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REVIEW 4 major objections 4 minor 31 references

Temperature-induced band shift in ferromagnetic Weyl semimetal Co3Sn2S2

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Temperature-dependent optical spectra reveal magnetization-driven band shifts in the ferromagnetic Weyl semimetal candidate Co3Sn2S2 and identify a low-energy transition tied to its Weyl nodes.

desk verdict Solid optical dataset, but the Weyl-node peak assignment depends on a global 1.33 rescaling that the paper's own numbers contradict. read the letter →

arxiv 1908.03895 v2 pith:PUR4EVR4 submitted 2019-08-11 cond-mat.supr-con cond-mat.mtrl-sci

Run Yang , Tan Zhang , Liqin Zhou , Yaomin Dai , Zhiyu Liao , Hongming Weng , Xianggang Qiu This is my paper · ORCID
classification cond-mat.supr-concond-mat.mtrl-sci PACS 72.15.-v74.70.-b78.30.-j
keywords WeylsemimetalCo3Sn2S2opticalconductivitybandrenormalizationexchangesplittingmagneticphasetransitionDrude-Lorentzanalysisfirst-principlescalculation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to show that Co3Sn2S2 is a magnetic Weyl semimetal whose Weyl nodes move as the magnetization changes, and that optical spectroscopy can observe that movement directly. It measures the optical conductivity from 300 K down to 5 K and compares the spectra with first-principles band structures computed with the Co moment constrained to values meant to represent the paramagnetic, 100 K, and 5 K states. After rescaling the experimental photon-energy axis by a factor of 1.33, the three observed interband peaks line up with specific calculated transitions, including a low-energy peak from spin-orbit-gapped bands near the Weyl nodes. A careful reader would care because a magnetic Weyl semimetal with magnetization-tunable Weyl nodes offers a practical temperature or magnetic-field knob on topological electronic properties.

What carries the argument

The load-bearing object is the magnetization-constrained first-principles band structure. The calculations hold the Co magnetic moment fixed at zero, 0.15, and 0.33 Bohr magnetons per Co to represent the paramagnetic, 100 K, and 5 K states, and the exchange splitting between spin channels is what shifts the bands. The optical conductivity is computed from the Kubo formula and compared with measurement after rescaling the experimental photon wavenumber by 1.33; the same rescaling is then used to attribute the observed peaks to calculated interband transitions. The linear-in-frequency optical conductivity below 100 K and the sharp plasma edge are the signatures used to tie InterA to three-dimensional linear bands near the Weyl nodes.

What would settle it

Measure the actual electronic bands of Co3Sn2S2 with angle-resolved photoemission at 5 K and 100 K and compare them with the density functional theory bands computed at moments of 0.33 and 0.15 Bohr magnetons per Co; if different bands need different rescaling factors rather than one global 1.33, the assignments of InterA, InterB, and InterC collapse. Alternatively, apply a magnetic field at fixed temperature near the Curie temperature: if the 310 cm-1 InterA peak does not shift in position or weight as magnetization grows, the Weyl-node attribution is not supported.

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Extended reading notes

Core claim

The paper's central claim is that the temperature evolution of Co3Sn2S2's optical conductivity is the optical fingerprint of magnetization-driven band shifts, not just thermal broadening. As the material cools below its Curie temperature near 177 K, exchange splitting separates the spin-up and spin-down bands, with the spin-up bands moving toward the Fermi level and the spin-down bands moving to higher energy. Comparing the measured spectra with density functional theory at constrained moments assigns the three interband peaks: InterC, insensitive to magnetization and arising from crystal-field-split Co 3d t2g/eg bands; InterB, which appears only after the magnetic transition and comes from same-spin-channel Co 3d transitions; and InterA near 310 cm-1, which comes from the bands gapped by spin-orbit coupling along the nodal line and surrounding the Weyl nodes. The paper further argues that the single 1.33 rescaling means electron correlation is moderate, and that the $T^2$ suppression of the Drude weight below 100 K matches the theoretical expectation for a Weyl semimetal. The asserted conclusion is that Co3Sn2S2 is a magnetic Weyl semimetal and its Weyl nodes can be tuned by magnetization through temperature change.

