A large anomalous Hall effect and Weyl nodes in bulk FeNi$_3$: a density functional theory study

Santu Baidya; Shivani Thakur

REVIEW 3 major objections 4 minor 1 cited by

A large anomalous Hall effect and Weyl nodes in bulk FeNi$_3$: a density functional theory study

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The authors predict that bulk FeNi3 is a ferromagnetic Weyl metal with 112 pairs of Weyl nodes and a large intrinsic anomalous Hall conductivity.

desk verdict FeNi3 is a plausible new ferromagnetic Weyl metal, but the uncontested lattice constant and missing convergence tests keep this at the conditional level. read the letter →

arxiv 2501.11025 v1 pith:GF3YT6CL submitted 2025-01-19 cond-mat.mtrl-sci

Shivani Thakur , Santu Baidya This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords FeNi3WeylmetalanomalousHalleffectspin-orbitcouplingferromagnetismdensityfunctionaltheoryWannierinterpolationinvaralloy

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 argues that ordinary bulk FeNi3, a well-known ferromagnetic intermetallic and water-splitting catalyst, is a magnetic Weyl metal rather than a trivial ferromagnet. Using spin-polarized density functional theory with spin-orbit coupling and Wannier interpolation, the authors find 112 pairs of Weyl nodes of nonzero chirality at the self-consistent Fermi level, away from high-symmetry points. These nodes produce an intrinsic anomalous Hall conductivity of roughly 10,000 S/m at the Fermi level, rising to about 70,000 S/m about 0.2 eV above it. If the prediction holds, an inexpensive and abundant 3d-metal alloy gains topological transport properties that could be exploited in spintronics and in proposals for topological catalysis.

What carries the argument

The argument is carried by Wannier-interpolated band structures from spin-orbit-coupled density functional theory and the Berry curvature computed from them. The central object is the set of Weyl nodes themselves: linear band crossings with nonzero chirality that act as monopoles of Berry curvature and therefore sources of anomalous Hall conductivity. To establish that the crossings are not avoided crossings, the authors use the irreducible representations G3 and G4 of the magnetic double point group D2: crossing bands carry different irreps, so the crossing is symmetry-allowed. The magnetic point group has eight symmetry elements, which constrains the total number of Weyl nodes to a multiple of eight, consistent with the 112 pairs reported.

What would settle it

Compute the Weyl-node count and anomalous Hall conductivity at a fully relaxed lattice constant and at the experimental lattice constants reported for L12 FeNi3; if 112 pairs of nodes and the ~70,000 S/m peak do not survive, the central claim fails. On the experimental side, a low-temperature Hall measurement on a single crystal or epitaxial film should show a zero-field anomalous Hall conductivity near 10,000 S/m with the easy axis along [001]; its absence would falsify the prediction.

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Extended reading notes

Core claim

The central discovery is that the DFT ground state of cubic FeNi3, when spin-orbit coupling is included, is a ferromagnetic Weyl metal. The authors find that Fe d–Ni d hybridization combined with spin-orbit coupling produces a dense set of 112 pairs of Weyl nodes with nonzero chirality at the self-consistent Fermi level, located away from high-symmetry planes, and additional type-I and type-II Weyl cones about 0.2 eV above the Fermi level along high-symmetry directions. The same band structure gives an intrinsic anomalous Hall conductivity of about 10,000 S/m at the Fermi level and an extremely large value near 70,000 S/m about 0.22 eV above it. The paper also reports a large magnetocrystalline anisotropy of about 1 meV per unit cell with easy axis along [001].

Load-bearing premise

The calculation assumes a cubic lattice constant of 3.4079 Å for FeNi3 without stating whether this value was optimized or measured; the predicted Weyl nodes and Hall conductivity depend on the band structure, so a substantially different lattice constant could remove or shift the topological features.

Editorial extensions

If this is right

Bulk FeNi3 becomes a concrete, abundant material for studying intrinsic magnetic Weyl physics, moving beyond the rare semimetals where such nodes are usually sought.
The predicted anomalous Hall conductivity of about 10,000 S/m at the Fermi level and about 70,000 S/m slightly above it should be measurable as a large zero-field Hall signal in single crystals or films.
Because Weyl cones sit about 0.2 eV above and 0.05 eV below the Fermi level, electron or hole doping, or moderate pressure, could put topological crossings directly at the Fermi level.
The coexistence of type-I and type-II Weyl cones in one material allows direct comparison of their distinct transport and thermodynamic signatures.

