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REVIEW 3 major objections 5 minor 64 references

In the altermagnet CoNb4Se8, phonon renormalization reveals a symmetry-dependent spin-orbit channel that links lattice vibrations to spin polarization.

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2026-08-01 16:28 UTC pith:6IATOOQI

load-bearing objection Raman data give a plausible first look at spin-phonon coupling in this altermagnet, but the SOC mechanism claim is undercut by the paper's own DFT numbers, and the 'beyond long-range order' discriminator relies on a heavily defective control. the 3 major comments →

arxiv 2607.17980 v1 pith:6IATOOQI submitted 2026-07-20 cond-mat.mtrl-sci

Spin-phonon interaction in a symmetry-enforced spin-polarized state

Suman Kalyan Pradhan , Dayal Das , Shubham Patel , Subhajit Mahapatra , Sachin Majee , Dibyendu Majee , Arnab Bera , Achintya Singha
show 3 more authors
Snehasish Nandy Samik DuttaGupta Atindra Nath Pal
This is my paper
classification cond-mat.mtrl-sci
keywords AltermagnetSpin-phonon couplingSpin-orbit couplingRaman spectroscopyLattice dynamicsCoNb4Se8Phonon renormalizationSymmetry-governed magnetism
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to show that spin-phonon coupling in symmetry-governed magnetic materials can arise not only from exchange striction tied to long-range magnetic order, but from a symmetry-dependent channel in which spin-orbit coupling lets lattice vibrations sense the spin-polarized electronic structure. It studies the g-type altermagnet CoNb4Se8 by temperature- and polarization-resolved Raman spectroscopy, finding pronounced mode-selective phonon renormalization across the magnetic transition, with A1g modes affected more than E2g modes. Crucially, similar anomalies persist in a Co-deficient analogue without well-defined long-range magnetic order, which the authors take as evidence that coherent exchange striction is not the whole story. First-principles calculations support the picture by showing that turning on spin-orbit coupling selectively renormalizes the same phonon branches that show the strongest experimental deviations. If correct, this makes phonons a practical probe of symmetry-derived spin polarization even in materials with no net magnetization, and offers a handle for engineering spin-lattice coupling.

Core claim

The central claim is that spin-orbit coupling establishes a symmetry-dependent interaction channel between phonons and the symmetry-generated spin-polarized electronic states of an altermagnet, and that this channel drives observable, mode-selective phonon renormalization independent of coherent magnetic order. In CoNb4Se8, Raman modes P2, P3, P5 and P8 deviate from anharmonic behavior near the Néel temperature while other modes such as P7 remain conventional; the effect is strongest for A1g modes. The same P5 anomaly appears in Co0.57Nb4Se8, whose magnetization shows no long-range order, and density-functional phonon calculations including spin-orbit coupling renormalize precisely the branc

What carries the argument

The load-bearing object is the altermagnetic order of CoNb4Se8, in which two Co sublattices are connected by a C6z screw rotation and an Mz glide mirror, producing momentum-space spin splitting without net magnetization. The mechanism proposed is a spin-orbit-coupling-mediated symmetry-dependent channel: lattice displacements change the orbital character of Co-Nb-Se states, and through SOC those orbital changes translate into spin-dependent electronic-structure changes that feed back into phonon self-energies. Two tools carry the argument: (i) polarization-resolved Raman spectroscopy, which assigns each mode to A1g or E2g symmetry and tracks the temperature evolution of frequency, linewidth,

Load-bearing premise

The argument that the coupling goes beyond long-range magnetic order rests on the assumption that Co0.57Nb4Se8 preserves the same crystal symmetry and that its ~180 K phonon anomaly has the same physical origin as the pristine anomaly, despite 43% Co vacancies that shift the Fermi level and introduce disorder.

