{"id":"ad282d9a-b924-4240-a589-a569e6e6e91a","arxiv_id":"2504.18313","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"NdGaGe, an antiferromagnet below 7.6 K, exhibits a large intrinsic anomalous Hall conductivity of about 368 Ω⁻¹ cm⁻¹, while GdGaGe shows a much smaller effect and a spin-flop transition.","lead":"Researchers grew single crystals of two rare-earth intermetallic compounds, NdGaGe and GdGaGe, and measured their magnetic and electrical properties. NdGaGe shows a large anomalous Hall effect, a signature of topologically nontrivial electron behavior that may be relevant for future spintronics.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 368 Ω⁻¹cm⁻¹ intrinsic AHC for NdGaGe depends on the unverified assumption that ρ_yx^A = S_Hρ_xx²M(B) holds field-by-field; Fig. 4(a) high-field linearity is only a consistency check, not a proof of the decomposition.","rationale":"The strongest claim about NdGaGe is the large intrinsic AHC, and the load-bearing condition for that claim is the validity of Eq. 1. The reader identified this same decomposition as the weakest assumption, and I agree. The concern is concrete and testable: the paper shows only high-field scaling curves, not a field-by-field check that the anomalous Hall resistivity follows S_Hρ_xx²M everywhere, and the GdGaGe analysis reveals a related inconsistency. However, this is an addressable experimental issue, not a fundamental flaw. The reported AHC magnitude is plausible for the RAlX family, and the paper provides independent magnetic and transport characterization. The appropriate disposition is therefore conditional, not rejection: the authors should supply the requested reanalysis and error bars before the intrinsic attribution is accepted. My read does not change the reader's verdict.","tokens_in":9179,"tokens_out":7501,"duration_ms":80388,"concrete_test":"","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central number, σ_xy^A ≈ 368 Ω⁻¹cm⁻¹ at 5 K, is extracted from Eq. 1, ρ_yx = R0B + S_Hρ_xx²M, by fitting ρ_yx/B versus ρ_xx²M/B in the high-field region (Fig. 4(a)). This decomposition assumes (i) the normal Hall resistivity is strictly linear in B with a field-independent R0, and (ii) the anomalous Hall resistivity is exactly proportional to the bulk net magnetization M(B) with a single scalar S_H. The observed linearity in Fig. 4(a) is a consistency check, not a uniqueness proof: because both plotted variables are constructed from the same measured M(B), any Hall contribution that tracks M(B) will produce a line regardless of whether the mechanism is intrinsic Berry curvature. No field-by-field comparison of ρ_yx^A with S_Hρ_xx²M below saturation or through the hysteresis loop is shown, so the reader cannot exclude a multi-band normal Hall effect or a field-dependent anomalous term tied to a sublattice moment rather than net M. The fragility of the procedure is exposed by the GdGaGe analysis, where the same scaling is abandoned above the spin-flop and replaced by a linear fit assuming a field-independent ρ_yx^A even though M(B) is explicitly unsaturated up to 7 T—an internal inconsistency with Eq. 1. With no error bars on R0, S_H, or σ_xy^A, the high-field intercept extrapolation carries unquantified uncertainty. If the scaling assumption fails, the quoted 368 Ω⁻¹cm⁻¹ is not established as the intrinsic AHC.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports the synthesis and characterization of single-crystalline NdGaGe and GdGaGe (tetragonal LaPtSi-type, space group I41md), including magnetic susceptibility, magnetization, magnetoresistance, and Hall effect measurements. NdGaGe orders antiferromagnetically at TN ≈ 7.6 K with strong c-axis anisotropy, shows negative magnetoresistance in the ordered state, and displays a large anomalous Hall conductance of about 368 Ω−1 cm−1 at 5 K. The authors argue this AHC is dominated by the intrinsic Berry-curvature mechanism because the anomalous Hall coefficient S_H ≈ 0.075–0.081 V−1 is nearly temperature independent and σ_xy^A scales as σ_xx^0.04. GdGaGe orders at TN ≈ 22.4 K, exhibits a spin-flop transition near 6.1 T, and is reported to have a much smaller AHC of about 23 Ω−1 