{"id":"9a179249-348d-4024-8c1d-f87544cb319f","arxiv_id":"2411.14045","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"In Cr1+δTe2, positive and negative Berry curvature contributions cancel, making the intrinsic anomalous Hall effect negligible and leaving skew scattering as the dominant mechanism.","lead":"Researchers studied a magnetic layered crystal and found its anomalous sideways voltage in a magnetic field comes from ordinary electron scattering, not from its exotic quantum band structure. Simulations show two topological contributions that would otherwise create the quantum part cancel out, and doping might turn that quantum part back on.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The intrinsic-AHC cancellation is computed for Cr1.25Te2 while the measured sample is Cr1.33Te2; because the paper itself cites δ-dependent Berry-curvature sign changes, this proxy is the principal unvalidated link in the central claim.","rationale":"I agree with the reader's weakest-assumption identification. The paper's central theoretical result is a near-cancellation of Berry-curvature contributions at two nodal points (Sec. IV, Fig. 7), and this cancellation is used to explain why the measured AHE is skew-scattering-dominated. The computed system is Cr1.25Te2, not the measured Cr1.33Te2; the paper calls this 'a close approximation' but provides no test of closeness. Because the paper's own concluding paragraph cites Fujisawa et al. [37] showing that σxy^int crosses zero and changes sign with δ, the burden is on the authors to show the cancellation survives at δ=0.33. The missing U-sensitivity scan is relevant because the Berry-curvature signal is concentrated at avoided crossings whose gaps are controlled by U and magnetic configuration; the stated U range of 0.5–0.8 eV is narrow and no AHC values are given at either endpoint. The requested check is specific and would settle whether the concern lands: a Cr4Te6 calculation with a U sweep would either reproduce the near-zero AHC or reveal that the proxy composition produced it. I do not elevate the lack of error bars in the ρ_AHE vs ρ_xx fit to the main concern because even a clean experimental decomposition still requires the intrinsic contribution to be evaluated at the measured composition. Since this is the same concern the reader flagged and the recommended condition is unchanged, the reader's CONDITIONAL verdict stands.","tokens_in":16341,"tokens_out":6796,"duration_ms":65287,"concrete_test":"Repeat the Wannier-interpolated Berry-curvature/AHC calculation on an ordered supercell with the measured composition δ=1/3, e.g. Cr4Te6 (or Cr8Te12) in the same P3m1 parent, using the same GGA+U and Wannier90 workflow, and compute σxy^int at EF as a function of U = 0, 0.5, 0.8, and 1.0 eV and of two inequivalent intercalant orderings. Also compute the same quantity for Cr10Te16 as the baseline. The central claim survives only if |σxy^int(EF)| for Cr4Te6 remains below roughly 10 S/cm across the U range and orderings; if it becomes comparable to the experimental σxy^AHE extracted from Fig. 6(b), or changes sign relative to the Cr10Te16 result, the near-cancellation is an artifact of the proxy composition.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the intrinsic AHC is effectively zero in Cr1.33Te2 because positive and negative Berry curvature at Γ-M and Γ-K cancel (Sec. IV, Fig. 7). The DFT calculation is not performed at the measured composition: Sec. IV states that 'Cr10Te16 (= Cr1.25Te2) provides a close approximation to the experimental structure.' Cr1.25Te2 is the δ=0.25 member (Cr5Te8), while EDXS and lattice parameters place the crystal at δ=0.33(1). The paper's own Sec. V cites Fujisawa et al. [37] showing that Ωz of Cr1+δTe2 'can switch from positive to negative as δ varies, and σxy^int also changes its sign, crossing through zero.' A δ offset of 0.08 is therefore not a harmless detail: the cancellation in Fig. 7(d) could be specific to the 0.25 supercell and its intercalant ordering. Fig. 7(d) itself shows AHC sign flips near EF, so a small shift in band filling or gap size can change the outcome. In addition, GGA+U is used with U in 0.5–0.8 eV, but no U dependence of the Berry curvature or AHC is reported, even though the gaps at avoided crossings depend on U and magnetic order. Without a calculation at the actual δ or a demonstrated insensitivity to δ and U, the theoretical explanation of the observed absence of intrinsic AHE has not been shown to apply to the measured sample.