Pith. sign in

REVIEW 2 major objections 3 minor 75 references

No phonon anomalies: GdGaI's band gap is electronic

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · deepseek-v4-flash

2026-08-01 12:03 UTC pith:OSRGLC3S

load-bearing objection Careful Raman work on GdGaI with a genuinely new experimental data set, but the no-CDW conclusion rests on an unquantified null result and the 'chiral phonon' language outruns the evidence. the 2 major comments →

arxiv 2607.19663 v1 pith:OSRGLC3S submitted 2026-07-22 cond-mat.mtrl-sci cond-mat.mes-hallcond-mat.str-el

Raman spectroscopy of van der Waals topological magnet GdGaI

classification cond-mat.mtrl-sci cond-mat.mes-hallcond-mat.str-el
keywords Raman spectroscopyexcitonic insulatorcharge density wavespin-phonon couplingchiral phononsvan der Waals magnetGdGaIcircular dichroism
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.

This paper tries to establish that the band reconstruction observed in the layered magnet GdGaI is electronic in origin—an excitonic insulator—rather than caused by a periodic lattice distortion like a charge-density wave. Using polarization-resolved Raman spectroscopy down to 4 K, it finds only the monotonic hardening expected from thermal contraction and anharmonicity: no extra peaks, no soft modes, and no zone-folded phonons that a 2×2×1 superlattice would produce. The paper argues this absence puts any lattice distortion below experimental sensitivity, and therefore supports an electron–electron-driven mechanism for the ARPES-observed gap opening. It also reports a field-reversible circular dichroism of the A1g phonons, attributed to chiral phonons with angular momentum generated by spin–phonon coupling, suggesting that circular-polarization Raman can detect the onset of short-range magnetic correlations.

Core claim

The central claim is that GdGaI's low-temperature band reconstruction is not accompanied by a detectable periodic lattice distortion. The Raman spectrum at 4 K is essentially identical in mode count to the 300 K spectrum; all six identified phonons (three A1g and three Eg) simply harden with cooling following a Grüneisen-type volume trend. Because the paper's DFT calculations predict that a 2×2×1 folding of the Brillouin zone would bring nine M-point phonons into the Raman-active window, the absence of these folded modes is taken as evidence that any CDW-type distortion is too small to matter. The authors also claim that under an out-of-plane magnetic field the A1g modes develop an antisymme

What carries the argument

The identifying machinery is the symmetry-based Raman tensor analysis for the D3d point group, combined with DFT phonon calculations. The Raman tensors dictate which phonons appear in helicity-conserving (RR/LL) versus helicity-exchanging (RL/LR) configurations, letting the authors assign all six modes. The decisive test is the predicted set of zone-folded M-point phonons: a 2×2×1 CDW superlattice would fold six Ag and three Bg modes below 300 cm−1 to the zone center and make them Raman-active; their absence is the observation that rules out a large lattice distortion. For the magnetic-field effect, the key object is the field-induced antisymmetric term e in the A1g Raman tensor, which makes

Load-bearing premise

The main conclusion depends on the assumption that the zone-folded M-point phonons predicted for a 2×2×1 superlattice would be intense enough to appear in these Raman spectra; if they are weak or the distortion is smaller than the detection limit, their absence would not rule out a lattice-driven transition.

What would settle it

A concrete falsifier would be a diffraction experiment: if x-ray or electron scattering finds superlattice reflections at the M-point wavevector below ~200 K, the no-distortion conclusion collapses. Conversely, a calculation or measurement showing that the folded M-point phonons have near-zero Raman cross-section would remove the detection argument. Inelastic x-ray scattering could also look for a soft phonon branch at M as the temperature drops.

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

If this is right

  • The band folding and gap seen by ARPES in GdGaI, if not lattice-driven, become a stronger case for excitonic order, placing GdGaI among the few materials where an excitonic insulator is seriously considered.
  • The absence of extra Raman peaks at 4 K sets an experimental upper bound on any CDW-type lattice distortion in this compound; future experiments can quantify this bound or detect a different ordering wavevector.
  • The field-reversible RR/LL asymmetry gives a magneto-Raman signature of the magnetization direction and magnitude; the degree of circular polarization can serve as a non-contact probe of short-range antiferromagnetic correlations.
  • The low-temperature deviations from the Grüneisen thermal-expansion trend, attributed to spin–phonon coupling, offer a route to quantify magnetoelastic coupling in GdGaI and other van der Waals magnets.
  • Circular-polarization-resolved Raman is demonstrated as a transferable technique for distinguishing electronic (excitonic) from lattice (CDW) mechanisms in other candidate materials.

