{"id":"4bd04453-6faf-4fc1-9600-be36f6f974b3","arxiv_id":"2501.05227","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In Eu(Ga1-xAlx)4, the maximal topological Hall effect does not coincide with the square skyrmion lattice; magnetocaloric boundaries mark the skyrmion phase instead.","lead":"This paper maps the magnetic and electronic phases of Ga-doped EuAl4 and finds that the strongest topological Hall signal appears outside the skyrmion-lattice region of the phase diagram. Instead, the magnetocaloric effect traces the square-skyrmion phase, suggesting the largest Hall response comes from topologically trivial spin fluctuations.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The sSkL-versus-THE mismatch rests on a two-band Hall subtraction that is not independently validated; the malformed subtraction equation and missing fit parameters leave the location of the maximal THE unsecured.","rationale":"The reader's weakest assumption identifies the same load-bearing concern: the THE extraction for x=0.9 is model-dependent and underdocumented. The strongest evidence in the paper is direct: SANS resolves the sSkL at Q1+Q2 in a high-temperature pocket, and MCE marks the corresponding phase boundaries. The weak link is the indirect Hall decomposition. The appendix itself concedes that the extraction is 'challenging due to the nonlinear field dependence,' and the written subtraction equation is malformed, yet no fit parameters, residuals, or alternative subtraction are provided. If the low-temperature maximum survives an independent two-band or magnetization-scaled subtraction, the central empirical claim stands; if not, the mismatch evaporates. The mechanism claim about frustrated spin fluctuations is more speculative, but it is not required for the primary conclusion that the maximal THE is not a skyrmion-lattice signature. Therefore the appropriate disposition remains CONDITIONAL, requesting a transparent re-analysis of the Hall data rather than acceptance or rejection.","tokens_in":16075,"tokens_out":3951,"duration_ms":39159,"concrete_test":"Re-analyze the raw Hall resistivity of x=0.9 (Fig. S2a,b) with at least two independent subtraction schemes: (i) the reported high-field two-band fit with all parameters and residuals stated; (ii) an anomalous-Hall subtraction ρ_yx^A = R_s(T) M(H) using the measured magnetization and R_s from the saturated-field slope, with any remaining nonlinearity treated as a normal-Hall multiband term. Compare the location and magnitude of the maximum of |Δρ_yx| in the H-T plane. If the maximum remains at T≲4 K and H≈1–2 T under both schemes, the mismatch with the sSkL pocket is robust; if it moves into the SANS sSkL region or disappears, the central claim fails. Report the two-band fit parameters and goodness-of-fit for each temperature.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's empirical foundation is the claim that the maximal topological Hall contribution in x=0.9 sits at low temperature (T≲4 K), far from the high-temperature square-skyrmion-lattice pocket found by SANS. That claim rests entirely on subtracting normal and anomalous Hall backgrounds from raw Hall data, but the subtraction is not shown to be unique. Appendix Fig. S2 states that the high-field (H>8 T) behavior is used for a two-band fit; no fitted carrier densities, mobilities, anomalous Hall coefficient, or residuals are reported, and the written equation Δρ_yx = ρ_yx − ρ_two-band − ρ_yx^AHE − ρ_yx^THE is not a well-defined extraction, since it subtracts the THE from the residual that is meant to define it. If the two-band extrapolation does not describe the low-field region, the apparent low-temperature maximum could be a subtraction artifact. Because the mismatch between the THE maximum and the sSkL is the basis for the conclusion that MCE should replace THE as the phase-diagram marker, an unvalidated subtraction is the single most load-bearing weakness. A secondary but related concern is that the low-temperature state is labeled 'fan-like' by inference from the absence of extra SANS peaks; absence of a skyrmion peak does not by itself establish zero scalar spin chirality, so the 'topologically trivial' mechanism is also underdetermined.