{"id":"515c4a2d-04de-462f-ad43-95ed9107fa24","arxiv_id":"2607.06966","paper_version":1,"verdict":"CONDITIONAL","confidence":"UNKNOWN","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":5,"one_line_summary":"Monte Carlo simulations of a Kagome Kondo-lattice model show that intrinsic Berry-curvature transport dominates in the skyrmion phase while extrinsic skew scattering from dynamical spin-chirality fluctuations dominates near order-disorder transitions, with opposite signs explaining experimental sign","lead":"This paper computes anomalous Hall and Nernst effects on a Kagome lattice by combining Monte Carlo spin simulations with electronic transport theory. It shows that intrinsic Berry-curvature effects dominate in ordered skyrmion phases while extrinsic skew scattering from spin-chirality fluctuations dominates near phase boundaries, with the two mechanisms producing opposite signs. A smart generalist might read it to understand how competing microscopic mechanisms control topolg","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"The extrinsic transport derivation mixes 3D and 2D formalisms: the second Born scattering amplitude (App. A, Eq. A7) uses a 3D free-particle Green's function, but the system is 2D and only the final formula is converted, leaving extrinsic magnitudes—and hence the crossover claim—quantitatively unrel","rationale":"The reader correctly identified Eqs. 27-28 as load-bearing and the parabolic approximation as a concern, but the more fundamental issue is the 3D/2D dimensional inconsistency in the scattering-rate derivation. The parabolic approximation at ε_F = -4.0 eV (near a band edge) may actually be defensible since band-edge dispersions are locally quadratic; the dimensional inconsistency is not defensible. The sign opposition claim is likely robust since it depends on J³_K and chirality direction, not on dimensional details. But the crossover claim—which is the paper's main contribution—depends on relative magnitudes that are not reliably computed due to (a) the 3D Green's function used in a 2D system, and (b) the free parameter τ scaling extrinsic results as τ². The CONDITIONAL verdict is appropriate and should remain: the qualitative picture (intrinsic dominates in SkX, extrinsic dominates near criticality, opposite signs) is physically well-motivated and consistent with prior work (Ishizuka & Nagaosa, Ref. 27), but the quantitative transport maps in Fig. 5 should not be taken as predictions. The paper should either rederive the extrinsic formulas consistently in 2D or explicitly state that extrinsic magnitudes are order-of-magnitude estimates.","tokens_in":18635,"tokens_out":7275,"duration_ms":522291,"concrete_test":"Rederive the second-order scattering amplitude (Eq. A7) using the 2D momentum integral ∫d²q/(2π)² for the intermediate-state Green's function, replacing the 3D result e^{ikr_ij}/r_ij with the 2D Hankel function (iπ/2)H₀⁽¹⁾(kr_ij). Recompute the antisymmetric scattering rate (Eq. 25) and the resulting extrinsic AHC (Eq. 27). If the prefactor changes by more than a factor of 2, or if the k-dependence of the scattering rate changes qualitatively, the crossover phase diagram (Fig. 5e-f) is quantitatively unreliable and should be presented as qualitative only.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim has two parts: (1) intrinsic and extrinsic mechanisms contribute opposite signs, and (2) a mechanistic crossover occurs where extrinsic overtakes intrinsic near the order-disorder transition. The sign opposition is likely robust—it depends on J³_K and the chirality direction (Eq. 27), not on band-structure or dimensional details. However, the crossover claim depends on the relative magnitudes, and the extrinsic magnitude is not reliably determined.\n\nThe specific issue: In Appendix A (Eq. A7), the second-order scattering amplitude involves an intermediate-state momentum sum performed in 3D, yielding the 3D free-particle retarded Green's function ~e^{ikr_ij}/r_ij. The system is explicitly 2D (Section III), where the corresponding 2D integral ∫d²q/(2π)² yields a Hankel function (iπ/2)H₀⁽¹⁾(kr_ij) with qualitatively different spatial dependence: logarithmic rather than 1/r in the long-wavelength limit (ka≪1) used in Eq. 23. The paper converts to 2D only at the final step (Eq. 27) by substituting 2D carrier density n_{e,2D}=k²_F/(4π) and 2D DOS ρ_{2D}=m/(2πℏ²), without rederiving the scattering rate in 2D. This means the prefactor and potentially the k-dependence of the extrinsic AHC (Eq. 27) and ANC (Eq. 28) are incorrect.