If correct, the work supplies a concrete orbital-selective mechanism for a comparatively rare ordering sequence in which pre-existing magnetism enables a subsequent structural MIT, and it ties that sequence to altermagnetism in a real material. The computational case is multi-pronged (magnetism- and U-dependent double well, matching-Q susceptibilities, nonmagnetic and δM-constrained controls, and a Cr-vs-V orbital contrast) and makes a falsifiable suggestion of precursor fluctuations between TN and TMI. That combination is of clear interest to the correlated-electron and altermagnet communities even though the free-energy coupling remains phenomenological.

major comments (2)
  1. [Free-energy paragraph after Fig. 4; Supplementary constraints] The central free-energy argument (F = F0 + (ramp/2)(δM)² + (rbond/2)Φbond² + g M0 δM Φbond, unstable when rbond ramp = g² M0²) treats g as a symmetry-allowed parameter that is never extracted. The double-well, the matching-Q RPA peaks of χamp and χbond, and the disappearance of the double well when M0=0 or when δM is constrained establish correlation and necessity of magnetism, but do not quantify the bilinear matrix element or rule out lattice-mediated or higher-order drivers. A constrained-DFT or frozen-phonon decomposition that isolates the cross term (or an explicit statement that g is only phenomenological) is needed for the claim that the MIT is “the” coupled sSDW–BO instability.
  2. [Fig. 2(a); Fig. 4; discussion of full relaxation and gap onset] Both the lattice double well (Fig. 2a: present at U=2,4 eV, absent at U=0) and the RPA enhancements (Fig. 4 at U=U'=3 eV) appear only inside a hand-chosen interaction window; the text also notes that full ionic relaxation pushes the global gap to still larger U. Without a constrained or first-principles estimate of U (or a broader scan showing the instability is robust rather than tuned), it remains unclear whether the coupled mode is an intrinsic property of the material or an artifact of the interaction range where the desired features coexist.
minor comments (5)
  1. [Susceptibility paragraphs and Fig. 4 caption] Define the secondary-SDW operator Â(M) and the precise RPA interaction matrix (density–density only vs full Kanamori) in the main text or a short methods paragraph; they are currently deferred entirely to the Supplementary Information.
  2. [Fig. 3] Fig. 3(c,d): state explicitly whether the DOS is spin-resolved or spin-summed and clarify the factor-of-two rescaling of S-pz so that orbital weights can be compared quantitatively.
  3. [Magnetic configurations, Fig. 1(c–j)] The Heisenberg mapping (J1, J2, J3 values) is used only to establish C-AFM stability; a brief note on whether non-collinear or spin-orbit corrections were checked would strengthen the claim that C-AFM is the unique relevant background.
  4. [Title block and methods] Typographical inconsistencies: “Metal-In sulator”, “V ASP”, “PA W”, and occasional missing spaces in chemical formulas should be cleaned for production.
  5. [Introduction / conclusions] The experimental companion (arXiv:2604.02114) is cited for structure and TN/TMI; a one-sentence comparison of calculated vs measured moment modulation and gap size would help the reader judge quantitative agreement.

Circularity Check

1 steps flagged · score 2.0 of 10

Mostly self-contained DFT narrative; mild circularity only in the phenomenological free energy that encodes the already-observed sSDW–BO locking rather than predicting it.

  1. self definitional [Phenomenological free-energy paragraph (after Fig. 4); eqs. for F, δM, reff_bond]
    "This coupling can be described by a minimal phenomenological free energy F = F0 + ramp/2 (δM)2 + rbond/2 Φ2bond + g M0 δM Φbond, where M0 is the pre-existing C-AFM order... δM ≡ ⟨Â(M)⟩ is the M-point sSDW order parameter... and Φbond ≡ ⟨Ôbond(M)⟩ is the Cr–S BO parameter. ... Minimizing the free energy with respect to δM gives δM = −(g M0/ramp) Φbond, and hence renormalizes the bonding stiffness to reffbond = rbond − g²M0²/ramp."

