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REVIEW 4 major objections 6 minor 70 references

Disorder driven crossover between anomalous Hall regimes in Fe$_3$GaTe$_2$

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper establishes that Fe3GaTe2, a single magnetic compound, exhibits the full disorder-driven crossover of the anomalous Hall effect: σxy ∝ σxx^1.6 in the dirty regime, crossing over to a disorder-independent plateau σxy ≈ 420…

desk verdict A plausible single-compound AHE crossover, but the mixed temperature/disorder data need to be disentangled before the headline claim holds. read the letter →

arxiv 2507.23243 v1 pith:HDBO2AZ7 submitted 2025-07-31 cond-mat.mtrl-sci

Sang-Eon Lee , Minkyu Park , W. Kice Brown , Vadym Kulichenko , Yan Xin , S. H. Rhim , Chanyong Hwang , Jaeyong Kim
show 3 more authors
Gregory T. McCandless Julia Y. Chan Luis Balicas
This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords anomalousHalleffectBerrycurvatureFe3GaTe2scalingcrossoverdirtyregimemoderatelyintrinsicmechanismfirst-ordermagnetictransition
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 show that the magnetic metal Fe3GaTe2, without changing its chemical composition, displays both known regimes of the anomalous Hall effect: in lower-conductivity crystals the Hall conductivity scales as σxy ∝ $σxx^{1}$.6, while in cleaner crystals it saturates at a disorder-independent value near 420 $Ω^{-1}$$cm^{-1}$. This crossover, between the 'dirty' and 'moderately dirty' regimes, had previously been assembled from measurements on different materials. The authors argue that the plateau is the intrinsic Berry-curvature contribution, whose calculated value from density functional theory (≈535 $Ω^{-1}$$cm^{-1}$) is slightly above the measured one. They also locate the dominant Berry curvature near the Γ-point, a few hundred meV below the Fermi level, rather than near the K-point emphasized in earlier work. If right, Fe3GaTe2 becomes a single testing ground for how disorder alone moves a ferromagnet through the anomalous Hall scaling regimes.

What carries the argument

The central machinery is the scaling plot of anomalous Hall conductivity σxy against longitudinal conductivity σxx across 19 crystals and many temperatures, fit to σxy = Aσxx^n + σ0 with n ≈ 1.6 in the dirty regime, together with band-resolved Berry curvature maps from DFT showing a dominant contribution near the Γ-point a few hundred meV below the Fermi energy. The Berry curvature acts as an effective magnetic field in momentum space that deflects electrons transversely; this is the mechanism that produces the intrinsic anomalous Hall plateau.

What would settle it

Measure σxy and σxx on a single Fe3GaTe2 crystal while introducing controlled disorder (for example, by electron irradiation or ion bombardment) at fixed temperature, and check whether the same σxy ∝ $σxx^{1}$.6 to plateau crossover appears with the same critical σxx near 4–7×$10^{3}$ $Ω^{-1}$$cm^{-1}$; alternatively, find two crystals with identical σxx but measurably different vacancy concentrations whose σxy differs by more than the scatter, which would break the functional dependence σxy(σxx).

Watch

Extended reading notes

Core claim

By measuring 19 Fe3GaTe2 single crystals spanning σxx from about 8×$10^{2}$ to 1×$10^{4}$ $Ω^{-1}$$cm^{-1}$ at 2 K, the authors find that σxy follows a power law σxy ∝ $σxx^{1}$.6 below σxx ≈ 4×$10^{3}$ $Ω^{-1}$$cm^{-1}$, then crosses over to a conductivity-independent plateau σxy ≈ 420 $Ω^{-1}$$cm^{-1}$ above σxx ≈ 7×$10^{3}$ $Ω^{-1}$$cm^{-1}$. They interpret the plateau as the intrinsic Berry-curvature contribution, noting its proximity to $e^{2}$/hd ≈ 477 $Ω^{-1}$$cm^{-1}$ and its robustness against elastic scattering, while the power-law regime is the dirty regime where disorder suppresses the intrinsic contribution. DFT calculations give σxy ≈ 535 $Ω^{-1}$$cm^{-1}$ and show the strongest Berry curvature comes from states a few hundred meV below the Fermi level near the Γ-point, with the K-point region providing a smaller, chemical-potential-sensitive contribution. Disorder is independently evidenced by broadening of the first-order ferromagnetic-to-ferrimagnetic transition in low-conductivity samples. The paper concludes that a single compound now displays the full dirty-to-intrinsic crossover previously inferred by combining data from different ferromagnets.