Reading between the lines

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

A natural next calculation is a full lattice relaxation and a scan of the anomalous Hall conductivity against lattice constant; the paper's stated 3.4079 Å value is the most fragile input, and the Weyl count may be sensitive to it.
The same Fe d–Ni d hybridization mechanism suggests that the other Fe–Ni invar phases, FeNi and Fe3Ni, deserve the same Wannier-based topological screening.
If FeNi3 nanoparticles used in electrocatalysis retain the bulk Weyl nodes, their surface electronic structure could inherit large Berry curvature; connecting that to catalytic activity would require a separate surface and interface calculation.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The genuinely new thing here is the prediction of Weyl nodes and a large intrinsic anomalous Hall effect in bulk FeNi3, a cheap and abundant catalyst material that had not been examined for topology before. The calculation pipeline is standard but executed reasonably: PBE+SOC band structures from Quantum ESPRESSO, Wannier90/WannierTools for the Berry curvature, an OpenMX cross-check for the bands, and an irreducible-representation argument (G3/G4 in D2) to show the crossings are not avoided. There are no fitted parameters and nothing circular; the claimed 112 Weyl pairs and AHC come straight from first-principles bands.

The soft spots are real, and they are mostly about verification. The load-bearing issue is the lattice constant, a = 3.4079 Å. The paper never says whether this is optimized or experimental, shows no equation-of-state check, and gives no sensitivity test. Common L12 FeNi3 parameters are near 3.55 Å, so 3.4079 Å is about 4% smaller. For a narrow d-band ferromagnet, that can move Weyl nodes off the Fermi level or change their chiralities. The phrase “optimized atomic positions” does not rescue this: in a cubic Pm-3m cell there are no internal coordinates to optimize, so the lattice constant is the uncontrolled degree of freedom. The stress-test note gets this right.

Also missing are convergence tests for the Wannier interpolation and the AHC k-mesh integration. WannierTools Berry integrals are sensitive to both the Wannierization and the k-grid, and the paper does not state either. The list of 112 Weyl pairs is said to be in a supplement, but the arXiv version has no supplement file, so the central table is not actually available. The units are also sloppy: the text reports AHC in S/m while Fig. 5 is labeled in 10^3 Ohm^-1 cm^-1; the numbers convert, but the mixing is careless.

The magnetic moments (Fe 3.03 µB, Ni ~0.58 µB, total 4.8 µB/f.u.) and the metallic ground state are consistent with earlier work, so the foundation is not in doubt. The AHC values are large but not off-scale. If the lattice constant is wrong, the topology could vanish; if it is right, FeNi3 becomes an interesting, inexpensive magnetic Weyl metal worth experimental attention.

This paper deserves a serious referee, not a desk reject. The referee should require the authors to justify the lattice constant, show a volume or strain sensitivity test, provide the Weyl node table and convergence tests, and clean up the units. I would send it to review with those conditions attached.

Referee Report

3 major / 4 minor

Summary. The paper reports first-principles PBE and PBE+SOC calculations for bulk cubic FeNi3, claiming that the ferromagnetic ground state is a Weyl metal. Using Wannier90-based interpolation and WannierTools, the authors identify 112 pairs of Weyl nodes with nonzero chirality at the self-consistent Fermi level, as well as type-I and type-II Weyl cones about 0.2 eV above the Fermi energy. They further compute an intrinsic anomalous Hall conductivity of about 10000 S/m at E_F, rising to about 70000 S/m at roughly 0.2 eV above E_F. The paper frames these results as a route toward topological catalysts and spintronic applications.

Significance. If the results are correct, FeNi3 would be a compelling candidate magnetic Weyl metal in a widely studied and easily synthesized material, with a large intrinsic anomalous Hall effect tunable by doping or pressure. The calculations are fully first-principles, with no fitted parameters, and the central predictions are falsifiable. The work would extend the list of magnetic Weyl systems beyond Co3Sn2S2 and similar compounds. However, the quantitative claims currently rest on an unverified structural input and on numerical details that are not documented, so the significance is conditional on resolving those gaps.

major comments (3)