    δM and Φbond are identified with the moment-amplitude modulation and Cr–S bonding already seen to lock in phase under S displacement in the DFT total-energy scans (Fig. 2b,c). The bilinear g M0 δM Φbond is postulated from that observed locking plus TR/momentum symmetry, not computed as a microscopic vertex. Minimizing F then recovers δM ∝ Φbond and a lowered reff_bond—i.e., restates the input correlation as an output of the free energy. The surrounding DFT checks remain independent; only this packaging step is self-definitional.

full rationale

The load-bearing evidence is independent first-principles content: C-AFM ground-state energetics; double-well only for C-AFM + U≥2 eV (absent at U=0 and in nonmagnetic cells); orbital-resolved DOS separating local dyz from itinerant dxz–Spz; RPA-enhanced χamp and χbond at the same M-point; constrained checks that M0=0 or δM=0 kill the double-well; and the V-compound orbital mismatch. None of these reduce by construction to their inputs. The only mild circularity is the minimal free-energy F = … + g M0 δM Φbond, which is written after the fact to encode the DFT-observed phase locking (S toward Cr2 suppresses its moment) and the TR-even symmetry of the product; minimizing it then ‘derives’ δM ∝ Φbond and a softened reff_bond—relations already read off Fig. 2. That is standard phenomenological packaging, not a fitted prediction or a self-citation uniqueness claim. U is scanned (0, 2, 4 eV) rather than secretly fitted to a target observable and re-sold as prediction. Score 2.

Assumptions & free parameters 4 free parameters · 5 assumptions · 3 invented entities

The claim rests on standard DFT+U/RPA practice plus one phenomenological free-energy coupling. Load-bearing numerical choices are the Hubbard U window and the RPA interaction; load-bearing modeling choices are collinear C-AFM, the local-orbital frame, the bonding operator definition, and the assumption that static mean-field plus RPA capture the instability that experiment sees near 305 K.

free parameters (4)
  • Hubbard U on Cr = 2–4 eV (main text); RPA at U=U'=3 eV
    Double-well and MIT appear only for U=2 and 4 eV (absent at U=0); gap onset shifts with relaxation. U is scanned, not computed from first principles or constrained DFT.
  • RPA interaction U=U' = 3 eV
    Static sSDW and bond susceptibilities are shown enhanced at a single interaction strength chosen inside the correlated window.
  • Sulfur displacement amplitude δxS = ~5% of in-plane Cr–Cr distance
    Structural, charge, moment, and gap results are reported along a constrained collective S displacement; minimum taken near 5%.
  • Phenomenological coupling g
    Free-energy term g M0 δM Φbond is postulated from symmetry; g is never extracted from a microscopic calculation.
assumptions (5)
  • domain assumption DFT+U with collinear spins and a static mean-field treatment of correlations adequately describes the C-AFM ground state and the lattice instability near room temperature.
    Used throughout total-energy, DOS, and phonon sections; no DMFT or dynamical vertex is employed.
  • domain assumption Maximally projected Wannier model on Cr-3d, S-3p, O-3p plus RPA ladder for multiorbital susceptibilities captures the leading sSDW and bond-order channels.
    Susceptibility section and SI definitions of χamp and χbond.
  • domain assumption Local Cr axes with y along Cr–O and x toward S correctly partition dyz (local-moment) from dxz (itinerant) physics.
    Orbital-selective narrative and DOS in Fig. 3(c) depend on this frame.
  • ad hoc to paper Symmetry-allowed free energy F = F0 + (ramp/2)(δM)² + (rbond/2)Φbond² + g M0 δM Φbond is the minimal description of the coupled instability.
    Introduced after the susceptibility discussion; g is not microscopically computed.
  • domain assumption Experimental C-AFM order below TN=326 K and structural MIT at TMI=305 K (Liu et al.) are the phenomena to be explained.
    Cited experimental anchor for the ordering sequence and Pmam distortion.
invented entities (3)
  • Secondary SDW (sSDW) order parameter δM on itinerant Cr-dxz
    purpose: Carries the M-point moment-amplitude modulation that locks to bond order on the C-AFM background.
    Defined as amplitude modulation superposed on primary C-AFM; supported by moment difference vs δxS and χamp(q) peak, but not measured directly as a separate order parameter.
  • Local Cr-dxz–S-pz bonding operator Ôbond
    purpose: Provides the electronic order parameter conjugate to the C4-breaking sulfur displacement.
    Defined in the text to compute bond susceptibility; standard bilinear hybridization operator, but the specific use as the BO parameter tied to sSDW is paper-specific.
  • Coupled sSDW–BO instability as the single driver of the MIT
    purpose: Unifies structural distortion, charge disproportionation, moment modulation, and gap opening.
    Composite ordered state asserted from concurrent appearance in DFT; no independent probe yet separates the coupled mode from ordinary magnetoelastic coupling.

