{"id":"c0924bdf-a881-451c-ab06-66c59ec7de01","arxiv_id":"2412.17020","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Optical spectroscopy shows spectral weight moves from below 0.4 eV to 0.8 to 1.5 eV across the CDW transition in FeGe, attributed to Ge1 distortion and a Hund-coupling-driven spin-state change.","lead":"In a kagome magnet FeGe, light reflection measurements show that when the material undergoes a charge-density-wave transition, low-energy excitations lose spectral weight and higher-energy excitations gain it, a sign of band reconstruction. Comparing samples annealed at different temperatures links this shift to distortion of germanium atoms and to growth of the iron magnetic moment.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Uniform 0.5–1 Å Ge1 displacement in a one-unit-cell DFT model is the least secure link; if it overestimates the partial-distortion band reconstruction, the common Ge1-distortion attribution collapses.","rationale":"The optical measurements themselves are direct and clearly show spectral-weight transfer in both samples, so the empirical observation is not in question. The weak point is the quantitative bridge from the measured spectra to the proposed microscopic mechanism: the paper's own DFT section admits that the realistic 1/4 partial distortion could not be calculated and a single-unit-cell uniform displacement was used instead. The reader's weakest assumption identifies exactly this modeling gap, and I agree. Because the central causal claim depends on this approximation, the manuscript needs either a supercell calculation or a quantitative comparison to known experimental displacements and ARPES data to support the 'confirmed' attribution. This does not warrant rejection—the optical data and prior literature make the proposed mechanism plausible—but it does justify a conditional verdict. I therefore leave the reader's conditional verdict unchanged.","tokens_in":10570,"tokens_out":4443,"duration_ms":44318,"concrete_test":"Compute the optical conductivity and integrated spectral weight for a 2×2×2 supercell with 1/4 of the Ge1 atoms displaced by the experimentally determined value (from refs [27,31]); compare the resulting Δσ1 and SW transfer (below 0.4 eV to 0.8–1.5 eV) with the measured difference between pristine and CDW states in S1. If the supercell result reproduces the measured transfer amplitude, the concern is resolved; if it is much smaller, the single-unit-cell model is not representative and the attribution needs revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is in Sec. II C: to model the effect of Ge1 distortion on the optical conductivity, the authors displace every Ge1 atom in a single unit cell by 0.5 and 1 Å, while the actual CDW in S1 distorts only 1/4 of the Ge1 atoms, and the magnitude of that displacement is not stated in this paper. The authors explicitly concede that a realistic supercell calculation 'surpasses our computational resources' and justify the single-cell model by citing earlier work [31] and ARPES. The central attribution—that the same band reconstruction explains both the abrupt transfer in S1 and the progressive transfer in S2—therefore rests on the assumption that a uniform, large displacement in one unit cell is quantitatively representative of a sparse, likely smaller, local distortion. If the single-cell calculation overestimates the band reconstruction, then the measured SW transfer could have a different origin (e.g., magnetic ordering or correlation effects), and the 'confirmed' language in Sec. III is unsupported. This is an external-modeling risk, not an internal inconsistency, but it is the least secure link in the causal chain.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports optical reflectivity measurements on two FeGe single crystals annealed at 320 °C (S1, with a CDW transition at 110 K) and 560 °C (S2, without CDW), together with DFT band-structure and optical-conductivity calculations. The authors observe that upon cooling, S1 abruptly transfers spectral weight from below 0.4 eV to the 0.8–1.5 eV range across the CDW transition, while S2 shows a similar but progressive transfer from 300 K to 5 K. They attribute the transfer in both samples to a band reconstruction caused by the c-axis distortion of Ge1 atoms, which they model in DFT by displacing all Ge1 atoms in one unit cell by 0.5 and 1 Å. The proposed mechanism is that Ge1 distortion weakens Ge1-p/Fe-d hybridization, changes Fe 3d orbital energies, and through Hund's coupling enhances the Fe magnetic moment.","tokens_in":10685,"tokens_out":2428,"duration_ms":25577,"significance":"If the attribution is correct, the paper provides a relatively direct optical signature of band reconstruction driven by a specific local lattice distortion, and it unifies the CDW sample and the annealed non-CDW sample under one mechanism. The raw optical spectra appear to show the claimed low-energy suppression and high-energy enhancement clearly, and the two-sample