{"id":"cf366cb3-426f-42e5-b37e-dcda654cd04c","arxiv_id":"2411.12134","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"The anomalous Hall conductivity in YMn6Sn5.45Ga0.55 is comparable to TbMn6Sn6 and is three-dimensional, so it cannot arise from a 2D Chern gap.","lead":"This paper measures the anomalous Hall effect in a doped kagome magnet and finds it is similar when the magnetic field is applied out of plane and in plane, so the effect comes from three-dimensional electronic structure rather than a two-dimensional Chern gap. The work also supports a new empirical formula that separates intrinsic, impurity, and spin-fluctuation contributions to the anomalous Hall effect.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"In-plane intrinsic AHC value rests on an unvalidated three-parameter fit and contradicts DFT by 10x; the qualitative 3D claim is robust, but the quantitative 'comparable magnitude' claim is not.","rationale":"The reader's verdict identifies the empirical scaling relation as the weakest premise, and I agree that the fitted c is the hinge. My stress-test sharpens this: the in-plane c=310 S/cm is not merely under-determined, it is contradicted by the authors' own first-principles calculation (36.76 S/cm). Since the abstract's 'comparable in magnitude' assertion and the phrase 'fully three-dimensional intrinsic AHC' rely on this number, the quantitative central claim is only as good as the three-parameter fit. At the same time, the direct observation of a large in-plane anomalous Hall signal in Fig. 6 is robust evidence for 3D Hall transport and suffices to refute a 2D Chern-gap-only origin. Therefore the paper's qualitative conclusion stands, but the paper should be conditioned on a test of the decomposition (e.g., low-temperature two-term fit or an explicit supercell DFT calculation). I therefore do not change the reader's CONDITIONAL verdict. The attack is partial agreement: I start from the same Eq. 2 issue but add the DFT magnitude check and the distinction between qualitative and quantitative claims.","tokens_in":16009,"tokens_out":6733,"duration_ms":72465,"concrete_test":"Refit the in-plane Hall conductivity data of Fig. 6 using only the low-temperature (T < 50 K) subset with the two-term scaling σxz = a σxx^2 + c, and compute bootstrap confidence intervals for c. If the interval includes the DFT value (~37 S/cm), the three-parameter decomposition is not sufficiently constrained to establish an intrinsic in-plane AHC of 310 S/cm, and the quantitative 'comparable magnitude' claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim that the intrinsic AHC is 'fully three-dimensional' and 'comparable in magnitude to TbMn6Sn6' rests on the fitted coefficient c in Eq. (2), σxy = aσxx^2 + d/σxx + c, for the in-plane geometry: c = 310 S/cm (Table III). No error bars, no alternative fit forms, and no microscopic derivation for the d/σxx term are provided. The paper's own DFT calculation (Sec. III F, Fig. 8) gives σzx = 36.76 S/cm for the same hole doping, an order of magnitude below the fitted c, and the discrepancy is acknowledged only with a caveat about rigid-band shifts. If the three-parameter fit is not the correct decomposition—for example, if the d/σxx term partially absorbs a temperature-dependent intrinsic contribution or if the anisotropic conductivity invalidates the isotropic scaling form—then the extracted c could be much smaller. That would remove the quantitative comparison to TbMn6Sn6 (140 S/cm) and leave the 'fully three-dimensional' intrinsic claim without a reliable magnitude. Notably, the qualitative 3D nature is not in question: a large anomalous Hall signal is directly observed in the in-plane geometry (Fig. 6), so the exclusion of a purely 2D Chern-gap origin survives even if the fitted c is wrong. The load-bearing weak spot is therefore the numerical value of the in-plane intrinsic AHC and the comparison built on it.