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Pith. "Pith review of Coupled Spin-Density-Wave and Bond-Order Driven Metal-Insulator Transition in Altermagnetic CsCr$_2$S$_2$O." pith.science (2026). https://pith.science/paper/MBN7FCF5

@misc{pith2026260728329,
  author       = {Pith},
  title        = {Pith review of: Coupled Spin-Density-Wave and Bond-Order Driven Metal-Insulator Transition in Altermagnetic CsCr$_2$S$_2$O},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MBN7FCF5}},
  note         = {Machine review of arXiv:2607.28329}
}
abstract

A metal-insulator transition (MIT) driven by bond order (BO) coupled with a secondary spin-density wave (SDW) is identified in CsCr$_2$S$_2$O. Such coupling is enabled as a result of the broken time-reversal symmetry due to the pre-existing C-type antiferromagnetic (C-AFM) order. First-principles calculations reveal an orbital-selective physics that Cr-$d_{yz}$ orbitals form local moments and establish the altermagnetic order, while the Cr-$d_{xz}$ orbitals remain metallic and hybridize with S-$p_z$. Thus the low-energy physics is governed by the Cr-$d_{xz}$ and S-$p_z$ orbitals. On-site interactions then enhance a secondary SDW ($s$SDW) instability of the itinerant $d_{xz}$ electrons, which couples to the Cr-$d_{xz}$-S-$p_z$ bonding order. The resulting coupled $s$SDW-BO simultaneously produces experimentally observed structural distortion, charge disproportionation, local Cr-moment modulation, and gap opening. Our results establish an orbital-selective mechanism upon which pre-existing altermagnetism and electronic correlations cooperate to drive a structural MIT.

Figures

Figures reproduced from arXiv: 2607.28329 by the authors.

Figure 1
Figure 1. FIG. 1. Crystal and magnetic structures of CsCr [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Electronic structures of CsCr [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Static susceptibilities of C-AFM CsCr [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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Works this paper leans on

48 extracted references · 2 linked inside Pith

  1. [1]

    Imada, A

    M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)

    1998

  2. [2]

    N. F. MOTT, Rev. Mod. Phys. 40, 677 (1968)

    1968

  3. [3]

    ADLER, Rev

    D. ADLER, Rev. Mod. Phys. 40, 714 (1968)

    1968

  4. [4]

    S. Y. Kim, M.-C. Lee, G. Han, M. Kratochvilova, S. Yun, S. J. Moon, C. Sohn, J.-G. Park, C. Kim, and T. W. Noh, Advanced Materials 30, 1704777 (2018)

    2018

  5. [5]

    Biermann, A

    S. Biermann, A. Poteryaev, A. I. Lichtenstein, and A. Georges, Phys. Rev. Lett. 94, 026404 (2005)

    2005

  6. [6]

    D. B. McWhan, A. Menth, J. P. Remeika, W. F. Brinkman, and T. M. Rice, Phys. Rev. B 7, 1920 (1973)

    1920

  7. [7]

    Mercy, J

    A. Mercy, J. Bieder, J. ´I˜ niguez, and P. Ghosez, Nat. Com- mun. 8, 1677 (2017)

    2017

  8. [8]

    Fagot, P

    S. Fagot, P. Foury-Leylekian, S. Ravy, J. P. Pouget, M. Anne, G. Popov, M. V. Lobanov, and M. Greenblatt, Solid State Sciences 7, 718 (2005)

    2005

Show all 48 references
  1. [9]

    P. G. Radaelli, Y. Horibe, M. J. Gutmann, H. Ishibashi, C. H. Chen, R. M. Ibberson, Y. Koyama, Y.-S. Hor, V. Kiryukhin, and S.-W. Cheong, Nature 416, 155 (2002)

    2002

  2. [10]

    P. C. Rogge, R. U. Chandrasena, A. Cammarata, R. J. Green, P. Shafer, B. M. Lefler, A. Huon, A. Arab, E. Arenholz, et al., Phys. Rev. Materials 2, 015002 (2018)

    2018

  3. [11]

    Gorelov, M

    E. Gorelov, M. Karolak, T. O. Wehling, F. Lechermann, A. I. Lichtenstein, and E. Pavarini, Phys. Rev. Lett. 104, 226401 (2010)

    2010

  4. [12]

    Asamitsu, Y

    A. Asamitsu, Y. Moritomo, Y. Tomioka, T. Arima, and Y. Tokura, Nature 373, 407 (1995)

    1995

  5. [13]

    Schmidt, W

    M. Schmidt, W. Ratcliff, P. G. Radaelli, K. Refson, N. M. Harrison, and S. W. Cheong, Phys. Rev. Lett. 92, 056402 (2004)

    2004

  6. [14]