comparison is an experimentally sensible design. The DFT calculation is genuinely first-principles and is not fitted to the optical data, which reduces circularity concerns. The paper also makes a testable claim about the role of Ge1 displacement magnitude, which is a useful step toward understanding the charge-lattice-spin coupling in FeGe. However, the quantitative support for the central mechanism is weakened by the single-unit-cell uniform-displacement modeling and by the absence of error estimates in the Drude-Lorentz analysis.","major_comments":[{"comment":"The central attribution rests on the assumption that a uniform displacement of all Ge1 atoms by 0.5–1 Å in a single unit cell reproduces the band reconstruction caused by a CDW that displaces only 1/4 of the Ge1 atoms (S1) or by 8% distorted Ge1 atoms (S2). The paper explicitly states that a realistic supercell calculation 'surpasses our computational resources' and does not report the actual displacement magnitude of the CDW-distorted Ge1 atoms. The word 'confirmed' in Section III is therefore too strong: the DFT result is at best qualitative evidence for the direction of the spectral-weight shift, not a quantitative confirmation of its magnitude. I ask the authors to either provide a supercell calculation with the actual partially displaced structure, or to demonstrate (e.g., by scaling or by comparing with published supercell results) that the single-unit-cell uniform displacement is representative. Without such a test, the central claim that Ge1 distortion, rather than other CDW or correlation effects, drives the measured transfer remains an unsupported quantitative step.","section":"Section II C, Fig. 3c-e, and Section III"},{"comment":"The quantitative spectral-weight analysis relies on a Drude-Lorentz decomposition into D1, D2, and L1–L6 oscillators, but the paper provides no error bars, no uniqueness test, and no discussion of how the oscillator set was chosen. The claim that 'the low-energy SW, encompassing both intraband responses (D1 and D2) and interband transitions (L1 to L3), undergoes suppression' while 'L4+L5' increases is a quantitative statement, and its robustness to alternative fits should be demonstrated. In particular, the separation between Drude and Lorentz components at low energy is notoriously non-unique, and the integrated spectral-weight ratios in Figs. 1c-f are more model-independent. I recommend adding an uncertainty analysis (e.g., fitting with different numbers of oscillators or imposing sum-rule constraints) and, if possible, reporting the temperature-dependent spectral weights directly from the integral of the measured σ1(ω) rather than only from the fitted components.","section":"Section II B, Figs. 2c and 2d"},{"comment":"The DFT optical conductivity σ1(ω) shown in Fig. 3e is only compared qualitatively with the measured spectra; the computational parameters (exchange-correlation functional, U value, spin ordering, k-point sampling, and broadening) are not given in the main text or in the available supplemental description. Since the paper claims that 'the consistency between observations and theoretical calculations confirmed' the mechanism, the reader needs enough information to assess whether the calculated shift is of the correct magnitude and energy scale. At minimum, the authors should provide the computational details and, ideally, an overlay of the calculated and measured σ1(ω) for the pristine and distorted cases so that the claimed agreement can be judged quantitatively.","section":"Section II C, Fig. 3e"}],"minor_comments":[{"comment":"The phrase 'both materials exhibit distinct mentality' appears to be a typo; presumably 'metallicity' is intended.","section":"Section II A, second paragraph"},{"comment":"The text says 'the Drude-Lorentz mode' but the intended word is likely 'model'.","section":"Section II B, first sentence"},{"comment":"The supplemental material is cited as '[28] Supplementary.' without a title or link; please provide a full reference and a description of its contents.","section":"Reference [28]"},{"comment":"The axis label 'c (103 cm-1)' in Figs. 1c and 1d appears to be a typo for the photon-energy axis; also, the caption could clarify that the insets in (c) and (d) show the lattice structure, as they are not mentioned in the caption body.","section":"Fig. 1 caption"},{"comment":"The phrase 'Hund’s rule coupling' should be 'Hund's coupling' or 'Hund-rule coupling' for consistency, and the notation JH should be defined before first use in Section III.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper presents a clear optical experimental comparison, and the qualitative direction of the spectral-weight transfer is convincing. My main concern is the quantitative gap between the measured effect and the DFT model: a uniform 0.5–1 Å displacement of all Ge1 atoms in one unit cell is not shown to represent the partial CDW distortion, and the paper uses 'confirmed' language that is not supported. This is fixable with additional calculations or with a carefully softened claim, so I recommend major revision rather than rejection. The authors should also provide computational details and Drude-Lorentz fit uncertainties, as these are needed for reproducibility."