What would settle it

Go look for a phonon anomaly in a fully nonmagnetic isostructural analogue with the same symmetry but no spin-polarized electronic states; if the same renormalization appears, the spin-orbit channel is not the cause. Conversely, a first-principles calculation of the Co-deficient supercell that reproduces the anomaly without any spin polarization or long-range order would disqualify Co0.57Nb4Se8 as evidence.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Phonon anomalies can serve as a local probe of symmetry-driven spin polarization even when the compound lacks net magnetization and well-defined long-range order.
  • Raman selection rules remain unchanged across the transition, so the magnetic response of the lattice can be read from mode-dependent renormalization rather than from structural symmetry breaking.
  • The symmetry-selective pattern—strongly affected A1g modes, weakly affected E2g modes—gives a fingerprint that distinguishes this SOC-mediated channel from ordinary exchange striction.
  • DFT with SOC identifies the anomalous branches, meaning first-principles phonon calculations can predict which modes will be most sensitive to the spin-polarized environment.
  • Because the effect survives in the Co-deficient analogue, short-range or symmetry-constrained magnetic correlations can couple to the lattice in similar fashion, extending the picture above the ordering temperature.

Where Pith is reading between the lines

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

  • A sharper discrimination test would be a first-principles phonon calculation for a realistic Co-deficient supercell (43% vacancies): if the anomaly cannot be reproduced without symmetry-breaking local moments or defect relaxations, the “beyond-long-range-order” attribution would need revision.
  • If the proposed SOC channel is the driver, the phonon anomalies should be tunable by replacing Co, Nb, or Se with heavier or lighter orbitals that change SOC strength, and should respond to uniaxial strain that alters the C6z/Mz connection between sublattices.
  • The symmetry-selective phonon fingerprint could be used as a tabletop diagnostic for altermagnetism in exfoliated flakes, complementing spin-resolved photoemission and transport, and could help identify new altermagnets from Raman data alone.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper reports temperature- and polarization-resolved Raman spectroscopy of the candidate g-type altermagnet CoNb4Se8 and a Co-deficient analogue Co0.57Nb4Se8. It observes symmetry-selective phonon renormalization across the magnetic transition near TN ≈ 175 K, with deviations from an anharmonic baseline for modes P2, P3, P5, and P8, and finds related anomalies in the deficient compound despite the absence of long-range magnetic order. First-principles phonon calculations with and without spin-orbit coupling are interpreted as evidence that SOC establishes a symmetry-dependent spin-phonon channel, leading to the claim that phonons can probe symmetry-driven spin polarization even without robust magnetic order.

Significance. If the mechanism were established, the paper would provide a valuable advance: phonon renormalization as a probe of altermagnetic-type spin polarization, with a symmetry-based route beyond conventional exchange striction. The experimental strengths are the careful symmetry assignment of eight Raman modes, the mode-selective temperature trends with small Lorentzian fitting errors, the dynamical-stability check from phonon dispersion, and the comparative Co-deficient sample. However, the DFT support is overclaimed: the with/without-SOC mode-resolved comparison does not match the observed anomaly pattern, and the calculation is a static harmonic comparison rather than a spin-phonon self-energy. The empirical phenomenology is interesting and potentially publishable, but the central mechanistic conclusion needs either new calculations or a substantial and honest reframing.