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a combined neutron scattering, magnetization, transport, and magnetocaloric-effect study of the centrosymmetric square-net compounds Eu(Ga1-xAlx)4 with x = 0.9 and x = 1, with H applied along the c-axis and in-plane. The authors use SANS to identify a square skyrmion lattice (sSkL) phase in the x = 0.9 compound at a high-temperature pocket near TN, and they compare its H-T location with the region of maximal topological Hall effect (THE) extracted from transport. They find that the maximal THE occurs at low temperatures in a state they identify as fan-like, well outside the sSkL pocket, and they argue that the magnetocaloric effect (MCE) boundaries, rather than the maximal THE, better mark the skyrmion-lattice phase. The central claim is that the maximal THE in this system is not a skyrmion signature but arises from itinerant-electron spin-fluctuation interactions in a topologically trivial magnetic state.","tokens_in":16225,"tokens_out":2979,"duration_ms":31097,"significance":"If the central claim holds, the paper provides an important counterexample to the common practice of using a maximal topological Hall response as a proxy for a skyrmion lattice in centrosymmetric magnets, and it promotes MCE as a complementary bulk probe for mapping skyrmion phase boundaries. The paper's strengths include a direct SANS identification of the sSkL peak in the doped compound, a thorough H-T phase diagram built from magnetization and neutron data, and a clean comparison of independent experimental probes (SANS, transport, bulk magnetization). The neutron refinement of the zero-field screw helix and the in-plane field phase diagram are solid contributions. However, the central interpretive conclusion depends on a Hall-subtraction procedure whose parameters are not reported and on an inferred low-temperature magnetic structure that is not directly refined.","major_comments":[{"comment":"The extraction of the topological Hall resistivity for x = 0.9 is not presented in a verifiable form. The supplement states that a two-band model is used for the high-field (H > 8 T) response, but it does not report the fitted carrier densities, mobilities, anomalous Hall coefficient, or the residuals of the fit. Moreover, the written equation Δρ_yx = ρ_yx − ρ_two-band − ρ_yx^AHE − ρ_yx^THE is not a well-defined extraction, because it subtracts the THE from the residual that is meant to define it. Since the central claim that the maximal THE at low temperature lies outside the sSkL region rests entirely on this subtraction, the authors should provide the fitted parameters, a plot of the residuals versus field at representative temperatures, and a sensitivity test (for example, varying the high-field fitting range) to demonstrate that the low-temperature maximum is not a subtraction artifact.","section":"Section III.B and Appendix Fig. S2"},{"comment":"The low-temperature, high-field magnetic state in x = 0.9 is labeled 'fan-like' based solely on the absence of extra SANS peaks and on the comparison with YMn6Sn6, without a direct magnetic-structure refinement. Absence of a skyrmion peak does not by itself establish zero scalar spin chirality, because a noncoplanar texture with zero net chirality, or a texture with too weak scattering to be observed, would also show no additional SANS peak. The conclusion that the maximal THE arises in a 'topologically trivial magnetic state' is therefore underdetermined. The authors should either refine the magnetic structure in this field/temperature region using the wide-angle CORELLI data already collected, or explicitly present the fan-like assignment as a hypothesis rather than a demonstrated result.","section":"Section III.B and Fig. 4"},{"comment":"The claim that the MCE 'better identifies' the sSkL phase is supported only by a visual overlap between the maximal entropy-change region and the SANS-determined sSkL boundaries. Since MCE is sensitive to all first-order phase transitions, not specifically to skyrmion formation, the evidence would be stronger with a quantitative comparison, for example overlaying the MCE maxima with the SANS sSkL boundaries and giving uncertainties. As written, the MCE result is a complementary indicator, but the phrase 'more accurately' overstates the quantitative support.","section":"Fig. 1(d) and 1(f), Section III.B"}],"minor_comments":[{"comment":"There is a typographical error: 'oberseved' should be 'observed' in the sentence 'thus raising the issue concerning the microscopic origin of the oberseved THE'.","section":"Introduction"},{"comment":"The phase labels are inconsistent: the main text uses 'phase ii' (Roman lowercase) in Section III.B while Fig. 1 and the rest of the text use 'phases II and III' (Roman uppercase). Please