{"id":"8264015e-291e-42e3-ba02-3abecd6ee4cf","arxiv_id":"2412.18824","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In annealed kagome antiferromagnet FeGe, a field-induced spin-flop transition produces a nonlinear Hall signal below the canting transition, interpreted as a topological Hall effect.","lead":"This paper reports electrical transport measurements on annealed crystals of the kagome antiferromagnet FeGe. It finds that resistivity and Hall signals are strongly anisotropic and that a magnetic field can induce a nonlinear Hall signal, which the authors attribute to a topological Hall effect from a canted spin texture.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The THE claim rests on subtracting a field-independent normal Hall baseline; the authors' own two-band analysis for the perpendicular configuration shows such baselines fail in FeGe, so the hump may be a multiband artifact rather than a topological signal.","rationale":"The central claim is the discovery of a field-induced topological Hall effect in the canted antiferromagnetic phase. The evidence is a hump in Δρ_yx after subtracting a linear normal Hall baseline. The most load-bearing assumption is that this baseline is R0*H with field-independent R0. In FeGe, a multiband semimetal with large magnetoresistance, this is not secure. The authors themselves demonstrate for the perpendicular geometry that a two-band model cannot consistently fit both Hall and MR, indicating that Hall nonlinearity of non-topological origin is present. They do not perform that check for the in-plane geometry. Additionally, the text explicitly acknowledges alternative explanations in the conclusion, which conflicts with the definitive 'discover' language in the abstract. A decisive check is to fit the in-plane Hall and MR with a two-band model; if it reproduces the hump, the THE attribution fails. I therefore agree with the reader's conditional verdict and recommend no change.","tokens_in":12374,"tokens_out":3856,"duration_ms":36503,"concrete_test":"Perform a simultaneous two-band fit of the field-dependent Hall conductivity σ_xy(H) = ρ_yx/(ρ_yx^2 + ρ_ab^2) and longitudinal conductivity σ_xx(H) for the H∥c, I∥ab data at T = 2, 10, 30, and 50 K, using the measured ρ_ab(H) as input. If the multiband model reproduces the hump in Δρ_yx within experimental scatter, the topological Hall effect is not required by the data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Section III (Figs. 3(c)-3(d)), the topological Hall resistivity is defined as Δρ_yx = ρ_yx − R0 μ0 H, with R0 obtained from the low-field slope. This subtraction assumes the normal Hall coefficient is constant and that no anomalous or magnetoresistance-induced nonlinearity contaminates the baseline. However, the same paper shows that for the perpendicular geometry (I∥c, H∥ab) a two-band fit fails to describe both MR and Hall simultaneously (Fig. 4(c) and accompanying text), and notes that 'other mechanisms such as skew/side-jump scattering or charge order induced unconventional Hall effect may be involved.' For the in-plane configuration that is the basis of the central claim, no equivalent multiband analysis is performed, even though ρ_ab magnetoresistance reaches 43% at 14 T and 2 K (Fig. 2(b)). A field-dependent R0 or multiband conduction with comparable carrier densities can generate a field-dependent bending of ρ_yx that resembles the hump assigned to THE. The paper's own conclusion further states that the phenomenon 'remains unclear' and 'may be explained by various models including the two-band modal, the charge order with a chiral loop-current effect or the topological Dirac points,' which undercuts the abstract's unqualified claim of having discovered a topological Hall effect.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports anisotropic resistivity, magnetization, and Hall-effect measurements on annealed FeGe single crystals, with current along the ab-plane and c-axis and magnetic fields in both orientations. The authors observe a first-order resistivity loop at the CDW transition T_cdw ≈ 108 K, a field-induced spin-flop transition near H_sf ≈ 6 T for H ∥ c, and a broad hump in the Hall resistivity at high fields in the canted antiferromagnetic phase below T_cant. This hump is interpreted as a topological Hall effect arising from noncollinear spin textures during the spin-flop process. The paper also reports a strongly nonlinear Hall resistivity for the perpendicular configuration (I ∥ c, H ∥ ab) and a magnetic field–temperature phase diagram.","tokens_in":12576,"tokens_out":3075,"duration_ms":31103,"significance":"If the topological Hall interpretation were established, the