major comments (3)
  1. [Table 1 / §III] The central theoretical claim is not supported by the paper's own data. The with-SOC minus without-SOC harmonic shifts in Table 1 are largest for P4 (+10.7), P5 (+15.5), P6 (+11.9), and P* (+12.9) cm−1, yet the measured anharmonic deviations Δω are largest for P5 (~1.15) and P8 (~1.04), and P6/P* have no quoted Δω. P8, one of the strongest anomalies, has a with-SOC shift of only +0.2 cm−1. Moreover, for P4 and P5 the with-SOC frequencies (223.92 and 237.53 cm−1) are farther from the 80 K experimental values (208.6 and 228.4 cm−1) than the without-SOC values (213.2 and 222.0 cm−1). Thus the DFT comparison demonstrates only static relativistic corrections to harmonic frequencies, not a spin-phonon self-energy, and does not support the statement in §III that the most affected modes are consistent with the strongest experimental anomalies. Please either compute mode-resolved spin-phonon coup
  2. [§II.H, Fig. 6] The comparative experiment on Co0.57Nb4Se8 is used to discriminate between coherent long-range magnetic order and symmetry-governed spin polarization, but the control is not faithful. A 43% Co vacancy concentration necessarily changes the Fermi level, introduces disorder and creates local defect/relaxation channels. The persistence of anomalies around 180 K in the deficient compound could therefore be due to these effects or to residual short-range correlations. The paper itself concedes (§II.I) that "short-range spin correlations or local symmetry-constrained magnetic textures may also contribute." To make the "beyond long-range order" claim load-bearing, the authors should either characterize the spin correlations in the deficient compound (e.g., through magnetic susceptibility fits, diffuse scattering, or a first-principles treatment of the deficient cell) or substantially weaken the
  3. [§II.G / Methods] The anomaly magnitude Δω is estimated as deviation from a three-phonon anharmonic model fitted only above TN. The largest deviations are ~0.7–1.15 cm−1, comparable to the stated spectral resolution of ~0.5 cm−1. Although the Lorentzian fitting errors are much smaller, the extrapolated baseline is a model-dependent construct; systematic errors from the fitting range, thermal expansion, and possible mode coupling are not quantified. Please report the 95% confidence intervals of Δω and test sensitivity to the fitting window/model.
minor comments (5)
  1. [§II.D] The values "P4 (213.2 cm−1)" and "P5 at 222 cm−1" appear to be without-SOC theoretical frequencies, while the experimental 300 K values are 216.4 and 226.5 cm−1. Please label all quoted frequencies consistently.
  2. [Fig. 5 caption / Table 1] The caption states P4 is "not clearly resolved," yet Table 1 lists experimental P4 frequencies at 300 and 80 K. Clarify the degree of confidence in the P4 fit and why Δω is not quoted.
  3. [§II.I] The statement that P6 "displays a pronounced spectral-weight redistribution" is not quantified in the main text; provide an integrated-intensity or linewidth plot if this is a central observation.
  4. [§III] The sentence "The phonon modes most affected in the calculations are consistent with those exhibiting the strongest experimental anomalies" repeats the unsupported claim from Table 1; this should be deleted or rewritten in light of the discrepancy.
  5. [Throughout] Minor grammatical issues, e.g., "P 5 exhibit noticeable deviations" should be "exhibits." The notation "w/" and "w/o" in Table 1 should be defined in the caption.

Circularity Check

1 steps flagged

Mild fit-defined anomaly in the Co-deficient control; central derivation is otherwise self-contained and not circular.

specific steps
  1. fitted input called prediction [§II.H, Fig. 6(c), page 7]
    "Both phonon modes exhibit pronounced temperature-dependent evolution, with distinct anomalies emerging around 180 K, close to the Néel temperature of CoNb4Se8 (Fig. S9). ... Notably, the P5 mode displays a pronounced deviation across this temperature scale [Fig. 6(c)] ... The violet solid line in (c) represents a fit using a Boltzmann sigmoidal function."

    The claimed ~180 K anomaly in the Co-deficient control is identified by fitting a Boltzmann sigmoid to the same P5 frequency data. A Boltzmann sigmoid has a built-in inflection point, so the 'distinct anomaly' is largely imposed by the fitting function rather than independently detected against a physically motivated baseline. Unlike the pristine compound, where deviations are measured relative to an anharmonic fit parameterized above TN, no such independent baseline or model comparison is provided for Co0.57Nb4Se8. The persistence of this anomaly is then used to argue that the lattice response persists beyond long-range order, making this fit-defined feature load-bearing for that specific comparison.

full rationale

The core derivation chain is not circular. The pristine-compound phonon renormalizations are experimental frequencies compared with an anharmonic phonon-phonon baseline fitted to data above TN; the reported Δω values are residuals of that comparison, not parameters fitted to produce the anomaly. The DFT with/without-SOC comparison is a parameter-free first-principles calculation and is not fitted to the measured Raman shifts; any disagreement with experiment (e.g., the Table 1 mode-by-mode mismatch noted by the skeptic) is a correctness/interpretation concern, not circularity. The altermagnetic classification and symmetry criteria are imported from external literature and prior experimental works, not from a self-citation chain by the present authors, and no uniqueness theorem is invoked to force the interpretation. The only mild circularity is in the Co-deficient control, where the anomaly position is displayed through the same Boltzmann sigmoid used to parameterize it. That step is supporting rather than the central derivation, so the overall circularity score is low.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The paper's own Raman measurements provide the phonon positions; the interpretive layer rides on (i) an anharmonic baseline fitted above TN, (ii) prior characterization of the magnetic structures of both compounds, (iii) a DFT comparison whose with-SOC branch fits experiment worse than without-SOC for the key mode P5, and (iv) the unvalidated control assumption that heavy Co deficiency leaves the symmetry-governed spin-lattice channel intact. No new entities (particles, fields, conserved quantities) are postulated; the 'symmetry-dependent interaction channel' is a mechanism label, not a new object.