Where Pith is reading between the lines

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

  • My inference: the paper's Raman detection limit for folded modes is not quantified, so a small-amplitude CDW cannot be fully excluded; a resonant Raman or higher-resolution study targeting the predicted M-point phonon energies could calibrate the sensitivity.
  • My inference: if the RR/LL asymmetry really reflects phonon angular momentum, then GdGaI should also show a magnetic-field-induced circular dichroism in infrared absorption and possibly a nonzero phonon thermal Hall conductivity; these would be independent, testable predictions.
  • My inference: the onset of circular dichroism around 100 K, well above the 40 K magnetic transition, may be a direct spectroscopic readout of short-range spin correlations; comparing with neutron scattering or spin-spin correlation calculations would test this assignment.
  • My inference: applying the same polarization-resolved Raman approach to monolayer or few-layer GdGaI, where the electronic structure changes, could reveal whether the excitonic instability strengthens or weakens with dimensionality, and whether any lattice distortion appears in the thinner limit.

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

2 major / 3 minor

Summary. The paper reports polarization-resolved Raman spectroscopy of the van der Waals compound GdGaI, a candidate excitonic insulator. Combining symmetry analysis with DFT phonon calculations, the authors identify six Raman-active phonons (three A1g and three Eg) and follow their temperature and magnetic-field evolution. The central claim is that the spectra show only anharmonic hardening down to 4 K, with no additional peaks, soft modes, or zone-folding signatures; this is taken as evidence that the band reconstruction seen in ARPES is electronically driven rather than caused by a CDW-type lattice distortion. The paper also reports a magnetic-field-induced RR/LL circular-intensity asymmetry for the A1g modes, which it models with an antisymmetric imaginary Raman-tensor component and interprets as evidence for chiral A1g phonons generated by spin-phonon coupling, with the degree of circular polarization tracking short-range antiferromagnetic correlations below ~100 K.

Significance. If the no-CDW conclusion holds, this is a valuable phonon-level discriminator for the excitonic-insulator interpretation of GdGaI: the Raman data are independent of the ARPES and susceptibility results they are compared with, and the null result provides a useful upper bound on any lattice distortion. The phonon assignments and symmetry analysis are carefully presented, and the authors include appropriate caveats. The circular-dichroism observation is also interesting and, if substantiated, would strengthen the case that helicity-resolved Raman can probe spin-phonon coupling in candidate excitonic systems. However, the two main interpretive steps — the conversion of an unquantified null result into support for an electronic mechanism, and the attribution of the intensity asymmetry to chiral phonons — currently outrun the evidence presented.

major comments (2)
  1. [Temperature Dependence of Raman Modes] The central no-CDW conclusion rests on the assertion that, for a 2×2×1 superlattice, the DFT-predicted M-point modes 'would become Raman active and should be observable within the spectral window.' This is not demonstrated. Raman activity after zone folding depends on the irreducible representations of the folded modes under the D3d point group, and the paper provides no decomposition of the M-point modes into Γ irreps, no calculated Raman intensities or cross-sections, and no noise-floor or detection-limit estimate. Folded modes can have small scattering cross-sections, and a distortion smaller than the experimental sensitivity would also produce no new peaks. A positive control (e.g., a known CDW material measured in the same apparatus) or an explicit quantitative upper bound on lattice distortion derived from the noise level is needed to convert the null result into support for an ele
  2. [Magnetic-field-induced circular dichroism, Eq. (5)] The RR/LL intensity asymmetry is reproduced by Eq. (5) with an imaginary antisymmetric component e ∝ M. This is a phenomenological magneto-optical modification of the Raman tensor (of the type already reported in CrI3 and VI3) and does not by itself demonstrate that A1g phonons carry angular momentum or are chiral. The same asymmetry would arise from field-induced changes to the optical response even without phonon angular momentum. The abstract and conclusion attribute the dichroic response to 'chiral A1g phonons with opposite angular momenta generated by spin-phonon coupling,' which goes beyond what Eq. (5) establishes. The authors should either soften this attribution or support it with independent evidence, such as a first-principles calculation of the phonon pseudo-angular momentum in the magnetized state or a symmetry analysis showing that the observed tensor form uniquely requires
minor comments (3)
  1. [Temperature Dependence of Raman Modes] The text refers to 'six Ag and three Bg modes at the M point' (Fig. S4). The D3d point group does not have Bg irreps; the notation is likely from the little group of the M point, but this should be stated explicitly to avoid confusion.
  2. [Magnetic-field-induced circular dichroism, Figs. 5(e)-5(f)] The caption lists 0 T (black) curves in the temperature dependence of the degree of circular polarization. Please clarify whether a nonzero zero-field signal is observed; if so, reconcile it with the statement that the effect is field-induced and that remanent magnetization is negligible. If the 0 T curves are zero, the text should state this explicitly, since 'emerges below about 100 K' could be misread as applying to zero field.
  3. [Temperature Dependence of Raman Modes, Eq. (4)] The effective Grüneisen parameter γ in Eq. (4) is fitted over 100–300 K and explicitly includes intrinsic anharmonic contributions. Calling this a 'thermal-expansion trend' is therefore somewhat misleading; the low-temperature deviations attributed to spin-phonon coupling could partly reflect anharmonic contributions not captured by the single-parameter fit. A brief clarification would help.

