{"id":"720afd23-1c69-4794-9706-bd90f2f0e8f4","arxiv_id":"2507.11182","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In Cr2Te3 thin films, electron-magnon scattering produces a negative skew-scattering contribution to the anomalous Hall resistivity that competes with impurity and Berry-curvature terms and explains the sign change around 100 K.","lead":"Measurements on thin films of the layered ferromagnet Cr2Te3 show that collisions between electrons and magnons contribute strongly to the anomalous Hall effect and can flip its sign as temperature changes. The result suggests this magnon-induced skew scattering may be a general feature of layered ferromagnets containing heavy elements.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Scaling decomposition assumes T-independent intrinsic AHE, but the paper admits Berry curvature varies with T; a T-dependent intrinsic term can masquerade as a2, undermining the magnon origin of the sign change.","rationale":"The reader identified electron-electron scattering as the weakest assumption; that is a legitimate concern, but I find it less load-bearing than the paper's own admission that the intrinsic Berry-curvature contribution can vary with temperature. The high-field suppression data (Fig. 5) provide independent evidence for a magnon contribution to the AHE, so even if part of the T^2 longitudinal resistivity were e-e, the qualitative claim that magnons scatter electrons significantly would survive. In contrast, if a temperature-dependent intrinsic AHE is present, the linear scaling used to extract a2 is not uniquely interpretable: a ρ0^2 ρT term from σ_xy^int(T) ∝ T^2 would be fitted as part of a2, and the sign change could be intrinsic rather than due to magnon skew scattering. The paper explicitly acknowledges this complication in Sec. II C, yet proceeds to extract a2 from linear fits without quantifying the intrinsic T-dependence. Precisely because the paper's novelty is the assignment of the sign change to magnons, this omission is the most load-bearing. The concrete test—a finite-temperature Berry-curvature calculation—is feasible and would settle whether the intrinsic term can account for Δρ_T_yx. The model calculation's use of λ as a fitting parameter weakens the quantitative agreement but is not the primary concern, since the T^2 scaling and proportionality of ρ_yx and ρ_xx are nontrivial predictions. Overall, the verdict remains CONDITIONAL: the experimental phenomenology is credible, but the central interpretation requires the proposed finite-T intrinsic calculation.","tokens_in":19347,"tokens_out":18233,"duration_ms":222572,"concrete_test":"Compute σ_xy^int(T) from the first-principles band structure of Cr2Te3 by integrating the Berry curvature with Fermi–Dirac occupations at T = 2, 50, 100, 150 K for the experimental lattice constants and Fermi level determined from the carrier density. Form ρ_yx^int(T) = σ_xy^int(T) ρ_xx(T)^2 using the measured ρ_xx(T) and compare with the measured Δρ̃_T_yx after subtracting the zero-field impurity contribution. If ρ_yx^int(T) reproduces the magnitude and sign change of Δρ̃_T_yx without invoking a2, the magnon-skew-scattering interpretation is not uniquely supported.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that the sign change in Δρ̃_yx is caused by magnon-induced skew scattering (a2 ≈ −0.067) rests on the scaling decomposition in Eq. 2, which assumes the intrinsic Berry-curvature contribution is cρ_xx^2 with a T-independent coefficient c. The paper itself states in Sec. II C that the Berry-curvature contribution in Cr2Te3 'can vary with temperature due to thermal broadening of the Fermi surface' and that this makes it difficult to extract b2 and c. If σ_xy^int(T) varies with T, then ρ_yx^int(T) = σ_xy^int(T) ρ_xx(T)^2 contains terms beyond cρ_xx^2; for example, a σ_xy^int ∝ T^2 component produces a term ∝ ρ0^2 ρT that is linear in ρT and is absorbed into the extracted a2 (and similarly contaminates the slope-vs-ρ0 intercept in Fig. 4e). The deviation-from-linearity estimate (≤25%) captures only nonlinear-in-ρT components; a linear-in-ρT intrinsic contribution would be hidden. Since prior work attributes the sign change to Berry curvature and the paper's own DFT shows σ_yx changes sign 0.06 eV below the Fermi level, finite-T smearing could produce a sizeable T-dependent intrinsic AHE. Without quantifying this, a2 cannot be unambiguously assigned to magnon skew scattering.