free parameters (2)
  • Three-phonon anharmonic model parameters (Balkanski-type fit per mode) = fitted to ω(T) for T > TN ≈ 175 K
    The 'anomalous' deviations Δω in Table 1 are defined relative to this extrapolated baseline; the magnitude and sign of the reported magnetic contribution depend on this fit (Fig. 5, §II.G).
  • Boltzmann sigmoid transition temperature for the deficient compound's P5 mode = ~180 K
    The anomaly position in Co0.57Nb4Se8 is the midpoint of a sigmoid fitted to the same frequency-vs-T curve (Fig. 6c, §II.H); the claim 'anomalies emerging around 180 K' is therefore a fitted value, not an independent measurement.
axioms (4)
  • domain assumption The magnetic ground state of CoNb4Se8 is the A-type collinear AFM with the moment arrangement of refs [41,43], and phonons are calculated in that ordered state.
    The spin-phonon interpretation presumes the established altermagnetic spin arrangement; §II.B states calculations are 'for the magnetically ordered phase' but Methods never document the spin configuration or its treatment in the phonon calculation.
  • domain assumption The Balkanski three-phonon decay model (ref 48) is an accurate non-magnetic baseline for ω(T) down to 80 K when fitted only for T > TN.
    Deviations in Table 1 and Fig. 5 are measured against this extrapolation; any systematic failure of the model below the fit range is read as 'magnetic renormalization' (§II.G).
  • domain assumption DFT as implemented (QE, norm-conserving PP, 70 Ry, no U stated) captures phonons of this Co-3d/Nb-4d correlated system with and without SOC.
    The SOC mechanism claim rests entirely on the w/o-SOC vs w/ SOC phonon comparison of Table 1; the quality of the baseline is questionable since experimental frequencies match the w/o-SOC column better for most modes.
  • ad hoc to paper Co0.57Nb4Se8 preserves the symmetry-governed electronic framework relevant to spin polarization; 43% Co deficiency leaves the spin-phonon channel intact.
    This is the load-bearing control assumption of §II.H. No electronic structure or spin dynamics of the deficient compound is calculated or measured beyond susceptibility; it is introduced specifically to make the 'beyond long-range order' argument.

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Cite this review

Pith. "Pith review of Spin-phonon interaction in a symmetry-enforced spin-polarized state." pith.science (2026). https://pith.science/paper/6IATOOQI

@misc{pith2026260717980,
  author       = {Pith},
  title        = {Pith review of: Spin-phonon interaction in a symmetry-enforced spin-polarized state},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6IATOOQI}},
  note         = {Machine review of arXiv:2607.17980}
}
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read the original abstract

Symmetry-governed magnetic materials have emerged as a promising platform for spintronic functionalities without net magnetization or stray magnetic fields, motivating the exploration of how lattice dynamics couple to symmetry-derived spin-polarized electronic states. Understanding spin-phonon coupling in these systems is therefore essential for uncovering the microscopic origin of spin-lattice interactions and for enabling their control in quantum materials. However, this mechanism remains poorly understood because spin polarization originates from crystal symmetry rather than conventional magnetic order. Here, we address this issue in the g-type altermagnet CoNb4Se8 using temperature- and polarization-resolved Raman spectroscopy, complemented by measurements on a structurally analogous Co-deficient compound lacking well-defined long-range magnetic order. We observe pronounced symmetry-selective phonon renormalization across the magnetic transition in CoNb4Se8, while related phonon anomalies persist in the Co-deficient system, demonstrating that the lattice response cannot be explained solely by conventional exchange-striction associated with coherent magnetic ordering. First-principles calculations reveal that spin-orbit coupling establishes a symmetry-dependent interaction channel between lattice vibrations and symmetry-governed electronic states. Our results identify an alternative mechanism for spin-phonon coupling in symmetry-governed magnetic materials and demonstrate that phonons provide a sensitive probe of symmetry-driven spin polarization even without robust magnetic order. More broadly, this work provides a framework for understanding and engineering spin-lattice functionality in symmetry-driven quantum materials, offering design principles for coupling lattice dynamics to spin-polarized electronic states.