Circularity Check

0 steps flagged

No significant circularity: the Raman measurements and the no-CDW null result are independent of the cited ARPES/magnetization inputs; the chiral-phonon interpretation leans on external symmetry results rather than on a fitted parameter.

full rationale

The paper's derivation chain is self-contained with respect to its own measurements. The phonon assignment combines symmetry selection rules (Eqs. 1–2) with DFT phonon calculations; the observed Raman peaks are measured directly, not produced by a fit. The central no-CDW conclusion rests on a null result: no additional peaks, no soft modes, and no zone folding down to 4 K. The authors explicitly state that folded M-point modes 'would become Raman active and should be observable within the spectral window of our experiment,' but this is a sensitivity/visibility assumption, not a circular reduction: the absence of peaks is not mathematically forced by any fitted parameter, and the unquantified folded-mode intensity is a correctness risk rather than a circularity. The Grüneisen analysis (Eq. 4) is used only to define a thermal-expansion baseline over 100–300 K and to identify low-temperature deviations; those deviations are then attributed to spin–phonon coupling based on the independent magnetic transition, not fitted into the conclusion. Self-citations appear (Ref. 55 for ARPES and susceptibility, Refs. 46–47 for phonon chirality), but they are external, falsifiable results used as context: the ARPES band reconstruction and the magnetic transition are not derived from the Raman data, and the Raman spectra are new measurements. No equation in the paper reduces to another by construction, and no fitted parameter is renamed as a prediction. Therefore no specific circular step can be exhibited, and the appropriate score is 0.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 1 invented entities

The central inference rests on the assumed observability of zone-folded modes, the validity of the D3d symmetry assignment, the ARPES/susceptibility results from Ref. [55], and the phenomenological tensor model for the dichroism. DFT phonon calculations are standard but the parameters are in the unavailable Supplemental Material. The only numerical fitted quantity affecting the interpretation is the per-mode effective Grüneisen parameter.

free parameters (2)
  • Effective Grüneisen parameter γ per phonon mode = Not given numerically in main text; annotated in Fig. 4 panels
    Fitted via Eq. (4) to the 100–300 K frequency data for each mode. Used to define the expected thermal-expansion baseline; deviations below 50–100 K are then attributed to spin–phonon coupling, so the attribution depends on this fitted baseline.
  • Antisymmetric Raman tensor component e = Not quantified; stated to be proportional to magnetization
    Introduced in Eq. (5) as the imaginary off-diagonal element of the A1g Raman tensor to reproduce the RR/LL intensity asymmetry. It is a phenomenological model parameter, not extracted from an independent measurement.
axioms (6)
  • domain assumption GdGaI crystallizes in space group P-3m1 with point group D3d in the paramagnetic state
    Taken from Refs. [53,54]; this is the basis for all Raman selection rules and mode assignments.
  • domain assumption A 2×2×1 CDW superlattice would fold M-point phonons to Γ and make them Raman-active and observable in the measured spectral window
    Stated in the Temperature Dependence section. Load-bearing for interpreting the null Raman result as excluding lattice distortion; relies on DFT-predicted mode frequencies and assumed cross-sections.
  • domain assumption The ARPES-observed band reconstruction and gap opening in GdGaI are real and onset near 200 K
    Taken from Ref. [55], which shares authors with this paper. The Raman null result is contrasted with this ARPES observation, so the ARPES interpretation is an input.
  • ad hoc to paper The field-induced RR/LL intensity asymmetry can be described by adding an imaginary antisymmetric component e ∝ M to the A1g Raman tensor
    Equation (5) is introduced to fit the observed asymmetry. Alternative mechanisms (e.g., Faraday rotation of light in the sample/optics) are not excluded.
  • domain assumption DFT phonon calculations (VASP/Phonopy with GGA-PBE, as referenced via the Supplemental Material) reliably predict mode frequencies and Raman activities
    Standard first-principles methodology, but the specific parameters are in the unavailable Supplemental Material; the M-point folding argument depends on these predicted modes.
  • standard math Standard Raman selection rules and Loudon tensors for D3d apply
    Used to derive the A1g and Eg Raman tensors and the RR/RL selection rules in the 'Raman selection rules and phonon assignment' section.
invented entities (1)
  • Chiral A1g phonons carrying angular momentum in the time-reversal-broken state no independent evidence
    purpose: Proposed microscopic origin of the RR/LL circular dichroism of A1g modes under magnetic field
    The paper presents no direct measurement of phonon angular momentum; the observed intensity asymmetry is equally captured by the phenomenological magneto-optical tensor in Eq. (5). A1g is non-degenerate in D3d/C3, so the mechanism by which it acquires finite angular momentum is not demonstrated.

pith-pipeline@v1.3.0-alltime-deepseek · 12370 in / 16771 out tokens · 187007 ms · 2026-08-01T12:03:46.065821+00:00 · methodology

