{"id":"b0e19f81-b8ce-4785-bfba-adb8576273c6","arxiv_id":"2507.16544","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"LuAuSn exhibits a record-large, cubic-in-field in-plane Hall effect with a 2π/3 angular periodicity, a first for a nonmagnetic material.","lead":"A nonmagnetic crystal called LuAuSn shows a giant sideways voltage when a magnetic field is applied flat in its plane, with a strength growing as the field cubed. The signal is the largest in-plane Hall effect reported so far and works up to room temperature.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The mechanism claim is underdetermined: Eq. (2) is fit with three correlated coefficients over a narrow 20–125 K window, and the authors concede side-jump/skew cannot be separated, so extrinsic dominance is not established.","rationale":"The reader's weakest assumption identifies exactly the same weak point: the scaling-law analysis cannot uniquely separate side-jump and skew-scattering contributions, and the conclusion relies on correlated parameters fitted over a restricted temperature range. I agree that the central experimental observation—a B³ in-plane Hall effect with 2π/3 angular periodicity in nonmagnetic LuAuSn—is well supported by the symmetry argument, the two-current-direction control, and the presented data. The mechanism attribution, however, is conditional at best. The fit in Fig. 5d omits the 2 K point where the signal is largest and the high-temperature range where phonon effects should be most visible; this makes the extracted coefficients sensitive to the chosen window. The authors' own admission that separating side-jump and skew scattering is in principle impossible in scaling analysis further weakens the claim that both impurity and phonon extrinsic mechanisms dominate. The first-principles calculations only rule out intrinsic and Lorentz-force contributions; they do not provide a positive identification of the extrinsic scattering channels. Therefore the paper's headline result stands, but the mechanism claim should be presented as suggestive rather than established. This matches the reader's CONDITIONAL verdict, so no change is needed.","tokens_in":11370,"tokens_out":5052,"duration_ms":59934,"concrete_test":"Refit Eq. (2) with the full data set (include T = 2 K and re-examine 125–300 K) and run a bootstrap over the 20–125 K points to obtain confidence intervals for C2+C1σxx0, C3, and C4. If the interval for C3 or C4 overlaps zero, or if including the 2 K point changes their signs, the claim that impurity and phonon side-jump/skew scattering dominate is not supported. Also report the covariance of C3 and C4; large anticorrelation would confirm the decomposition is underdetermined.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing soft spot is the attribution of the observed IPHE to extrinsic side-jump and skew scattering. The evidence is the fit of Eq. (2) to σxy^i versus σxx over 20–125 K in Fig. 5d. That fit uses three effective parameters (C2+C1σxx0, C3, C4) over a narrow range of σxx/σxx0 (about 0.6–1.0), after excluding the 2 K point where the signal is largest and the 125–300 K data. The fitted values C3 = −855 Ω⁻¹cm⁻¹ and C4 = +664 Ω⁻¹cm⁻¹ partly cancel in the combinations appearing in Eq. (2), and the authors explicitly state that separating side-jump and skew-scattering contributions is in principle impossible in scaling analysis. First-principles calculations only show that the intrinsic and Lorentz-force terms are small (~1 S/cm); they do not positively identify the extrinsic scattering channels. Thus the central mechanism claim—that impurity and phonon side-jump/skew scattering dominate—rests on an underdetermined fit rather than a falsifiable decomposition. The headline observation of a B³, 2π/3-period IPHE in nonmagnetic LuAuSn is not threatened by this issue; only the mechanism conclusion is.