paper would provide a interesting platform for studying the interplay of charge order, magnetism, and topology in a kagome antiferromagnet. The raw transport and magnetization data appear internally consistent, and the observation of a first-order CDW signature in resistivity, a field-induced spin-flop transition, and strong transport anisotropy is a useful experimental contribution. The symmetrized Hall measurements and the comparison of in-plane and out-of-plane configurations are well conceived, and the phase diagram in Fig. 5 is a useful summary. The central claim, however, rests on a subtraction procedure whose assumptions are not validated for the key configuration, and the authors themselves list alternative explanations in the conclusion. The strength of the paper therefore depends on whether the topological Hall effect claim can be either supported by additional analysis or appropriately weakened.","major_comments":[{"comment":"The topological Hall effect extraction is not robust. The residual is defined as Δρ_yx = ρ_yx − R0 μ0 H, where R0 is obtained from a low-field linear fit to the same ρ_yx(H) curves. This assumes a field-independent normal Hall coefficient and no anomalous or magnetoresistance-induced nonlinearity. The paper's own data show a 43% in-plane magnetoresistance at 14 T and 2 K (Fig. 2(b)), so a field-dependent multi-band normal Hall contribution can mimic the observed hump. No two-band or multiband analysis is presented for the H ∥ c, I ∥ ab configuration that is the basis of the central claim, in contrast to the analysis for the perpendicular geometry in Fig. 4(c). To support the topological Hall claim, the authors should either provide an independently determined baseline (for example, a two-band fit constrained by the measured magnetoresistance, or a high-field slope check) or reframe the finding as a nonlinear Hall effect of unresolved origin.","section":"Section III, Fig. 3(c)-(d)"},{"comment":"The conclusion explicitly states that the phenomenon 'remains unclear, which may be explained by various models including the two-band modal, the charge order with a chiral loop-current effect or the topological Dirac points.' This statement undercuts the abstract's unqualified claim of having 'discovered' a topological Hall effect. The situation is made more serious by Fig. 4(c), where the authors show that a two-band model fails for the perpendicular geometry and invoke skew/side-jump scattering or charge-order-induced unconventional Hall effects as alternatives. A falsifiable distinction between the topological spin-texture mechanism and these alternatives is needed, or the central claim must be revised to a more cautious statement about a field-induced nonlinear Hall effect with several candidate mechanisms.","section":"Section IV (Conclusion)"},{"comment":"Plotting Δρ_yx as a function of magnetization Mc does not by itself establish a topological origin. Since Mc is nearly linear above H_sf (Fig. 1(g)), a field-dependent normal Hall contribution or a multiband effect will also produce a nonlinear Δρ_yx(Mc) trace. A quantitative comparison with the scalar spin chirality expected from the canted double-cone structure, or an independent probe of the spin texture (for example, field-dependent neutron scattering or a control measurement on a non-canted sample), would be required to distinguish the topological mechanism from the alternatives the authors themselves list.","section":"Section III, Fig. 3(e)"}],"minor_comments":[{"comment":"The caption of Fig. 3(a) refers to magnetization data plotted in 'figure 4(a)', and the caption of Fig. 3(e) refers to 'figure 2f'; these should be corrected to the actual magnetization panels in Fig. 1.","section":"Captions of Figs. 3(a) and 3(e)"},{"comment":"The phrase 'anomalous/topopolocal Hall effect/Nernst effect' contains a typo; 'topopolocal' should be 'topological'.","section":"Section I (Introduction)"},{"comment":"The term 'two-band modal' appears twice (Section III and Section IV) and should be 'two-band model'.","section":"Throughout"},{"comment":"The description of the two rectangular pieces could be clarified by stating which piece was used for the in-plane and which for the out-of-plane transport measurements, and by giving the contact geometry for the Hall measurements.","section":"Section II (Experimental Details)"}],"recommendation":"major_revision","confidential_remarks":"I see no indication of data fabrication; the raw resistivity, magnetization, and Hall data are broadly self-consistent. The main issue is interpretive overreach: the topological Hall effect is extracted by subtracting a linear baseline fitted to the same curves, and the paper itself offers several alternative explanations. I would be willing to accept a revised version that either presents a quantitative multiband test for the H ∥ c, I ∥ ab configuration or substantially softens the claim to a field-induced nonlinear Hall effect with candidate mechanisms. The anisotropic transport results and phase diagram are useful even if the topological Hall interpretation is not yet proven."