{"id":"02e294ef-b179-4b06-bdc5-fe6f32757e04","arxiv_id":"2507.23243","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Measurements on 19 Fe3GaTe2 crystals show a dirty-regime scaling σxy ∝ σxx^1.6 below σxx ≈ 4×10^3 Ω^-1cm^-1, crossing over to a disorder-independent anomalous Hall conductivity of about 420 Ω^-1cm^-1.","lead":"This paper reports the first observation, in a single compound Fe3GaTe2, of a crossover between two anomalous Hall regimes as crystal disorder varies. The result supports the intrinsic Berry-curvature origin of the large anomalous Hall effect and identifies the dominant band-structure source.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Temperature and disorder are treated as interchangeable in Fig. 2(a); the 2 K-only data are never shown, so the crossover may be a T-mixing artifact.","rationale":"The central claim is that Fe3GaTe2 alone exhibits the dirty-to-moderately-dirty crossover, with σxy ∝ σxx^1.6 below σxx ≈ 4×10^3 Ω^-1cm^-1 and a disorder-independent plateau near 420 Ω^-1cm^-1 above. For this to be true, σxy must be a single-valued function of σxx regardless of whether σxx is changed by quenched disorder or by temperature. The reader identified this as the weakest assumption, and I agree. The paper's own text is inconsistent: it claims the analysis was done at 2 K to exclude inelastic effects, yet Fig. 2(a) and Fig. 3 deliberately include data up to 200 K and 350 K. The authors also state that in the moderately dirty regime σxy decreases rapidly with T, showing that temperature does not merely rescale σxx but changes the AHE amplitude through inelastic channels. If the crossover curve in Fig. 2(a) is populated by high-temperature points of clean crystals, the apparent power-law and the onset of the plateau may be a temperature artifact. The fixed-temperature fits in Fig. 3(a) provide some support: at each T, the dirty-regime exponent appears consistent across samples, which suggests disorder tuning works for the low-σxx branch. But no fixed-T plot spanning the full σxx range is shown; without the T=2 K subset alone, the crossover cannot be separated from temperature effects. The proposed test—replotting Fig. 2(a) with only 2 K data and checking whether the break and plateau persist—would settle this. If the 2 K data alone are scattered and do not define the two regimes, the central claim is not supported by the present evidence. If the 2 K data alone do show the crossover, then the concern is resolved and the conditional acceptance can proceed. Because this concern is exactly the reader's condition, the verdict remains CONDITIONAL pending the 2 K-only analysis.","tokens_in":12940,"tokens_out":8202,"duration_ms":91130,"concrete_test":"Re-plot Fig. 2(a) using only the T=2 K points for all 19 crystals. Fit the points with σxx < 4×10^3 Ω^-1cm^-1 to σxy = Aσxx^n + σ0 and check whether the high-σxx points saturate near 420 Ω^-1cm^-1. Additionally, overlay each sample's T-trajectory (2–200 K) on the same plot: if a clean sample's trajectory follows the disorder-tuned curve, T and disorder are equivalent; if it cuts across the curve, the combined dataset is mixing regimes. The crossover claim stands only if the 2 K-only data alone exhibit the break and plateau.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption is that temperature and static disorder are interchangeable tuning knobs for σxx. The authors state 'Our analysis was performed at the lowest temperature of T = 2 K to exclude inelastic effects due to phonons, or magnons,' yet Fig. 2(a) plots σxy versus σxx for all samples 'within the temperature range T = 2 K – 200 K' and Fig. 3 uses fits up to 350 K to establish the n ≈ 1.6 exponent. The crossover and plateau are therefore identified on a curve that mixes sample-to-sample disorder with temperature sweeps. The authors themselves note that for the clean crystal C1, σxy decreases rapidly with T in the moderately dirty regime, i.e., inelastic scattering suppresses the AHE independently of σxx. If high-T points from clean crystals populate the crossover region, the apparent n ≈ 1.6 power law and the break near σxx ≈ 4×10^3 Ω^-1cm^-1 could be an artifact of combining two different physical mechanisms (elastic disorder vs. phonon/magnon scattering) rather than evidence for a disorder-driven crossover. The fixed-T fits in Fig. 3(a) do mitigate the concern for the dirty-regime exponent, but they do not establish that the crossover and plateau at high σxx are disorder-driven.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13240,"tokens_out":8499,"duration_ms":95848,"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":[{"comment":"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.","section":"Fig. 2(a); text near 'Our analysis was performed at the lowest temperature of T = 2 K' and 'within the temperature…"},{"comment":"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.","section":"Fig. 4 and text 'We identified two distinctive regimes...'"