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an experimental and theoretical study of the anomalous Hall effect (AHE) in layered ferromagnet Cr2Te3 thin films. The authors measure the longitudinal resistivity and anomalous Hall resistivity as functions of temperature and thickness, decompose the data using a multivariable scaling relation (Eq. 2), and extract a dynamic skew-scattering coefficient a2 ≈ −0.067. They attribute the T^2 longitudinal resistivity to electron-magnon scattering and the negative a2 term to magnon-induced skew scattering, arguing that the sign change of the AHE near 100 K results from competition between this negative term and positive impurity-induced side-jump/Berry-curvature terms. A model calculation based on a spin-orbit-modified p-d exchange interaction reproduces the T^2 scaling and, after adjusting the spin-orbit parameter λ to −0.84, the magnitude of the ratio Δρ_yx/ρ_xx.","tokens_in":19644,"tokens_out":7193,"duration_ms":75131,"significance":"If the central claim is correct, the paper identifies magnon-induced skew scattering as a significant and potentially dominant AHE mechanism in layered ferromagnets with heavy elements, going beyond the usual Berry-curvature and impurity-scattering pictures. The experimental strengths include the systematic thickness dependence, the use of multivariable scaling, the linear magnetoresistance and high-field suppression data that support a magnon-related dynamic contribution, and the first-principles band-structure context. The main limitations are that the model's magnitude agreement is obtained by fitting λ, and that the scaling analysis may be contaminated by a temperature-dependent intrinsic Berry-curvature contribution that the paper itself acknowledges. These issues are addressable and do not invalidate the qualitative conclusion, but they must be resolved before the quantitative assignment of a2 to magnon skew scattering is fully established.","major_comments":[{"comment":"The scaling decomposition assumes the intrinsic Berry-curvature contribution is cρ_xx^2 with a temperature-independent c. The paper states in Sec. II C that the Berry-curvature contribution in Cr2Te3 can vary with temperature due to thermal broadening and that this makes it difficult to extract b2 and c. If σ_xy^int(T) varies with T, then ρ_yx^int(T) = σ_xy^int(T) ρ_xx(T)^2 contains terms that are linear in ρ_T (for example, a T-linear part of σ_xy^int produces a term proportional to ρ0^2 ρ_T). Such a term would be absorbed into the fitted a2 in the slope versus ρ0 analysis of Fig. 4(e). The reported upper bound of about 25% for the quadratic (b2 and c) contributions is estimated from deviations from linearity and therefore only constrains nonlinear-in-ρ_T terms, not a linear-in-ρ_T contamination. Since the DFT calculation in Sec. VI C shows that σ_yx changes sign only 0.06 eV below the Fermi level, finite-temperature smearing can produce a sizeable T-dependent intrinsic term. I request a quantitative estimate of σ_xy^int(T) from the calculated band structure with thermal broadening, and a propagation of that estimate through Eq. (2) to bound the resulting linear-in-ρ_T contribution to a2.","section":"Sec. II C, Eq. (2)"},{"comment":"The model ratio Δρ_cal_yx / ρ_cal_xx is made equal to the extracted a2 = −0.067 by choosing λ = −0.84, as stated in the text and in Table I footnote 4. The magnitude agreement is therefore by construction rather than a predictive test of the model. The model's nontrivial content lies in the T^2 scaling and the negative sign (which requires λ < 0), and the resulting λJpd ≈ 0.084 eV is indeed of the order of the Te atomic spin-orbit coupling. The authors should state this limitation clearly and provide an independent estimate or bound on λ from band-structure or SOC matrix elements if possible; otherwise the model should be presented as an illustrative mechanism rather than a quantitative confirmation.","section":"Sec. III, Eq. (16) and Table I footnote 4"},{"comment":"The decomposition of the longitudinal resistivity uses ρ_T_xx ≡ ρ_xx − ρ0_xx entirely as electron-magnon scattering, with the statement 'we neglect electron-electron scattering' in Sec. II B. Since electron-electron scattering also scales as T^2, a substantial e-e contribution would weaken the correlation between Δρ̃_T_yx and ρ_m_xx in Fig. 4(f) and the assignment of a2 to magnons. The linear magnetoresistance and high-field suppression in Figs. 3 and 5 indicate that magnons contribute to ρ_T_xx, but they do not exclude a coexisting T^2 e-e channel. Please provide an estimate of the possible e-e contribution (for example, from the Kadowaki-Woods ratio or from comparing ρ_m_xx across samples with different residual resistivities) or otherwise justify why the entire T^2 term can be attributed to magnons.","section":"Sec. II B"},{"comment":"The key coefficients a1 ≈ −0.034, b1+c ≈ 1.5×10^−4 (µΩ cm)^−1, a2 ≈ −0.067, and b3+2c ≈ 0.7×10^−4 (µΩ cm)^−1 are quoted without