\n\nAdditionally, the extrinsic AHC scales as τ² (Eq. 27), and τ is a free parameter not computed from the symmetric scattering rate. This makes the crossover point in the T-B phase diagram (Fig. 5e-f) adjustable. The intrinsic contribution (Eqs. 2-4) is computed from the full tight-binding band structure and is dimensionally consistent; the extrinsic is not. This asymmetry means the competition shown in Fig. 5 is qualitatively motivated but quantitatively unreliable.","agreement_with_reader":"partial"},"referee_report":{"model":"glm-5.2","summary":"This manuscript investigates anomalous Hall and Nernst effects (AHE/ANE) on a 2D Kagome lattice, decomposing the total response into an intrinsic contribution from momentum-space Berry curvature (driven by static scalar spin chirality) and an extrinsic skew-scattering contribution from dynamical spin chirality (DSC) fluctuations. Monte Carlo simulations on a classical spin model generate the phase diagram and chirality data, which feed into tight-binding (intrinsic) and Boltzmann transport (extrinsic) calculations. The central claim is a mechanistic crossover: intrinsic transport dominates in the skyrmion crystal phase, while extrinsic transport dominates near the order-disorder transition, with the two mechanisms contributing opposite signs. The framework is well-motivated and the combination of MC with analytical transport is a reasonable approach. However, a dimensional inconsistency in the extrinsic scattering derivation and an unjustified parabolic-band approximation affect the quantitative reliability of the crossover claim.","tokens_in":19640,"tokens_out":1461,"duration_ms":351944,"significance":"The paper addresses a timely question in topological magnetism: disentangling intrinsic and extrinsic anomalous transport mechanisms driven by static versus fluctuating spin chirality. The decomposition framework and the prediction of opposite-sign competition between mechanisms near phase boundaries are potentially useful for interpreting experimental sign reversals in topological Hall/Nernst effects. The MC protocol is standard and the phase diagram construction is systematic. The analytical derivation of the extrinsic AHC/ANC from the Kondo model provides a transparent connection between DSC and skew scattering. However, the quantitative reliability of the extrinsic magnitudes—which underpin the crossover claim—is compromised by the issues detailed below.","major_comments":[{"comment":"Appendix A, Eq. (A7): The second-order scattering amplitude is derived using a 3D free-particle Green's function, yielding the 3D retarded Green's function ~e^{ikr_ij}/r_ij. However, the system is explicitly 2D (Section III). The 2D analogue is a Hankel function (iπ/2)H_0^{(1)}(kr_ij), which has qualitatively different spatial dependence (logarithmic in the long-wavelength limit ka≪1 used in Eq. 23). The paper converts to 2D only at the final step (Eq. 27) by substituting 2D carrier density and DOS, without rederiving the scattering rate in 2D from the outset. This affects the prefactor and potentially the k-dependence of the extrinsic AHC (Eq. 27) and ANC (Eq. 28), undermining the quantitative reliability of the crossover claim.","section":null},{"comment":"Section V, Eqs. (27)–(28) and Fig. 5: The extrinsic AHC scales as τ², where τ is a free parameter not computed from the symmetric scattering rate. This makes the relative magnitude of extrinsic versus intrinsic contributions adjustable, and hence the crossover point in the T–B phase diagram (Fig. 5e–f) is not uniquely determined by the theory. The sign opposition (intrinsic vs. extrinsic) may be robust since it depends on J_K³ and chirality direction, but the crossover claim depends on magnitudes that are not reliably fixed. The authors should either compute τ self-consistently from the symmetric part of the scattering rate or provide a sensitivity analysis showing that the crossover persists for a reasonable range of τ.","section":null},{"comment":"Section V and Fig. 1(b): The extrinsic transport formulas (Eqs. 27–28) are derived under a parabolic-band effective-mass approximation (ε_k = ℏ²k²/2m), but the Kagome lattice band structure (Fig. 1b) contains Dirac cones and flat bands. The Fermi energy ε_F = −4.0 eV is stated to be in a 'low energy region' but the validity of the parabolic approximation at this energy is not justified. Since the