Load-bearing premise

The analysis assumes that temperature-induced changes in a crystal and disorder-induced differences between crystals both move the system along the same σxy(σxx) curve, so that σxx is the only variable controlling the anomalous Hall regime.

Editorial extensions

If this is right

  • Fe3GaTe2 provides a platform where disorder alone can be tuned to move a device between the dirty and intrinsic anomalous Hall regimes without changing chemical composition.
  • The measured plateau close to e^2/hd ≈ 477 Ω^-1cm^-1 and the DFT value ≈535 Ω^-1cm^-1 imply that the intrinsic Berry-curvature mechanism is the dominant anomalous Hall source in clean Fe3GaTe2, so Berry-curvature spintronics applications can expect stable Hall output in clean crystals.
  • Locating the dominant Berry curvature near the Γ-point, a few hundred meV below the Fermi energy, means the large anomalous Hall conductivity is robust to small Fermi-level shifts, guiding band engineering in Fe3GaTe2 and related Fe3XTe2 compounds.
  • The scaling exponent n ≈ 1.6 persisting up to 350 K indicates the dirty-regime scaling law holds over a wide temperature range in this material, providing a quantitative test for theory in a single compound.

Reading between the lines

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

  • The paper's σxy versus σxx curve combines temperature slices and crystal-to-crystal variations; a cleaner test would be to vary disorder at fixed temperature, for example by electron irradiation, to see if the same crossover curve is followed without thermal effects.
  • The DFT overestimate of σxy (≈535 Ω^-1cm^-1) relative to the measured plateau (≈420 Ω^-1cm^-1) remains unresolved; it could reflect disorder even in the cleanest crystals, finite-temperature corrections, or limitations of the exchange-correlation functional.
  • The observation of a Weyl node along the K-H direction with opposite-sign Berry curvature suggests that Fermi-level placement could separate the K-point and Γ-point contributions, allowing independent engineering of the total anomalous Hall response.
  • Using the broadening of a first-order magnetic transition as a disorder meter could be extended to other layered ferromagnets to predict where they sit on the universal anomalous Hall scaling plot.
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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 / 6 minor

Summary. The paper reports measurements of the anomalous Hall effect in 19 Fe3GaTe2 single crystals whose longitudinal conductivity spans roughly 800 to 10^4 Ω^-1cm^-1. It claims a dirty-regime scaling σxy ∝ σxx^1.6 below σxx ≈ 4×10^3 Ω^-1cm^-1, a crossover region, and a disorder-independent plateau σxy ≈ 420 Ω^-1cm^-1 above σxx ≈ 7×10^3 Ω^-1cm^-1, which it attributes to the intrinsic Berry-curvature mechanism. Supporting DFT/Wannier calculations yield σxy ≈ 535 Ω^-1cm^-1 and locate the dominant Berry-curvature contributions near the Γ-point, a few hundred meV below the Fermi energy. Disorder is argued from structural characterization and from the broadening of a first-order magnetic transition in lower-conductivity crystals.

Significance. If the central claim holds, the paper would provide a single-material observation of the crossover between the dirty and moderately dirty anomalous Hall regimes, complementing earlier multi-material scaling studies. The strengths of the work include a large number of crystals, a wide conductivity range, combined transport, magnetization, structural, and first-principles characterization, and a concrete prediction for the Berry-curvature hot spots. The DFT calculation is independent of the experimental scaling fits and therefore provides a non-circular check on the intrinsic mechanism. The main weakness is that the crossover and plateau are identified from a plot that mixes temperature sweeps with sample-to-sample disorder, and the regime boundaries are not defined by a quantitative criterion.