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nKnow this: the paper reports a clean optical comparison of FeGe annealed at 320°C and 560°C, showing that spectral weight moves from below 0.4 eV to 0.8–1.5 eV either abruptly (below the CDW at 110 K) or progressively (in the 560°C sample). That is a solid, reproducible observation and a useful fingerprint. The authors tie it to Ge1 distortion, which is plausible and consistent with earlier ARPES and DFT work.\n\nWhat is genuinely new is the comparative SW-transfer data and the explicit link between the optical response and the Ge1 distortion/Hund-coupling picture. The raw spectra and the SW integrals are convincing; the claim that both paths—CDW and annealing—act on the same structural coordinate is attractive. The DFT calculation is qualitative but honestly labeled; the authors admit the single-cell approximation.\n\nSoft spots: (1) The Drude-Lorentz decomposition has no error bars, and the quantitative SW per component is fit output, not direct data. The integrated SW in Fig 1 is direct, so the qualitative shift survives. (2) No structural measurement on the measured samples; the 8% Ge1-distortion premise is imported from the authors' own PRL (ref 27). That is not circular, but it means the central premise is not verified on these crystals. (3) The DFT displaces all Ge1 by 0.5–1 Å in a one-unit-cell model, whereas the CDW displaces only 1/4 of Ge1 and the actual magnitude is not stated. The supercell is beyond resources, so the calculated σ1 is a qualitative guide, not a quantitative reproduction. Given that, the \"confirmed\" language in Sec III is too strong. The data support a consistent interpretation, not a proof.\n\nFor whom: anyone following FeGe or kagome magnets, and anyone doing optical spectroscopy on materials with small structural distortions will get value from the methodology and the cautionary example. The paper deserves serious refereeing; it has a genuine experimental result that the community should see. I'd recommend asking for uncertainty estimates, structural characterization, and a toned-down conclusion, but not a rejection.\n\nBest.","headline":"Clean optical data show spectral-weight transfer in both annealing regimes, but the single-cell DFT and imported structural premises make the Ge1-distortion attribution plausible, not confirmed.","tokens_in":11352,"tokens_out":2477,"would_cite":true,"duration_ms":22894,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper attributes the optical spectral-weight transfer in the kagome magnet FeGe to c-axis displacement of Ge1 atoms, which reshapes the Fe 3d bands and, through Hund's rule coupling, enhances the iron magnetic moment.","keywords":["FeGe","kagome lattice","charge-density wave","optical conductivity","spectral weight transfer","band reconstruction","Hund's coupling","Ge1 lattice distortion"],"falsifier":"Determining the Ge1 distortion fraction in the 560°C-annealed sample by single-crystal diffraction and measuring the optical spectral-weight transfer in a series of samples annealed to different temperatures would test the structural premise: if the transfer does not scale with the measured distortion fraction, the attribution is wrong. A supercell density-functional calculation with only one quarter of Ge1 atoms displaced—explicitly beyond the paper's resources—would test the modeling premise: it should reproduce the same qualitative transfer, and if it does not, the single-unit-cell approximation is the weak point.","tokens_in":10251,"feed_emoji":"🧲","tokens_out":14924,"duration_ms":113745,"temperature":0.7,"pith_summary":"This paper tries to establish that the dramatic redistribution of optical spectral weight in the kagome magnet FeGe—both the abrupt change at the charge-density-wave transition and the gradual change in an annealed sample without such a transition—has a single microscopic cause: displacement of the Ge1 germanium atoms along the c-axis. Using reflectivity measurements converted to optical conductivity, the authors show that low-energy excitations below 0.4 eV lose spectral weight that reappears between 0.8 and 1.5 eV, and that the high-energy weight tracks the iron magnetic moment. First-principles calculations with a displaced Ge1 atom reproduce the transfer and show that the distortion moves the iron $3d$ orbital energies closer together, so that Hund's rule coupling tips Fe from a low-spin toward a high-spin state. If correct, the result identifies a concrete lattice motion—not the charge order by itself—as the driver of both the electronic reconstruction and the magnetic enhancement, and it suggests that annealing can tune magnetism in kagome metals.","feed_headline":"Germanium atoms, not charge