[Section IIA, Table I] The cubic lattice constant is fixed at a = 3.4079 Å without any statement of its origin (experimental, optimized, or otherwise), and no volume relaxation or equation-of-state check is reported. This is load-bearing because FeNi3 is a narrow d-band metal in which Weyl node creation/annihilation and the Fermi-level Berry curvature are controlled by small band inversions. Commonly cited L12 FeNi3 lattice parameters are near 3.55 Å, so the adopted value is roughly 4% smaller in linear dimension. The sentence 'optimized atomic positions' in Section IIA does not resolve this, because the cubic Pm-3m L12 cell has no internal coordinates; the lattice constant itself is the uncontrolled degree of freedom. The authors should state the provenance of a, verify it against a volume optimization, and test the Weyl-node count and AHC at least one nearby lattice constant to show robustness.
[Section IIB] The central quantitative claim of 112 Weyl-node pairs is only summarized in the text and Fig. 3(a), with the detailed table of positions and chiralities relegated to a supplementary document that is not included with the arXiv submission. Without that table, the chirality sum and the consistency with the magnetic point group's eight symmetry elements cannot be checked. Additionally, no convergence information is given for the Wannier interpolation (number of Wannier functions, disentanglement/frozen windows, k-mesh used in WannierTools for the node search), so the reader cannot assess whether the 112-pair count is converged or an artifact of the interpolation grid.
[Section IIC, Fig. 5] The anomalous Hall conductivity calculation is presented without any k-mesh convergence test for the Berry curvature integral, and the units are mixed: the text quotes 10000 S/m and 70000 S/m, while the Fig. 5 axis label is in units of 10^3 Ω^-1 cm^-1. Since 1 Ω^-1 cm^-1 = 100 S/m, the quoted Fermi-level value of 10000 S/m corresponds to 0.1 in the axis units, but the conversion is never stated. The figure should be replotted in a single unit and the integration parameters (k-mesh density, number of bands, smearing) should be reported so that the quantitative AHC prediction can be reproduced.

minor comments (4)

[Section IIA] The phrase 'time-reversal symmetry from partially filled d-orbitals' is physically unclear and likely incorrect: ferromagnetic order breaks time-reversal symmetry, and the Weyl nodes arise because of this broken symmetry combined with spin-orbit coupling. The sentence should be reworded.
[Throughout] There are numerous typographical errors, including 'inver' for 'invar', 'conductivty', 'conducvity', 'ORIBITALS', 'Brilluin', and 'correspdoning'. A careful proofreading pass is needed.
[Section IIC] The equation for the anomalous Hall conductivity, Eq. (1), uses f(E_k) as the occupation factor, but the notation for the Fermi window over which the integration is performed is not defined. Clarifying the energy window and the temperature/smearing used would improve reproducibility.
[Conclusions] The statement that the study 'may help in further studying Fe-Ni invar materials for understanding physics of topological catalysts and applications in superconductivity due to presence of Weyl nodes' is speculative; the superconductivity connection is not developed elsewhere and should be either removed or supported.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Weyl node count and AHC are direct first-principles outputs with no fitted inputs or self-citation load-bearing steps.

full rationale

The paper's central claims—112 pairs of Weyl nodes of nonzero chirality at the self-consistent Fermi level and an intrinsic anomalous Hall conductivity near 10000 S/m at EF—are obtained by a direct first-principles pipeline: PBE+SOC DFT band structure, Wannier90 interpolation, and WannierTools chirality identification and Berry-curvature integration via Eq. (1). No parameter is fitted to the claimed Weyl-node count or AHC value, and no benchmark quantity from experiment or prior theory is used to constrain the calculation. The lattice constant a = 3.4079 Å and the pseudopotentials are fixed inputs, not adjustable parameters tuned to reproduce the topological output. The symmetry argument that the magnetic point group requires the number of nodes to be a multiple of eight is a consistency check, not an input equivalent to the result. The only coauthor self-citation (Ref. [2], Baidya and Vanderbilt) supports general background on obtaining Weyl semimetals from Dirac semimetals and is not load-bearing for the FeNi3 prediction; the CrPt3 comparison (Ref. [16]) is external to the present authors. The lack of stated provenance for the lattice constant and the absence of a lattice-constant sensitivity study are correctness and robustness risks, but they do not make the derivation circular: the computed quantities are not defined in terms of the claimed outputs, and there is no equation in the paper that reduces to its own input by construction. The analysis is therefore self-contained against the stated DFT-based derivation chain, and no circular step is identified.

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

The main calculation uses PBE+SOC with a fixed lattice constant and ferromagnetic order along [001]. No parameters are fitted to experimental data; the Hubbard U scan is only a sensitivity check. The prediction thus rests on the adequacy of PBE, the assumed magnetic ordering, and the fidelity of the Wannier interpolation.

assumptions (4)

domain assumption PBE-GGA exchange-correlation functional accurately describes the magnetic and electronic ground state of FeNi3
Used throughout for band structure, Weyl node positions, and AHC; no hybrid functional or GW correction tested (Section II A).
domain assumption Ferromagnetic ordering along [001] is the magnetic ground state
The symmetry reduction to P4mm'm' and the distinction between Ni1c and Ni2e sites rely on this assumed ordering (Section II A).
domain assumption Wannier90 interpolation is accurate enough to locate Weyl nodes and compute Berry curvature
All Weyl node positions and AHC values are obtained from Wannier-interpolated bands; no convergence tests are reported (Sections II B and II C).
standard math The magnetic double point group D2 and its irreducible representations G3 and G4 are correctly assigned
Used to argue that crossings are not avoided (Section II B, Fig. 4).

