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REVIEW 3 major objections 6 minor 63 references

Anomalous and parallel Hall effects in ferromagnetic Weyl semimetal Cr$_3$Te$_4$

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Calculations predict Cr3Te4 is a room-temperature magnetic Weyl semimetal.

desk verdict Prediction of a room-temperature magnetic Weyl semimetal in Cr3Te4 with large Fermi arcs and parallel AHE, but the assumed collinear magnetic order clashes with the canted structure the paper itself cites. read the letter →

arxiv 2411.16184 v1 pith:6E77C6ZT submitted 2024-11-25 cond-mat.mtrl-sci

Anumita Bose , Shubham Purwar , Setti Thirupathaiah , Awadhesh Narayan This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords Cr3Te4WeylsemimetalanomalousHalleffectparallelNernstBerrycurvatureferromagnetismfirst-principlescalculations
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 aims to establish that the layered, monoclinic ferromagnet Cr$_3$Te$_4$ is an intrinsic magnetic Weyl semimetal, with multiple Weyl points—gapless band crossings that act as sources and sinks of Berry curvature—close to the Fermi level and Fermi arcs long enough to be seen in photoemission. It argues that the Berry curvature produced by these Weyl points generates both a conventional anomalous Hall conductivity of about $260\ \Omega^{-1}\mathrm{cm}^{-1}$ and an unconventional 'parallel' anomalous Hall conductivity of about $100\ \Omega^{-1}\mathrm{cm}^{-1}$ along an in-plane direction. It further derives anomalous Nernst conductivities of about $0.39$ and $0.72\ \mathrm{A\,m^{-1}K^{-1}}$ at 300 K from the same Berry curvature via the Mott relation. Complementary magnetization measurements put the Curie temperature near 327 K, so a correct prediction would make Cr$_3$Te$_4$ a candidate for room-temperature topological and spintronic applications.

What carries the argument

The load-bearing object is the magnetic space group of monoclinic Cr$_3$Te$_4$ in its assumed ferromagnetic state. The centrosymmetric crystal (space group C2/m) becomes magnetic when chromium moments order along $a$, breaking time reversal but preserving the combined symmetries $\tau M_y$ and $\tau C_{2y}$. These combined symmetries dictate which Berry curvature components survive, constrain the Weyl-point partners, enforce $\sigma_{zx}=0$, and permit the coexistence of the conventional Hall conductivity $\sigma_{yz}$ and the parallel Hall conductivity $\sigma_{xy}$; the parallel component is the low-symmetry effect called the parallel anomalous Hall effect. The numerical machinery is first-principles electronic structure with tight-binding interpolation, followed by Berry curvature integration; the Nernst conductivities are obtained from the Hall conductivities through the Mott relation.

What would settle it

A low-temperature neutron or resonant X-ray scattering experiment that resolves the magnetic structure would settle it: if the chromium moments form the canted configuration described in Ref. [51] rather than collinear order along $a$, the combined symmetries $\tau M_y$ and $\tau C_{2y}$ are broken, and the predicted Weyl points and in-plane Hall conductivities should disappear. Alternatively, ARPES on the $(\bar{1}\bar{1}0)$ surface that fails to find Fermi arcs of roughly $0.83\ \mathrm{\AA}^{-1}$ would contradict the surface-state prediction.

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Extended reading notes

Core claim

On its own terms, the paper claims that ferromagnetic Cr$_3$Te$_4$, with chromium moments aligned along the $a$ axis, hosts multiple pairs of Weyl points near the Fermi level. Under the combined symmetry operations $\tau M_y$ and $\tau C_{2y}$ (time reversal followed by a mirror or a twofold rotation), the Berry curvature components $\Omega_x$ and $\Omega_z$ are allowed to be nonzero while $\Omega_y$ vanishes, which forces $\sigma_{zx}=0$ and leaves two independent transverse Hall conductivities: the conventional $\sigma_{yz}\sim260\ \Omega^{-1}\mathrm{cm}^{-1}$ at the Fermi level and the unconventional parallel $\sigma_{xy}\sim100\ \Omega^{-1}\mathrm{cm}^{-1}$. The same Berry curvature yields anomalous Nernst conductivities $\alpha_{yz}\sim0.39$ and $\alpha_{xy}\sim0.72\ \mathrm{A\,m^{-1}K^{-1}}$ at 300 K. Surface calculations on the $(\bar{1}\bar{1}0)$ face show Fermi arcs extending about $0.83\ \mathrm{\AA}^{-1}$, roughly three-quarters of the surface reciprocal vector, which the authors expect to be detectable by ARPES and STM.