Load-bearing premise

The peak assignments depend on the assumption that a single factor of 1.33 uniformly rescales all calculated bands to match experiment, and that the two constrained Co moments faithfully represent the 100 K and 5 K states.

Editorial extensions

If this is right

  • If the identification is right, the position and strength of the 310 cm-1 InterA peak track the spin-orbit-gapped bands that form the Weyl nodes, so bulk optical measurements can report on Weyl-node formation without surface-sensitive probes.
  • Because one global 1.33 rescaling reproduces three peaks, the correlation correction in Co3Sn2S2 is a moderate, mostly momentum-independent renormalization, making density functional theory band assignments reliable for this material.
  • The $T^2$ suppression of the Drude weight below 100 K, if caused by Weyl physics, gives a simple optical and transport signature for recognizing magnetic Weyl semimetals.
  • The magnetization-sensitive InterB appears only below the magnetic transition, so its onset marks the ferromagnetic phase in optical data.
  • If the Weyl nodes move with magnetization, then temperature or magnetic field can be used to tune the anomalous Hall response and related topological properties in this compound.

Reading between the lines

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

  • At fixed temperature below the Curie temperature, an applied magnetic field should shift and reshape InterA and InterB by changing the net magnetization; the paper does not test this field dependence, and it would provide a direct confirmation of the magnetization-tuning claim.
  • The single-factor 1.33 renormalization suggests that other cobalt-based shandites with similar Co 3d character might show the same global rescaling; checking that would reveal whether the moderate-correlation picture is specific to Co3Sn2S2 or generic to the family.
  • If the constrained moments truly represent the 100 K and 5 K states, then the measured temperature-dependent peak positions effectively map out the temperature dependence of the local Co moment, allowing optical data to be inverted into a magnetization curve.
  • The paper suggests a Lifshitz transition below 100 K as parabolic bands move away from the Fermi level; a search for this transition in quantum oscillation or thermoelectric measurements would be a testable consequence beyond the optical data.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper reports temperature-dependent in-plane optical conductivity measurements of Co3Sn2S2 between 5 K and 300 K, together with first-principles simulations in the paramagnetic state and in ferromagnetic states with constrained Co moments of 0.15 and 0.33 μB/Co. The authors identify three interband absorption features, InterA, InterB, and InterC, and assign them to calculated band-structure transitions: InterC is described as magnetization-insensitive, InterB as magnetization-sensitive, and InterA as arising from bands near the Weyl nodes. To obtain the assignments, the experimental wavenumber axis is rescaled by a global factor of 1.33, attributed to electron correlation, and the Drude scattering rates in the simulations are parameterized to mimic the temperature evolution. The paper concludes that Co3Sn2S2 is a magnetic Weyl semimetal and that its Weyl nodes can be tuned by magnetization and temperature.

Significance. If the peak assignments and the band-resolved interpretation are correct, the work would provide a clear optical-spectroscopy signature of magnetization-driven band shifts in a magnetic Weyl semimetal candidate, and would add quantitative evidence about the strength of electron correlation in Co3Sn2S2. The experimental data are careful and internally consistent: the extrapolated dc conductivity matches transport data, the spectral-weight analysis is physically reasonable, and the observation of temperature-dependent interband features is robust. However, the two quantitative pillars of the paper, namely the global 1.33 renormalization factor and the identification of InterA with Weyl-node-related transitions, are not established with sufficient rigor, and the constrained-moment calculations rely on parameters chosen to match the data. These issues do not invalidate the raw experimental findings, but they currently prevent the paper from supporting the strong claims in the abstract.