cm−1.","tokens_in":9601,"tokens_out":5779,"duration_ms":51953,"significance":"If the central AHC claim is robust, the work adds a new antiferromagnetic RGaGe member to the family of non-centrosymmetric rare-earth compounds with a large intrinsic anomalous Hall response, which is of interest for both Berry-curvature physics and spintronics. The manuscript is strengthened by high-quality single-crystal synthesis, standard Rietveld refinement of powder XRD, careful antisymmetrization of Hall data, and systematic magnetization and transport measurements over a wide temperature range. However, the headline number is extracted under a decomposition assumption that is only partially tested, and the GdGaGe analysis is not consistent with the proposed model; these issues, together with the absence of uncertainty estimates, prevent the paper from establishing the intrinsic origin of the reported AHC as firmly as the text claims.","major_comments":[{"comment":"The central claim of an intrinsic AHC of about 368 Ω−1 cm−1 rests on the assumption that ρ_yx^A = S_H ρ_xx^2 M(B) holds field by field with the bulk net magnetization M(B). The linearity of the high-field scaling plot in Fig. 4(a) is a consistency check, not a demonstration of uniqueness: any anomalous contribution that tracks M(B) will produce a line in that plot, regardless of whether it is intrinsic Berry-curvature, skew scattering, or side jump. To support the decomposition, the authors should show a field-by-field comparison of the measured ρ_yx^A with S_H ρ_xx^2 M over the full field range, including below saturation and through the hysteresis loop. Without such a check, a multi-band normal Hall effect or an anomalous term tied to a sublattice moment rather than net M is not excluded, and the quoted 368 Ω−1 cm−1 is not established as the intrinsic value.","section":"Hall-effect analysis, Eq. (1) and Fig. 4(a)"},{"comment":"The treatment of GdGaGe is internally inconsistent with Eq. (1). Above Bflop, the paper performs a linear fit of ρ_yx(B) with a field-independent intercept ρ_yx^A, even though M(B) is explicitly unsaturated up to 7 T. If Eq. (1) applied with a constant S_H, the anomalous term S_H ρ_xx^2 M would continue to increase with field in this region. The extracted values ρ_yx^A ≈ 0.027 μΩ cm and σ_xy^A ≈ 23 Ω−1 cm−1 therefore do not follow from the stated model. The authors need to justify the constant-intercept assumption or re-analyze the data with the same scaling decomposition used for NdGaGe.","section":"GdGaGe Hall analysis, Eq. (1) and Fig. 3(d)"},{"comment":"No uncertainties are reported for R0, S_H, σ_xy^A, or the scaling exponent. The claim that S_H is temperature independent (0.075–0.081 V−1) and the exponent 0.04 is obtained from a range of only a few temperatures (2–10 K) in which σ_xy^A is nearly constant while σ_xx changes by a small factor; without confidence intervals and the number of fitted points, the exponent is not meaningfully distinguished from zero. Please provide error bars for all reported fitting parameters and statistical details of the linear fits.","section":"Fig. 4 and related text"},{"comment":"The phrase that 'the observed linear behavior confirms that the AHE originates predominantly from the intrinsic mechanism' overstates what the data demonstrate. Temperature-independent S_H and a small scaling exponent are consistent with an intrinsic contribution, but they do not rule out extrinsic skew-scattering contributions with similar phenomenology. A direct comparison with a band-structure/Berry-curvature calculation, or a broader test of the scaling law, would be needed to substantiate 'dominated by the intrinsic mechanism'. At minimum, the wording should be softened to 'consistent with'.","section":"Discussion of the intrinsic mechanism, Fig. 4"}],"minor_comments":[{"comment":"The word 'Recently' is repeated at the start of the first two sentences, and 'Specially' should be 'Specifically'.","section":"Abstract and introductory text"},{"comment":"The sentence 'S_H ρ_xx^2 represents the ordinary and anomalous Hall coefficient' is inconsistent with Eq. (1), where S_H alone is the anomalous Hall coefficient; please correct this wording.","section":"Eq. (1)"},{"comment":"The phrase 'rare-earth