Load-bearing premise

The prediction rests on the assumption that the magnetic ground state is collinear ferromagnetic order with all chromium moments along the $a$ axis, while the paper's own magnetization data and cited neutron diffraction suggest a canted configuration with antiferromagnetic components along $a+b$.

Editorial extensions

If this is right

  • If the prediction holds, Cr$_3$Te$_4$ becomes a bulk, room-temperature magnetic Weyl semimetal, a category with very few confirmed members.
  • The long Fermi arcs should be observable in surface-sensitive ARPES and STM experiments, providing a direct test of the Weyl topology.
  • Electron or hole doping could tune the Hall responses substantially, for example raising $\sigma_{xy}$ to about $320\ \Omega^{-1}\mathrm{cm}^{-1}$ at a Fermi-level shift of 0.14 eV and $\alpha_{xy}$ to about $1.19\ \mathrm{A\,m^{-1}K^{-1}}$ at a shift of 65 meV.
  • The coexistence of conventional and parallel anomalous Hall effects, plus sizable anomalous Nernst responses, suggests possible Berry-curvature-based thermoelectric and spintronic devices operating near room temperature.

Reading between the lines

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

  • The symmetry argument implies a strong sensitivity to magnetic structure: if the low-temperature canted phase suggested by neutron diffraction is the true ground state, the combined symmetries $\tau M_y$ and $\tau C_{2y}$ may be lost and the predicted Weyl points and parallel Hall effect may not survive.
  • A natural extension is to compute the band topology using the experimentally reported canted magnetic configuration; this would directly show whether the Weyl phase is a property of the actual magnetic ground state or only of the idealized collinear order.
  • The same symmetry analysis could be applied to other chromium telluride intercalates (such as CrTe, Cr$_2$Te$_3$, and Cr$_5$Te$_8$) to search for parallel Hall effects and Weyl points as a family-wide feature.
  • Because the parallel Hall conductivity is allowed only when mirror and twofold rotational symmetries are broken by the moment direction, rotating the magnetization with an external field should switch the pattern of allowed Hall components; this is a testable prediction the paper does not spell out.
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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

3 major / 6 minor

Summary. The paper predicts, from PBE-GGA density-functional calculations with spin-orbit coupling and Wannier interpolation, that monoclinic Cr3Te4 in a collinear ferromagnetic state with Cr moments along the a direction is a magnetic Weyl semimetal. The authors report multiple Weyl points near the Fermi level, long Fermi arcs on the (1-bar-1-bar-0) surface (0.83 inverse Angstroms), a conventional anomalous Hall conductivity sigma_yz of about 260 inverse Ohm-centimeter, a parallel anomalous Hall conductivity sigma_xy of about 100 inverse Ohm-centimeter at the Fermi level, and anomalous Nernst conductivities alpha_yz of about 0.39 and alpha_xy of about 0.72 Ampere per meter-Kelvin at 300 K. They support these calculations with experimental XRD and magnetization data, including a Curie temperature of 327 K and a second magnetic transition near 70 K. The symmetry analysis uses the anti-unitary operations tau My and tau C2y to conclude sigma_zx = 0 and to allow nonzero sigma_xy and sigma_yz.