standardize the phase nomenclature.","section":"Section III.B and Appendix"},{"comment":"Reference [28] is incomplete; it lists only author names and a year. Please provide the full citation with journal, volume, and article number.","section":"References"},{"comment":"The notation for the Hall contributions is confusing: the same symbol ρ_yx is used for the raw measured Hall resistivity and for its components, and the equation for Δρ_yx should be rewritten as a definition of the residual after subtracting the normal and anomalous contributions, without including the THE on the right-hand side.","section":"Appendix Fig. S2"}],"recommendation":"major_revision","confidential_remarks":"The paper's core message—maximal THE is not a reliable skyrmion marker in this family, while MCE is—is timely and would interest the condensed-matter community if the supporting analysis is made rigorous. The main risk is that the load-bearing Hall subtraction for x = 0.9 is not independently validated. The authors may also consider whether the inference of a 'fan-like' state should be softened until direct magnetic-structure refinement is available. The reliance on Ref. [35] for the x = 0.9 transport analysis is acceptable, but the current manuscript should stand alone for the new claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the first neutron scattering study of Eu(Ga0.1Al0.9)4: the SANS identification of the square skyrmion lattice pocket, the magnetic structure refinement showing the zero-field screw helix, and the mapping of the in-plane and c-axis phase diagrams. The MCE comparison is also a useful addition, and the observation that MCE boundaries track the sSkL better than the THE contour does is credible because it relies on independent probes: SANS, magnetization, and transport. That part deserves credit.\n\nThe soft spot is exactly where you put it. The entire mismatch narrative—maximal THE at low temperature, far from the high-temperature sSkL pocket—rests on the two-band subtraction for x = 0.9. The supplement says the extraction is challenging and 'requires a multiband description,' but no carrier densities, mobilities, or residuals are reported, and the written equation in Fig. S2 is genuinely malformed: it subtracts the THE from the residual you are trying to define. Without knowing how the two-band extrapolation behaves below the fit region, the low-temperature maximum could be a subtraction artifact. This is load-bearing. If the low-T THE is an artifact, the spin-fluctuation mechanism claim collapses, and the paper becomes mostly a phase-diagram mapping paper.\n\nSecondary issue: the low-temperature state is called 'fan-like' by inference from the absence of extra SANS peaks. That absence is evidence against a skyrmion lattice, but it does not by itself prove zero net scalar spin chirality or establish a specific spin-fluctuation scattering mechanism. The conclusion would need either direct refinement of that state or much softer wording.\n\nMinor points: the contour maps lack error bars, and the parent-compound mismatch was already known from Refs. 14 and 31, so the conceptual novelty is moderate. Still, the x = 0.9 SANS data are new and could be valuable to the skyrmion community.\n\nBottom line: worth a serious referee, but the revision must include the subtraction parameters, residual plots, and a validation of the two-band fit, or the central claim should be scaled back. I would not desk-reject this.","headline":"Solid new SANS data on the doped compound, but the central claim that maximal THE is a topologically trivial artifact leans on an unvalidated two-band Hall subtraction.","tokens_in":16936,"tokens_out":1474,"would_cite":false,"duration_ms":17084,"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":"In Eu(Ga1-xAlx)4, neutron scattering shows that the square skyrmion lattice is best identified by the magnetocaloric effect, while the maximal topological Hall effect arises from a topologically trivial fan-like magnetic state.","keywords":["Eu(Ga1-xAlx)4","square skyrmion lattice","topological Hall effect","magnetocaloric effect","neutron scattering","spin fluctuations","centrosymmetric magnet","H-T phase diagram"],"falsifier":"Re-analyze the x = 0.9 Hall resistivity data with an alternative subtraction that does not assume a two-band model above 8 T; if the extracted rho^T_xy maximum moves into the sSkL pocket of the H-T diagram, the paper's central conclusion would be