    Bansal, J

    D. Bansal, J. L. Niedziela, S. Calder, T. Lanigan-Atkin s, R. Rawl, A. H. Said, D. L. Abernathy, A. I. Kolesnikov, H. Zhou, and O. Delaire, Nat. Phys. 16, 669 (2020)

    2020

  7. [15]

    Braden, G

    M. Braden, G. Andr´ e, S. Nakatsuji, and Y. Maeno, Phys. Rev. B 58, 847 (1998)

    1998

  8. [16]

    P. M. Woodward, D. E. Cox, E. Moshopoulou, A. W. Sleight, and S. Morimoto, Phys. Rev. B 62, 844 (2000)

    2000

  9. [17]

    D. C. Peets, J.-H. Kim, P. Dosanjh, M. Reehuis, A. Maljuk, N. Aliouane, C. Ulrich, and B. Keimer, Phys. Rev. B 87, 214410 (2013)

    2013

  10. [18]

    Millange, S

    F. Millange, S. d. Brion, and G. Chouteau, Phys. Rev. B 62, 5619 (2000)

    2000

  11. [19]

    Huang, Y

    Q. Huang, Y. Qiu, W. Bao, M. A. Green, J. W. Lynn, Y. C. Gasparovic, T. Wu, G. Wu, and X. H. Chen, Phys. Rev. Lett. 101, 257003 (2008)

    2008

  12. [20]

    A. I. Goldman, D. N. Argyriou, B. Ouladdiaf, T. Chat- terji, A. Kreyssig, S. Nandi, N. Ni, S. L. Bud’ko, P. C. Canfield, and R. J. McQueeney, Phys. Rev. B 78, 100506(R) (2008)

    2008

  13. [21]

    Jesche, N

    A. Jesche, N. Caroca-Canales, H. Rosner, H. Borrmann, A. Ormeci, D. Kasinathan, H. H. Klauss, H. Luetkens, R. Khasanov, A. Amato, A. Hoser, K. Kaneko, C. Krell- ner, and C. Geibel, Phys. Rev. B 78, 180504(R) (2008)

    2008

  14. [22]

    Warmuth, M

    J. Warmuth, M. Bremholm, P. Hofmann, J. Wiebe, and R. Wiesendanger, npj Quantum Materials 3, 21 (2018)

    2018

  15. [23]

    Liu, Z.-Y

    Y. Liu, Z.-Y. Liu, J.-K. Bao, P.-T. Yang, L.-W. Ji, S.- Q. Wu, Q.-X. Shen, J. Luo, J. Yang, J.-Y. Liu, C.-C. Xu, W.-Z. Yang, W.-L. Chai, J.-Y. Lu, C.-C. Liu, B.-S. Wang, H. Jiang, Q. Tao, Z. Ren, X.-F. Xu, C. Cao, Z.-A. Xu, R. Zhou, J.-G. Cheng, and G.-H. Cao, Nature 632, 1032 (2024)

    2024

  16. [24]

    Liu, C.-C

    Y. Liu, C.-C. Xu, J.-K. Bao, B.-J. Lv, H. Li, J. Li, Y.- Q. Lin, H.-X. Li, Y.-M. Lu, X.-Y. Zhao, W.-Z. Yang, Z.-Y. Zhang, X.-Y. Chen, W.-H. Jiao, J.-Y. Liu, B.-R. Zhu, and G.-H. Cao, arXiv preprint arXiv:2604.02114 (2026), arXiv:2604.02114 [cond-mat.str-el]

    2026

  17. [25]

    X. Sun, P. Chen, X. Wen, and H. Chen, Crystals 16, 56 (2026)

    2026

  18. [26]

    P. Doan, M. Gooch, Z. Tang, B. Lorenz, A. M¨ oller, J. Tapp, P. C. W. Chu, and A. M. Guloy, Journal of the American Chemical Society 134, 16520 (2012)

    2012

  19. [27]

    B. A. Frandsen, E. S. Bozin, H. Hu, Y. Zhu, Y. Nozaki, H. Kageyama, Y. J. Uemura, W.-G. Yin, and S. J. L. Billinge, Nature Communications 5, 5761 (2014)

    2014

  20. [28]

    Yajima, K

    T. Yajima, K. Nakano, F. Takeiri, J. Hester, T. Ya- mamoto, Y. Kobayashi, N. Tsuji, J. Kim, A. Fujiwara, and H. Kageyama, Journal of the Physical Society of Japan 82, 013703 (2013)