uncertainties, goodness-of-fit measures, or the number of independent devices included in each fit. Because the central quantitative claim is that a2 is negative and comparable in magnitude to a1, the fits in Figs. 4(d) and 4(e) should be reported with standard errors (and ideally confidence intervals), and the fitting ranges and weighting schemes should be specified.","section":"Sec. II C, Figs. 4(d) and 4(e)"}],"minor_comments":[{"comment":"Please specify the temperature range over which Eq. (1) is fitted (the text says 'for T < TC' but does not state the upper bound used in the fit) and the units of T (K).","section":"Eq. (1) and Fig. 2(b)"},{"comment":"The transverse voltage probe configuration is shown schematically but not described in the text; please state whether the V_yx contacts are placed symmetrically with respect to the current path to avoid longitudinal pickup.","section":"Sec. V B and Fig. 8"},{"comment":"The parabolic fitting shown in Fig. 4(b) is for a 10 nm-thick film; please clarify whether the T^2 scaling of Δρ̃_yx is verified for all thicknesses or only for selected samples.","section":"Fig. 4(b)"},{"comment":"Please state the sign convention connecting Δσ_yx and Δρ_yx in the model calculations and in Fig. 9, since the main text switches between resistivities and conductivities.","section":"Sec. VI D, Eq. (12)"},{"comment":"The model is cited to an arXiv preprint from 1998; if a published version exists (e.g., Irkhin and Irkhin, Phys. Rev. B 75, 104412 (2007)), it should be cited instead of or in addition to the arXiv listing.","section":"References [45]"}],"recommendation":"major_revision","confidential_remarks":"The manuscript presents a substantial dataset and a plausible mechanism for the temperature-dependent anomalous Hall effect in Cr2Te3. The main risk is that the scaling analysis may absorb a temperature-dependent intrinsic Berry-curvature term into a2; the authors already have the DFT machinery to test this, so the requested calculation is feasible. The model's free λ and the neglect of e-e scattering are secondary but should be addressed for the quantitative claim. I do not see a need to reject the manuscript; the requested revisions are within the scope of a major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a solid experimental paper that makes a new claim about the AHE sign change in Cr2Te3 — it's driven by magnon-induced skew scattering, not just Berry curvature or static impurities. The experiments are thorough: films of five thicknesses, Hall bars, magnetoresistance up to 140 kOe, and the high-field suppression of the Hall signal is a nice piece of evidence. The T^2 longitudinal resistivity and the scaling decomposition are mutually consistent, and extending the Hou multivariable scaling to include a dynamic skew term a2 is a reasonable step.\n\nWhat I'd push back on is the strength of the assignment of a2 to magnons. The paper itself says the Berry curvature contribution can vary with temperature due to thermal broadening of the Fermi surface and that this makes b2 and c hard to extract. That creates a real problem for the central claim. If the intrinsic anomalous Hall conductivity varies with T, an intrinsic term of the form σ_xy^int(T) ρ_xx^2 contains a piece linear in ρT — exactly what gets absorbed into a2. The paper's 25% bound on quadratic terms only covers nonlinear-in-ρT components; a linear-in-ρT intrinsic term would be hidden. The DFT sign change 0.06 eV below the Fermi level makes this concrete. So the decomposition alone cannot cleanly separate magnon skew scattering from a T-dependent intrinsic contribution. The high-field suppression and correlation with ρm_xx help, but they co-vary with T and do not by themselves pin down the microscopic origin.\n\nThe microscopic model also has a circularity: λ is adjusted so that the calculated ratio equals the measured a2. That makes the magnitude agreement by construction. The T^2 scaling and sign competition are consistent, but the model doesn't independently confirm the mechanism.\n\nMinor issues: no uncertainties on the fitted coefficients, and the explicit neglect of electron-electron scattering (also T^2) is a simplification that the interpretation inherits.