falsified.","tokens_in":1627,"feed_emoji":"🧲","tokens_out":1803,"duration_ms":82845,"temperature":0.7,"pith_summary":"This paper combines neutron scattering, Hall transport, and magnetization measurements to map the magnetic field-temperature phase diagram of Eu(Ga1-xAlx)4 for x = 0.9 and x = 1. It establishes that the square skyrmion lattice (sSkL), a spin texture with nonzero scalar spin chirality, is present in both compounds but occupies a small pocket of phase space near the magnetic ordering temperature. The largest topological Hall effect (THE) appears at low temperatures, far from this sSkL pocket, making the THE an unreliable marker for skyrmions in this family. The paper argues that the maximal THE comes from interactions of itinerant electrons with frustrated spin fluctuations in a topologically trivial fan-like magnetic state, and shows that the magnetocaloric effect (MCE) tracks the sSkL boundaries more accurately. The conclusion matters because it separates topological spin textures from a transport signature that is often treated as their fingerprint.","feed_headline":"Maximal Hall signal bypasses skyrmion lattice in Eu(Ga,Al)4","feed_subtitle":"Neutron and transport maps show the largest topological Hall response arises from spin fluctuations, not skyrmions.","key_machinery":"The argument rests on comparing three probes on the same H-T phase diagram: small-angle neutron scattering (SANS), which locates the square skyrmion lattice by its Q1+Q2 satellite peak; Hall resistivity measurements with a multi-band subtraction that isolates the topological Hall contribution rho^T_xy; and magnetocaloric maps built from dM/dT, where Delta_SM(T,H) = integral_0^H (dM/dT)_H' dH'. The mismatch between the THE maximum and the sSkL region, together with the match between the MCE maximum and the sSkL boundaries, is the load-bearing evidence. The fan-like magnetic structure, refined from neutron diffraction, provides the topologically trivial state in which the maximal THE is argued to arise from spin fluctuations rather than scalar spin chirality.","core_discovery":"The central discovery is a clear separation in H-T phase space between the square skyrmion lattice and the maximal topological Hall response in both EuAl4 and the 10% gallium-doped compound. Small-angle neutron scattering identifies the sSkL through its characteristic Q1+Q2 reflection near TN, while Hall measurements show the THE peaking at low temperatures, roughly twice as large, in a regime where neutron data reveal only a fan-like deformation of the zero-field screw helix. Because the fan structure has vanishing net scalar spin chirality, its large Hall response cannot be a conventional topological Hall effect; the authors attribute it to scattering of itinerant electrons off frustrated spin fluctuations. They then show that the strongest magnetocaloric signal, computed from magnetization via the Maxwell relation Delta_SM(T,H) = integral (dM/dT) dH, coincides with the sSkL phase boundaries. The paper's conclusion is that the sSkL phase is better identified by maximal MCE, while the maximal THE is a non-topological probe in this system.","pith_inferences":["The same probe-comparison approach could be applied to other centrosymmetric skyrmion hosts, such as Gd2PdSi3 or GdRu2Si2, to test whether their reported THE maxima actually coincide with the skyrmion phases.","If the low-temperature Hall response is truly driven by frustrated spin fluctuations, its magnitude should be sensitive to disorder and to the strength of magnetic frustration; controlled Ga doping or pressure studies could test this prediction.","Because the MCE is a bulk thermodynamic probe, it could be used to locate skyrmion phases in polycrystalline samples or thin films where SANS is impractical, extending the paper's method beyond single crystals."],"forward_implications":["In the Eu(Ga1-xAlx)4 family, a maximal topological Hall response should no longer be used as a fingerprint for a skyrmion lattice in transport-only studies.","The square skyrmion lattice in Eu(Ga1-xAlx)4 can be mapped reliably from magnetization data through the magnetocaloric effect, without requiring neutron scattering.","The low-temperature rhombic skyrmion and vortex lattice phases present in EuAl4 are absent in the 10% Ga-doped compound, so the topological phase diagram is highly sensitive to chemical substitution.","A modest topological Hall signal does coexist with the square skyrmion lattice, so the skyrmion chirality contributes to the Hall effect, but it is not