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reports a combined experimental and first-principles study of the ferromagnetic kagome compound YMn6Sn5.45Ga0.55. Single crystals are characterized by X-ray diffraction, magnetization, resistivity, angular magnetoresistance, and Hall-effect measurements in two field geometries (B||[001] and B||[120]). The anomalous Hall conductivity (AHC) is fitted to the empirical scaling law σxy = aσxx^2 + d/σxx + c, yielding intrinsic AHC values c = 121 S/cm (out-of-plane) and c = 310 S/cm (in-plane). DFT Berry-curvature calculations give σxy = 77.62 S/cm and σzx = 36.76 S/cm for the assumed hole doping. The authors conclude that the intrinsic AHC is three-dimensional and comparable in magnitude to TbMn6Sn6, and that the d/σxx term reflects spin fluctuations.","tokens_in":16395,"tokens_out":7535,"duration_ms":71339,"significance":"The paper addresses a topical debate: whether the anomalous Hall effect in RMn6Sn6 kagome magnets arises from 2D Chern gaps or from a bulk 3D Berry-curvature distribution. The experimental observation of a large in-plane AHC in a Tb-free compound is a direct and convincing falsification of a purely 2D Chern-gap origin, independent of any scaling analysis. The DFT AHC calculation is a state-of-the-art parameter-free integration of Berry curvature over a dense k mesh using Wannier interpolation, with Ueff fixed from earlier work. The paper also provides an independent test of the scaling law proposed in Ref. [12]. However, the quantitative intrinsic AHC values, especially the in-plane value, rest on an empirical three-parameter decomposition that is not yet adequately justified.","major_comments":[{"comment":"The central quantitative claim in the abstract—that the intrinsic AHC in YMn6Sn5.45Ga0.55 is comparable in magnitude to TbMn6Sn6 and is fully three-dimensional—relies on the fitted coefficient c in Eq. (2): c = 121 S/cm for B||[001] and c = 310 S/cm for B||[120] (Table III). No uncertainty estimates for a, d, or c are provided, and no alternative decomposition forms are tested. The in-plane fitted value is nearly an order of magnitude larger than the authors' own DFT value σzx = 36.76 S/cm (Sec. III.F, Fig. 8), and the brief caveat about rigid-band shifts does not quantify whether this discrepancy is consistent with the experimental c. Because this discrepancy directly affects the comparison to TbMn6Sn6 (140 S/cm), the manuscript needs either a robust statistical and systematic error analysis of the fit, or a reformulation of the quantitative claims.","section":"III.E, Table III, Eq. (2)"},{"comment":"The three-term scaling relation σxy = aσxx^2 + d/σxx + c is introduced as an empirical formula from Ref. [12]; the d/σxx term is attributed to spin fluctuations, but no microscopic derivation or independent verification is given in the present manuscript. The nonzero d observed in the Tb-free Y166-Ga is suggestive, but the manuscript does not analyze whether the magnitude and temperature dependence of d correlate with any spin-fluctuation measure, nor does it report goodness-of-fit statistics. Since this empirical relation is the only basis for extracting the intrinsic c values, its lack of a derivation or falsifiable test is a load-bearing assumption for the paper's quantitative conclusions.","section":"III.E, Eq. (2)"},{"comment":"The scaling law in Eq. (2) is written for a single longitudinal conductivity σxx, but the material is strongly anisotropic in transport: σ[001]/σ[100] > 2 over the whole temperature range (Sec. III.D, Fig. 3(b)). For the in-plane Hall geometry (B||[120], I||[100]), the Hall resistivity is converted to conductivity using σzx = -ρzx/(ρxxρzz), and the scaling plot in Fig. 6(c) uses the same σxx = 1/ρxx as in the out-of-plane case. The manuscript does not justify that the isotropic form of Eq. (2) remains valid for an anisotropic conductor, or that the appropriate longitudinal conductivity for the in-plane geometry is σxx rather than some combination of σxx and σzz. Without such a justification, the in-plane fitted c = 310 S/cm is not a reliable intrinsic AHC.","section":"III.D, III.E"}],"minor_comments":[{"comment":"The text gives the composition as 'YMn6Sn6.45Ga0.55' in the sentence 'selected one particular composition YMn6Sn6.45Ga0.55 for the study'; this should be 'YMn6Sn5.45Ga0.55' to match the abstract and the rest of the paper.","section":"Section I"},{"comment":"The Hall conductivity component is denoted inconsistently; the text defines σzx (and Table III uses |σxz|), while the caption of Fig. 6 labels it |σA_xz|. Please use a single convention throughout.","section":"Section III.E and Fig. 6"},{"comment":"The statement 'σxx = 1/ρxx' is imprecise; in the in-plane geometry the longitudinal resistivity is ρxx but the Hall-conductivity conversion uses both ρxx and ρzz, so the notation should distinguish the tensor components.","section":"Section