Significance. If the predictions are correct, Cr3Te4 would be a room-temperature magnetic Weyl semimetal with large Berry-curvature charge and thermoelectric responses, including a sizable parallel anomalous Hall effect. Strengths of the paper are that the transport coefficients are computed from the ab initio band structure without fitting any parameter to Hall or Nernst data, and that the symmetry reasoning is transparent and falsifiable by future ARPES and transport experiments. However, the central topological and transport claims rely on a collinear ferromagnetic ground state that appears to be inconsistent with the canted magnetic structure described in the authors' own experimental section, so the significance of the results for the actual material is not yet established.

major comments (3)
  1. [Sec. III A and Sec. III D] The symmetry analysis and Weyl-partner mapping presume a collinear ferromagnetic state with all Cr moments along x, but the authors' own Sec. III A states that neutron diffraction [51] finds a canted spin configuration with antiferromagnetic components along (a+b) and that M(T) shows a second transition near 70 K. In a canted or non-collinear ground state, the magnetic space group generically lacks the anti-unitary operations tau My and tau C2y that are used in Sec. III D to enforce sigma_zx=0 and to allow nonzero sigma_xy and sigma_yz. The predicted Weyl points, Fermi arcs, and both Hall conductivities therefore may not survive in the experimentally relevant magnetic phase. The manuscript must either repeat the electronic-structure and transport calculations for the canted magnetic configuration, or provide an explicit justification for why the collinear approximation captures the topological and transport properties.
  2. [Sec. III D and Sec. III E] The quantitative values sigma_yz of about 260, sigma_xy of about 100, alpha_yz of about 0.39, and alpha_xy of about 0.72 are obtained from Brillouin-zone integrals of the Berry curvature over Wannier-interpolated bands, yet the paper reports no convergence tests with respect to k-mesh density or smearing width, and no error estimates. Because the crossings are described as lying slightly away from high-symmetry paths and the Berry curvature is sharply peaked near such crossings, the reported numerical values are not robustly established. The authors should provide a convergence study (for example, increasing the k-mesh for the AHC integration and varying the smearing) and, ideally, a check of the sensitivity to the PBE exchange-correlation choice.
  3. [Sec. III B and Sec. III C] The claim of 'multiple Weyl points' is not documented with a quantitative inventory. No table or list reports the k-space coordinates, energies, chiralities, or pairing of the Weyl points, and the text notes that the actual crossings occur slightly away from the high-symmetry paths shown in Fig. 1(c). In addition, the 0.83 inverse Angstrom Fermi-arc length in Table I is quoted at the Fermi energy, while the text states that arcs are prominent in a 0.0-0.15 eV window and that part of the arcs merge into bulk states; the definition of the measured arc length and the specific Weyl pair connected by the longest arc need to be stated explicitly.
minor comments (6)
  1. [Fig. 4] The caption lists panels as (a) Omega_x, (b) Omega_y, and (c) Omega_z, but the text refers to 'Fig. 4(c)' for Omega_y and 'Fig. 4(b) and (d)' for Omega_x and Omega_z; the panel labels and references should be reconciled.
  2. [Table II] The entry 'Cd' for a conventional ferromagnet appears to be a typo for Co, since the text and Ref. [57] refer to Fe, Co, FePt, FePd, and Ni.
  3. [Sec. III D] The notation switches between sigma_zx and sigma_xz; for consistency one symbol should be used throughout.
  4. [Eq. (1)] The symbol epsilon is used both for the Levi-Civita symbol and for the band energy, and the sign convention for the Hall tensor is not fixed; please disambiguate the notation.
  5. [Sec. III A] The sentence beginning 'In our system ferromagnetically aligned magnetic moments are predominantly present on the Cr atoms are aligned along the x direction' is grammatically incomplete and should be rewritten.
  6. [Appendix A] Table III lists 'Theoretical' and 'Experimental' cell parameters that differ, although the Methods section states that the experimental structure was used; please clarify whether relaxation was performed and, if so, report the relaxation settings.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Hall and Nernst conductivities are first-principles Berry-curvature integrals with no fitted parameters, and the self-citations are contextual rather than load-bearing.