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports the observation of a giant in-plane Hall effect (IPHE) in the nonmagnetic half-Heusler compound LuAuSn. The authors show that, for the magnetic field applied in the (111) plane, the Hall resistivity exhibits a 2π/3 angular period and a cubic magnetic-field dependence up to 3 T, consistent with the predicted magneto-cubic IPHE under C3z symmetry. They extract an in-plane Hall conductivity of about 306 Ω⁻¹cm⁻¹ at 2 K and 3 T, which they claim exceeds all previously reported values. They also present two-current-direction experiments that distinguish the effect from an anisotropic magnetoresistance (planar Hall) response. First-principles calculations are used to show that intrinsic and Lorentz-force contributions are small, and a scaling-law analysis based on Eq. (2) is used to argue that extrinsic side-jump and skew-scattering processes from both impurities and phonons dominate the effect.","tokens_in":11634,"tokens_out":4277,"duration_ms":46185,"significance":"If the central observation holds, this is an important advance: it provides the first experimental realization of the magneto-cubic in-plane Hall effect in a nonmagnetic material, and the magnitude is genuinely large, exceeding prior IPHE reports. The two-current-direction control (Fig. 3) is a particularly strong piece of evidence that the effect is not a planar Hall/AMR artifact, and the clean B³ scaling up to 3 T is directly demonstrated. The paper also has the strength of including first-principles estimates of the intrinsic and Lorentz-force contributions, which bound those channels. However, the mechanism claim (extrinsic side-jump and skew scattering from impurities and phonons) is less secure and relies on a scaling fit with correlated parameters; this weakens the interpretational part of the paper but does not threaten the headline transport observation.","major_comments":[{"comment":"The scaling-law analysis does not establish that side-jump and skew-scattering mechanisms dominate. The fit uses three effective parameters (C2+C1σxx0, C3, and C4) over a restricted range σxx/σxx0 ≈ 0.6–1.0, after excluding the 2 K point where the signal is largest and the 125–300 K data. The fitted values C3 = −855 Ω⁻¹cm⁻¹ and C4 = +664 Ω⁻¹cm⁻¹ partially cancel, and the authors themselves state that separating side-jump and skew-scattering contributions is in principle impossible in scaling analysis (ref. 39). The first-principles calculations only exclude intrinsic and Lorentz-force contributions; they do not positively compute the extrinsic contributions. Therefore the conclusion that both impurity and phonon side-jump/skew scattering dominate is underdetermined. I recommend either providing explicit disorder-model calculations for the extrinsic channels or tempering the mechanism claim to state that intrinsic and Lorentz mechanisms are excluded, with the microscopic origin of the dominant extrinsic contribution left as an open question.","section":"Discussion on the physical mechanisms, Eq. (2) and Fig. 5d"},{"comment":"The decomposition of the angular Hall signal into sin(3φ) and sin(φ+φ0) components assumes a single out-of-plane misalignment with free phase φ0. The robustness of the extracted in-plane component should be demonstrated, for example by showing that the 2π/3 component is stable under reasonable variations of φ0 and that the amplitude of the sin(φ+φ0) term is consistent with the independently measured out-of-plane Hall response. Without such a sensitivity analysis, the decomposition could in principle absorb part of the signal into the misalignment term, although the two-current-direction control in Fig. 3 does provide additional support that the 2π/3 component is a genuine IPHE.","section":"Observation in nonmagnetic LuAuSn, Eq. (1) and Fig. 2e"},{"comment":"The scaling relation of Eq. (2) is taken from the anomalous Hall effect literature (ref. 39), where it is derived for ferromagnets with an established magnetization. Its applicability to a nonmagnetic material where the magnetic field only induces a Zeeman splitting is not self-evident and should be justified, either by derivation or by citing a specific theory for the IPHE that yields the same functional form. As written, the fit in Fig. 5d is essentially a quadratic polynomial, and the physical interpretation of the fitted coefficients relies on the validity of that borrowed scaling form.","section":"Discussion on the physical mechanisms, use of Eq. (2)"}],"minor_comments":[{"comment":"The caption refers to 