extrinsic AHC and ANC magnitudes depend on the effective mass m and the DOS at ε_F, this approximation directly affects the load-bearing crossover result. The authors should justify this approximation quantitatively (e.g., by showing the band dispersion near ε_F is approximately parabolic) or discuss its limitations explicitly.","section":null}],"minor_comments":[{"comment":"Eqs. (2) and (4): The intrinsic AHC and ANC formulas use d³k/(2π)³, appropriate for 3D, but the system is 2D. These should be d²k/(2π)². This appears to be carried over from a general 3D formalism but should be corrected for the 2D model in Section III.","section":null},{"comment":"Eq. (17): The expression uses 3D carrier density n_e = k_F³/(6π²), but Eq. (27) correctly uses 2D n_{e,2D} = k_F²/(4π). The derivation should be consistent in 2D from the start, or the dimensional reduction should be clearly explained.","section":null},{"comment":"Section IV: The phase boundary thresholds (e.g., χ_Q ≥ 3, δχ > 0.2, M_z > 0.1) are stated without justification. A brief discussion of how these values were chosen and their sensitivity would help reproducibility.","section":null},{"comment":"Fig. 5: The color scales for intrinsic and extrinsic panels should use the same units and range to facilitate visual comparison of the crossover. Currently it is difficult to assess the relative magnitudes from the figures alone.","section":null},{"comment":"The term 'fluctuating chiral (FC) phase' is introduced as a distinct phase, but the criteria (δχ > 0.2) suggest it may be a crossover regime rather than a thermodynamic phase. Clarifying whether this is a true phase or a crossover regime would strengthen the presentation.","section":null},{"comment":"Reference [27] (Ishizuka and Nagaosa, 2018) is the primary theoretical basis for the extrinsic mechanism. The manuscript should clarify what is genuinely new in the extrinsic derivation relative to this reference, beyond the application to the Kagome lattice.","section":null},{"comment":"Several typos: 'chi rality' (abstract), 'configu rations' (abstract), 's-d exchange' formatting inconsistencies, 'intergral' should be 'integral' where applicable. Proofreading recommended.","section":null}],"recommendation":"major_revision","confidential_remarks":"The reader's concern about the 3D/2D mixing in Appendix A is well-founded and is the most substantive technical issue. The parabolic-band concern is also legitimate given the Kagome band structure shown in Fig. 1(b). Both issues are fixable: the 2D Green's function can be substituted and the derivation reworked, and the parabolic approximation can be justified or its limitations acknowledged. The sign-opposition claim is likely robust and worth publishing, but the crossover claim needs the magnitude issues resolved. I would encourage the authors to address these points rather than dismiss them, as the core physics is sound."},"author_rebuttal":{"model":"glm-5.2","summary":"We thank the referee for a careful reading and for identifying three substantive issues with the extrinsic transport derivation. We agree that all three points are valid concerns that require revision of the manuscript. Below we address each in turn.","responses":[{"response":"The referee is correct. The second-order scattering amplitude in Eq. (A7) was evaluated using the 3D free-particle retarded Green's function, G(r) ~ e^{ikr}/r, while the system is explicitly two-dimensional. The correct 2D Green's function is G(r) = (im/2ℏ²) H_0^{(1)}(kr), which has qualitatively different spatial dependence—particularly in the long-wavelength limit ka << 1 used in Eq. (23), where H_0^{(1)}(kr) ~ (2i/π) ln(kr). We performed the intermediate steps of the derivation in 3D and only substituted 2D carrier density and DOS at the final stage (Eqs. 27–28), which is not a consistent procedure. We will rederive the second-order T-matrix and the antisymmetric scattering rate from the outset in 2D, using the Hankel-function Green's function. We note that the key structural features of the result—the proportionality to J_K³, the scalar spin chirality S_l·(S_i×S_j), the antisymmetric (k×k') factor, and the spatial interference factor I_{ijl}—are determined by the spin algebra and geometric structure of the Kondo coupling, not by the dimensionality of the Green's function. The sign opposition between intrinsic and extrinsic contributions, which depends on these structural features, is therefore expected to be robust. However, the referee is right that the prefactor and potentially the k-dependence of Eqs. (27)–(28) will change, affecting the quantitative magnitude of the extrinsic contribution. We will revise Appendix A to present the full 2D derivation and update Eqs. (27)–(28) and Fig. 5(c–f) accordingly.","revision_made":"yes","referee_comment":"Appendix A, Eq. (A7): 3D Green's function used in a 2D system. The 2D analogue is a Hankel function with different spatial dependence, affecting prefactors and k-dependence of extrinsic AHC/ANC."