III.E"},{"comment":"The calculation is described as performed for 'YMn6Sn5Ga', but the experimental composition is YMn6Sn5.45Ga0.55; please clarify whether the calculation uses an ordered x=1 model and whether this is intended.","section":"Fig. 4 caption"},{"comment":"The conclusion contains a duplicated word: 'may be important for not only for the large family' should read 'for not only the large family'.","section":"Section IV"}],"recommendation":"major_revision","confidential_remarks":"The experimental data are of high quality and the qualitative 3D conclusion is robust. The main reservation is that the quantitative intrinsic AHC values are derived from an empirical scaling law whose microscopic basis is not established, and the in-plane DFT discrepancy is large. I believe the manuscript can be made acceptable by adding error analysis, testing alternative decomposition forms, and either softening the quantitative comparison or providing a microscopic justification of Eq. (2). The paper is well within the scope of cond-mat.mtrl-sci."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe qualitative central claim is likely right: measuring a large anomalous Hall conductivity in the in-plane geometry directly rules out a purely 2D Chern-gap origin in this kagome family. The quantitative claim that the intrinsic AHC is comparable in magnitude to TbMn6Sn6 is weaker, but the 3D nature does not rest on the disputed number.\n\nWhat is new: this is the first in-plane AHE measurement in the RMn6Sn6 family, made possible by the soft ferromagnetism of the Ga-doped Y compound, and it tests the group's own three-term scaling law on a Tb-free system. The sample growth, single-crystal X-ray, magnetization, and transport appear careful. The out-of-plane intrinsic AHC from the fit (121 S/cm) agrees reasonably with the DFT rigid-band value (77.6 S/cm), and the DFT AHC calculation is parameter-free aside from U_eff fixed in earlier work, with a dense 256^3 k-mesh.\n\nSoft spots, in order of importance. First, the in-plane fitted intrinsic AHC (310 S/cm) is about an order of magnitude larger than the DFT value (36.8 S/cm); the authors acknowledge this but do not resolve it. The discrepancy weakens the quantitative magnitude of the in-plane intrinsic part and the comparison to TbMn6Sn6 built on it, though the qualitative 3D conclusion survives. Second, the scaling relation (Eq. 2) remains purely empirical: no error bars on the fitted coefficients, no microscopic derivation of the d/σxx term, and no check against alternative decompositions. This matters because the paper's headline numbers are the fitted c coefficients. Third, the abstract's claim that the scaling law is 'universally governed by spin fluctuations' overreaches from two compounds, which have different fluctuating species (Tb vs Mn). Fourth, minor: the AMR calculation underestimates the measured value by a factor of three, which the authors attribute to anisotropic scattering or SOC underestimation.\n\nIf I were refereeing, I would ask for error bars on the fits, a discussion of whether the low-temperature data alone give a robust in-plane intrinsic AHC without the three-term decomposition, and a softened universality claim. None of these are deal-breakers. The paper is a solid experimental contribution that deserves a serious referee and likely publication after revision.\n\nBest","headline":"The experimental case against 2D Chern-gap AHE in this kagome family is strong; the quantitative in-plane intrinsic value is weakened by an unvalidated fit and a large DFT mismatch.","tokens_in":16971,"tokens_out":5707,"would_cite":true,"duration_ms":55465,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper establishes that the intrinsic anomalous Hall conductivity in YMn6Sn5.45Ga0.55 is fully three-dimensional and comparable to TbMn6Sn6, ruling out 2D Chern gaps as its origin in the RMn6Sn6 family.","keywords":["kagome lattice","anomalous Hall effect","YMn6Sn6","Chern gap","spin fluctuations","Berry curvature","ferrimagnet","empirical scaling relation"],"falsifier":"A first-principles calculation that includes explicit Ga disorder at the experimental composition and still predicts the in-plane intrinsic AHC far below the fitted 310 S/cm — the paper's own rigid-band estimate is 36.76 S/cm — would undercut the claim that the fitted in-plane value is intrinsic; if the discrepancy persists with disorder properly treated, the