\n\nStill, this deserves a serious referee. The experimental phenomenology is new and the proposed mechanism is testable. The referee should demand a quantitative estimate of the T-dependent intrinsic contribution — or a more direct probe separating the two channels — before the magnon-skew-scattering attribution becomes the headline. My call: send to peer review, expecting that the interpretation section needs to be reworked or substantially hedged.","headline":"Solid experimental evidence for a dynamic AHE term in Cr2Te3, but the magnon attribution is less certain than the authors claim because T-dependent Berry curvature can masquerade as the culprit.","tokens_in":20208,"tokens_out":2966,"would_cite":true,"duration_ms":35163,"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":"This paper reports that electron-magnon scattering, not only Berry curvature or impurity scattering, controls the anomalous Hall effect in Cr2Te3 and explains its sign change near 100 K.","keywords":["anomalous Hall effect","electron-magnon scattering","skew scattering","Cr2Te3","layered ferromagnet","spin-orbit coupling","Berry curvature","magnetoresistance"],"falsifier":"Measure the anomalous Hall resistivity of Cr$_2$Te$_3$ at magnetic fields strong enough to suppress magnons almost completely (several hundred kOe): if the $a_2$ term is magnon-induced skew scattering, the $T^2$ part of $\\Delta\\rho_{yx}$ should vanish under full magnon suppression, whereas it should persist if another $T^2$ channel such as electron-electron scattering contributes.","tokens_in":19164,"feed_emoji":"🧲","tokens_out":7704,"duration_ms":82938,"temperature":0.7,"pith_summary":"Using longitudinal and Hall transport measurements on Cr$_2$Te$_3$ thin films below the Curie temperature, this paper argues that the temperature-dependent part of the anomalous Hall effect comes from magnon-induced skew scattering rather than from band Berry curvature or static impurity scattering alone. The authors fit the anomalous Hall resistivity with a multivariable scaling decomposition and extract a dynamic skew-scattering coefficient $a_2 \\approx -0.067$. They attribute the sign change of the anomalous Hall resistivity near 100 K to competition between this negative magnon term and positive impurity side-jump or Berry-curvature terms. A model calculation with $p$-$d$ exchange plus spin-orbit coupling reproduces the observed quadratic temperature scaling and magnitude, pointing to exchange between itinerant Te $p$-electrons and localized Cr $d$-moments as the microscopic origin.","feed_headline":"Electron-magnon scattering flips Cr2Te3's Hall sign","feed_subtitle":"Temperature-dependent Hall data show magnon skew scattering competes with Berry curvature to reverse the sign near 100 K.","key_machinery":"The load-bearing objects are the multivariable scaling relation for the anomalous Hall resistivity, $\\Delta\\tilde{\\rho}_{yx}=a_1\\rho^0_{xx}+a_2\\rho^T_{xx}+\\dots$, which separates static from dynamic disorder contributions, and the spin-orbit-modified $p$-$d$ exchange Hamiltonian $H_{pd}=i\\lambda J_{pd}a_0^2\\sum_{k,k'}(k\\times k')\\cdot(\\delta S)_{k-k'}c_k^\\dagger c_{k'}$. The $a_2$ term isolates the dynamic skew scattering caused by magnons; the Hamiltonian generates both the $T^2$ longitudinal resistivity and the $T^2$ anomalous Hall resistivity from the same electron-magnon collision process. The ratio of the two model resistivities is then used to fix the spin-orbit parameter $\\lambda$ against the measured $a_2$.","core_discovery":"The central claim is that electron-magnon scattering is a leading source of the anomalous Hall effect in the layered ferromagnet Cr$_2$Te$_3$. Experimentally, the longitudinal resistivity below $T_C$ follows $\\rho_{xx}=\\rho^0_{xx}+\\rho^m_{xx}T^2$, and the anomalous Hall resistivity $\\Delta\\tilde{\\rho}_{yx}$ shows the same quadratic temperature dependence. Using the multivariable scaling of Ref. [39] extended with a dynamic skew term, the paper decomposes $\\Delta\\tilde{\\rho}_{yx}$ into static and dynamic parts and finds the dynamic coefficient $a_2\\simeq -0.067$. The temperature-dependent contribution is positively correlated with the electron-magnon scattering coefficient $\\rho^m_{xx}$ and is suppressed by magnetic fields that freeze magnons. The authors conclude that magnon-induced skew scattering, arising from a spin-orbit-coupled $p$-$d$ exchange interaction, competes with impurity side-jump and Berry-curvature contributions and drives the sign change near 100 K.","pith_inferences":["The paper leaves open whether the same magnon skew-scattering mechanism dominates in other heavy-element layered ferromagnets; a direct test would be to apply the same scaling decomposition to a Te-free ferromagnet with weak spin-orbit coupling and check whether $a_2$ nearly vanishes.","Since $\\lambda$ is fixed by matching the measured $a_2$, the microscopic assignment could be tested independently by first-principles calculation of the spin-orbit matrix element between Te $p$ and Cr $d$ states; agreement with $\\lambda J_{pd}\\approx 0.084$ eV would not rely on transport data.","The analysis assigns all of $\\rho^T_{xx}$ to magnons; if part of the $T^2$ term is electron-electron