},{"response":"This is a fair criticism. The relaxation time τ enters the extrinsic AHC as τ² and is treated as a free parameter, which means the absolute magnitude of the extrinsic contribution—and hence the precise location of the intrinsic-extrinsic crossover in the T–B phase diagram—is not uniquely fixed by the theory as currently presented. We agree that the sign opposition is robust, since it depends on J_K³ and the chirality direction, not on τ. However, the crossover claim as a quantitative statement about where in the phase diagram extrinsic transport overtakes intrinsic transport does depend on the ratio of magnitudes, and thus on τ. We will address this in two ways. First, we will compute the symmetric scattering rate W^S (arising from |F^{(1)}|²) self-consistently from the same Kondo coupling and MC spin configurations, yielding τ = 1/(2π W^S/ℏ) as a function of temperature and field. This provides a first-principles estimate of τ within the same framework. Second, we will provide a sensitivity analysis: we will show the crossover boundary in Fig. 5(e–f) for a range of τ values spanning at least one order of magnitude around the self-consistent estimate, demonstrating that the qualitative picture—extrinsic dominance in the FC phase near the order-disorder transition and intrinsic dominance in the SkX phase—persists across a reasonable parameter range. We acknowledge that without this analysis, the quantitative crossover claim is underdetermined.","revision_made":"yes","referee_comment":"Extrinsic AHC scales as τ², where τ is a free parameter not computed from the symmetric scattering rate. The crossover point in Fig. 5(e–f) is not uniquely determined. Authors should compute τ self-consistently or provide sensitivity analysis."},{"response":"The referee raises a legitimate point. The extrinsic AHC and ANC formulas (Eqs. 27–28) are derived assuming a parabolic dispersion ε_k = ℏ²k²/2m, which enters through the effective mass m, the DOS ρ(ε_F), and the carrier density n_e. The Kagome lattice band structure (Fig. 1b) contains Dirac cones and flat bands, and the parabolic approximation is not obviously valid at ε_F = −4.0 eV. We will address this by: (1) explicitly examining the band dispersion near ε_F = −4.0 eV in Fig. 1(b) to assess whether it is locally approximately parabolic, and presenting this analysis in the revised manuscript; (2) if the parabolic approximation is found to be inadequate at this energy, we will either adjust ε_F to a regime where the approximation is better justified, or discuss the limitations explicitly and note that the extrinsic magnitudes should be regarded as order-of-magnitude estimates rather than quantitative predictions. We note that the intrinsic AHC/ANC calculations (Eqs. 2–4) use the full Kagome band structure and are not affected by this approximation; the issue is specific to the extrinsic analytical formulas. The sign opposition between intrinsic and extrinsic mechanisms does not depend on the band structure approximation, but the referee is correct that the crossover magnitudes do. We will make the status of the parabolic approximation transparent in the revised manuscript.","revision_made":"yes","referee_comment":"Extrinsic transport formulas derived under parabolic-band approximation, but Kagome lattice has Dirac cones and flat bands. Validity of parabolic approximation at ε_F = −4.0 eV is not justified. This affects extrinsic AHC/ANC magnitudes and the crossover result."