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe one line you need: this is a solid new dataset on annealed FeGe, but the topological Hall effect claim is not yet backed by the analysis. The paper is worth engaging with, not because the THE is established, but because the anisotropic transport and phase diagram are new and the interpretation exposes a common methodological problem.\n\nWhat's actually new: this is the first transport work on annealed FeGe crystals. The authors see anisotropic resistivity (ρ_ab roughly 3× ρ_c), a resistivity loop at the CDW transition that is a good sign of first-order character, a spin-flop transition that shifts with temperature but leaves T_cdw alone, and angle-dependent Hall data that kill the THE when H is rotated away from c. Those results look internally consistent and should survive contact with experiment.\n\nThe soft spot is exactly where the stress-test puts it. The THE is defined as the residual after subtracting R0 μ0 H, with R0 from the low-field slope of the same curve. That is only legitimate if R0 is field-independent. Here, ρ_ab shows 43% MR at 14 T and 2 K, which suggests the carriers' mobility or density may well be field dependent. The authors' own two-band fit for the perpendicular geometry fails to explain both MR and Hall simultaneously, and the conclusion explicitly says the phenomenon 'remains unclear' and could be explained by two-band effects, loop currents, or Dirac points. That sentence alone should temper the abstract's claim. I don't think the stress-test is overstating; if anything, it is generous—the in-plane geometry gets no multiband check at all. So the THE hump may just be a multiband artifact.\n\nMinor things: no error bars on transport, no data release, and the paper uses 'topological Hall' in the abstract while the conclusion hedges to near-falsification.\n\nThis is for a serious referee, but the referee should treat the THE as an interpretation to be tested, not a result. I would accept it for peer review, because the material and data are timely and the field can use a clear example of why baseline subtraction alone is not enough. I would not cite it as evidence for THE in its current form.","headline":"New transport data on annealed FeGe; the topological Hall claim needs a multiband check before it will persuade.","tokens_in":13217,"tokens_out":3198,"would_cite":false,"duration_ms":31521,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["71.45.Lr","73.43.–f","73.23.–b","75.50.Ee"],"model":"deepseek-v4-flash","headline":"Annealed FeGe shows a field-induced topological Hall effect in its canted antiferromagnetic state.","keywords":["kagome magnet","FeGe","charge density wave","topological Hall effect","spin-flop transition","anisotropic transport","canted antiferromagnet","Berry phase"],"falsifier":"Measure Hall and longitudinal resistivity on the same annealed FeGe crystal using a six-contact geometry with the magnetic field rotated through the c-axis, and fit the full conductivity tensor with a two-band model that includes field-dependent mobilities and magnetoresistance. If the fitted ordinary terms alone reproduce the $0.2\\,\\mu\\Omega\\,\\text{cm}$ hump above $H_{sf}$, the topological Hall assignment is falsified; if the hump persists only when the spin texture is noncollinear and vanishes when the field approaches the ab-plane, the Berry-phase reading survives.","tokens_in":12115,"feed_emoji":"🧲","tokens_out":6681,"duration_ms":57046,"temperature":0.7,"pith_summary":"This paper studies annealed single crystals of the kagome antiferromagnet FeGe, where a charge density wave (CDW) forms inside the A-type antiferromagnetic order. It reports that transport is strongly anisotropic: with current in the ab-plane, resistivity shows a first-order anomaly near the CDW transition at 108 K and is about three times larger than the c-axis resistivity. The central claim is that when the magnetic field is applied along the c-axis, a spin-flop transition around 6 T transforms the canted double-cone antiferromagnetic state into a noncollinear spin texture, and that this texture produces a large topological Hall effect below the CDW transition. The evidence is a broad hump in the Hall resistivity above the