    2013

  21. [29]

    Ablimit, Y.-L

    A. Ablimit, Y.-L. Sun, H. Jiang, S.-Q. Wu, Y.-B. Liu, and G.-H. Cao, Physical Review B 97, 214517 (2018)

    2018

  22. [30]

    Jiang, M

    B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei, Y.-J. Sun, Y. Huang, X. Zheng, Y. Peng, L. He, S. Li, J. Luo, Z. Li, G. Chen, H. Li, H. Weng, and T. Qian, Nature Physics 21, 754 (2025)

    2025

  23. [31]

    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, Nature Physics 21, 760 (2025)

    2025

  24. [32]

    Kresse and J

    G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993)

    1993

  25. [33]

    Kresse and D

    G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999)

    1999

  26. [34]

    P. E. Bl¨ ochl, Phys. Rev. B 50, 17953 (1994)

    1994

  27. [35]

    Pizzi, V

    G. Pizzi, V. Vitale, R. Arita, S. Bl¨ ugel, F. Freimuth, G. G´ eranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Iba˜ nez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, S. Ponc´ e, T. Pon- wei...

    2020

  28. [36]

    G.-X. Zhi, C. Xu, S.-Q. Wu, F. Ning, and C. Cao, Com- puter Physics Communications 271, 108196 (2022)

    2022

  29. [37]

    Monacelli, R

    L. Monacelli, R. Bianco, M. Cherubini, M. Calandra, I. Errea, and F. Mauri, Journal of Physics: Condensed Matter 33, 363001 (2021)

    2021

  30. [38]

    Errea, M

    I. Errea, M. Calandra, and F. Mauri, Physical Review B 89, 064302 (2014)

    2014

  31. [39]

    Bianco, I

    R. Bianco, I. Errea, L. Paulatto, M. Calandra, and F. Mauri, Physical Review B 96, 014111 (2017)

    2017

  32. [40]

    Monacelli, I

    L. Monacelli, I. Errea, M. Calandra, and F. Mauri, Phys- ical Review B 98, 024106 (2018)

    2018

  33. [41]

    Giustino, Reviews of Modern Physics 89, 015003 (2017)

    F. Giustino, Reviews of Modern Physics 89, 015003 (2017)

    2017

  34. [42]

    Sanville, S

    E. Sanville, S. D. Kenny, R. Smith, and G. Henkelman, Journal of Computational Chemistry 28, 899 (2007)

    2007

  35. [43]

    W. Tang, E. Sanville, and G. Henkelman, Journal of Physics: Condensed Matter 21, 084204 (2009)

    2009

  36. [44]

    Y. Xu, H. Zhang, M. Feng, and F. Tian, Phys. Rev. B 112, 125141 (2025)

    2025

  37. [45]

    Parthenios, P

    N. Parthenios, P. M. Bonetti, R. Gonz´ alez-Hern´ andez , W. H. Campos, L. ˇSmejkal, and L. Classen, Phys. Rev. B 112, 214410 (2025)

    2025

  38. [46]

    Z. Wang, S. Yu, X. Cheng, X. Xiao, W. Ma, F. Quan, H. Song, K. Zhang, Y. Zhang, Y. Ma, W. Liu, P. Yadav, X. Shi, Z. Wang, Q. Niu, Y. Gao, B. Xiang, J. Liu, Z. Wang, and X. Chen, arXiv preprint arXiv:2512.23290 10.48550/arXiv.2512.23290 (2025), arXiv:2512.23290 [cond-mat.mes-hall]

    2025 doi

  39. [47]

    D. Fu, L. Yang, Y. Shen, K. Xiao, Y. Wang, W. Jiang, Z. Wang, Y. Yao, Q.-K. Xue, and W. Li, arXiv preprint arXiv:2512.24114 10.48550/arXiv.2512.24114 (2025), arXiv:2512.24114 [cond-mat.mtrl-sci]

    2025 doi arXiv

  40. [48]

    G. Yang, C. Li, C. Wang, X. Zhao, Y. Wan, H. Gui, G. Zeng, S. Cao, C. Hu, D. Chen, Y. Liu, Y. Song, F. Liu, L.-H. Hu, L. Jiao, and H. Yuan, Visualizing spin- polarization of an altermagnet kv 2se2o via spin-selective tunneling (2026), arXiv:2603.21969 [cond-mat.mtrl-sci]

    2026 arXiv

Pith tools

Reviewed July 31, 2026 · model on record in the stance chip above.