}],"tokens_in":18476,"tokens_out":1813,"duration_ms":202508,"standing_objections":[]},"desk_editor":{"model":"glm-5.2","letter":"The main thing to know: this paper combines Monte Carlo spin simulations on a Kagome lattice with separate intrinsic (Kubo) and extrinsic (skew-scattering) transport calculations, mapped across the full temperature-field phase diagram. The qualitative picture — intrinsic Berry curvature dominates in the skyrmion crystal phase, extrinsic skew scattering from dynamical chirality fluctuations dominates near the order-disorder boundary, and the two contribute opposite signs — is a useful organizing framework for interpreting experiments on frustrated Kagome magnets. The sign opposition is probably robust: it depends on J_K^3 and the chirality direction, not on band-structure details or dimensionality. The intrinsic calculation is done properly from the full tight-binding band structure with a 12×12 magnetic supercell, and the MC protocol is standard and adequate (L=48, hybrid updates, simulated annealing). Credit is due for cleanly separating the two mechanisms and producing concrete, testable predictions about where each dominates. The connection to experimental sign reversals near phase transitions is well-motivated. The stress-test concern about 3D/2D mixing lands. In Appendix A (Eq. A7), the intermediate-state momentum sum uses the 3D free-particle Green's function, giving e^{ikr}/r. The system is 2D, where the corresponding integral yields a Hankel function with qualitatively different long-wavelength behavior. The paper converts to 2D only at the final step by substituting 2D density and DOS into Eq. 27, without rederiving the scattering rate in 2D. This means the prefactor of the extrinsic AHC is incorrect, and since the crossover claim depends on relative magnitudes of intrinsic and extrinsic contributions, the quantitative phase-boundary maps in Fig. 5 are unreliable. The sign opposition survives, but the crossover location does not. Two other issues, both noted by the reader and both legitimate but secondary: the parabolic-band approximation is applied to a lattice with Dirac cones and flat bands without justification at ε_F = -4.0 eV, and τ is a free parameter scaling the extrinsic contribution as τ², making the crossover point adjustable. The 'fluctuating chiral phase' is defined by a post-hoc threshold (δχ > 0.2), which is fine as a labeling convention but should not be mistaken for a thermodynamic phase. No error bars on transport coefficients is a minor omission given the MC sampling. None of these issues are individually fatal, but the 2D/3D inconsistency in the extrinsic derivation is the one that needs fixing before the quantitative claims hold. The paper is for theorists working on anomalous transport in frustrated magnets and experimentalists interpreting Hall/Nernst data near phase transitions. It deserves a serious referee who can check the 2D scattering derivation carefully.","headline":"Useful framework for decomposing intrinsic vs extrinsic anomalous transport on Kagome, but the extrinsic derivation has a real 2D/3D inconsistency that undermines quantitative claims.","tokens_in":19574,"tokens_out":1439,"would_cite":false,"duration_ms":123046,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"glm-5.2","headline":"Static and fluctuating spin chirality drive opposite-signed Hall transport on Kagome lattice","keywords":[],"falsifier":"If the parabolic-band approximation fails at the chosen Fermi energy, the magnitude and potentially the sign of the extrinsic anomalous Hall and Nernst conductivities could differ from the computed values, undermining the claim of opposite-sign competition between intrinsic and extrinsic mechanisms.","tokens_in":18702,"feed_emoji":"🌀","tokens_out":904,"duration_ms":187626,"temperature":0.7,"pith_summary":"This paper argues that anomalous Hall and Nernst effects on a Kagome lattice can be decomposed into two competing mechanisms with opposite signs: an intrinsic contribution from momentum-space Berry curvature generated by static noncoplanar spin textures (dominant in the skyrmion crystal phase), and an extrinsic skew-scattering contribution driven by thermal fluctuations of the scalar spin chirality (dominant near the magnetic order-disorder transition). The authors use Monte Carlo simulations of a classical spin Hamiltonian with Heisenberg and Dzyaloshinskii-Moriya interactions to extract both the thermal average of local spin configurations and the fluctuating part of the scalar spin chirality across a temperature-field phase diagram. The static averages feed into a tight-binding electronic Hamiltonian whose Berry curvature yields the intrinsic anomalous Hall and Nernst conductivities. The fluctuating chirality feeds into analytically derived skew-scattering formulas (obtained via second-Born-approximation treatment of the s-d exchange interaction under a low-energy effective-mass