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents a combined experimental and ab initio study of self-intercalated Cr1+δTe2 single crystals with δ ≈ 0.33. Magnetization, magnetocaloric effect, synchrotron X-ray diffraction, resistivity, and Hall resistivity measurements characterize a ferromagnet with TC ≈ 191 K and strong c-axis anisotropy. The anomalous Hall data are analyzed with a modified scaling law (Eq. 5) to conclude that skew scattering dominates the AHE. DFT + GGA+U calculations on a Cr10Te16 (Cr1.25Te2) supercell find gapped nodal points along Γ-M and Γ-K with Berry curvature of opposite signs; the Kubo-formula intrinsic AHC is argued to be near zero because of this cancellation.","tokens_in":16748,"tokens_out":4764,"duration_ms":45944,"significance":"If confirmed, the paper offers a plausible resolution of the puzzle of why a compound with sizable Berry curvature shows no intrinsic AHE. The theoretical part is a genuine first-principles calculation of the Berry curvature and AHC via the Kubo formula, not a fit to the measured Hall data; the near-cancellation is computed rather than assumed. The paper also provides a useful experimental dataset on the magnetocaloric effect and thermal expansion, and it makes a falsifiable prediction that electron doping should induce a large intrinsic AHE when the Fermi level reaches the conduction-band nodal point. The main weakness is the gap between the measured composition (δ ≈ 0.33) and the calculated one (δ = 0.25), which is not tested for sensitivity.","major_comments":[{"comment":"The DFT calculation is performed for Cr10Te16, i.e., Cr1.25Te2, while the measured crystals are Cr1.33Te2 according to EDXS and lattice parameters (Sec. III.A). The text calls the supercell \"a close approximation\" but provides no calculation at the actual composition and no test of how the Berry-curvature cancellation depends on δ. The paper itself cites Fujisawa et al. [37] to state that Ωz and σxy^int can switch sign as δ varies and cross through zero. A δ difference of 0.08 is therefore potentially material. The authors should either compute σxy^int for a Cr1.33Te2 supercell or show explicitly that the cancellation is robust over the measured δ range and over intercalant arrangements.","section":"Sec. IV, Fig. 7"},{"comment":"The conclusion that skew scattering dominates the AHE rests on a three-parameter fit to ρAHE_xy versus ρxx, but the paper reports only the best-fit values α′ = -0.042, α′′ = 0.037, β = 4.41 S/cm. No uncertainties, correlation matrix, or goodness-of-fit statistic are given, and alternative scaling forms (e.g., a single exponent q, or different separation of residual and phonon terms) are not discussed. The authors should provide error bars and a measure of fit quality, and demonstrate that the βρxx^2 term is negligible within the uncertainties.","section":"Sec. III.E, Eq. (5)"},{"comment":"The central theoretical claim is that the intrinsic AHC is \"effectively zero,\" but the manuscript gives no numerical value of σxy^int at EF and no quantitative comparison with the experimental σAHE_xy shown in Fig. 6(b). Because Fig. 7(d) shows sign flips near EF, the exact position of EF is critical. The authors should state the computed AHC at EF, including its sensitivity to k-mesh, smearing, and Hubbard U, and compare it with the experimental magnitude to make the cancellation claim quantitative.","section":"Sec. IV, Eq. (7) and Fig. 7(d)"},{"comment":"The Hubbard U is chosen in the range 0.5-0.8 eV to match magnetic moments, but no U dependence of the Berry curvature or AHC is reported. Since the gaps at the avoided crossings, and hence the Berry curvature and σxy^int, are expected to depend on U and on the magnetic order, the near-cancellation could be specific to the chosen interaction strength. A short U-dependence scan of σxy^int would test this directly.","section":"Sec. II.B, Fig. 7"}],"minor_comments":[{"comment":"In the conclusion, \"δS\" should be ΔSM, matching the notation used in Sec. III.B.","section":"Sec. V"},{"comment":"\"V ASP\" should be \"VASP.\"","section":"Sec. II.B"},{"comment":"The Fig. 7(a) caption and the main text disagree on the colors used for the bands with and without SOC; please align them.","section":"Sec. IV, Fig. 7(a)"},{"comment":"The phrase \"the inset shows the enlarge view\" should be \"the inset shows an enlarged view.