},{"comment":"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.","section":"Fig. 3 and the discussion of the n ≈ 1.6 exponent"},{"comment":"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.","section":"Sections on structural characterization (XRD, STEM) and Fig. 5"}],"minor_comments":[{"comment":"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.","section":"Text near Fig. 2(a)"},{"comment":"The caption says 'the dirty regime below σxy = 4 ×10^3 Ω^-1cm^-1' but should refer to σxx, not σxy.","section":"Fig. 4 caption"},{"comment":"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.","section":"Discussion of DFT results"},{"comment":"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.","section":"Fig. 2(b)"},{"comment":"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.","section":"Fig. 5(b) and text following"},{"comment":"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.","section":"Methods text near Fig. 2(a)"}],"recommendation":"major_revision","confidential_remarks":"The data set is valuable and the paper addresses an important question in the anomalous Hall effect literature. The main risk is the conflation of temperature-driven changes with disorder-driven changes in Fig. 2(a); if the authors can present a clean fixed-temperature analysis and quantify the regime boundaries, the paper could become a strong contribution. I do not see evidence of circular reasoning in the DFT comparison, but the sample classification into regimes does rely on the same hand-drawn boundaries used to define the regimes."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Frankly, this is the clearest single-compound claim yet for the dirty-to-moderately-dirty AHE crossover, and the paper does a lot right. Nineteen crystals spanning σxx from 8×10^2 to 10^4 Ω⁻¹cm⁻¹, no chemical substitution, TEM and magnetization evidence for disorder, and a DFT calculation that puts the dominant Berry curvature near Γ rather than K. That is a solid, useful package.\n\nThe central scaling in the dirty regime, n≈1.6, is supported by fixed-temperature fits in Fig. 3(a), which is the right way to test a disorder-driven exponent. The saturation value σxy≈420 Ω⁻¹cm⁻¹ is close to e2/hd, so the intrinsic plateau claim is plausible.\n\nThe soft spots are real but not fatal. The biggest one: the text says the analysis is at 2 K to exclude inelastic effects, but Fig. 2(a) plots data from 2 K to 200 K for all samples. The crossover and plateau are therefore identified on a curve that mixes sample-to-sample disorder with temperature sweeps. The authors themselves note that σxy for the cleanest crystal drops rapidly with T in the moderately dirty regime, so high-T points could populate the crossover region and create an apparent n≈1.6 power law that is actually a T-mixing artifact. The fixed-T fits in Fig. 3(a) do mitigate this for the dirty-regime exponent, but they do not establish that the crossover and the plateau are disorder-driven. The paper needs a 2 K-only version of Fig. 2(a).\n\nOther issues: no error bars on σxx or σxy, hand-drawn regime boundaries, and a placeholder data DOI. The DFT overestimate by ~27% is acknowledged and within the usual range, so I would not treat that as a flaw.\n\nBottom line: the paper deserves a serious referee. The data set is rich, the question is well posed, and the Γ-point attribution is a genuine contribution. But the referee should ask for the 2 K-only analysis, error bars, and the actual data before this is publishable. I would bring it to our reading group if the authors post the data; until then, maybe.","headline":"A plausible single-compound AHE crossover, but the mixed temperature/disorder data need to be disentangled before the headline claim holds.","tokens_in":13726,"tokens_out":2114,"would_cite":true,"duration_ms":24125,"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":"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…","keywords":["anomalous Hall effect","Berry curvature","Fe3GaTe2","scaling crossover","dirty regime","moderately dirty regime","intrinsic mechanism","first-order magnetic transition"],"falsifier":"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}$$cm^{-1}$; alternatively, find two crystals with identical σxx but measurably different vacancy concentrations whose σxy differs by more than the scatter, which would break the functional dependence σxy(σxx).","tokens_in":12786,"feed_emoji":"🧲","tokens_out":6126,"duration_ms":59715,"temperature":0.7,"pith_summary":"The paper aims to show that the magnetic metal Fe3GaTe2, without changing its chemical composition, displays both known regimes of the anomalous Hall effect: in lower-conductivity crystals the Hall conductivity scales as σxy ∝ $σxx^{1}$.6, while in cleaner crystals it saturates at a disorder-independent value near 420 $Ω^{-1}$$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}$$cm^{-1}$) is slightly above the measured one. They also locate the dominant Berry curvature near the Γ-point, a few hundred meV