'equation (2)' when describing the fitting curve for the angular dependence; this should be equation (1).","section":"Fig. 2e caption"},{"comment":"The paragraph describing the extraction of σxyH contains garbled typesetting (e.g., 'herer,', 'teansvresr', 'mrasuerd'), which makes the formulas difficult to verify. Please ensure the final version has clean mathematical typesetting.","section":"Giant in-plane Hall conductivity section"},{"comment":"The phrase 'A -period of IPHE' is incomplete; it should read 'A 2π/3-period'.","section":"Abstract"},{"comment":"The sentence 'C3z forbids IPHE in the linear order of B12' appears to have a typo; it should be 'linear order of B'.","section":"Results, symmetry analysis"},{"comment":"Several references (e.g., refs. 16, 17, 21, 27, 28) lack complete page numbers or article numbers; please check the journal style.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The central experimental observation is strong and well supported by the two-current-direction control and the B³ scaling. The main weakness is the mechanism attribution in the scaling analysis, which is underdetermined as the authors themselves concede. A revision that softens the mechanism claim or adds a disorder-model calculation would make the paper's conclusions more secure. The fit to the journal's scope is good: this is a solid transport experiment with symmetry-based analysis. I would not reject, but the mechanism section needs substantial reworking before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear Colleague,\n\nThe headline result is real: LuAuSn shows a cubic-in-B in-plane Hall effect with 2π/3 angular periodicity, a clean nonmagnetic platform, and a record Hall conductivity of about 306 S/cm at 2 K and 3 T. The experimental work is careful: the angular decomposition separates the in-plane component from a small out-of-plane misalignment, the two-current-direction control distinguishes IPHE from planar Hall, and the B^3 scaling is directly demonstrated. The symmetry analysis is standard, and the comparison with existing IPHE systems is useful.\n\nThe soft spot is the mechanism claim. The authors attribute the effect to extrinsic side-jump and skew scattering from both impurities and phonons, but that rests on a scaling-law fit over 20–125 K with correlated parameters and a narrow range of σxx. They themselves state that separating side-jump from skew scattering is in principle impossible in scaling analysis, so the claim that both channels contribute equally goes beyond the fit. The first-principles calculations show the intrinsic and Lorentz-force terms are small, but that only rules out those two; it does not positively identify the extrinsic channels. So I would treat the mechanism as a plausible hypothesis, not an established result. This is a genuine weakness, but it does not undercut the central observation.\n\nWhat would make the paper stronger: deposit raw data, add error bars on the extracted σxy^i, and either extend the scaling fit or soften the mechanism language. As is, it deserves serious peer review—the observation is important enough that a referee should spend time on it and push the authors on the scaling analysis.\n\nWho it's for: experimentalists and theorists working on Hall effects in nonmagnetic/topological materials, and anyone interested in in-plane Hall families. I'd bring it to a reading group and would cite the experimental result if I worked in that area.\n\nMy recommendation: send to review, but the referee should focus on the scaling analysis and request raw data and a more cautious mechanism statement.