major comments (4)
  1. [Fig. 2(a); text near 'Our analysis was performed at the lowest temperature of T = 2 K' and 'within the temperature…] The central claim of a disorder-driven crossover is identified from Fig. 2(a), which plots σxy versus σxx for all samples at T = 2, 10, 25, 50, 100, 150, and 200 K. This mixes temperature sweeps with sample-to-sample variation, although the text states that the analysis was performed at T = 2 K to exclude inelastic phonon or magnon effects. For the clean crystal C1, the text also states that σxy decreases rapidly with T in the moderately dirty regime, i.e., inelastic scattering suppresses the AHE independently of σxx. The apparent power law and crossover could therefore be an artifact of combining two different physical mechanisms. Please show the 2 K-only data with distinct symbols, identify the regimes using only those points, and verify that the n ≈ 1.6 exponent and the ≈ 420 Ω^-1cm^-1 plateau persist at fixed temperature. The fixed-T fits in Fig. 3(a) mitigate the concern for the dirty-regime exponent but do not establish the disorder-driven crossover or plateau.
  2. [Fig. 4 and text 'We identified two distinctive regimes...'] The regime boundaries at σxx ≈ 4×10^3 and 7×10^3 Ω^-1cm^-1 are introduced as shaded regions without an objective criterion. Please define a quantitative procedure, for example fits to σxy = A σxx^n and σxy = const with a residual-based or intersection-based crossover determination, and report the resulting boundary values with uncertainties. The classification of C6 as a 'boundary' sample in Fig. 5 also relies on these hand-drawn boundaries, so an independent criterion is needed to avoid circular sample classification.
  3. [Fig. 3 and the discussion of the n ≈ 1.6 exponent] The exponent n ≈ 1.6 is load-bearing for the dirty-regime claim, but the paper does not report uncertainties on the individual σxy and σxx values or fit-quality metrics such as R² and confidence intervals for n. Given that the text states that σ0 displays large error bars, the distinction between n = 1.6 and, say, n = 1.5 or 1.8 needs to be quantified. Please provide these uncertainties, at least for the fixed-temperature fits in Fig. 3(a), and for the plateau value in the moderately dirty regime.
  4. [Sections on structural characterization (XRD, STEM) and Fig. 5] The title and abstract attribute the crossover to disorder, but the paper does not provide a quantitative disorder metric across the 19 crystals. X-ray diffraction was performed on four crystals, STEM is shown for a representative image, and the susceptibility broadening is shown for three crystals; no correlation between a measured disorder parameter and σxx is established. Since the claim is specifically that disorder drives the crossover, please quantify the variation in Fe2 occupancy, Fe3 intercalation, or positional disorder, or show that the conductivity variation tracks a measurable disorder parameter.
minor comments (6)
  1. [Text near Fig. 2(a)] The text states that the two regimes are separated by 'σxx ≃ 4 mΩ^-1cm^-1'; the units should be 4×10^3 Ω^-1cm^-1.
  2. [Fig. 4 caption] The caption says 'the dirty regime below σxy = 4 ×10^3 Ω^-1cm^-1' but should refer to σxx, not σxy.
  3. [Discussion of DFT results] The calculated σxy ≈ 535 Ω^-1cm^-1 overestimates the measured plateau by about 27%; please discuss possible sources of this difference, such as the sensitivity to chemical potential, disorder, or temperature effects, since the comparison is used to support the intrinsic mechanism.
  4. [Fig. 2(b)] When comparing Fe3GaTe2 with literature data in Fig. 2(b), please state whether the literature points are base-temperature values; mixing multi-temperature Fe3GaTe2 data with single-temperature literature points could bias the apparent crossover location.
  5. [Fig. 5(b) and text following] The observation that the intermediate-quality sample C6 has a higher first-order transition temperature (T ≈ 184 K) than the cleaner sample C1 (T ≈ 161 K) is not explained; since this is presented as disorder evidence, a brief interpretation would be helpful.
  6. [Methods text near Fig. 2(a)] The scaling plot uses σxy at μ0H = 1 T and σxx at μ0H = 0 T; please justify this choice or show that the magnetoresistance is negligible, so that σxx at zero field is the correct scaling variable.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the σxy(σxx) scaling is an empirical fit, the crossover assignment is descriptive, and the DFT Berry-curvature result is an independent first-principles calculation.

full rationale

The central empirical claims are observational fits, not predictions derived from the fitted parameters. The paper measures σxy and σxx on 19 crystals, fits σxy = A σxx^n + σ0 in Fig. 3, and reports n ≈ 1.6; this is a fit to data labeled as an observation, not a parameter renamed as a prediction. The crossover boundary at σxx ≈ 4×10^3 Ω^-1 cm^-1 is a descriptive regime assignment placed on the same data, which is a classification rather than a derivation and therefore not circular. The DFT calculation of Berry curvature and σxy ≈ 535 Ω^-1 cm^-1 is independent of the experimental AHE fits and is compared to, not fitted from, the measured plateau of ≈ 420 Ω^-1 cm^-1. No load-bearing argument reduces to a self-citation: theoretical references such as Onoda et al. (Refs. [7,61]) and Nagaosa et al. (Ref. [62]) are external prior work, and the few self-citations that occur (e.g., Refs. [28,32] for skyrmion context) are not load-bearing for the AHE crossover claim. The paper's own caveat that the 2 K analysis excludes phonon/magnon inelastic effects while Fig. 2(a) includes data up to 200 K is a possible validity concern about mixing temperature and disorder as tuning parameters, but that is a scientific/correctness issue, not a circularity of the derivation chain. No equation is defined in terms of the result it purports to establish, and no fitted quantity is later called a prediction. Therefore no circularity is found.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claims rest on empirical fits (n, A, σ0) and hand-chosen regime boundaries; no new physical entities are introduced. The DFT calculation is a standard computation with well-documented approximations.