order, drive the optical shift in FeGe","feed_subtitle":"Both the CDW sample and the annealed sample show the same band reconstruction, linking lattice motion to magnetism.","key_machinery":"The paper's load-bearing observable is the integrated spectral weight $SW(\\omega_c,T) = (Z_0/\\pi^2)\\int_0^{\\omega_c} \\sigma_1(\\omega')d\\omega'$, computed from Kramers-Kronig-transformed reflectivity and decomposed into Drude and Lorentz components; the central identity is that this weight is conserved and moves from below about 0.4 eV into the 0.8–1.5 eV window. The explanatory machinery on the theory side is a density-functional band calculation in which the Ge1 atoms are displaced along the c-axis by 0.5 and 1 Å within a single unit cell; this displacement lowers the Fe $d_{yz}$ orbital, raises the $d_{xy}/d_{x^2-y^2}$ orbitals, pushes the van Hove singularity at the $M$ point toward the Fermi level, and—because the crystal-field splitting narrows below the Hund's coupling energy $J_H\\approx 0.8$ eV—favors a high-spin configuration. The same Ge1 displacement parameter thus accounts for both the optical transfer and the enhanced Fe moment.","core_discovery":"The paper's central claim is that the spectral-weight transfer seen in both FeGe samples—abrupt below the 110 K CDW transition in the 320°C-annealed crystal, gradual from 300 to 5 K in the 560°C-annealed crystal—has a single microscopic origin: the displacement of Ge1 atoms along the c-axis. In the 320°C sample, the CDW displaces one quarter of the Ge1 atoms; in the 560°C sample, annealing already leaves about 8% of them distorted. Density-functional band structures computed for Ge1 displacements of 0.5 and 1 Å reproduce the optical changes: flat bands move up, the Fe $d_{yz}$ orbital at $\\Gamma$ drops and gains occupancy, the $d_{xy}/d_{x^2-y^2}$ orbitals at $K$ and $H$ rise, the van Hove singularity at $M$ approaches the Fermi level, and the density of states at the Fermi level falls, suppressing the Drude response. Because the distortion narrows the crystal-field splitting between the Fe $3d$ orbital groups to below the Hund's coupling energy ($J_H \\approx 0.8$ eV), Fe shifts from a low-spin Fe$^{2+}$ toward a high-spin state, which the authors identify with the enhanced magnetic moment and the increased Néel temperature in the 560°C sample.","pith_inferences":["Not claimed by the paper: a supercell calculation with only one quarter of the Ge1 atoms displaced—the calculation the paper says exceeded its resources—would provide the decisive check of whether the single-unit-cell uniform displacement faithfully represents the partial distortion; if the spectral-weight transfer differs qualitatively, the central attribution would need revision.","Not claimed by the paper: uniaxial stress or strain along the c-axis of a pristine FeGe crystal should produce the same spectral-weight transfer and magnetic-moment enhancement without any CDW transition, because it directly drives the Ge1 displacement that the paper identifies as the cause.","Not claimed by the paper: the high-energy spectral weight tracking the Fe moment suggests that optical reflectivity in this energy range could serve as a fast bulk probe of magnetism in kagome metals where neutron scattering is impractical.","Not claimed by the paper: the proposed mechanism—p–d hybridization controlling the crystal-field splitting relative to Hund's coupling—may generalize to other transition-metal germanides and pnictides with similar anion-site distortions."],"forward_implications":["If the attribution is right, the abrupt suppression of low-frequency spectral weight below 110 K in the 320°C sample and the gradual suppression from 300 K in the 560°C sample are the same band reconstruction, making the CDW transition's optical signature a secondary consequence of the Ge1 displacement.","The high-frequency spectral weight in the 0.8–1.5 eV window becomes a bulk optical proxy for the Fe magnetic moment, tracking the neutron-scattering temperature dependence including the downturn below the ~40 K spin canting.","Annealing at 560°C pre-distorts enough Ge1 sites to suppress the CDW and raise the Néel temperature, so the lattice distortion and magnetic properties are tunable by processing without requiring the CDW state.","The density-functional results predict that further Ge1 displacement monotonically increases the Fe moment, linking the degree of lattice distortion quantitatively to magnetism."],"supporting_citations":[{"why":"It supplies the annealing control that the argument builds on: 320°C annealing preserves the CDW transition, while 560°C annealing distorts about 8% of Ge1 atoms along the c-axis, suppresses the CDW, and raises the Néel temperature.","marker":"[27]"},{"why":"It provides the structural and band-structure basis for modeling only the Ge1 distortion, reporting that other lattice sites barely move and that the related band changes match supercell calculations and photoemission.","marker":"[31]"},{"why":"It