full rationale

The paper's derivation chain is self-contained. Bulk and surface electronic structures are obtained from DFT with SOI plus Wannier interpolation; Weyl points are identified by computed finite chiralities; Fermi arcs are read from computed surface spectral functions. The anomalous Hall conductivity is obtained by integrating the computed Berry curvature through Eq. (1), and the anomalous Nernst conductivity is obtained from that same AHC through the standard Mott-type relation, Eq. (4). No parameter is fitted to any claimed Hall, Nernst, or Fermi-arc value, and the symmetry constraints (tau M_y, tau C_2y) are used to decide which conductivity components can be nonzero, not to impose their magnitudes. Self-citations (Refs. 22, 35, 38, 39) appear only as background on Cr-Te materials and prior work; none carries the weight of the Weyl-point or transport claims, and no uniqueness theorem is imported from the authors' earlier papers. The manuscript's own Sec. III A and Ref. [51] raise a real concern that the assumed collinear FM order along a may not be the true ground state, since a 70 K transition and a canted spin configuration with antiferromagnetic components along (a+b) are reported; this is an assumption-validity and robustness risk, not a circular reduction of the predictions to their inputs. The calculated quantities are therefore not equivalent, by construction, to the paper's inputs.

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

The paper introduces no new entities. The main assumptions are the DFT exchange-correlation functional, the collinear FM magnetic order, and the use of standard linear-response formulas. No free parameters are fitted to the target observables.

assumptions (4)
  • domain assumption PBE-GGA without Hubbard U adequately describes the band structure and magnetism of Cr3Te4.
    The calculation uses standard PBE; no U or hybrid functional is applied. For 3d transition metal tellurides, correlations can shift bands and alter Weyl points.
  • ad hoc to paper The magnetic ground state is a collinear ferromagnet with Cr moments along the x direction.
    Experiment suggests a canted structure (Ref. 51). The paper assumes collinear FM, which determines the symmetry analysis for the Weyl points and Hall conductivity components.
  • standard math The Kubo formula for intrinsic anomalous Hall conductivity via Berry curvature is valid.
    Equation (1), linear response theory. This is a standard relation in the field.
  • standard math The Mott relation connects anomalous Nernst conductivity to the energy derivative of AHC.
    Used to compute anomalous Nernst conductivity from energy-dependent AHC via Eq. (4).

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Cite this review

Pith. "Pith review of Anomalous and parallel Hall effects in ferromagnetic Weyl semimetal Cr$_3$Te$_4$." pith.science (2026). https://pith.science/paper/6E77C6ZT

@misc{pith2026241116184,
  author       = {Pith},
  title        = {Pith review of: Anomalous and parallel Hall effects in ferromagnetic Weyl semimetal Cr$_3$Te$_4$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6E77C6ZT}},
  note         = {Machine review of arXiv:2411.16184}
}
abstract

Recently, time-reversal symmetry broken magnetic Weyl semimetals (WSMs) have attracted extensive attention and have provided an intriguing platform for exploring fundamental physical phenomena. The study of chromium telluride-based systems has also drawn significant interest towards spintronics applications owing to their high Curie temperatures. Here, using \textit{ab initio} calculations, we propose the emergence of multiple Weyl points (WPs) near the Fermi level in such an intrinsic ferromagnetic system, Cr$_3$Te$_4$. The large, well-separated, nontrivial Fermi arcs and surface states, suggest that the WPs are highly robust and resilient to perturbations. A substantial Berry curvature contribution in the vicinity of the Fermi energy not only serves as the origin of large conventional anomalous Hall conductivity (AHC), but also produces unconventional parallel AHC in this material, owing to the low structural symmetry. In addition to the charge Hall conductivity, we also find significant anomalous Nernst conductivities originating from the Berry curvature. Alongside our theoretical predictions, we present complementary experimental results, including X-ray diffraction (XRD) analysis and an examination of the magnetic properties, which demonstrate a Curie temperature of 327 K. Our study advances the understanding of magnetic WSMs, and also encourages further studies in the context of topological properties of our proposed material.

Figures

Figures reproduced from arXiv: 2411.16184 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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