three-dimensionality conclusion is not supported by the data.","tokens_in":15815,"feed_emoji":"🧲","tokens_out":10721,"duration_ms":100539,"temperature":0.7,"pith_summary":"This paper sets out to settle where the anomalous Hall effect comes from in the RMn6Sn6 kagome metals, using Ga-doped YMn6Sn6 as a testbed. It argues that the intrinsic anomalous Hall conductivity is comparable to that of TbMn6Sn6 (fitted 121 S/cm out-of-plane versus 140 S/cm) yet persists with larger magnitude (310 S/cm) when the magnetic field lies in the kagome plane, where a 2D Chern gap cannot contribute. A sympathetic reader would take this as experimental evidence that the intrinsic Hall response is a three-dimensional property of the ferrimagnetic band structure rather than a topological 2D gap feature. The paper also reads its three-term scaling law as confirmed, since the fitted spin-fluctuation term remains nonzero in a compound that contains no Tb, implying fluctuating Mn moments are sufficient to generate it.","feed_headline":"Kagome magnet's Hall effect is 3D, not a 2D Chern gap","feed_subtitle":"Intrinsic Hall signal persists with the field in-plane, pointing to ferrimagnetic bands instead of 2D topology.","key_machinery":"The central device is the empirical scaling law $\\sigma_{xy}=a\\sigma_{xx}^2+d/\\sigma_{xx}+c$, which extends the standard Berry-phase-plus-impurity scaling by adding a term that grows when $\\sigma_{xx}$ is small, i.e., at high temperature. Fitting the measured Hall conductivity to this law partitions it into impurity scattering ($a\\sigma_{xx}^2$), spin-fluctuation scattering ($d/\\sigma_{xx}$), and an intrinsic part $c$ identified with the Berry-curvature integral. The second device is geometric: comparing the $B\\parallel[001]$ configuration, in which a 2D Chern gap would contribute, with the $B\\parallel[120]$ configuration, in which it cannot, converts the scaling fit into a dimensional test of the intrinsic AHC.","core_discovery":"The central claim is that, in YMn6Sn5.45Ga0.55, the intrinsic (Berry-curvature) contribution to the anomalous Hall conductivity is fully three-dimensional. Fitting the Hall conductivity over 1.8–300 K to $\\sigma_{xy}=a\\sigma_{xx}^2+d/\\sigma_{xx}+c$ gives $c=121$ S/cm for $B\\parallel[001]$, comparable to the TbMn6Sn6 value of 140 S/cm, and $c=310$ S/cm for $B\\parallel[120]$. Because a 2D Chern gap, an energy gap in a two-dimensional band with a nonzero Chern number, would contribute only in the out-of-plane geometry, the large in-plane value shows that the Hall conductivity does not originate from those gaps. The nonzero fitted $d$ in a Tb-free compound is presented as confirmation that the extra $d/\\sigma_{xx}$ term is a spin-fluctuation contribution universal to the RMn6Sn6 family.","pith_inferences":["Editorial inference: if the fitted $c$ values are true Berry-curvature contributions, the larger in-plane value (310 vs 121 S/cm) implies the dominant Berry-curvature hot spots are most active when the moment lies in the kagome planes; this could be checked with momentum-resolved Berry-curvature maps for in-plane magnetization.","Editorial inference: the $d/\\sigma_{xx}$ term is empirical and not microscopically derived here; a controlled test would tune the Mn moment fluctuation amplitude (by pressure, doping, or field) and check that the fitted $|d|$ tracks the fluctuation strength rather than the residual resistivity.","Editorial inference: the same two-geometry protocol applied to a compound whose Fermi level genuinely sits in a 2D Chern gap should show a strong out-of-plane intrinsic AHC and a near-zero in-plane one; finding such a compound would sharpen the contrast the paper draws."],"forward_implications":["If the decomposition is correct, the 2D Chern gap near 130 meV above the Fermi energy cannot be the source of the measured AHC, because the in-plane geometry does not couple to it yet gives a comparable or larger intrinsic value.","The three-term scaling law should replace the two-term law when extracting intrinsic AHC from spin-fluctuating magnets; the two-term law would misattribute the high-temperature $d/\\sigma_{xx}$ contribution.","The nonzero fitted $d$ in YMn6Sn5.45Ga0.55, a compound without Tb, means the spin-fluctuation term is not tied to a specific rare earth and is expected throughout the RMn6Sn6 ferrimagnets.","Ga substitution is a practical route to a saturable kagome ferromagnet whose