Figures

Figures reproduced from arXiv: 2607.17980 by Achintya Singha, Arnab Bera, Atindra Nath Pal, Dayal Das, Dibyendu Majee, Sachin Majee, Samik DuttaGupta, Shubham Patel, Snehasish Nandy, Subhajit Mahapatra, Suman Kalyan Pradhan.

Figure 1
Figure 1. Figure 1: FIG. 1. Magnetic structure of CoNb [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Phonon dispersion relations and the correspond [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Raman spectra of CoNb [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Temperature-dependent Raman spectra of CoNb [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) False-color map of Raman intensity in the 50–350 cm [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Temperature dependence of magnetization mea [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

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Works this paper leans on

64 extracted references · 2 linked inside Pith

  1. [1]

    J. Cao, L. I. Vergara, J. L. Musfeldt, A. P. Litvinchuk, Y. J. Wang, S. Park, and S.-W. Cheong, Phys. Rev. Lett. 100, 177205 (2008)

    2008

  2. [2]

    L. I. Vergara, J. Cao, N. Rogado, Y. Q. Wang, R. P. Chaudhury, R. J. Cava, B. Lorenz, and J. L. Musfeldt, Phys. Rev. B80, 052303 (2009)

    2009

  3. [3]

    G. Go, S. K. Kim, and K.-J. Lee, Phys. Rev. Lett.123, 237207 (2019)

    2019

  4. [4]

    Calero, E

    C. Calero, E. M. Chudnovsky, and D. A. Garanin, Phys. Rev. Lett.95, 166603 (2005)

    2005

  5. [5]

    Y. Tian, M. J. Gray, H. Ji, R. J. Cava, and K. S. Burch, 2D Materials3, 025035 (2016)

    2016

  6. [6]

    Bansal, J

    D. Bansal, J. L. Niedziela, S. Calder, T. Lanigan-Atkins, R. Rawl, A. H. Said, D. L. Abernathy, A. I. Kolesnikov, H. Zhou, and O. Delaire, Nature Physics16, 669 (2020)

    2020

  7. [7]

    D. A. Bozhko, V. I. Vasyuchka, A. V. Chumak, and A. A. Serga, Low Temperature Physics46, 383 (2020)

    2020

  8. [8]

    A. Bera, P. Sarathi Rana, S. Kalyan Pradhan, M. Palit, S. Saha, S. Kalimuddin, S. Bera, T. Debnath, S. Das, D. Singha Roy, S. Datta, and M. Mondal, Journal of Physics: Condensed Matter37, 125403 (2025-01)

    2025

  9. [9]

    Badola, S

    S. Badola, S. Mukherjee, G. Sunil, B. Ghosh, D. Negi, G. Vaitheeswaran, A. C. Garcia-Castro, and S. Saha, Phys. Rev. B109, L060104 (2024)

    2024

  10. [10]

    R. Pal, M. N. Hasan, C. Nayak, M. Deka, N. Salehi, M. Pereiro, S. Mondal, A. Misra, A. Singha, P. Man- dal, D. Karmakar, and A. N. Pal, Spin reorienta- tion driven renormalization of spin-phonon coupling in fe4gete2 (2025), arXiv:2512.18544 [cond-mat.mes-hall]

    arXiv 2025

  11. [11]

    N´ eel, Rev

    L. N´ eel, Rev. Mod. Phys.25, 58 (1953)

    1953

  12. [12]

    N´ eel, Science174, 985 (1971)

    L. N´ eel, Science174, 985 (1971)

    1971

  13. [13]

    Granado, A

    E. Granado, A. Garc ´ ıa, J. A. Sanjurjo, C. Rettori, I. Tor- riani, F. Prado, R. D. S´ anchez, A. Caneiro, and S. B. Oseroff, Phys. Rev. B60, 11879 (1999)