irons' should be 'rare-earth ions'.","section":"Discussion before the Summary"},{"comment":"In the reference list entry for ref. [19], there is a stray 's' in 'attention s[19-48]'; please fix this typographical error.","section":"References"},{"comment":"The MR definition in the caption uses ρ(B) and ρ(0) while the main text uses ρ_xx(B) and ρ_xx(0); please unify the notation for clarity.","section":"Fig. 3 caption"},{"comment":"The S_H(T) inset would benefit from error bars and a clearer statement of the temperature range; at present the constancy claim is based on inspection only.","section":"Fig. 4(a) inset"}],"recommendation":"major_revision","confidential_remarks":"The reference list contains several works by the same group (refs. 20, 41, 47) and two arXiv preprints; the novelty of the present NdGaGe/GdGaGe results relative to those earlier studies should be stated explicitly in the revision. This is a presentation and framing concern rather than a grounds for rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things worth knowing about arXiv:2504.18313. First, it reports the first single-crystal growth and characterization of NdGaGe and GdGaGe, and the NdGaGe AHC of ~368 Ω⁻¹ cm⁻¹ at 5 K is a legitimate new data point for the RGaX family. Second, that headline number is less secure than the text suggests: it rests entirely on Eq. 1's decomposition and is not checked field-by-field, and the GdGaGe analysis uses an inconsistent assumption.\n\nCredit: The manuscript is clearly written. The basic characterization (XRD, susceptibility, magnetization, resistivity) is standard and the NdGaGe scaling analysis is internally consistent: ρ_yx/B versus ρ_xx²M/B is linear, S_H is roughly temperature-independent, and the scaling exponent 0.04 supports intrinsic dominance in the stated range. The comparison with the RAlX family is appropriate, and the self-citations are to genuinely related work. The magnetic data—strong anisotropy for Nd, spin-flop for Gd—are useful.\n\nSoft spots: (1) No error bars anywhere on R0, S_H, σ_xy^A, or the exponent. Given that the main claim is a large AHC with an intrinsic interpretation, this matters. (2) The stress-test concern is on target: the linearity in Fig. 4(a) is a consistency check, not a uniqueness proof. Because the anomalous term is defined as S_H ρ_xx² M, any contribution tracking M(B) will linearize. The authors do not show a direct comparison of ρ_yx^A to S_Hρ_xx²M through the hysteresis loop or below saturation, so multi-band normal Hall or field-dependent sublattice Berry curvature cannot be excluded. (3) The GdGaGe extraction is genuinely problematic: above Bflop they fit a field-independent ρ_yx^A even though M(B) is explicitly unsaturated; that contradicts the form of Eq. 1 and should be fixed or toned down. (4) No raw data or analysis code deposited.\n\nProportionate: the first two soft spots are addressable; the third is minor because the GdGaGe AHC is a small side claim. The central NdGaGe result is plausible and fits family trends, but I would not call the 368 value established until the decomposition is validated.\n\nWho benefits: experimentalists working on magnetic topological semimetals, especially RAlX/RGaX AHE. It deserves serious peer review; I would send it out with a request for error bars, a field-by-field decomposition check, and either raw data or a clear deposition plan. I would not cite the 368 number in my own work until that is done.","headline":"A useful new data point for the RGaX family, but the headline AHC in NdGaGe rests on an unvalidated decomposition and the GdGaGe extraction is inconsistent.","tokens_in":10143,"tokens_out":3078,"would_cite":false,"duration_ms":27858,"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":"The antiferromagnet NdGaGe shows a large anomalous Hall conductance of about 368 Ω⁻¹ cm⁻¹ at 5 K, and the paper argues from scaling evidence that the effect is intrinsic Berry-curvature physics.","keywords":["anomalous Hall effect","antiferromagnet","NdGaGe","GdGaGe","Berry curvature","intrinsic mechanism","spin-flop transition","rare-earth intermetallics"],"falsifier":"Compute the intrinsic anomalous Hall conductivity of NdGaGe from first-principles Berry curvature