below the Fermi level, rather than near the K-point emphasized in earlier work. If right, Fe3GaTe2 becomes a single testing ground for how disorder alone moves a ferromagnet through the anomalous Hall scaling regimes.","feed_headline":"Fe3GaTe2 shows the full anomalous Hall crossover in one compound","feed_subtitle":"Hall conductivity scales as σxx^1.6 in dirty crystals and saturates at 420 Ω^-1cm^-1 in clean ones.","key_machinery":"The central machinery is the scaling plot of anomalous Hall conductivity σxy against longitudinal conductivity σxx across 19 crystals and many temperatures, fit to σxy = Aσxx^n + σ0 with n ≈ 1.6 in the dirty regime, together with band-resolved Berry curvature maps from DFT showing a dominant contribution near the Γ-point a few hundred meV below the Fermi energy. The Berry curvature acts as an effective magnetic field in momentum space that deflects electrons transversely; this is the mechanism that produces the intrinsic anomalous Hall plateau.","core_discovery":"By measuring 19 Fe3GaTe2 single crystals spanning σxx from about 8×$10^{2}$ to 1×$10^{4}$ $Ω^{-1}$$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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the quantum transport theory defining the dirty, moderately dirty, and super-clean anomalous Hall regimes and the σxy ∝ σxx^1.6 dirty-regime scaling.","marker":"[7]"},{"why":"Distinguishes intrinsic (Berry-curvature) from extrinsic anomalous Hall mechanisms and provides the intrinsic conductivity framework for the plateau comparison.","marker":"[61]"},{"why":"Empirical crossover behavior of the anomalous Hall effect in itinerant ferromagnets that the Fe3GaTe2 data are compared against.","marker":"[43]"},{"why":"Reports large anomalous Hall conductivity in the isomorphic compound Fe3GeTe2 with nodal-line Berry curvature, the work this paper extends toward the moderately dirty regime.","marker":"[26]"},{"why":"Prior claim of a singular Hall response in Fe3GaTe2 emphasizing Berry curvature near the K-point, which this paper contrasts with its Γ-point finding.","marker":"[27]"},{"why":"Proposes the TYJ scaling based on temperature and sample-dependent conductivity, an alternative scaling approach that does not include the dirty regime.","marker":"[44]"},{"why":"Proposes a multivariable scaling for anomalous Hall effect beyond the low-conductivity regime, another scaling framework the paper positions itself against.","marker":"[45]"}],"fun_headline_variants":["One material reveals full dirty-to-clean Hall transition","Fe3GaTe2 maps the complete anomalous Hall crossover","From dirty to clean: Hall conductivity crossover in Fe3GaTe2","Single compound shows disorder-driven Hall conductivity regimes","Anomalous Hall crossover captured in a single crystal family"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["One material reveals full dirty-to-clean Hall transition","Fe3GaTe2 maps the complete anomalous Hall crossover","From dirty to clean: Hall conductivity crossover in Fe3GaTe2","Single compound shows disorder-driven Hall conductivity regimes","Anomalous Hall crossover captured in a single crystal family"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000841,"raw_usage":{"total_tokens":3715,"prompt_tokens":1045,"completion_tokens":2670,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":661,"completion_tokens_details":{"reasoning_tokens":2590}},"tokens_in":661,"tokens_out":2670,"duration_ms":18880,"temperature":1.0,"reasoning_tokens":2590,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T10:54:23.354102+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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).","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Distinguishes intrinsic (Berry-curvature) from extrinsic anomalous Hall mechanisms and provides the intrinsic conductivity framework for the plateau comparison."},{"cited_title":"Iguchi, N","cited_arxiv_id":null,"evidence_quote":"Empirical crossover behavior of the anomalous Hall effect in itinerant ferromagnets that the Fe3GaTe2 data are compared against."},{"cited_title":"Figure 1(c) shows 3 FIG","cited_arxiv_id":null,"evidence_quote":"Reports large anomalous Hall conductivity in the isomorphic compound Fe3GeTe2 with nodal-line Berry curvature, the work this paper extends toward the moderately dirty regime."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior claim of a singular Hall response in Fe3GaTe2 emphasizing Berry curvature near the K-point, which this paper contrasts with its Γ-point finding."},{"cited_title":"Miyasato, N","cited_arxiv_id":null,"evidence_quote":"Proposes the TYJ scaling based on temperature and sample-dependent conductivity, an alternative scaling approach that does not include the dirty regime."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proposes a multivariable scaling for anomalous Hall effect beyond the low-conductivity regime, another scaling framework the paper positions itself against."}],"review_version":1}