    1999

  14. [14]

    J. Wu, Y. Yao, M.-L. Lin, M. R¨ osner, Z. Du, K. Watan- abe, T. Taniguchi, P.-H. Tan, S. Haas, and H. Wang, Advanced Materials34, 2108506 (2022)

    2022

  15. [15]

    M. C. Weber, M. Guennou, D. M. Evans, C. Toulouse, A. Simonov, Y. Kholina, X. Ma, W. Ren, S. Cao, M. A. Carpenter, B. Dkhil, M. Fiebig, and J. Kreisel, Nature Communications13, 443 (2022)

    2022

  16. [16]

    Q.-C. Sun, S. N. Baker, A. D. Christianson, and J. L. Musfeldt, Phys. Rev. B84, 014301 (2011)

    2011

  17. [17]

    J. H. Lee, L. Fang, E. Vlahos, X. Ke, Y. W. Jung, L. F. Kourkoutis, J.-W. Kim, P. J. Ryan, T. Heeg, M. Roeck- erath, V. Goian, M. Bernhagen, R. Uecker, P. C. Ham- mel, K. M. Rabe, S. Kamba, J. Schubert, J. W. Free- land, D. A. Muller, C. J. Fennie, P. Schiffer, V. Gopalan, E. Johnston-Halperin, and D. G. Schlom, Nature466, 954 (2010)

    2010

  18. [18]

    J. Son, B. C. Park, C. H. Kim, H. Cho, S. Y. Kim, L. J. Sandilands, C. Sohn, J.-G. Park, S. J. Moon, and T. W. Noh, npj Quantum Materials4, 17 (2019)

    2019

  19. [19]

    A. P. Roy, J. SS, V. Dwij, A. Khandelwal, M. K. Chat- topadhyay, V. Sathe, R. Mittal, P. U. Sastry, S. N. Achary, A. K. Tyagi, P. D. Babu, M. D. Le, and D. Bansal, Phys. Rev. Lett.132, 026701 (2024)

    2024

  20. [20]

    Huang, P

    B. Huang, P. Hao, and Z. Sheng, Phys. Rev. B113, 094435 (2026)

    2026

  21. [21]

    I. I. Mazin, K. Koepernik, M. D. Johannes, R. Gonz´ alez- Hern´ andez, and L.ˇSmejkal, Proceedings of the National Academy of Sciences118, e2108924118 (2021)

    2021

  22. [22]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Phys. Rev. X 12, 031042 (2022)

    2022

  23. [23]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Phys. Rev. X 12, 040501 (2022)

    2022

  24. [24]

    Krempasky, L

    J. Krempasky, L. ˇSmejkal, S. W. DSouza, 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. Wadley, J. Sinova, D. Kriegner, J. Min´ ar, J. H. Dil, and T. Jungwirth, Nature62...

    2024

  25. [25]

    X. Zhou, W. Feng, R.-W. Zhang, L. ˇSmejkal, J. Sinova, Y. Mokrousov, and Y. Yao, Phys. Rev. Lett.132, 056701 (2024)

    2024

  26. [26]

    Cheong and F.-T

    S.-W. Cheong and F.-T. Huang, npj Quantum Materials 10, 38 (2025)

    2025

  27. [27]

    Jungwirth, J

    T. Jungwirth, J. Sinova, R. M. Fernandes, Q. Liu, H. Watanabe, S. Murakami, S. Nakatsuji, and L.ˇSmejkal, Nature649, 837 (2026)

    2026

  28. [28]

    L. Bai, W. Feng, S. Liu, L. ˇSmejkal, Y. Mokrousov, and Y. Yao, Advanced Functional Materials34, 2409327 (2024)

    2024

  29. [29]

    B. Chi, L. Jiang, Y. Zhu, G. Yu, C. Wan, J. Zhang, and X. Han, Phys. Rev. Appl.21, 034038 (2024)

    2024

  30. [30]

    Leraand, K

    K. Leraand, K. Mæland, and A. Sudbø, Phys. Rev. B 112, 104510 (2025)

    2025

  31. [31]

    S. S. Fender, O. Gonzalez, and D. K. Bediako, J. Am. Chem. Soc.147, 2257 (2025-01)

    2025

  32. [32]