0 comments
read the original abstract

We report polarization-resolved Raman spectroscopy of a van der Waals compound GdGaI that is a candidate for excitonic insulators. By combining the symmetry analysis with density functional theory calculations, we identify six Raman-active phonons. The spectra exhibit only the expected anharmonic hardening down to 4 K: no additional peaks, no soft modes, and no signatures of zone folding are observed. This result indicates that any lattice distortion is below our experimental sensitivity, supporting an electronically driven origin for the band reconstruction reported by angle-resolved photoemission spectroscopy rather than an electron-phonon-driven mechanism. Moreover, we observe a pronounced circular dichroism of the $A_{1g}$ modes under an out-of-plane magnetic field. Based on symmetry considerations, we attribute this dichroic response to chiral $A_{1g}$ phonons with opposite angular momenta generated by spin-phonon coupling in the time-reversal-broken state. The temperature evolution of the degree of circular polarization further suggests that circularly polarized Raman spectroscopy detects the emergence of short-range antiferromagnetic correlations. Our results highlight GdGaI as a promising platform in which excitonic order, magnetism, and circularly polarized phonons can be intertwined, and demonstrate that circular-polarization Raman provides a sensitive probe of spin-phonon coupling in excitonic systems.

Figures

Figures reproduced from arXiv: 2607.19663 by Jun-ichi Yamaura, Kenji Watanabe, Nan Jiang, Ryutaro Okuma, Takashi Taniguchi, Tiantian Zhang, Tomo Higashihara, Tomoki Machida, Yasuhiro Niimi, Yijin Zhang, Yoshinori Okada, Yujie Xia.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Crystal structure of GdGaI. The black solid line [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) (a) Calculated phonon dispersion relations [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Polarized Raman spectra of GdGaI at several [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Temperature dependence of the fitted (a–f) peak [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a-c) Polarized Raman spectra of the 16- [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

75 extracted references · 3 linked inside Pith

  1. [1]

    N. F. Mott, The transition to the metallic state, The Philosophical Magazine: A Journal of Theoretical Ex- perimental and Applied Physics6, 287 (1961)

  2. [2]

    L. V. Keldysh and Y. V. Kopaev, Possible instability of semimetallic state toward Coulomb interaction., Sov. Phys. Solid State6, 2219 (1965)

  3. [3]

    J. D. Cloizeaux, Exciton instability and crystallographic anomalies in semiconductors, Journal of Physics and Chemistry of Solids26, 259 (1965)

  4. [4]

    J´ erome, T

    D. J´ erome, T. M. Rice, and W. Kohn, Excitonic Insula- tor, Phys. Rev.158, 462 (1967)

  5. [5]

    Zittartz, Anisotropy Effects in the Excitonic Insulator, Phys

    J. Zittartz, Anisotropy Effects in the Excitonic Insulator, Phys. Rev.162, 752 (1967)

  6. [6]

    Kohn, Excitonic Phases, Phys

    W. Kohn, Excitonic Phases, Phys. Rev. Lett.19, 439 (1967)

  7. [7]

    B. I. HALPERIN and T. M. RICE, Possible Anomalies at a Semimetal-Semiconductor Transistion, Rev. Mod. Phys.40, 755 (1968)

  8. [8]

    Kaneko and Y

    T. Kaneko and Y. Ohta, A New Era of Excitonic Insula- tors, Journal of the Physical Society of Japan94, 012001 (2025)

  9. [9]

    Cercellier, C

    H. Cercellier, C. Monney, F. Clerc, C. Battaglia, L. De- spont, M. G. Garnier, H. Beck, P. Aebi, L. Patthey, H. Berger, and L. Forr´ o, Evidence for an Excitonic In- sulator Phase in 1T−TiSe 2, Phys. Rev. Lett.99, 146403 (2007)

  10. [10]

    Kogar, M

    A. Kogar, M. S. Rak, S. Vig, A. A. Husain, F. Flicker, Y. I. Joe, L. Venema, G. J. MacDougall, T. C. Chiang, E. Fradkin, J. van Wezel, and P. Abbamonte, Signatures of exciton condensation in a transition metal dichalco- genide, Science358, 1314 (2017)

  11. [11]

    M. Holt, P. Zschack, H. Hong, M. Y. Chou, and T.-C. Chiang, X-Ray Studies of Phonon Softening in TiSe 2, Phys. Rev. Lett.86, 3799 (2001)

  12. [12]

    Wakisaka, T

    Y. Wakisaka, T. Sudayama, K. Takubo, T. Mizokawa, M. Arita, H. Namatame, M. Taniguchi, N. Katayama, M. Nohara, and H. Takagi, Excitonic Insulator State in Ta2NiSe5 Probed by Photoemission Spectroscopy, Phys. Rev. Lett.103, 026402 (2009)

  13. [13]