major comments (4)
  1. [Fig. 3f and text after it] The global rescaling of the experimental wavenumber axis by a factor of 1.33 is introduced specifically to match the calculated position of InterC, and the same rescaling is then used to claim that electron correlation in Co3Sn2S2 is moderate. This argument is partly circular: the renormalization factor is fitted to one peak and is not derived from any independent many-body calculation, and no uncertainty is attached to any of the three peak positions. A quantitative demonstration that the same factor consistently aligns InterA, InterB, and InterC, with stated tolerances, is required before the conclusion about moderate correlation can be accepted.
  2. [Discussion of InterA, p. 4] The assignment of InterA (310 cm−1) to transitions between bands near the Weyl nodes is not consistent with the stated rescaling. The manuscript says that the Wannier/SOC calculation gives a peak around 350 cm−1 that is consistent with the position of InterA in Fig. 1c, but on the rescaled abscissa used in Fig. 3f the measured 310 cm−1 feature would appear near 412 cm−1, which is an 18 percent discrepancy. Thus the comparison either ignores the 1.33 rescaling or, if the rescaling is applied, the match is poor. In either case a single global renormalization factor does not consistently support all three peak assignments, and the identification of InterA with Weyl-node-related transitions is not established.
  3. [Sec. on first-principles simulations] The constrained Co moments of 0.15 and 0.33 μB/Co are chosen to mimic the 100 K and 5 K states, but no independent relationship between temperature and magnetic moment is given. Without such a link, the comparison between experimental spectra and calculations at different fixed moments only demonstrates that the data can be reproduced by tuning two additional parameters; it does not by itself prove that the temperature-induced band shift is driven by magnetization. The authors should connect the constrained moments to measured magnetization values or to a temperature-dependent moment from first-principles or experiment.
  4. [Fig. 3f and simulated Drude parameters] The simulated spectra are generated with Drude scattering rates of 0.17, 0.05, and 0.03 eV, selected to match the experimental spectra. Because these choices affect the visibility of low-energy interband structure, the assertion that InterA is present below 100 K but cannot be resolved in the calculated spectra should be tested by varying the Drude parameters and by checking the robustness of the low-energy peak, rather than made on the basis of a single set of fitted scattering rates.
minor comments (4)
  1. [Throughout] The manuscript contains several typographical errors, including 'tow-dimensional' in the introduction and 'repspectively' in the discussion of Fig. 3, which should be corrected in a revised version.
  2. [Eq. (1) and Fig. 2] The parameters of the Drude-Lorentz fits used in Eq. (1) are not reported; a table listing the plasma frequencies, scattering rates, oscillator positions, widths, and strengths for the temperatures shown would improve reproducibility and allow readers to judge the quality of the fits.
  3. [Fig. 2b and text on ω-linear conductivity] The claim that the ω-linear conductivity from 130 to 230 cm−1 indicates the presence of 3D linear bands would be more convincing if accompanied by a quantitative comparison with the calculated joint density of states in the corresponding energy range, rather than only a linear extrapolation.
  4. [Abstract and summary] The phrase 'the results strongly support that Co3Sn2S2 is a magnetic WSM' is too strong relative to the evidence presented, which is based on peak assignments with the fitted rescaling; the wording should be moderated to reflect the assumptions involved.

Circularity Check

2 steps flagged · score 6.0 of 10

The 1.33 band renormalization is a fitted rescaling chosen to align InterC, the constrained moments and Drude rates are fitted to mimic the data, and the InterA/Weyl-node match switches between raw (310 cm^-1) and rescaled (412 cm^-1) axes, so the magnetic-WSM band attribution is partly built from inputs rather than independently predicted.

  1. fitted input called prediction [Fig. 3(f) and following paragraph (also abstract)]
    "It is noted that the experimental spectra are replotted with the incident photon wavenumber being scaled by a factor of 1.33 to match the InterC in Fig. 1c with the calculated position. This difference between the experimental and theoretical results comes from the correlation effect due to 3d orbitals of Co, which is not considered during the calculation within local density approximation."