    Ghosh, M

    A. Ghosh, M. Palit, S. Maity, V. Dwij, S. Rana, and S. Datta, Phys. Rev. B103, 064431 (2021)

    2021

  33. [33]

    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, Phys. Rev. Lett.132, 036702 (2024)

    2024

  34. [34]

    Osumi, S

    T. Osumi, S. Souma, T. Aoyama, K. Yamauchi, A. Honma, K. Nakayama, T. Takahashi, K. Ohgushi, and T. Sato, Phys. Rev. B109, 115102 (2024). 11

    2024

  35. [35]

    R. D. Gonzalez Betancourt, J. Zub´ aˇ c, R. Gonzalez- Hernandez, K. Geishendorf, Z. ˇSob´ aˇ n, G. Springholz, K. Olejn ´ ık, L.ˇSmejkal, J. Sinova, T. Jungwirth, S. T. B. Goennenwein, A. Thomas, H. Reichlov´ a, J.ˇZelezn´ y, and D. Kriegner, Phys. Rev. Lett.130, 036702 (2023)

    2023

  36. [36]

    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, Nature Communi- cations15, 2116 (2024)

    2024

  37. [37]

    Zeng, M.-Y

    M. Zeng, M.-Y. Zhu, Y.-P. Zhu, X.-R. Liu, X.-M. Ma, Y.- J. Hao, P. Liu, G. Qu, Y. Yang, Z. Jiang, K. Yamagami, M. Arita, X. Zhang, T.-H. Shao, Y. Dai, K. Shimada, Z. Liu, M. Ye, Y. Huang, Q. Liu, and C. Liu, Advanced Science11, 2406529 (2024)

    2024

  38. [38]

    R. B. Regmi, H. Bhandari, B. Thapa, Y. Hao, N. Sharma, J. McKenzie, X. Chen, A. Nayak, M. El Gazzah, B. G. M´ arkus, L. Forr´ o, X. Liu, H. Cao, J. F. Mitchell, I. I. Mazin, and N. J. Ghimire, Nature Communications16, 4399 (2025)

    2025

  39. [39]

    A. P. Sakhya, M. I. Mondal, M. Sprague, R. B. Regmi, A. K. Kumay, H. Sheokand, I. I. Mazin, N. J. Ghimire, and M. Neupane, Electronic structure of a layered alter- magnetic compound conb4se8 (2025), arXiv:2503.16670 [cond-mat.mes-hall]

    Pith/arXiv arXiv 2025

  40. [40]

    Candelora, M

    C. Candelora, M. Xu, S. Cheng, A. D. Vita, D. Ro- manin, C. Bigi, M. B. Petersen, A. LaFleur, M. Ca- landra, J. Miwa, Y. Hwang, Z. Wang, F. Mazzola, and I. Zeljkovic, Discovery of magnetic-field-tunable density waves in a layered altermagnet (2025), arXiv:2503.03716 [cond-mat.str-el]

    Pith/arXiv arXiv 2025

  41. [41]

    N. Dale, O. A. Ashour, M. Vila, R. B. Regmi, J. Fox, C. W. Johnson, A. Fedorov, A. Stibor, N. J. Ghimire, and S. M. Griffin, Non-relativistic spin splitting above and below the fermi level in ag-wave altermagnet (2024), arXiv:2411.18761 [cond-mat.mtrl-sci]

    arXiv 2024

  42. [42]

    A. D. 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. Antonelli, G. Sangiovanni, L. D. Re, I. Vobornik, J. Fujii, F. M. Granozio, A. Sambri, ...

    arXiv 2025

  43. [43]

    H. C. Mandujano, P. Y. Zavalij, A. Manj´ on-Sanz, H. Cao, and E. E. Rodriguez, Phys. Rev. Mater.9, 014403 (2025)

    2025

  44. [44]

    X. Wei, M. Li, X. He, Q. Xie, L. Chen, L. Ma, and G. Cheng, Applied Physics Letters126, 252201 (2025- 06)

    2025

  45. [45]

    M. P. Erodici, T. T. Mai, L. S. Xie, S. Li, S. S. Fender, S. Husremovi´ c, O. Gonzalez, A. R. Hight Walker, and D. K. Bediako, The Journal of Physical Chemistry C127, 9787 (2023)