    K. Seki, Y. Wakisaka, T. Kaneko, T. Toriyama, T. Kon- ishi, T. Sudayama, N. L. Saini, M. Arita, H. Namatame, M. Taniguchi, N. Katayama, M. Nohara, H. Takagi, T. Mizokawa, and Y. Ohta, Excitonic Bose-Einstein con- densation in Ta 2NiSe5 above room temperature, Phys. Rev. B90, 155116 (2014)

  14. [14]

    Y. F. Lu, H. Kono, T. I. Larkin, A. W. Rost, T. Takayama, A. V. Boris, B. Keimer, and H. Takagi, Zero-gap semiconductor to excitonic insulator transition in Ta2NiSe5, Nature Communications8, 14408 (2017)

  15. [15]

    Werdehausen, T

    D. Werdehausen, T. Takayama, M. H¨ oppner, G. Al- brecht, A. W. Rost, Y. Lu, D. Manske, H. Takagi, and S. Kaiser, Coherent order parameter oscillations in the ground state of the excitonic insulator Ta2NiSe5, Science Advances4, eaap8652 (2018)

  16. [16]

    Mazza, M

    G. Mazza, M. R¨ osner, L. Windg¨ atter, S. Latini, H. H¨ ubener, A. J. Millis, A. Rubio, and A. Georges, Nature of Symmetry Breaking at the Excitonic Insula- tor Transition: Ta 2NiSe5, Phys. Rev. Lett.124, 197601 (2020)

  17. [17]

    Y. Jia, P. Wang, C.-L. Chiu, Z. Song, G. Yu, B. J¨ ack, S. Lei, S. Klemenz, F. A. Cevallos, M. Onyszczak, N. Fishchenko, X. Liu, G. Farahi, F. Xie, Y. Xu, K. Watanabe, T. Taniguchi, B. A. Bernevig, R. J. Cava, 7 L. M. Schoop, A. Yazdani, and S. Wu, Evidence for a monolayer excitonic insulator, Nature Physics18, 87 (2022)

  18. [18]

    B. Sun, W. Zhao, T. Palomaki, Z. Fei, E. Runburg, P. Malinowski, X. Huang, J. Cenker, Y.-T. Cui, J.-H. Chu, X. Xu, S. S. Ataei, D. Varsano, M. Palummo, E. Molinari, M. Rontani, and D. H. Cobden, Evidence for equilibrium exciton condensation in monolayer WTe2, Nature Physics18, 94 (2022)

  19. [19]

    Gao, Y.-h

    Q. Gao, Y.-h. Chan, Y. Wang, H. Zhang, P. Jinxu, S. Cui, Y. Yang, Z. Liu, D. Shen, Z. Sun, J. Jiang, T. C. Chiang, and P. Chen, Evidence of high-temperature exciton con- densation in a two-dimensional semimetal, Nature Com- munications14, 994 (2023)

  20. [20]

    Gao, Y.-h

    Q. Gao, Y.-h. Chan, P. Jiao, H. Chen, S. Yin, K. Tang- prapha, Y. Yang, X. Li, Z. Liu, D. Shen, S. Jiang, and P. Chen, Observation of possible excitonic charge density waves and metal–insulator transitions in atomically thin semimetals, Nature Physics20, 597 (2024)

  21. [21]

    Gr¨ uner,Density Waves in Solids, Frontiers in Physics (Addison–Wesley, Reading, MA, 1994)

    G. Gr¨ uner,Density Waves in Solids, Frontiers in Physics (Addison–Wesley, Reading, MA, 1994)

  22. [22]

    H. Lu, M. Rossi, J.-h. Kim, H. Yavas, A. Said, A. Nag, M. Garcia-Fernandez, S. Agrestini, K.-J. Zhou, C. Jia, B. Moritz, T. P. Devereaux, Z.-X. Shen, and W.-S. Lee, Evolution of the electronic structure in Ta 2NiSe5 across the structural transition revealed by resonant inelastic x-ray scattering, Phys. Rev. B103, 235159 (2021)

  23. [23]

    Sugai, Lattice Vibrations in the Charge-Density-Wave States of Layered Transition Metal Dichalcogenides, physica status solidi (b)129, 13 (1985)

    S. Sugai, Lattice Vibrations in the Charge-Density-Wave States of Layered Transition Metal Dichalcogenides, physica status solidi (b)129, 13 (1985)

  24. [24]

    D. Lin, S. Li, J. Wen, H. Berger, L. Forr´ o, H. Zhou, S. Jia, T. Taniguchi, K. Watanabe, X. Xi, and M. S. Bahramy, Patterns and driving forces of dimensionality- dependent charge density waves in 2H-type transition metal dichalcogenides, Nature Communications11, 2406 (2020)

  25. [25]

    Y. Tian, M. J. Gray, H. Ji, R. J. Cava, and K. S. Burch, Magneto-elastic coupling in a potential ferromagnetic 2D atomic crystal, 2D Materials3, 025035 (2016)

  26. [26]