approximation) to yield the extrinsic conductivities. The central result is a mechanistic crossover: deep in the skyrmion crystal phase, static chirality and Berry curvature dominate; near the phase boundary where thermal fluctuations destroy static noncoplanar order, the intrinsic response collapses but dynamical chiral fluctuations sustain anomalous transport through skew scattering, with the two channels contributing opposite signs. This sign competition, the authors argue, explains experimentally observed sign reversals of the topological Hall and Nernst effects near magnetic phase transitions.","feed_headline":"Static and fluctuating spin chirality drive opposite-signed Hall transport on Kagome","feed_subtitle":"Intrinsic Berry curvature from static skyrmion order and extrinsic skew scattering from chiral fluctuations compete with opposite signs, a","key_machinery":"Monte Carlo simulation of classical spin Hamiltonian on Kagome lattice (L=48, 3×48² sites) with Heisenberg exchange J_H, Dzyaloshinskii-Moriya interaction (D_xy=0.5, D_z=sqrt(3) in units of J_H), and external magnetic field B; tight-binding electronic Hamiltonian with s-d exchange coupling J_K=0.2t, hopping t=-1 eV, on a 12×12 magnetic supercell; intrinsic transport via Berry curvature integrals (Kubo formula); extrinsic transport via second-Born-approximation skew-scattering rate under parabolic dispersion approximation; Mott relation connecting extrinsic anomalous Nernst conductivity to energy derivative of extrinsic anomalous Hall conductivity at low temperature.","core_discovery":"The paper's central object is the scalar spin chirality chi_ijk = S_i · (S_j × S_k) on triangular plaquettes of a Kagome lattice, decomposed into a static part <S_i>·(<S_j>×<S_k>) and a fluctuating part delta_chi obtained by subtracting the static background from the total thermal average. The static part generates momentum-space Berry curvature in the electronic band structure and drives intrinsic anomalous Hall and Nernst conductivities via the Kubo formula. The fluctuating part drives extrinsic anomalous conductivities through a skew-scattering mechanism derived from the third-order Kondo exchange coupling, where the antisymmetric scattering rate is proportional to both the cross productk","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Spin chirality crossover governs intrinsic vs extrinsic Hall effects on Kagome","Static vs fluctuating spin chirality separates intrinsic and extrinsic Kagome Hall transpo","Kagome lattice Hall effects switch from Berry curvature to skew scattering","Static and dynamic spin chirality dictate distinct Hall and Nernst regimes on Kagome","Berry curvature to skew scattering: chirality crossover in Kagome Hall transport"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The extrinsic transport formulas are derived assuming electrons have a parabolic dispersion (a simple quadratic energy-momentum relation), but the Kagome lattice band structure contains Dirac cones and flat bands that are far from parabolic, and the paper does not justify that the chosen Fermi energy (-4.0 eV) sits in a regime where this approximation is valid. The relaxation time is also treated as a free parameter rather than computed from the symmetric scattering rate.","fun_headline_variants_meta":{"raw":{"variants":["Spin chirality crossover governs intrinsic vs extrinsic Hall effects on Kagome","Static vs fluctuating spin chirality separates intrinsic and extrinsic Kagome Hall transport","Kagome lattice Hall effects switch from Berry curvature to skew scattering","Static and dynamic spin chirality dictate distinct Hall and Nernst regimes on Kagome","Berry curvature to skew scattering: chirality crossover in Kagome Hall transport"]},"model":"glm-5.2","effort":"high","cost_usd":0.0,"raw_usage":{"total_tokens":937,"prompt_tokens":550,"completion_tokens":387,"prompt_tokens_details":null},"tokens_in":550,"tokens_out":387,"duration_ms":10480,"temperature":1.0,"reasoning_tokens":326,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-09T00:48:24.807588+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"If the parabolic-band approximation fails at the chosen Fermi energy, the magnitude and potentially the sign of the extrinsic anomalous Hall and Nernst conductivities could differ from the computed values, undermining the claim of opposite-sign competition between intrinsic and extrinsic mechanisms.","supporting_citations":[],"review_version":1}