the dominant contribution."],"supporting_citations":[{"why":"Identifies the square and rhombic skyrmion lattices in EuAl4 via SANS; provides the sSkL peak and phase assignments used as the reference.","marker":"[14]"},{"why":"Gives the anomalous Hall and topological Hall extraction for EuAl4 that the x = 1 analysis follows.","marker":"[31]"},{"why":"Established the transport and magnetization phase diagrams of Eu(Ga1-xAlx)4 and the THE analysis for x = 0.9 used here.","marker":"[35]"},{"why":"Shows a field-induced topological Hall effect from a double-fan spin structure in YMn6Sn6, the comparative example of a topologically trivial spin texture producing THE.","marker":"[23]"},{"why":"Provides the metamagnetic multiband Hall effect in ErGa2 whose magnitude is compared with the low-temperature THE in Eu(Ga1-xAlx)4.","marker":"[26]"},{"why":"Established magnetoentropic (MCE) signatures of skyrmion phase behavior in FeGe, the method adopted to map the sSkL boundaries.","marker":"[37]"}],"fun_headline_variants":["Skyrmion lattice hides from maximal Hall effect in Eu(Ga,Al)4","Magnetocaloric effect pinpoints skyrmion phase; Hall effect does not","Maximal topological Hall signal is not topological in Eu(Ga,Al)4","Frustrated spins drive Hall peak, while MCE tracks skyrmions"],"cache_read_input_tokens":18944,"weakest_assumption_plain":"The argument that the maximal topological Hall effect sits outside the skyrmion region depends on the two-band model subtraction used to separate normal, anomalous, and topological Hall contributions in the x = 0.9 compound; if that subtraction is not unique, the location and magnitude of the maximal THE could be an artifact.","fun_headline_variants_meta":{"raw":{"variants":["Skyrmion lattice hides from maximal Hall effect in Eu(Ga,Al)4","Magnetocaloric effect pinpoints skyrmion phase; Hall effect does not","Maximal topological Hall signal is not topological in Eu(Ga,Al)4","Frustrated spins drive Hall peak, while MCE tracks skyrmions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000202,"raw_usage":{"total_tokens":1404,"prompt_tokens":991,"completion_tokens":413,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":607,"completion_tokens_details":{"reasoning_tokens":326}},"tokens_in":607,"tokens_out":413,"duration_ms":4171,"temperature":1.0,"reasoning_tokens":326,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:14:09.693280+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-analyze the x = 0.9 Hall resistivity data with an alternative subtraction that does not assume a two-band model above 8 T; if the extracted rho^T_xy maximum moves into the sSkL pocket of the H-T diagram, the paper's central conclusion would be falsified.","supporting_citations":[{"cited_title":"Square and rhombic lattices of magnetic skyrmions in a centrosymmetric binary compound","cited_arxiv_id":null,"evidence_quote":"Identifies the square and rhombic skyrmion lattices in EuAl4 via SANS; provides the sSkL peak and phase assignments used as the reference."},{"cited_title":"Anomalous Hall resistivity and possible topological Hall effect in the ${\\mathrm{EuAl}}_{4}$ antiferromagnet","cited_arxiv_id":null,"evidence_quote":"Gives the anomalous Hall and topological Hall extraction for EuAl4 that the x = 1 analysis follows."},{"cited_title":"Real-space and reciprocal-space topology in the ${{\\mathrm{Eu}(\\mathrm{Ga}}_{1\\ensuremath{- }x}{\\mathrm{Al}}_{x})}_{4}$ square net system","cited_arxiv_id":null,"evidence_quote":"Established the transport and magnetization phase diagrams of Eu(Ga1-xAlx)4 and the THE analysis for x = 0.9 used here."},{"cited_title":"Field-induced topological Hall effect and double-fan spin structure with a c-axis component in the metallic kagome antiferromagnetic compound YMn6Sn6","cited_arxiv_id":null,"evidence_quote":"Shows a field-induced topological Hall effect from a double-fan spin structure in YMn6Sn6, the comparative example of a topologically trivial spin texture producing THE."},{"cited_title":"Metamagnetic multiband Hall effect in Ising antiferromagnet ErGa2","cited_arxiv_id":null,"evidence_quote":"Provides the metamagnetic multiband Hall effect in ErGa2 whose magnitude is compared with the low-temperature THE in Eu(Ga1-xAlx)4."},{"cited_title":"Magnetoentropic signatures of skyrmionic phase behavior in FeGe","cited_arxiv_id":null,"evidence_quote":"Established magnetoentropic (MCE) signatures of skyrmion phase behavior in FeGe, the method adopted to map the sSkL boundaries."}],"review_version":1}