    2023

  46. [46]

    X. Xi, L. Zhao, Z. Wang, H. Berger, L. Forr´ o, J. Shan, and K. F. Mak, Nature Nanotechnology10, 765 (2015)

    2015

  47. [47]

    Kroumova, M

    E. Kroumova, M. I. Aroyo, J. M. Perez-Mato, A. Kirov, C. Capillas, S. Ivantchev, and H. Wondratschek, Phase Transitions76, 155 (2003)

    2003

  48. [48]

    Balkanski, R

    M. Balkanski, R. F. Wallis, and E. Haro, Phys. Rev. B 28, 1928 (1983)

    1928

  49. [49]

    Zhu and W

    S. Zhu and W. Zheng, J. Phys. Chem. Lett.12, 5261 (2021)

    2021

  50. [50]

    Steurer, A

    W. Steurer, A. Apfolter, M. Koch, W. E. Ernst, E. Sønderg ˚ ard, J. R. Manson, and B. Holst, Phys. Rev. Lett.100, 135504 (2008)

    2008

  51. [51]

    Schilberth, M

    F. Schilberth, M. Kond´ akor, D. Ukolov, A. Pawbake, K. Vasin, O. Ercem, L. Prodan, V. Tsurkan, A. A. Tsir- lin, C. Faugeras, P. Lemmens, K. Penc, I. K´ ezsm´ arki, S. Bord´ acs, and J. Deisenhofer, npj Quantum Materials 11, 26 (2026)

    2026

  52. [52]

    A. Paul, P. Sharma, and U. V. Waghmare, Phys. Rev. B 92, 054106 (2015)

    2015

  53. [53]

    T. Kim, C. H. Kim, J. Jeong, P. Park, K. Park, K. H. Lee, J. C. Leiner, D. Ishikawa, A. Q. R. Baron, Z. Hiroi, and J.-G. Park, Phys. Rev. B102, 201101 (2020)

    2020

  54. [54]

    Lunghi, F

    A. Lunghi, F. Totti, S. Sanvito, and R. Sessoli, Chemical science8, 6051 (2017)

    2017

  55. [55]

    Albino, S

    A. Albino, S. Benci, M. Atzori, L. Chelazzi, S. Ciattini, A. Taschin, P. Bartolini, A. Lunghi, R. Righini, R. Torre, et al., The Journal of Physical Chemistry C125, 22100 (2021)

    2021

  56. [56]

    R. Nabi, J. K. Staab, A. Mattioni, J. G. Kragskow, D. Reta, J. M. Skelton, and N. F. Chilton, Journal of the American Chemical Society145, 24558 (2023)

    2023

  57. [57]

    Winkler,Spin–Orbit Coupling Effects in Two- Dimensional Electron and Hole Systems, Springer Tracts in Modern Physics, Vol

    R. Winkler,Spin–Orbit Coupling Effects in Two- Dimensional Electron and Hole Systems, Springer Tracts in Modern Physics, Vol. 191 (Springer, 2003)

    2003

  58. [58]

    Y. Liu, X. Chen, Y. Yu, J. Etxebarria, J. M. Perez-Mato, and Q. Liu, Nature652, 869 (2026)

    2026

  59. [59]

    MAUD-Materials Analysis Using Diffraction version- 2.9993 (2023)

    2023

  60. [60]

    Momma and F

    K. Momma and F. Izumi, Journal of Applied Crystallog- raphy44, 1272 (2011)

    2011

  61. [61]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococ- cioni, I. Dabo,et al., Journal of physics: Condensed mat- ter21, 395502 (2009)

    2009

  62. [62]

    Giannozzi, O

    P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni,et al., Journal of physics: Condensed matter29, 465901 (2017)

    2017

  63. [63]

    Giannozzi, O

    P. Giannozzi, O. Baseggio, P. Bonf` a, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. De Gironcoli, P. Delugas, F. Ferrari Ruffino,et al., The Journal of chemical physics 152, 154105 (2020)

    2020

  64. [64]

    Troullier and J

    N. Troullier and J. L. Martins, Phys. Rev. B43, 1993 (1991)

    1993

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