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Pith. "Pith review of A large anomalous Hall effect and Weyl nodes in bulk FeNi$_3$: a density functional theory study." pith.science (2026). https://pith.science/paper/GF3YT6CL

@misc{pith2026250111025,
  author       = {Pith},
  title        = {Pith review of: A large anomalous Hall effect and Weyl nodes in bulk FeNi$_3$: a density functional theory study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GF3YT6CL}},
  note         = {Machine review of arXiv:2501.11025}
}

abstract

In this work, we report the study of electronic structure, magnetism, and the existence of Weyl nodes in a pristine bulk FeNi$_{3}$, a member of Fe-Ni inver alloy compounds, known as good metal catalysts with high activity and stability for water splitting for a very long time. Our observation of Weyl points in the bulk FeNi$_{3}$ may lead to a new technology to design highly efficient topological catalysts. While the previous literature \cite{PhysRev.97.304} mainly focused on the thermal and catalytic properties of FeNi$_{3}$ we report the interplay of Fe $d$-Ni $d$ hybridization and spin-orbit coupling give rise to the ferromagnetic Weyl nodes in the bulk FeNi$_{3}$. Our study shows that the ground state of the bulk FeNi$_{3}$ is a Weyl metal with a large number of Weyl nodes at the Fermi energy away from high-symmetry $k$-points. Furthermore, we predict a large intrinsic anomalous Hall conductivity of about $10000~S/m$ at the ground state. In addition, we show the existence of Weyl nodes along the high symmetry $k$-points $~0.2eV$ above and $~0.05eV$ below self-consistent Fermi level that may be achieved either by the electron or hole doping, or by external perturbation. In this article, FeNi$_{3}$ has been studied to explore this scenario using first-principles density functional theory and subsequent Wannier90-based tight-binding method. Furthermore, we report the existence of two types of Weyl cones, type-I and type-II, $~0.2eV$ above the Fermi level. Our report provides a realistic material to further explore the intrinsic properties related to Weyl cones, and the spintronic applications.

Figures

Figures reproduced from arXiv: 2501.11025 by the authors.

**Figure 2.** FIG. 2. (a) Variation of spin magnetic moment of Fe and Ni [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. (a) The Weyl map at the scf Fermi energy [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. PBE+SOC band structure shows (a) the position [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5. The PBE+SOC band structure along with the vari [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

C. G. Shull and M. K. Wilkinson, Neutron diffraction studies of the magnetic structure of alloys of transition elements, Phys. Rev. 97, 304 (1955)

work page 1955

[2] [2]

Baidya and D

S. Baidya and D. Vanderbilt, First-principles theory of the dirac semimetal cd 3as2 under zeeman magnetic field, Phys. Rev. B 102, 165115 (2020)

work page 2020

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Okamura, S

Y. Okamura, S. Minami, Y. Kato, Y. Fujishiro, Y. Kaneko, J. Ikeda, J. Muramoto, R. Kaneko, K. Ueda, V. Kocsis, N. Kanazawa, Y. Taguchi, T. Koretsune, K. Fujiwara, A. Tsukazaki, R. Arita, Y. Tokura, and Y. Takahashi, Giant magneto-optical responses in mag- netic weyl semimetal Co3Sn2S2, Nature Communications 11, 4619 (2020)

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C. Li, J. Zhang, Y. Wang, H. Liu, Q. Guo, E. Rienks, W. Chen, F. Bertran, H. Yang, D. Phuyal, H. Fed- derwitz, B. Thiagarajan, M. Dendzik, M. H. Berntsen, Y. Shi, T. Xiang, and O. Tjernberg, Emergence of weyl fermions by ferrimagnetism in a noncentrosymmetric magnetic weyl semimetal, Nature Communications 14, 7185 (2023)

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J. W. Drijver, F. van der Woude, and S. Radelaar, M¨ ossbauer study of atomic order in ni3fe. ii. the order- disorder transition, Phys. Rev. B 16, 993 (1977)

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T. E. Cranshaw, The electronic and magnetic structure of ordered ni3fe studied by mossbauer spectroscopy, Journal of Physics F: Metal Physics 17, 967 (1987)

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S. Yi, H. Jiang, X. Bao, S. Zou, J. Liao, and Z. Zhang, Recent progress of pt-based catalysts for oxygen re- duction reaction in preparation strategies and catalytic mechanism, Journal of Electroanalytical Chemistry 848, 113279 (2019)

work page 2019