free parameters (5)
  • n (scaling exponent) = 1.6 (over 2-350 K)
    Exponent in the fit σxy = Aσxx^n + σ0; obtained from log-log linear regression in Fig. 3(a).
  • A (prefactor) = Varies with T, follows magnetization
    Prefactor in the same fit; its T-dependence is compared to magnetization.
  • σ0 (offset) = Near zero within error bars
    Vertical offset in the fit; large error bars reported.
  • Regime boundary σxx = 4×10^3 Ω^-1cm^-1 = 4×10^3 Ω^-1cm^-1
    Boundary between dirty and crossover regimes, chosen by visual inspection of Fig. 4.
  • Regime boundary σxx = 7×10^3 Ω^-1cm^-1 = 7×10^3 Ω^-1cm^-1
    Boundary between crossover and moderately dirty regimes, chosen by visual inspection.
assumptions (4)
  • domain assumption Anomalous Hall scaling law σxy ∝ σxx^1.6 in the dirty regime
    Taken from Onoda-Nagaosa theory and empirical studies (Refs. [7,61,62]); the paper uses it to interpret the observed exponent.
  • domain assumption DFT with PBE and Wannier interpolation captures the Berry curvature relevant to AHC
    Quantum ESPRESSO and WannierBerri calculations, as cited in SM; disorder (9% Fe vacancies) is not included in the calculation.
  • domain assumption σxy measured at μ0H = 1 T represents the saturated anomalous Hall value for all samples
    The field dependence in Fig. 1 indicates saturation for the displayed crystal, but the same field is used for all 19 crystals without per-sample saturation checks.
  • ad hoc to paper The combined T and sample variation adequately samples one universal scaling curve
    The paper pools data from different crystals and temperatures and assumes they fall on a single σxy(σxx) curve.

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Cite this review

Pith. "Pith review of Disorder driven crossover between anomalous Hall regimes in Fe$_3$GaTe$_2$." pith.science (2026). https://pith.science/paper/HDBO2AZ7

@misc{pith2026250723243,
  author       = {Pith},
  title        = {Pith review of: Disorder driven crossover between anomalous Hall regimes in Fe$_3$GaTe$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HDBO2AZ7}},
  note         = {Machine review of arXiv:2507.23243}
}
abstract

The large anomalous Hall conductivity (AHC) of the Fe$_3$(Ge,Ga)Te$_2$ compounds has attracted considerable attention. Here, we expose the intrinsic nature of AHC in Fe$_3$GaTe$_2$ crystals characterized by high conductivities, which show disorder-independent AHC with a pronounced value $\sigma_{xy}^{\text{c}}\approx$ 420 $\Omega^{-1}$cm$^{-1}$. In the low conductivity regime, we observe the scaling relation $\sigma_{xy}\propto\sigma_{xx}^{1.6}$, which crosses over to $\sigma_{xy} \simeq \sigma_{xy}^{\text{c}}$ as $\sigma_{xx}$ increases. Disorder in low-conductivity crystals is confirmed by the broadening of a first-order transition between ferromagnetism and the ferrimagnetic ground state. Through density functional theory (DFT) calculations, we reveal that the dominant sources of Berry curvature are located a few hundred meV below the Fermi energy around the $\Gamma$-point. Therefore, Fe$_3$GaTe$_2$ clearly exposes the disorder-induced crossover among distinct AHC regimes, previously inferred from measurements on different ferromagnets located in either side of the crossover region.

Figures

Figures reproduced from arXiv: 2507.23243 by the authors.

Figure 1
Figure 1. FIG. 1. Magnetization and anomalous Hall effect for Fe [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Experimental evidence for a crossover between distinct anomalous Hall regimes in Fe [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Scaling analysis of the anomalous Hall response of Fe [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Anomalous Hall coefficient [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Electronic band structure and distribution of Berry curvature in Fe [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

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