\n\nBest.","headline":"A genuine new experimental observation of a giant B^3 in-plane Hall effect in a nonmagnetic material, with an underdetermined mechanism attribution that should be softened.","tokens_in":12233,"tokens_out":2894,"would_cite":true,"duration_ms":28932,"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":"In the nonmagnetic half-Heusler LuAuSn, an in-plane magnetic field produces a giant Hall effect with $2\\pi/3$ angular period and cubic field dependence, reaching 306 S/cm at 2 K and 3 T, and the authors attribute it to extrinsic side-jump…","keywords":["in-plane Hall effect","magneto-cubic","half-Heusler","LuAuSn","side jump","skew scattering","nonmagnetic transport","C3z symmetry"],"falsifier":"Grow LuAuSn crystals with substantially different residual resistivity ratios and measure the 2 K, 3 T in-plane Hall conductivity: if impurity side-jump and skew scattering dominate, the impurity coefficient extracted from Eq. (2) should track the impurity level, while a coefficient that stays fixed across samples of different purity would falsify the extrinsic-scattering claim.","tokens_in":11161,"feed_emoji":"🧲","tokens_out":11148,"duration_ms":103977,"temperature":0.7,"pith_summary":"This paper claims that a nonmagnetic material can produce a large Hall voltage when the magnetic field lies in the transport plane, an effect usually studied in magnets. In the half-Heusler LuAuSn, the Hall signal has a $2\\pi/3$ angular period and grows as $B^3$ below 3 T, matching a prediction for crystals with threefold rotational symmetry. At 2 K and 3 T the in-plane Hall conductivity reaches about 306 $\\Omega^{-1}\\mathrm{cm}^{-1}$, exceeding previously reported in-plane Hall conductivities, and the effect remains measurable at room temperature. If the claim holds, the in-plane Hall effect becomes a phenomenon that nonmagnetic materials can host, with scattering rather than magnetic order as its source.","feed_headline":"Nonmagnetic LuAuSn delivers cubic in-plane Hall effect","feed_subtitle":"A 2π/3-period Hall signal with B³ scaling reaches 306 S/cm at 2 K, topping all prior in-plane Hall systems.","key_machinery":"The load-bearing symmetry is the threefold rotation $C_{3z}$ of the (111) surface of LuAuSn, whose point group is $3m$. A symmetry analysis of the Hall vector shows that $C_{3z}$ forbids a linear-in-$B$ in-plane Hall response, so the leading allowed term is cubic in the field and carries a $\\sin(3\\varphi)$ angular dependence. The argument then uses a multivariable scaling relation (Eq. 2) that assigns coefficients to impurity and phonon side-jump and skew-scattering processes, together with first-principles estimates of the intrinsic and Lorentz-force contributions, to conclude that extrinsic scattering, not band topology, generates the observed signal.","core_discovery":"The paper reports the first observation of a magneto-cubic in-plane Hall effect in a three-dimensional nonmagnetic material. In LuAuSn, the in-plane Hall resistivity extracted from angle-dependent measurements follows a $\\sin(3\\varphi)$ angular dependence with no phase shift, and below 3 T it scales as $B^3$. At 2 K and 3 T the corresponding in-plane Hall conductivity is about 306 $\\Omega^{-1}\\mathrm{cm}^{-1}$, an order of magnitude larger than in the nonmagnetic benchmark ZrTe$_5$ and larger than previously reported in-plane Hall conductivities in magnetic systems; at 7 T it reaches about 687 $\\Omega^{-1}\\mathrm{cm}^{-1}$. The signal persists up to room temperature. First-principles calculations put the intrinsic Berry-curvature and Lorentz-force contributions two orders of magnitude below the measured value, and a scaling-law fit indicates that extrinsic side-jump and skew scattering from both impurities and phonons dominate.","pith_inferences":["By extension, other nonmagnetic crystals with a $C_{3z}$ surface direction, such as other half-Heuslers or trigonal metals, should show the same $\\sin(3\\varphi)$, $B^3$ in-plane Hall term, making this a likely materials class rather than a single-compound effect.","A cleaner LuAuSn sample with a higher residual resistance ratio should shift the balance among the scaling terms, so measuring IPHE in samples with deliberately varied impurity content would directly test the impurity-scattering part of the mechanism claim.","The same symmetry argument suggests thermal analogs, an in-plane Nernst effect and an in-plane thermal Hall effect, should exist in this material, a direction the paper names as future work."],"forward_implications":["Magnetic order is not required for an in-plane Hall effect: a magnetic field alone, acting on a $C_{3z}$-symmetric nonmagnetic conductor, can generate a large transverse Hall voltage.","The clean $B^3$ dependence and $2\\pi/3$ angular period give an experimental fingerprint