    Milosavljevi´ c, A.ˇSolaji´ c, S

    A. Milosavljevi´ c, A.ˇSolaji´ c, S. Djurdji ´ c Mijin, J. Peˇ si´ c, B. Viˇ si´ c, Y. Liu, C. Petrovic, N. Lazarevi´ c, and Z. V. Popovi´ c, Lattice dynamics and phase transitions in Fe3−xGeTe2, Phys. Rev. B99, 214304 (2019)

  27. [27]

    K. Kim, S. Y. Lim, J. Kim, J.-U. Lee, S. Lee, P. Kim, K. Park, S. Son, C.-H. Park, J.-G. Park, and H. Cheong, Antiferromagnetic ordering in van der Waals 2D mag- netic material MnPS 3 probed by Raman spectroscopy, 2D Materials6, 041001 (2019)

  28. [28]

    Pawbake, T

    A. Pawbake, T. Pelini, N. P. Wilson, K. Mosina, Z. Sofer, R. Heid, and C. Faugeras, Raman scattering signatures of strong spin-phonon coupling in the bulk magnetic van der Waals material CrSBr, Phys. Rev. B107, 075421 (2023)

  29. [29]

    Wang, S.-J

    Y.-M. Wang, S.-J. Tian, C.-H. Li, F. Jin, J.-T. Ji, H.-C. Lei, and Q.-M. Zhang, Raman scattering study of two- dimensional magnetic van der Waals compound VI3, Chi- nese Physics B29, 056301 (2020)

  30. [30]

    K. Kim, S. Y. Lim, J.-U. Lee, S. Lee, T. Y. Kim, K. Park, G. S. Jeon, C.-H. Park, J.-G. Park, and H. Cheong, Sup- pression of magnetic ordering in XXZ-type antiferromag- netic monolayer NiPS3, Nature Communications10, 345 (2019)

  31. [31]

    J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J.-G. Park, and H. Cheong, Ising- Type Magnetic Ordering in Atomically Thin FePS 3, Nano Letters16, 7433 (2016)

  32. [32]

    X. Wang, K. Du, Y. Y. Fredrik Liu, P. Hu, J. Zhang, Q. Zhang, M. H. S. Owen, X. Lu, C. K. Gan, P. Sen- gupta, C. Kloc, and Q. Xiong, Raman spectroscopy of atomically thin two-dimensional magnetic iron phospho- rus trisulfide (FePS 3) crystals, 2D Materials3, 031009 (2016)

  33. [33]

    Kim, J.-U

    K. Kim, J.-U. Lee, and H. Cheong, Raman spectroscopy of two-dimensional magnetic van der Waals materials, Nanotechnology30, 452001 (2019)

  34. [34]

    Zhang, X

    Y. Zhang, X. Wu, B. Lyu, M. Wu, S. Zhao, J. Chen, M. Jia, C. Zhang, L. Wang, X. Wang, Y. Chen, J. Mei, T. Taniguchi, K. Watanabe, H. Yan, Q. Liu, L. Huang, Y. Zhao, and M. Huang, Magnetic Order-Induced Po- larization Anomaly of Raman Scattering in 2D Magnet CrI3, Nano Letters20, 729 (2020)

  35. [35]

    S. Li, Z. Ye, X. Luo, G. Ye, H. H. Kim, B. Yang, S. Tian, C. Li, H. Lei, A. W. Tsen, K. Sun, R. He, and L. Zhao, Magnetic-Field-Induced Quantum Phase Transitions in a van der Waals Magnet, Phys. Rev. X10, 011075 (2020)

  36. [36]

    Huang, J

    B. Huang, J. Cenker, X. Zhang, E. L. Ray, T. Song, T. Taniguchi, K. Watanabe, M. A. McGuire, D. Xiao, and X. Xu, Tuning inelastic light scattering via symme- try control in the two-dimensional magnet CrI 3, Nature Nanotechnology15, 212 (2020)

  37. [37]

    McCreary, T

    A. McCreary, T. T. Mai, F. G. Utermohlen, J. R. Simp- son, K. F. Garrity, X. Feng, D. Shcherbakov, Y. Zhu, J. Hu, D. Weber, K. Watanabe, T. Taniguchi, J. E. Goldberger, Z. Mao, C. N. Lau, Y. Lu, N. Trivedi, R. Vald´ es Aguilar, and A. R. Hight Walker, Distinct magneto-Raman signatures of spin-flip phase transitions in CrI3, Nature Communications11, 3879 (2020)

  38. [38]

    B. Lyu, Y. Gao, Y. Zhang, L. Wang, X. Wu, Y. Chen, J. Zhang, G. Li, Q. Huang, N. Zhang, Y. Chen, J. Mei, H. Yan, Y. Zhao, L. Huang, and M. Huang, Probing the Ferromagnetism and Spin Wave Gap in VI 3 by Helicity- Resolved Raman Spectroscopy, Nano Letters20, 6024 (2020)

  39. [39]