spin-flop field that does not track magnetization, reaches $0.2\\,\\mu\\Omega\\,\\text{cm}$, and disappears when the field is rotated toward the ab-plane.","feed_headline":"Annealed FeGe shows topological Hall effect after spin-flop transition","feed_subtitle":"A c-axis field flips FeGe's canted spins into a noncollinear texture that adds a 0.2 μΩ cm Hall bump.","key_machinery":"The load-bearing object is the field-induced spin-flop transition in the canted double-cone antiferromagnetic state of FeGe. With field along the easy c-axis and current in the ab-plane, the spin flop rotates the magnetic moments, yielding the basal-plane moment component $M_{ij}=M_0\\sin(-\\mathbf{q}\\cdot\\mathbf{r}_i+\\phi)$ and a noncollinear spin texture. The mechanism that converts this texture into a Hall voltage is the real-space Berry phase from finite scalar spin chirality $\\chi_{ijk}=\\mathbf{S}_i\\cdot(\\mathbf{S}_j\\times\\mathbf{S}_k)$; subtracting the normal and anomalous terms via $\\rho_{yx}=R_0\\mu_0 H+\\rho^A_{yx}+\\rho^T_{yx}$ isolates the topological contribution $\\rho^T_{yx}$ as the hump in $\\Delta\\rho_{yx}$ above $H_{sf}$.","core_discovery":"For $\\mathbf{H}$ along the c-axis and current along the ab-plane, the Hall resistivity $\\rho_{yx}(H)$ is linear at low fields, defining a normal Hall coefficient $R_0$ with carrier density near $6\\times10^{22}\\,\\text{cm}^{-3}$. Above the spin-flop field $H_{sf}\\sim 6\\,\\text{T}$ and below $T_{cdw}=108\\,\\text{K}$, the authors observe a broad hump in $\\Delta\\rho_{yx}=\\rho_{yx}-R_0\\mu_0 H$ that grows with decreasing temperature and reaches about $0.2\\,\\mu\\Omega\\,\\text{cm}$. This hump is strongest in the canting antiferromagnetic phase below $T_{cant}=56\\,\\text{K}$, weakens between $T_{cant}$ and $T_{cdw}$, and is absent above $T_{cdw}$; the authors attribute it to the real-space Berry phase acquired by electrons moving through the field-induced noncollinear spin texture of the canted double-cone AFM state. In contrast, with current along the c-axis and field in the ab-plane, no spin-flop transition appears and the Hall resistivity bends at low fields but is discussed in terms of two-band or alternative mechanisms. The paper also constructs a magnetic phase diagram in which $H_{sf}$ jumps from about $6\\,\\text{T}$ to $9\\,\\text{T}$ across $T_{cdw}$, indicating that the CDW order stabilizes the low-field magnetic texture responsible for the effect.","pith_inferences":["A sharp test follows from the Berry-phase picture: the topological Hall resistivity should be proportional to the sample-averaged scalar spin chirality, so a combined neutron-diffraction and Hall measurement sweeping through the spin-flop region could confirm the mechanism or force a multiband explanation.","The same subtraction logic, applied to the c-axis current data, classifies the low-field bending in $\\rho_{zx}$ as non-topological; if the two-band fit fails at 5 K because of strong scattering, a Corbino or six-terminal geometry could separate the intrinsic Hall term from contact and magnetoresistance artifacts.","The authors leave open why $\\rho_{zx}(T)$ changes sign below $T_{cant}$; an editorial guess is that the sign reversal marks a crossover from CDW-dominated to spin-texture-dominated transport, which could be tested by doping or pressure that suppresses $T_{cdw}$ without fully killing the canting."],"forward_implications":["If the topological Hall interpretation is correct, the observed hump is a direct electrical signature of a field-induced noncollinear magnetic state, so Hall measurements can be used to track the spin-flop reconstruction in FeGe.","The phase diagram shows $H_{sf}$ jumps from about $6\\,\\text{T}$ below $T_{cdw}$ to about $9\\,\\text{T}$ above it, implying the CDW order pins or stabilizes the low-field magnetic texture; tuning $T_{cdw}$ should tune the field range of the topological Hall effect.","The angle-dependent data, where $\\rho_{yx}$ vanishes once $\\mathbf{H}$ is rotated more than roughly $60^\\circ$ from the c-axis, give a practical geometric criterion for when the chiral texture contributes; the same criterion can be tested in other canted antiferromagnets.","Because the effect only appears below $T_{cant}$, where the cone half-angle of the canted double-cone structure grows, the magnitude of the topological Hall signal should correlate with the cone angle across the magnetic phase diagram."],"supporting_citations":[{"why":"Reports the discovery of a CDW inside the AFM state of FeGe and gives the baseline as-grown Hall and transport data that the present annealed-crystal study compares against.","marker":"[7]"},{"why":"Establishes the canted