    The factor 1.33 is not derived from an independent many-body calculation; it is imposed as a rescaling of the experimental wavenumber axis chosen so that InterC coincides with the calculated peak. The conclusion that Co 3d correlations renormalize the bands by 'a factor about 1.33' is therefore a restatement of that imposed match, not a prediction. The 'overall consistency' cited as evidence is guaranteed by construction for InterC, and the claim that the single factor works for the other peaks is asserted from the same scaled spectra rather than established by an independent calculation.

  2. fitted input called prediction [First-principles section before Fig. 3(f), and Fig. 3 caption]
    "To mimic the T effect, the magnetic moment on Co is constrained at different values during the self-consistent calculation. ... The scattering rate 1/τD is parameterized as 0.17 eV, 0.05 eV and 0.03 eV to mimic the decreasing (increasing) of T (lifetime) and to well fit the experimental spectra. Within these settings, the theoretical spectra are shown in Fig. 3(f) together with the experimental ones."

    The magnetic moments used to represent the 100 K and 5 K states are chosen to mimic the temperature effect; 0.33 μB/Co is the unconstrained ground-state moment, but 0.15 μB/Co is not independently tied to 100 K, and the paper provides no measured moment-temperature link. The Drude scattering rates are explicitly parameterized to fit the experimental spectra. The agreement in Fig. 3(f) therefore incorporates the experimental trend through these inputs, so the conclusion that increasing exchange splitting renormalizes the bands and that Weyl nodes are controlled by magnetization follows in part from the magnetizations inserted into the calculation rather than from a parameter-free prediction.

full rationale

The measured temperature-dependent optical conductivity, including the appearance of InterA below 100 K, the suppression of the Drude weight, and the spectral-weight transfer to InterB/InterC, is an independent experimental result and does not reduce to the DFT comparison. The circularity is confined to the theory-to-experiment mapping. The paper fixes a global wavenumber rescaling of 1.33 by matching InterC and then presents this same value as the measured band renormalization and as evidence of moderate correlation, which is a fitted parameter renamed as a result. Similarly, the constrained moments and scattering rates are chosen to mimic the data, so the calculated spectra in Fig. 3(f) are not a blind prediction of the magnetization-driven evolution; the magnetization dependence fed into the calculation is recovered as the conclusion. One additional consistency problem, noted rather than counted as a separate circular step, is that the Wannier-derived InterA peak at 'around 350 cm^-1' is said to be 'consistent with the position of InterA in Fig. 1c' (raw 310 cm^-1), whereas the global 1.33 rescaling used for all other comparisons would put InterA near 412 cm^-1; if the rescaling is applied, the Weyl-node feature does not match, and if it is not applied, the renormalization factor is not global. This does not affect the measured T-dependence, but it means the identification of the Weyl-node-derived transition is not robustly tied to the stated first-principles comparison. No external benchmarks are needed to see that the 1.33 factor and the moment/scattering parameters are fit-determined; the central empirical content, however, remains non-circular, so the overall score is partial rather than total.

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

The central comparison rests on a small number of fitted or hand-chosen inputs: a global 1.33 energy rescaling, constrained cobalt moments used to mimic temperatures, and parameterized Drude scattering rates. The underlying DFT and Kubo-formula framework is standard for this field. No new physical entity is introduced; the Weyl nodes and spin-orbit gapped nodal lines are carried over from prior predicted topology.