and compare it with the measured $\\approx 368\\ \\Omega^{-1}\\,\\mathrm{cm}^{-1}$; or, experimentally, remeasure the Hall effect at higher fields and along multiple crystallographic directions and refit with a multi-band model. If the calculated value misses the measurement, or if a multi-band fit changes the extracted anomalous conductance substantially, the intrinsic claim would be falsified.","tokens_in":8961,"feed_emoji":"🧲","tokens_out":11618,"duration_ms":103737,"temperature":0.7,"pith_summary":"The paper reports that NdGaGe, a non-centrosymmetric antiferromagnet, displays an anomalous Hall conductance of $\\approx 368\\ \\Omega^{-1}\\,\\mathrm{cm}^{-1}$ at 5 K, a magnitude usually seen in ferromagnetic Weyl semimetals. It argues that the effect is intrinsic, arising from Berry curvature rather than from scattering, because the anomalous Hall coefficient $S_H$ stays near $0.075$--$0.081\\ \\mathrm{V}^{-1}$ between 2 and 10 K and the anomalous Hall conductivity scales as $\\sigma_{xy}^A \\propto \\sigma_{xx}^{0.04}$. The companion compound GdGaGe is antiferromagnetic with a spin-flop transition near 6.1 T and shows a much smaller anomalous Hall conductance of about $23\\ \\Omega^{-1}\\,\\mathrm{cm}^{-1}$. The deeper claim is that the rare-earth element controls both the magnetic structure and the Berry-curvature response in the RGaGe family, making these crystals a tunable platform for antiferromagnetic spintronics.","feed_headline":"NdGaGe's anomalous Hall conductance reaches 368 Ω⁻¹ cm⁻¹","feed_subtitle":"A temperature-independent coefficient and a 0.04 exponent mark the effect as intrinsic Berry-curvature physics.","key_machinery":"The load-bearing object is the two-term decomposition of the Hall resistivity in Eq. (1), $\\rho_{yx} = R_0 B + S_H \\rho_{xx}^2 M$, where $R_0B$ is the ordinary Hall term and $S_H \\rho_{xx}^2 M$ is the anomalous term. The analytic lever is a scaling plot of $\\rho_{yx}/B$ against $\\rho_{xx}^2 M/B$ in the high-field region: the intercept gives $R_0$ and the slope gives $S_H$, and a straight line is read as evidence for a single intrinsic contribution. Temperature-independent $S_H$ and the nearly zero scaling exponent $\\sigma_{xy}^A \\propto \\sigma_{xx}^{0.04}$ then identify the mechanism as Berry-curvature-dominated. For GdGaGe, where the same scaling is not clean, the paper instead fits Eq. (1) above the spin-flop field to extract a small anomalous resistivity.","core_discovery":"On its own terms, the central result is that NdGaGe combines antiferromagnetic order at $T_N\\approx 7.6$ K with a large anomalous Hall conductance of $\\sigma_{xy}^A\\approx 368\\ \\Omega^{-1}\\,\\mathrm{cm}^{-1}$ at 5 K, and that this large response is dominated by the intrinsic Karplus--Luttinger mechanism. The evidence is threefold: the coefficient $S_H$ in $\\rho_{yx}^A = S_H \\rho_{xx}^2 M$ is essentially constant at $0.075$--$0.081\\ \\mathrm{V}^{-1}$ in the range 2--10 K, $\\sigma_{xy}^A$ barely changes with temperature, and $\\sigma_{xy}^A \\propto \\sigma_{xx}^{0.04}$. In contrast, GdGaGe ($T_N\\approx 22.4$ K) has nearly isotropic susceptibility, a spin-flop transition near $B_{\\mathrm{flop}}\\approx 6.1$ T, and a much weaker anomalous Hall conductance of about $23\\ \\Omega^{-1}\\,\\mathrm{cm}^{-1}$. The paper reads this contrast as evidence that the rare-earth ion tunes the electronic structure and therefore the Berry-curvature contribution to transport.","pith_inferences":["If the intrinsic picture is correct, a parameter-free first-principles calculation should reproduce the 368 value; the paper does not report such a calculation, so this is a direct test of its central claim.","The paper ties the anomalous term to the net c-axis magnetization, but an antiferromagnet can also generate Berry curvature from a sublattice or staggered moment; measuring the AHC through the spin-reorientation feature below $T_N$ would distinguish these options.","The same crystal-growth and measurement recipe could be extended to other RGaGe compounds; the Nd/Gd contrast predicts a trend across the rare-earth series that a small systematic study could confirm or overturn."],"forward_implications":["NdGaGe becomes a low-temperature