double-cone AFM structure with a temperature-dependent cone half-angle that the topological Hall effect is attributed to.","marker":"[20]"},{"why":"Shows that post-annealing produces long-range CDW order in FeGe, the sample quality on which the anisotropic transport measurements rely.","marker":"[34]"},{"why":"Provides the MnBi2Te4 comparison case where a spin-flop transition induces a topological Hall effect in an antiferromagnet, used as the interpretive template for FeGe.","marker":"[45]"},{"why":"Supplies the Berry-phase and Berry-curvature theory connecting noncollinear spin textures and magnetic order to anomalous and topological Hall contributions.","marker":"[53]"},{"why":"Gives the frustrated-magnet example whose angle-dependent Hall response matches the observed cos-theta behavior and the vanishing of the signal when the field nears the plane.","marker":"[49]"},{"why":"Shows a nonmagnetic kagome compound where bending Hall resistivity is attributed to loop-current or two-band effects, used to discuss alternative explanations for the out-of-plane Hall data.","marker":"[51]"}],"fun_headline_variants":["Spin flop in FeGe yields topological Hall effect","Kagome FeGe: 6 T spin flop triggers topological Hall","Field-induced topological Hall bump in annealed FeGe","Anisotropic transport and topological Hall in kagome FeGe","Topological Hall effect from canted spins in FeGe"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper treats the low-field linear slope of the Hall resistivity as a field-independent normal Hall coefficient $R_0$, so every deviation above the spin-flop field is assigned to anomalous or topological terms; if ordinary magnetoresistance or multiband conduction also bends $\\rho_{yx}(H)$ in the same way, the topological Hall effect claim collapses.","fun_headline_variants_meta":{"raw":{"variants":["Spin flop in FeGe yields topological Hall effect","Kagome FeGe: 6 T spin flop triggers topological Hall","Field-induced topological Hall bump in annealed FeGe","Anisotropic transport and topological Hall in kagome FeGe","Topological Hall effect from canted spins in FeGe"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000257,"raw_usage":{"total_tokens":1668,"prompt_tokens":1126,"completion_tokens":542,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":742,"completion_tokens_details":{"reasoning_tokens":458}},"tokens_in":742,"tokens_out":542,"duration_ms":5076,"temperature":1.0,"reasoning_tokens":458,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T04:25:40.222134+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure Hall and longitudinal resistivity on the same annealed FeGe crystal using a six-contact geometry with the magnetic field rotated through the c-axis, and fit the full conductivity tensor with a two-band model that includes field-dependent mobilities and magnetoresistance. If the fitted ordinary terms alone reproduce the $0.2\\,\\mu\\Omega\\,\\text{cm}$ hump above $H_{sf}$, the topological Hall assignment is falsified; if the hump persists only when the spin texture is noncollinear and vanishes when the field approaches the ab-plane, the Berry-phase reading survives.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the discovery of a CDW inside the AFM state of FeGe and gives the baseline as-grown Hall and transport data that the present annealed-crystal study compares against."},{"cited_title":"Instability of the charge density wave in Kagome magnet FeGe","cited_arxiv_id":"2302.04490","evidence_quote":"Shows that post-annealing produces long-range CDW order in FeGe, the sample quality on which the anisotropic transport measurements rely."},{"cited_title":"Li and J","cited_arxiv_id":null,"evidence_quote":"Provides the MnBi2Te4 comparison case where a spin-flop transition induces a topological Hall effect in an antiferromagnet, used as the interpretive template for FeGe."},{"cited_title":"Quantum oscillations revealing topological band in kagome metal ScV6Sn6","cited_arxiv_id":"2305.04683","evidence_quote":"Supplies the Berry-phase and Berry-curvature theory connecting noncollinear spin textures and magnetic order to anomalous and topological Hall contributions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the frustrated-magnet example whose angle-dependent Hall response matches the observed cos-theta behavior and the vanishing of the signal when the field nears the plane."},{"cited_title":"Roychowdhury, S","cited_arxiv_id":null,"evidence_quote":"Shows a nonmagnetic kagome compound where bending Hall resistivity is attributed to loop-current or two-band effects, used to discuss alternative explanations for the out-of-plane Hall data."}],"review_version":1}