free parameters (4)
  • Energy rescaling factor (band renormalization) = 1.33
    Applied to all experimental photon wavenumbers to match the calculated InterC peak position; this fitted value is the basis for claiming a 1.33 band renormalization and moderate correlations.
  • Constrained Co magnetic moments = 0.15 and 0.33 μB/Co
    Chosen to mimic the magnetic state at selected temperatures; 0.33 μB is the DFT ground-state moment, while 0.15 μB is an intermediate hand-picked value with no data-derived justification.
  • Drude scattering rates in simulated spectra = 0.17, 0.05, 0.03 eV for PM, FM 0.15, FM 0.33
    Parameterized in the text to mimic decreasing temperature and to fit the experimental spectra; these values are not predicted from first principles.
  • Drude-Lorentz oscillator parameters in experimental fits = Peak positions 310, 1600, 5100 cm^-1 at 100 K, plus T-dependent widths and strengths
    The measured conductivity is decomposed with fitted Drude and Lorentz oscillators; the peak positions are fit outputs used to identify the interband transitions discussed in the paper.
assumptions (4)
  • domain assumption Density functional theory in the local density approximation with spin-orbit coupling gives a reliable single-particle description of the band structure and optical conductivity of Co3Sn2S2.
    Used throughout the simulation section; the paper argues that a 1.33 rescaling makes this sufficient, but the approximation itself is not proven.
  • standard math The measured optical conductivity can be represented as a sum of Drude and Lorentz oscillators with the dielectric function in Eq. 1.
    Standard Drude-Lorentz parameterization; the fit quality is shown at selected temperatures, not at every temperature.
  • domain assumption A linear-in-frequency optical conductivity between 130 and 230 cm^-1 is a reliable signature of 3D linear bands near the Fermi level.
    The interpretation follows Refs [18,20,28,29]; other mechanisms could in principle produce similar low-energy conductivity.
  • ad hoc to paper Constraining the Co magnetic moment to 0.15 μB mimics the 100 K state while 0.33 μB mimics the 5 K ground state.
    The text says the moment is constrained to mimic the temperature effect, but no direct link between moment value and temperature is established.

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Cite this review

Pith. "Pith review of Temperature-induced band shift in ferromagnetic Weyl semimetal Co3Sn2S2." pith.science (2026). https://pith.science/paper/PUR4EVR4

@misc{pith2026190803895,
  author       = {Pith},
  title        = {Pith review of: Temperature-induced band shift in ferromagnetic Weyl semimetal Co3Sn2S2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PUR4EVR4}},
  note         = {Machine review of arXiv:1908.03895}
}
abstract

The discovery of nonmagnetic Weyl semimetals (WSMs) in TaAs compounds has triggered lots of efforts in finding its magnetic counterpart. While the direct observation of the Weyl nodes and Fermi arcs in a magnetic candidate through angle-resolved photoemission spectroscopy is hindered by the complex magnetic domains. The transport features of magnetic WSMs, including negative magnetoresistivity and anomalous Hall conductivity, are not conclusive since these are sensitive to extrinsic factors like defects and disorders in lattice or magnetic ordering. Here, we systematically study the temperature-dependent optical spectra of ferromagnetic Co$_3$Sn$_2$S$_2$ experimentally and simulated by first-principles calculations. The many-body correlation effect due to Co $3d$ electrons leads to the renormalization of bands by a factor about 1.33, which is moderate and the description within density functional theory is suitable. As the temperature drops down, the magnetic phase transition happens and the magnetization drives the band shift through exchange splitting. The optical spectra can well detect these changes, including the transitions sensitive and insensitive to the magnetization, and those from the bands around the Weyl nodes. The results strongly support that Co$_3$Sn$_2$S$_2$ is a magnetic WSM and the Weyl nodes can be tuned by magnetization with temperature change.

Figures

Figures reproduced from arXiv: 1908.03895 by the authors.

Figure 1
Figure 1. (a)The dc resistivity (ρ) of Co3Sn2S2 (solid line) with the zero-frequency values of optical conductivities(red circles). (b) The T dependence of magnetic susceptibil￾ity χ(T) with zero-field-cooling and field-cooling mode at µ0H=30 Oe for H||c. The black arrow denotes the Curie Weiss temperature TC ∼ 177 K. (c) The T-dependent opti￾cal conductivity σ1(ω) from 30 to 7 000 cm−1 . Inset shows the optical conductivity … view at source ↗
Figure 2
Figure 2. (a)The Drude-Lorentz fit to the complex optical [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. (a) The band structure along high-symmetry paths with (red) and without (black) spin-orbital coupling (SOC). The [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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