    Cenker, B

    J. Cenker, B. Huang, N. Suri, P. Thijssen, A. Miller, T. Song, T. Taniguchi, K. Watanabe, M. A. McGuire, D. Xiao, and X. Xu, Direct observation of two- dimensional magnons in atomically thin CrI 3, Nature Physics17, 20 (2021)

  40. [40]

    Zhang and Q

    L. Zhang and Q. Niu, Chiral Phonons at High-Symmetry Points in Monolayer Hexagonal Lattices, Phys. Rev. Lett. 115, 115502 (2015)

  41. [41]

    H. Zhu, J. Yi, M.-Y. Li, J. Xiao, L. Zhang, C.-W. Yang, R. A. Kaindl, L.-J. Li, Y. Wang, and X. Zhang, Obser- vation of chiral phonons, Science359, 579 (2018)

  42. [42]

    Zhang and S

    T. Zhang and S. Murakami, Chiral phonons and pseu- doangular momentum in nonsymmorphic systems, Phys- ical Review Research4, L012024 (2022)

  43. [43]

    H. Ueda, M. Garc ´ ıa-Fern´ andez, S. Agrestini, C. P. Ro- mao, J. van den Brink, N. A. Spaldin, K.-J. Zhou, and U. Staub, Chiral phonons in quartz probed by X-rays, Nature618, 946 (2023)

  44. [44]

    Ishito, H

    K. Ishito, H. Mao, Y. Kousaka, Y. Togawa, S. Iwasaki, T. Zhang, S. Murakami, J.-i. Kishine, and T. Satoh, Truly chiral phonons inα-HgS, Nature Physics19, 35 (2023)

  45. [45]

    Zhang, Z

    T. Zhang, Z. Huang, Z. Pan, L. Du, G. Zhang, and S. Mu- rakami, Weyl phonons in chiral crystals, Nano Letters23, 7561 (2023). 8

  46. [46]

    Zhang, Z

    S. Zhang, Z. Huang, M. Du, T. Ying, L. Du, and T. Zhang, Comprehensive study of phonon chirality under symmetry constraints, Physical Review B113, 024302 (2026)

  47. [47]

    Zhang, Y

    T. Zhang, Y. Liu, H. Miao, and S. Murakami, Advances in phonons: From band topology to phonon chirality, arXiv preprint arXiv:2505.06179 (2025)

  48. [48]

    Zhang and Q

    L. Zhang and Q. Niu, Angular Momentum of Phonons and the Einstein–de Haas Effect, Phys. Rev. Lett.112, 085503 (2014)

  49. [49]

    W. Jin, Z. Ye, X. Luo, B. Yang, G. Ye, F. Yin, H. H. Kim, L. Rojas, S. Tian, Y. Fu, S. Yan, H. Lei, K. Sun, A. W. Tsen, R. He, and L. Zhao, Tunable layered-magnetism-assisted magneto-Raman effect in a two-dimensional magnet CrI 3, Proceedings of the Na- tional Academy of Sciences117, 24664 (2020)

  50. [50]

    F. G. G. Hernandez, A. Baydin, S. Chaudhary, F. Tay, I. Katayama, J. Takeda, H. Nojiri, A. K. Okazaki, P. H. O. Rappl, E. Abramof, M. Rodriguez-Vega, G. A. Fiete, and J. Kono, Observation of interplay between phonon chirality and electronic band topology, Science Advances9, eadj4074 (2023)

  51. [51]

    Yang, Y.-Y

    R. Yang, Y.-Y. Zhu, M. Steigleder, Y.-C. Liu, C.-C. Liu, X.-G. Qiu, T. Zhang, and M. Dressel, Inherent Circu- lar Dichroism of Phonons in Magnetic Weyl Semimetal Co3Sn2S2, Phys. Rev. Lett.134, 196905 (2025)

  52. [52]

    M. Che, J. Liang, Y. Cui, H. Li, B. Lu, W. Sang, X. Li, X. Dong, L. Zhao, S. Zhang, T. Sun, W. Jiang, E. Liu, F. Jin, T. Zhang, and L. Yang, Magnetic Or- der Induced Chiral Phonons in a Ferromagnetic Weyl Semimetal, Phys. Rev. Lett.134, 196906 (2025)

  53. [53]

    Lukachuk, C

    M. Lukachuk, C. Zheng, H. Mattausch, R. K. Kre- mer, A. Simon, and M. G. Banks, RE 2+xI2M2+y (RE = Ce,Gd, Y; M = Al, Ga): Reduced Rare Earth Halides with a Hexagonal Metal Atom Network, Zeitschrift f¨ ur Naturforschung B62, 633 (2007)

  54. [54]

    Kaneko, R

    T. Kaneko, R. Mizuno, S. Kamiyama, H. Miyamoto, and M. Ochi, Electronic band structure, phonon dispersion, and magnetic triple-qstate in gdgai, Phys. Rev. B113, 045156 (2026)

  55. [55]