\"","section":"Sec. III.E"},{"comment":"\"alternative staking\" should be \"alternative stacking.\"","section":"Sec. I"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable combined experimental and theoretical study, but the central theoretical explanation is computed at a proxy composition with no sensitivity check; this needs to be addressed before publication. The experimental Hall scaling analysis also needs full statistical reporting. If these issues are resolved, the paper would be a solid contribution for the journal's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: this is a careful experiment-plus-DFT paper on AHE in Cr1.33Te2, and the central idea—that opposing Berry curvature at two gapped nodal points cancels the intrinsic AHC—is plausible and nicely worked out. The catch is that the DFT is computed for Cr1.25Te2, not the measured δ=0.33, and the paper's own reference [37] shows that δ tunes the sign of the Berry curvature. So the theory demonstrates a mechanism at a nearby composition, but it doesn't yet prove that this is why the measured sample has no intrinsic AHE.\n\nWhat I like: the experimental side is thorough. SCXRD, PXRD, EDXS, magnetization, MCE, resistivity, Hall—they characterize the crystal well. The AHE scaling fit to Eq. 5 is standard and the conclusion that skew scattering dominates is a reasonable read of the data. The DFT is a genuine first-principles calculation: they identify the Γ-M (Cr-d/Cr-d) and Γ-K (Cr-d/Te-p) crossings, show SOC opens gaps, compute Berry curvature with opposite signs, and show the integrated AHC is near zero at EF. The predicted unoccupied node at K that could produce large AHE under electron doping is a nice falsifiable claim. They also argue against the previously reported THE, attributing the staircase to spin-flop instead.\n\nSoft spots, in order of severity. First, the composition issue. Cr10Te16 is δ=0.25, but the crystals are δ≈0.33. The authors call it a 'close approximation', but [37] shows δ-driven sign flips in BC. A calculation at the real composition, or a scan over δ and U, would close the loop. Without that, the theory is suggestive, not demonstrative. Second, the scaling fit has no error bars or goodness-of-fit; the α′, α″, β values are reported without uncertainties, and the decomposition into linear vs quadratic terms is model dependent. Minor, but it would help. Third, the absence of THE is asserted rather than quantitatively shown—no attempt to extract a topological Hall contribution in the field range where it might appear.\n\nWho should read this? People working on AHE in Cr-Te and related layered magnets. It's a useful data point and the doping prediction is testable. I'd send it to a serious referee, but with a request that the authors either compute at δ=0.33 or explicitly test sensitivity to δ and U. The paper is honest and well cited; the gap is a validation gap, not a fabrication. My verdict: conditional, but worth engaging.","headline":"Solid experiment-plus-DFT study; the Berry-curvature-cancellation story is plausible but not yet proven at the measured composition, and the paper's own cited δ-dependence is the load-bearing loose end.","tokens_in":17294,"tokens_out":3543,"would_cite":true,"duration_ms":36320,"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":"Rival Berry curvature contributions cancel the intrinsic anomalous Hall effect in Cr1+δTe2","keywords":["Cr1+δTe2","anomalous Hall effect","Berry curvature","skew scattering","self-intercalated van der Waals ferromagnet","density functional theory","spin-orbit coupling","magnetocrystalline anisotropy"],"falsifier":"Recompute the Berry curvature and intrinsic anomalous Hall conductivity for a supercell that exactly matches the measured Cr1.33Te2 composition and intercalation pattern; if the integrated value is non-negligible at the Fermi level, the cancellation argument is falsified. Alternatively, electron-dope the crystal to move the Fermi level onto the conduction-band node at K; if a large intrinsic Hall signal does not appear, the predicted node contribution is wrong.","tokens_in":16150,"feed_emoji":"🧲","tokens_out":9414,"duration_ms":73758,"temperature":0.7,"pith_summary":"This paper tries to explain why the self-intercalated ferromagnet Cr1+δTe2 (δ≈0.33) shows a sizable anomalous Hall effect that is nevertheless not intrinsic. Magnetization, magnetocaloric, and magnetotransport measurements on single crystals show strong uniaxial anisotropy, a first-order-like hysteresis, and a Hall response dominated by skew scattering according to the modified scaling relation. Density functional theory with spin-orbit coupling finds gapped nodal points near the Fermi energy with substantial Berry curvature of opposite signs along the Γ–M and Γ–K directions, and these contributions nearly cancel in the anomalous Hall conductivity. The authors conclude that the intrinsic Berry-curvature channel is effectively zero, and that extrinsic skew scattering accounts for the observed AHE.","feed_headline":"Rival Berry curvatures cancel the intrinsic Hall effect in Cr1+δTe2","feed_subtitle":"Magnetotransport and DFT show skew scattering, not band topology, drives the anomalous Hall signal.","key_machinery":"The load-bearing object is the momentum-space Berry curvature $\\Omega^z_n(\\mathbf{k})$ computed from a tight-binding model derived from DFT+U+SOC bands. Opposite-sign curvature contributions at the gapped Γ–M (Cr d–d) and Γ–K (Cr d–Te p) nodal points cancel in the linear-response integral for the intrinsic anomalous Hall conductivity, reducing it to near zero. The same machinery predicts a sign change in the intrinsic Hall response upon shifting the Fermi level, which is why the authors suggest electron doping as a route to switch on a topological Hall signal.","core_discovery":"The central discovery is that the intrinsic anomalous Hall contribution in Cr1+δTe2 is suppressed by cancellation of Berry curvature from different momentum-space nodal points. In the Cr10Te16 supercell used to approximate the experimental composition, density functional theory plus spin-orbit coupling opens gaps at band crossings along Γ–M and Γ–K; the resulting Berry curvature is positive near one node and negative near the other. Integrating this Berry curvature over occupied states yields an intrinsic anomalous Hall conductivity that is effectively zero, even though individual Berry-curvature values are large. The paper therefore attributes the measured anomalous Hall effect to the extrinsic skew-scattering mechanism, and notes that electron doping could move the Fermi level to a conduction-band node where a large intrinsic Hall effect would reappear.","pith_inferences":["Because the DFT model uses Cr1.25Te2 instead of the measured Cr1.33Te2, and because earlier work shows the Berry curvature changes sign with Cr concentration, the exact cancellation may be a composition-specific accident; a slightly different doping could restore a finite intrinsic AHE.","The symmetry and orbital-hybridization picture at the conduction-band K node suggests a design rule for centrosymmetric intercalated chalcogenides: the sign of Berry curvature is controlled by which orbitals hybridize at a crossing, so tuning orbital character could balance or amplify the two contributions.","The staircase features in magnetization and Hall resistivity, interpreted here as spin-flop transitions, could be tested directly by neutron diffraction on a single crystal in a magnetic field; if they are spin-flop, the magnetic structure should reorient without forming a skyrmion phase.","The prediction that electron doping should turn on a large intrinsic Hall effect is testable by electrostatic gating or chemical intercalation; observing such a signal would confirm both the K-node origin and the cancellation picture."],"forward_implications":["The observed anomalous Hall effect in Cr1+δTe2 (δ≈0.33) is extrinsic, dominated by skew scattering, rather than Berry-curvature-driven.","Nontrivial band topology with gapped nodal points can coexist with a vanishing intrinsic Hall response when opposite-sign Berry curvature cancels.","Electron doping of Cr1+δTe2 should shift the Fermi level toward the conduction-band node at K and produce a measurable intrinsic anomalous Hall effect.","The near-zero thermal expansion between roughly 115 and 150 K is coupled to the magnetic hysteresis, indicating magneto-structural coupling in the same temperature window.","The absence of a topological Hall effect in this centro-symmetric crystal contrasts with earlier reports on Cr1.33Te2, suggesting the topological Hall signal may require a non-centrosymmetric