that distinguishes this effect from planar Hall and anisotropic magnetoresistance signals.","The in-plane Hall conductivity of LuAuSn at 2 K and 3 T is about 306 $\\Omega^{-1}\\mathrm{cm}^{-1}$, exceeding all previously reported in-plane Hall conductivities, with a value near 687 $\\Omega^{-1}\\mathrm{cm}^{-1}$ at 7 T.","The effect operates from 2 K to room temperature, with about 17 $\\Omega^{-1}\\mathrm{cm}^{-1}$ at 300 K and 9 T, so IPHE-based devices would not need cryogenic conditions.","The mechanism attribution implies that impurity and phonon scattering, not intrinsic Berry curvature or the Lorentz force, should be the focus of future IPHE engineering."],"supporting_citations":[{"why":"Predicted that in-plane magnetization can induce the quantum anomalous Hall effect, establishing the theoretical basis for in-plane Hall physics.","marker":"7"},{"why":"Proposed possible quantization and half-quantization of the anomalous Hall effect caused by an in-plane magnetic field, part of the prediction the paper realizes in a nonmagnetic material.","marker":"8"},{"why":"Discussed why the anomalous Hall effect is absent in planar Hall geometry and analyzed side-jump and skew-scattering channels for the in-plane Hall effect.","marker":"9"},{"why":"Supplies the multivariable scaling relation (Eq. 2) used to separate impurity and phonon scattering contributions.","marker":"39"},{"why":"Reported anomalous Hall effect in ZrTe$_5$, the prior nonmagnetic benchmark whose in-plane Hall conductivity LuAuSn exceeds by an order of magnitude.","marker":"1"},{"why":"Reported a heterodimensional superlattice with an in-plane anomalous Hall effect, one of the magnetic-system values compared in Fig. 4f.","marker":"3"},{"why":"Developed the theory of the phonon side-jump contribution to the anomalous Hall effect, supporting the claimed phonon scattering channel.","marker":"42"},{"why":"Derived universal classes of disorder scatterings in the in-plane anomalous Hall effect, supporting the side-jump and skew-scattering attribution.","marker":"31"}],"fun_headline_variants":["Record cubic in-plane Hall effect found in nonmagnetic LuAuSn","LuAuSn shows giant magneto-cubic Hall effect without magnetism","Cubic in-plane Hall effect reaches record 306 S/cm in LuAuSn","Nonmagnetic LuAuSn delivers first B³-scaled in-plane Hall effect","Unexpected nonmagnetic host yields giant cubic Hall response"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The mechanism conclusion rests on the scaling relation with four correlated coefficients fitted only over the 20-125 K window, and the paper itself concedes that scaling analysis cannot in principle separate side-jump from skew-scattering contributions.","fun_headline_variants_meta":{"raw":{"variants":["Record cubic in-plane Hall effect found in nonmagnetic LuAuSn","LuAuSn shows giant magneto-cubic Hall effect without magnetism","Cubic in-plane Hall effect reaches record 306 S/cm in LuAuSn","Nonmagnetic LuAuSn delivers first B³-scaled in-plane Hall effect","Unexpected nonmagnetic host yields giant cubic Hall response"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000816,"raw_usage":{"total_tokens":3569,"prompt_tokens":936,"completion_tokens":2633,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":552,"completion_tokens_details":{"reasoning_tokens":2536}},"tokens_in":552,"tokens_out":2633,"duration_ms":21485,"temperature":1.0,"reasoning_tokens":2536,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:07:06.124105+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Grow LuAuSn crystals with substantially different residual resistivity ratios and measure the 2 K, 3 T in-plane Hall conductivity: if impurity side-jump and skew scattering dominate, the impurity coefficient extracted from Eq. (2) should track the impurity level, while a coefficient that stays fixed across samples of different purity would falsify the extrinsic-scattering claim.","supporting_citations":[{"cited_title":"Anomalous Hall effect in ZrTe5","cited_arxiv_id":null,"evidence_quote":"Reported anomalous Hall effect in ZrTe$_5$, the prior nonmagnetic benchmark whose in-plane Hall conductivity LuAuSn exceeds by an order of magnitude."}],"review_version":1}