in-plane and out-of-plane AHC can both be measured in a 9 T laboratory magnet, as opposed to TbMn6Sn6 whose in-plane saturation would require much higher fields.","First-principles calculations for YMn6Sn6 reproduce the same 3D pattern—appreciable $\\sigma_{xy}$ for out-of-plane magnetization and appreciable $\\sigma_{yz}/\\sigma_{zx}$ for in-plane magnetization—consistent with the experimental conclusion."],"supporting_citations":[{"why":"Supplies the three-term scaling law and the TbMn6Sn6 comparison values (c = 140 S/cm), and the DFT conclusion that AHC comes from 3D bands.","marker":"[12]"},{"why":"Proposes the 2D Chern gap near 130 meV above the Fermi energy that the paper's in-plane measurement rules out as the AHC source.","marker":"[20]"},{"why":"DFT results showing the 2D Chern gap lies about 700 meV above the Fermi energy, challenging its relevance to transport.","marker":"[16]"},{"why":"Establishes the Ga-substituted YMn6Sn6 compositions that order ferromagnetically, providing the platform for the experiments.","marker":"[31]"},{"why":"Provides the exchange-coupling model and the fluctuating-moment picture for Mn in Y166 that motivates the spin-fluctuation interpretation.","marker":"[17]"},{"why":"Gives the standard two-term scaling law that the paper extends with the d/σxx term.","marker":"[28]"},{"why":"Photoemission on parent YMn6Sn6 showing no topological feature above the Fermi energy, supporting the non-Chern interpretation.","marker":"[47]"}],"fun_headline_variants":["Kagome Hall effect is 3D, not a Chern gap","Hall conductivity in kagome magnet is 3D, not 2D","3D Berry curvature drives kagome Hall effect, no Chern gap","Kagome magnet's Hall effect: 3D, not from Chern gaps"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything rests on the empirically fitted three-term formula $\\sigma_{xy}=a\\sigma_{xx}^2+d/\\sigma_{xx}+c$ being the true decomposition of the measured Hall conductivity; the 'intrinsic' values are fitted coefficients $c$, not directly measured quantities, and the paper gives no microscopic derivation of the $d$ term. If that decomposition is wrong, the comparison with TbMn6Sn6 and the 3D claim lose their quantitative footing.","fun_headline_variants_meta":{"raw":{"variants":["Kagome Hall effect is 3D, not a Chern gap","Hall conductivity in kagome magnet is 3D, not 2D","3D Berry curvature drives kagome Hall effect, no Chern gap","Kagome magnet's Hall effect: 3D, not from Chern gaps"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001399,"raw_usage":{"total_tokens":5692,"prompt_tokens":1014,"completion_tokens":4678,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":630,"completion_tokens_details":{"reasoning_tokens":4597}},"tokens_in":630,"tokens_out":4678,"duration_ms":29351,"temperature":1.0,"reasoning_tokens":4597,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T17:52:09.092681+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A first-principles calculation that includes explicit Ga disorder at the experimental composition and still predicts the in-plane intrinsic AHC far below the fitted 310 S/cm — the paper's own rigid-band estimate is 36.76 S/cm — would undercut the claim that the fitted in-plane value is intrinsic; if the discrepancy persists with disorder properly treated, the three-dimensionality conclusion is not supported by the data.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the three-term scaling law and the TbMn6Sn6 comparison values (c = 140 S/cm), and the DFT conclusion that AHC comes from 3D bands."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proposes the 2D Chern gap near 130 meV above the Fermi energy that the paper's in-plane measurement rules out as the AHC source."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the Ga-substituted YMn6Sn6 compositions that order ferromagnetically, providing the platform for the experiments."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the exchange-coupling model and the fluctuating-moment picture for Mn in Y166 that motivates the spin-fluctuation interpretation."},{"cited_title":"Cr´ epieux and P","cited_arxiv_id":null,"evidence_quote":"Gives the standard two-term scaling law that the paper extends with the d/σxx term."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Photoemission on parent YMn6Sn6 showing no topological feature above the Fermi energy, supporting the non-Chern interpretation."}],"review_version":1}