antiferromagnetic reference in which a large anomalous Hall conductance does not require a net ferromagnetic moment.","The same scaling tools applied to other RGaGe members should reveal how rare-earth substitution moves the Fermi level and the Berry curvature, giving a systematic tuning map for the family.","The nearly constant anomalous Hall angle near 0.9% means the transport signal can serve as a reliable low-temperature probe of the magnetic state.","The strong c-axis anisotropy in NdGaGe means measurements aligned with the easy axis will access the full anomalous response, while the gadolinium compound offers a field-controlled spin-flop switch."],"supporting_citations":[{"why":"Supplies the standard classification of the anomalous Hall effect into intrinsic and extrinsic mechanisms and the scaling framework used throughout.","marker":"[1]"},{"why":"Provides the criterion that a temperature-independent anomalous Hall coefficient marks the intrinsic mechanism.","marker":"[2]"},{"why":"Gives the original Karplus--Luttinger intrinsic mechanism that the paper invokes for the Berry-curvature contribution.","marker":"[6]"},{"why":"Supplies the modern Berry-curvature formalism for anomalous Hall transport.","marker":"[8]"},{"why":"Establishes the LaAlSi-type crystal structure of the parent family that places NdGaGe and GdGaGe in the non-centrosymmetric RTX class.","marker":"[20]"},{"why":"Reports a large anomalous Hall conductance in CeAlSi, the ferromagnetic comparison point that makes the 368 value in an antiferromagnet a meaningful benchmark.","marker":"[22]"},{"why":"Documents the temperature-dependent anomalous Hall behavior in NdAlGe that motivates the rare-earth tuning narrative for the family.","marker":"[38,40]"},{"why":"Older experimental references cited for using an essentially constant S_H as evidence of intrinsic anomalous Hall effect.","marker":"[56,57]"}],"fun_headline_variants":["NdGaGe's intrinsic anomalous Hall conductance hits 368 Ω⁻¹cm⁻¹","Anomalous Hall in antiferromagnet: rare-earth tunes the effect","Intrinsic Berry-curvature Hall effect in antiferromagnetic NdGaGe","Rare-earth contrast: NdGaGe's 368 vs GdGaGe's 23 Ω⁻¹cm⁻¹"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire Hall analysis assumes that the anomalous Hall resistivity is exactly proportional to the measured bulk magnetization along the c axis and that the normal and anomalous terms separate cleanly, so no hidden multi-band ordinary Hall effect or field-dependent magnetic contribution distorts the extracted value of about 368 Ω⁻¹ cm⁻¹.","fun_headline_variants_meta":{"raw":{"variants":["NdGaGe's intrinsic anomalous Hall conductance hits 368 Ω⁻¹cm⁻¹","Anomalous Hall in antiferromagnet: rare-earth tunes the effect","Intrinsic Berry-curvature Hall effect in antiferromagnetic NdGaGe","Rare-earth contrast: NdGaGe's 368 vs GdGaGe's 23 Ω⁻¹cm⁻¹"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001089,"raw_usage":{"total_tokens":4621,"prompt_tokens":1089,"completion_tokens":3532,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":705,"completion_tokens_details":{"reasoning_tokens":3438}},"tokens_in":705,"tokens_out":3532,"duration_ms":26080,"temperature":1.0,"reasoning_tokens":3438,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:19:08.230696+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the intrinsic anomalous Hall conductivity of NdGaGe from first-principles Berry curvature and compare it with the measured $\\approx 368\\ \\Omega^{-1}\\,\\mathrm{cm}^{-1}$; or, experimentally, remeasure the Hall effect at higher fields and along multiple crystallographic directions and refit with a multi-band model. If the calculated value misses the measurement, or if a multi-band fit changes the extracted anomalous conductance substantially, the intrinsic claim would be falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the LaAlSi-type crystal structure of the parent family that places NdGaGe and GdGaGe in the non-centrosymmetric RTX class."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports a large anomalous Hall conductance in CeAlSi, the ferromagnetic comparison point that makes the 368 value in an antiferromagnet a meaningful benchmark."}],"review_version":1}