REVIEW 3 major objections 5 minor 1 cited by
Giant magneto-cubic in-plane Hall effect in a nonmagnetic material
T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash
Pith's one-line read 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…
desk verdict 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. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
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.
What would settle it
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.
Extended reading notes
Core claim
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.
Load-bearing premise
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.
Editorial extensions
If this is right
- 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.
Reading between the lines
- 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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
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.
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 (3)
- [Discussion on the physical mechanisms, Eq. (2) and Fig. 5d] 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.
- [Observation in nonmagnetic LuAuSn, Eq. (1) and Fig. 2e] 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.
- [Discussion on the physical mechanisms, use of Eq. (2)] 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.
minor comments (5)
- [Fig. 2e caption] The caption refers to 'equation (2)' when describing the fitting curve for the angular dependence; this should be equation (1).
- [Giant in-plane Hall conductivity section] 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.
- [Abstract] The phrase 'A -period of IPHE' is incomplete; it should read 'A 2π/3-period'.
- [Results, symmetry analysis] The sentence 'C3z forbids IPHE in the linear order of B12' appears to have a typo; it should be 'linear order of B'.
- [References] Several references (e.g., refs. 16, 17, 21, 27, 28) lack complete page numbers or article numbers; please check the journal style.
Circularity Check
No significant circularity: the core IPHE observation is a direct measurement, and the mechanism interpretation, though underdetermined, does not reduce to its own inputs by construction.
full rationale
The paper's central claim is an experimental observation: a sin(3φ), B³ in-plane Hall effect in nonmagnetic LuAuSn, extracted from measured transverse resistivity via the angular decomposition of Eq. (1). The decomposition is a fit to the data, but the 2π/3 periodicity and the cubic field dependence are not imposed by the fitting form; they are properties of the extracted component and are verified independently in Figs. 2d–g. The theoretical prediction of magneto-cubic IPHE under C3z symmetry is attributed to external references (refs. 7–9) with no overlap of the present authors, so no self-citation chain forces the result. The mechanism discussion uses the scaling relation Eq. (2) from ref. 39, which includes one present co-author (S. A. Yang), but that relation is a general, parameter-free theoretical result for the anomalous Hall effect, not fitted to LuAuSn data or derived from the observation being explained. The first-principles estimates of the intrinsic and Lorentz-force contributions are independent DFT-based calculations that do not use the measured IPHE as input. The conclusion that extrinsic side-jump and skew scattering dominate is inferred by elimination after showing the intrinsic and Lorentz terms are small. The authors explicitly acknowledge that side-jump and skew-scattering contributions cannot be separated in scaling analysis, and the fit window (20–125 K) is narrow with correlated coefficients; however, this is a limitation of the evidence for the mechanism, not a circular reduction. No step in the paper equates a prediction to a fitted input by construction, and no load-bearing claim depends solely on a self-citation. The honest finding is therefore no significant circularity.
Assumptions & free parameters
free parameters (3)
- Misalignment phase φ0 in Eq. (1) =
Not stated
- Scaling coefficients C1, C2, C3, C4 in Eq. (2) =
C2+C1σxx0 = 311 Ω⁻¹cm⁻¹, C3 = -855 Ω⁻¹cm⁻¹, C4 = 664 Ω⁻¹cm⁻¹
- Relaxation time τ =
0.1 ps
assumptions (5)
- standard math The Hall vector transforms under proper rotations as a polar vector, and C3z symmetry permits a B^3 IPHE while forbidding a B-linear IPHE.
- domain assumption The (111) transport plane realizes C3z/3m symmetry and the measured response is a bulk property of that plane.
- domain assumption LuAuSn is nonmagnetic, with no magnetic ordering contributing to the observed Hall signal.
- domain assumption The scaling relation Eq. (2) from anomalous Hall transport theory applies to the in-plane Hall effect in this nonmagnetic material.
- domain assumption The DFT+U band structure and Zeeman-dressed Berry-curvature calculation correctly capture the intrinsic and Lorentz-force contributions.
Cite this review
Pith. "Pith review of Giant magneto-cubic in-plane Hall effect in a nonmagnetic material." pith.science (2026). https://pith.science/paper/TK67FR7E
@misc{pith2026250716544,
author = {Pith},
title = {Pith review of: Giant magneto-cubic in-plane Hall effect in a nonmagnetic material},
year = {2026},
howpublished = {\url{https://pith.science/paper/TK67FR7E}},
note = {Machine review of arXiv:2507.16544}
}
read the original abstract
In-plane Hall effect (IPHE) triggered by an external magnetic field applied in the transport plane has attracted significant experimental attentions in recent few years 1-6. However, most experiments focus on magnetic materials, where the existence of magnetic ordering may complicate understanding the physics behind, and the relatively small signal magnitudes limit the application of the effect. Here, we report a giant IPHE in a nonmagnetic half-Heusler compound LuAuSn, with a magnitude exceeding all the previously reported values. A -period of IPHE and the consistent cubic dependence on the magnetic field are observed, realizing the long-sought theoretical prediction of magneto-cubic IPHE under threefold rotational symmetry7-9 in an unexpected material. The scaling law analysis and first-principles calculations indicate that extrinsic side jump and skew scattering processes from both impurity and phonon scatterings dominate the observed effect. These findings unravel a new type of magneto-nonlinear IPHE, and its large magnitude and wide-temperature operation may open the door to practical applications of IPHE.
Forward citations
Cited by 1 Pith paper
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Magneto-cubic and magneto-linear dependence observed in an in-plane anomalous Hall magnet
In-plane anomalous Hall resistivity in EuCd2Sb2 shows B cubed behavior around zero field in paramagnetic and antiferromagnetic phases and B linear behavior at high fields in the forced ferromagnetic phase.
Reference graph
Works this paper leans on
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[1]
Anomalous Hall effect in ZrTe5
1.Liang T, et al. Anomalous Hall effect in ZrTe5. Nat Phys 14, 451-455 (2018). 2.Chen J, et al. Unconventional Anomalous Hall Effect in the Canted Antiferromagnetic Half-Heusler Compound DyPtBi. Adv Funct Mater 31, 2107526 (2021). 3.Zhou J, et al. Heterodimensional superlattice with in -plane anomalous Hall effect. Nature 609, 46-51 (2022). 4.Lesne E , et...
work page 2018
Reviewed August 6, 2026 · model on record in the stance chip above.
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