environment."],"supporting_citations":[{"why":"Shows that the Berry curvature in this material family changes sign as the Cr concentration varies, which the paper relies on to explain why the cancellation at the modeled composition is consistent with the experimental absence of intrinsic AHE.","marker":"[37]"},{"why":"Reported a topological Hall effect in the same nominal composition, the prior result this paper re-examines and does not reproduce, supporting its extrinsic interpretation.","marker":"[41]"},{"why":"Supplies the Berry-curvature formula used to compute $\\Omega^z_n$ from the tight-binding bands.","marker":"[73]"},{"why":"Describes the construction of maximally-localized orbitals used to make the tight-binding Hamiltonian from the DFT band structure.","marker":"[47]"},{"why":"Introduced the modified scaling law that separates skew scattering from intrinsic and side-jump contributions, which the paper fits to its Hall data.","marker":"[70]"},{"why":"Extends that scaling law to include the temperature-linear term, strengthening the assignment of the dominant contribution to skew scattering.","marker":"[71]"},{"why":"Provides the standard classification of anomalous Hall mechanisms (skew scattering, side-jump, intrinsic) that frames the experimental analysis.","marker":"[23]"},{"why":"Establishes the intrinsic band-structure mechanism for AHE, which the paper's cancellation argument tests against.","marker":"[25]"},{"why":"Gives the linear-response expression used to integrate the Berry curvature into the intrinsic anomalous Hall conductivity.","marker":"[31]"}],"fun_headline_variants":["Rival Berry curvatures cancel intrinsic Hall effect in Cr1+δTe2","Skew scattering dominates as Berry curvature contributions cancel in Cr1+δTe2","Intrinsic Hall effect suppressed by sign-opposite Berry curvatures","Cr1+δTe2: competing Berry nodes quench intrinsic anomalous Hall contribution","Berry curvature cancellation explains missing intrinsic Hall in Cr1+δTe2"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The theoretical model approximates the measured Cr1.33Te2 crystal with a Cr10Te16 (Cr1.25Te2) supercell, and the conclusion of near-zero intrinsic Hall effect assumes that this substitution preserves the near-cancellation of Berry curvature.","fun_headline_variants_meta":{"raw":{"variants":["Rival Berry curvatures cancel intrinsic Hall effect in Cr1+δTe2","Skew scattering dominates as Berry curvature contributions cancel in Cr1+δTe2","Intrinsic Hall effect suppressed by sign-opposite Berry curvatures","Cr1+δTe2: competing Berry nodes quench intrinsic anomalous Hall contribution","Berry curvature cancellation explains missing intrinsic Hall in Cr1+δTe2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000637,"raw_usage":{"total_tokens":2931,"prompt_tokens":938,"completion_tokens":1993,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":554,"completion_tokens_details":{"reasoning_tokens":1892}},"tokens_in":554,"tokens_out":1993,"duration_ms":13187,"temperature":1.0,"reasoning_tokens":1892,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:35:59.852443+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the Berry curvature and intrinsic anomalous Hall conductivity for a supercell that exactly matches the measured Cr1.33Te2 composition and intercalation pattern; if the integrated value is non-negligible at the Fermi level, the cancellation argument is falsified. Alternatively, electron-dope the crystal to move the Fermi level onto the conduction-band node at K; if a large intrinsic Hall signal does not appear, the predicted node contribution is wrong.","supporting_citations":[{"cited_title":"Fujisawa, M","cited_arxiv_id":null,"evidence_quote":"Shows that the Berry curvature in this material family changes sign as the Cr concentration varies, which the paper relies on to explain why the cancellation at the modeled composition is consistent with the experimental absence of intrinsic AHE."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reported a topological Hall effect in the same nominal composition, the prior result this paper re-examines and does not reproduce, supporting its extrinsic interpretation."},{"cited_title":"Gradhand, D","cited_arxiv_id":null,"evidence_quote":"Gives the linear-response expression used to integrate the Berry curvature into the intrinsic anomalous Hall conductivity."}],"review_version":1}