scattering, then $a_2$ as extracted would be an upper bound for the magnon skew-scattering coefficient, and a cleaner test would be to compare films where the carrier density is tuned so the electron-electron contribution changes independently of magnon population."],"forward_implications":["The sign change of the anomalous Hall resistivity near 100 K is explained by competition between negative magnon-induced skew scattering and positive impurity side-jump or Berry-curvature terms, so a separate topological Hall mechanism is not required to account for it.","Below $T_C$, the quadratic temperature dependence of the longitudinal resistivity is dominated by electron-magnon scattering, corroborated by the linear decrease of magnetoresistance with out-of-plane field.","The dynamic skew-scattering coefficient $a_2\\approx -0.067$ is comparable in magnitude to skew-scattering coefficients extracted in other ferromagnetic systems.","High magnetic fields suppress magnon population and thereby reduce both the magnetoresistance and the temperature-dependent part of the anomalous Hall resistivity.","The model calculation shows that the same $p$-$d$ exchange interaction with spin-orbit coupling yields $T^2$ scaling for both longitudinal and Hall resistivities, consistent with the experiments."],"supporting_citations":[{"why":"Provides the multivariable scaling relation for anomalous Hall resistivity that the paper extends by adding a dynamic skew-scattering term.","marker":"[39]"},{"why":"Gives the spin-orbit-modified p-d exchange Hamiltonian and the model formulas for magnon-induced skew scattering.","marker":"[45]"},{"why":"Documents the linear magnetoresistance and magnetic-field suppression of electron-magnon scattering used to corroborate the magnon origin.","marker":"[33]"},{"why":"Supplies the standard anomalous Hall effect formalism and normalization used to analyze the Hall data.","marker":"[37]"},{"why":"Provides earlier Berry curvature calculations for Cr2Te3 used as a comparison for the first-principles results here.","marker":"[20]"}],"fun_headline_variants":["Magnon scattering drives Cr2Te3 Hall sign flip","Cr2Te3 Hall sign change traced to magnons","Electron-magnon scattering controls Cr2Te3 AHE","Magnon skew scattering reverses Hall sign in Cr2Te3","Why Cr2Te3's Hall effect flips: magnons"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The analysis assumes that all of the observed $T^2$ longitudinal resistivity below $T_C$ comes from electron-magnon scattering and explicitly neglects electron-electron scattering, which also scales as $T^2$; if a substantial part of that term has another origin, the identification of $a_2$ with magnon skew scattering is weakened.","fun_headline_variants_meta":{"raw":{"variants":["Magnon scattering drives Cr2Te3 Hall sign flip","Cr2Te3 Hall sign change traced to magnons","Electron-magnon scattering controls Cr2Te3 AHE","Magnon skew scattering reverses Hall sign in Cr2Te3","Why Cr2Te3's Hall effect flips: magnons"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000479,"raw_usage":{"total_tokens":2365,"prompt_tokens":929,"completion_tokens":1436,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":545,"completion_tokens_details":{"reasoning_tokens":1350}},"tokens_in":545,"tokens_out":1436,"duration_ms":11254,"temperature":1.0,"reasoning_tokens":1350,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:15:03.935852+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the anomalous Hall resistivity of Cr$_2$Te$_3$ at magnetic fields strong enough to suppress magnons almost completely (several hundred kOe): if the $a_2$ term is magnon-induced skew scattering, the $T^2$ part of $\\Delta\\rho_{yx}$ should vanish under full magnon suppression, whereas it should persist if another $T^2$ channel such as electron-electron scattering contributes.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the multivariable scaling relation for anomalous Hall resistivity that the paper extends by adding a dynamic skew-scattering term."},{"cited_title":"Kikkawa, K","cited_arxiv_id":null,"evidence_quote":"Gives the spin-orbit-modified p-d exchange Hamiltonian and the model formulas for magnon-induced skew scattering."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the linear magnetoresistance and magnetic-field suppression of electron-magnon scattering used to corroborate the magnon origin."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the standard anomalous Hall effect formalism and normalization used to analyze the Hall data."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides earlier Berry curvature calculations for Cr2Te3 used as a comparison for the first-principles results here."}],"review_version":1}