supplies the neutron-scattering magnetic-moment data whose temperature dependence the high-energy spectral weight is compared with, including the spin-canting downturn.","marker":"[17]"},{"why":"It establishes the near-degenerate energy scales of lattice, charge, and spin in FeGe and places the van Hove singularity close to the Fermi level when electron correlations are included, motivating the structural instability.","marker":"[20]"},{"why":"It gives the crystal-field grouping of the Fe 3d orbitals and the Hund's coupling scale $J_H \\approx 0.8$ eV, the quantitative input for the low-spin-to-high-spin argument.","marker":"[34]"},{"why":"It provides the high-energy pseudo-gap behavior in iron-based superconductors used as the analogy for the gradual spectral-weight transfer in the 560°C-annealed sample.","marker":"[29]"},{"why":"It supports the assignment that Fe sits in a low-spin Fe$^{2+}$ state in the undistorted lattice, the starting point for the spin-state crossover.","marker":"[35]"}],"fun_headline_variants":["Ge1 motion, not charge order, drives FeGe's optical shift","Anneal or CDW: same Ge1 distortion remakes FeGe bands","FeGe's hidden twist: Ge1 atoms rewire bands and spin","One atomic shift explains FeGe's CDW and anneal optical changes","Bending Ge1 bonds links charge, lattice, and spin in FeGe"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument rests on the structural premise, taken from earlier work, that annealing at 560°C distorts 8% of Ge1 atoms and that the CDW displaces one quarter of Ge1 atoms along the c-axis, together with the modeling assumption that a single-unit-cell density-functional calculation with a uniform 0.5 to 1 Å Ge1 displacement captures the band reconstruction of the real partially distorted crystal.","fun_headline_variants_meta":{"raw":{"variants":["Ge1 motion, not charge order, drives FeGe's optical shift","Anneal or CDW: same Ge1 distortion remakes FeGe bands","FeGe's hidden twist: Ge1 atoms rewire bands and spin","One atomic shift explains FeGe's CDW and anneal optical changes","Bending Ge1 bonds links charge, lattice, and spin in FeGe"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000238,"raw_usage":{"total_tokens":1608,"prompt_tokens":1137,"completion_tokens":471,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":753,"completion_tokens_details":{"reasoning_tokens":387}},"tokens_in":753,"tokens_out":471,"duration_ms":5302,"temperature":1.0,"reasoning_tokens":387,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T05:51:31.947250+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Determining the Ge1 distortion fraction in the 560°C-annealed sample by single-crystal diffraction and measuring the optical spectral-weight transfer in a series of samples annealed to different temperatures would test the structural premise: if the transfer does not scale with the measured distortion fraction, the attribution is wrong. A supercell density-functional calculation with only one quarter of Ge1 atoms displaced—explicitly beyond the paper's resources—would test the modeling premise: it should reproduce the same qualitative transfer, and if it does not, the single-unit-cell approximation is the weak point.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the annealing control that the argument builds on: 320°C annealing preserves the CDW transition, while 560°C annealing distorts about 8% of Ge1 atoms along the c-axis, suppresses the CDW, and raises the Néel temperature."},{"cited_title":"Zhang, J","cited_arxiv_id":null,"evidence_quote":"It provides the structural and band-structure basis for modeling only the Ge1 distortion, reporting that other lattice sites barely move and that the related band changes match supercell calculations and photoemission."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the neutron-scattering magnetic-moment data whose temperature dependence the high-energy spectral weight is compared with, including the spin-canting downturn."},{"cited_title":"Wang, Physical Review Materials 7, 104006 (2023)","cited_arxiv_id":null,"evidence_quote":"It establishes the near-degenerate energy scales of lattice, charge, and spin in FeGe and places the van Hove singularity close to the Fermi level when electron correlations are included, motivating the structural instability."},{"cited_title":"Huang and H","cited_arxiv_id":null,"evidence_quote":"It gives the crystal-field grouping of the Fe 3d orbitals and the Hund's coupling scale $J_H \\approx 0.8$ eV, the quantitative input for the low-spin-to-high-spin argument."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It provides the high-energy pseudo-gap behavior in iron-based superconductors used as the analogy for the gradual spectral-weight transfer in the 560°C-annealed sample."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supports the assignment that Fe sits in a low-spin Fe$^{2+}$ state in the undistorted lattice, the starting point for the spin-state crossover."}],"review_version":1}