    Okuma, K

    R. Okuma, K. Yamagami, Y. Fujisawa, C. H. Hsu, Y. Obata, N. Tomoda, M. Dronova, K. Kuroda, H. Ishikawa, K. Kawaguchi, K. Aido, K. Kindo, Y. H. Chan, H. Lin, Y. Ihara, T. Kondo, and Y. Okada, Emer- gent topological magnetism in hund’s excitonic insulator (2024), arXiv:2405.16781 [cond-mat.str-el]

  56. [56]

    Zhang, D

    Y. Zhang, D. Zhao, Q. Wang, and J. H. Smet, In situ Raman spectroscopy across superconducting transition of liquid-gated MoS2, Applied Physics Letters120, 053106 (2022)

  57. [57]

    Sun, S.-M

    Y.-J. Sun, S.-M. Pang, and J. Zhang, Review of raman spectroscopy of two-dimensional magnetic van der waals materials, Chinese Physics B30, 117104 (2021)

  58. [58]

    T. Wang, H. Sun, X. Li, and L. Zhang, Chiral phonons: Prediction, verification, and application, Nano Letters 24, 4311 (2024)

  59. [59]

    Zhang, M

    S. Zhang, M. Wang, and T. Zhang, General ab initio framework for chiral phonons induced by electronic order, arXiv preprint arXiv:2509.09253 (2025)

  60. [60]

    D. M. Juraschek, R. M. Geilhufe, H. Zhu, M. Basini, P. Baum, A. Baydin, S. Chaudhary, M. Fechner, B. Fle- bus, G. Grissonnanche,et al., Chiral phonons, Nature Physics21, 1532 (2025)

  61. [61]

    The Supplemental Material also contains Refs

    See Supplemental Material at [URL will be inserted by publisher] for details of sample preparation, x-ray diffrac- tion measurements, device fabrication, polarized Ra- man measurements, first-principles calculations, room- temperature polarized Raman spectra, Raman-intensity maps, Raman-active modes at the M point, lattice con- stants, magnetic-field-depe...

  62. [62]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Physical review B54, 11169 (1996)

  63. [63]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Physical review let- ters77, 3865 (1996)

  64. [64]

    A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Imple- mentation strategies in phonopy and phono3py, Journal of Physics: Condensed Matter35, 353001 (2023)

  65. [65]

    Loudon, The Raman effect in crystals, Advances in Physics13, 423 (1964)

    R. Loudon, The Raman effect in crystals, Advances in Physics13, 423 (1964)

  66. [66]

    Men´ endez and M

    J. Men´ endez and M. Cardona, Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, andα−Sn: Anharmonic effects, Phys. Rev. B29, 2051 (1984)

  67. [67]

    Irmer, M

    G. Irmer, M. Wenzel, and J. Monecke, The temperature dependence of the LO(T) and TO(T) phonons in GaAs and InP, physica status solidi (b)195, 85 (1996)

  68. [68]

    A. Link, K. Bitzer, W. Limmer, R. Sauer, C. Kirchner, V. Schwegler, M. Kamp, D. G. Ebling, and K. W. Benz, Temperature dependence of the E2 and A1(LO) phonons in GaN and AlN, Journal of Applied Physics86, 6256 (1999)

  69. [69]

    R. W. Munn, Gr¨ uneisen parameters for molecular crys- tals, Phys. Rev. B12, 3491 (1975)

  70. [70]

    E. T. Ritz, S. J. Li, and N. A. Benedek, Thermal expan- sion in insulating solids from first principles, Journal of Applied Physics126, 171102 (2019)

  71. [71]

    T. Yin, K. A. Ulman, S. Liu, A. Granados del ´Aguila, Y. Huang, L. Zhang, M. Serra, D. Sedmidubsky, Z. Sofer, S. Y. Quek, and Q. Xiong, Chiral Phonons and Giant Magneto-Optical Effect in CrBr3 2D Magnet, Advanced Materials33, 2101618 (2021)

  72. [72]

    Liu, M.-Q

    S. Liu, M.-Q. Long, and Y.-P. Wang, Theoretical investi- gations on the magneto-Raman effect of CrI3, Phys. Rev. B108, 184414 (2023)

  73. [73]

    R. Rao, J. Jiang, R. Pachter, T. T. Mai, V. Mohau- gen, M. F. Mu˜ noz, R. Siebenaller, E. Rowe, R. Selhorst, A. N. Giordano, A. R. H. Walker, and M. A. Susner, Anomalous Raman scattering in layered AgCrP2Se6: He- lical modes and excitation energy-dependent intensities (2025), arXiv:2501.17565 [cond-mat.mes-hall]

  74. [74]

    Anastassakis, E

    E. Anastassakis, E. Burstein, A. Maradudin, and R. Min- nick, Morphic effects — III. Effects of an external mag- netic field on the long wavelength optical phonons, Jour- nal of Physics and Chemistry of Solids33, 519 (1972)

  75. [75]

    Momma and F

    K. Momma and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, Journal of Applied Crystallography44, 1272 (2011)