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REVIEW 3 major objections 4 minor 41 references

Magneto-cubic and magneto-linear dependence observed in an in-plane anomalous Hall magnet

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read In a trigonal antiferromagnet, the in-plane anomalous Hall resistivity is cubic in the in-plane field near zero field and linear above saturation, across magnetic phases.

desk verdict A plausible power-law taxonomy of in-plane AHE that deserves refereeing, but the fits need more rigor before the B^3 and B-linear claims are locked in. read the letter →

arxiv 2507.21458 v1 pith:O5O4LLS7 submitted 2025-07-29 cond-mat.str-el cond-mat.mtrl-sci

Ayano Nakamura , Shinichi Nishihaya , Mitsuru Akaki , Motoi Kimata , Kenta Sudo , Yuki Deguchi , Hsiang Lee , Tadashi Yoneda
show 4 more authors
Masaki Kondo Hiroaki Ishizuka Masashi Tokunaga Masaki Uchida
This is my paper · ORCID
classification cond-mat.str-elcond-mat.mtrl-sci
keywords in-planeanomalousHalleffectmagneto-cubicresponseoctupolartensorEuCd2Sb2trigonalantiferromagnetWeylpointshigh-fieldtransportBerrycurvature
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

EuCd2Sb2 is a trigonal antiferromagnet whose in-plane magnetic field produces a transverse Hall signal. This paper measures that in-plane anomalous Hall effect in each magnetic phase and claims that near zero field the Hall resistivity follows $\rho_{yx,\mathrm{AHE}} \propto B_y^3$ both below and above the Néel temperature $T_N = 7.5$ K. The cubic coefficient is an off-diagonal octupolar component, $o_{zyyy}$, which decays above $T_N$ roughly as $T^{-3}$, while the conventional out-of-plane coefficient decays only as $T^{-1}$. In the forced ferromagnetic phase, the leading dependence switches to linear in $B_y$ and remains linear up to 24 T. If correct, the result shows that the leading multipolar order of the in-plane Hall coupling is phase-dependent and that quantum-geometric band changes, not spin saturation, continue to drive the response at high field.

What carries the argument

The load-bearing object is the off-diagonal coupling between the applied in-plane field and the out-of-plane Hall vector, written through multipolar response coefficients: the octupolar component $o_{zyyy}$, the third-order Hall response to the in-plane field, in $\rho_z = o_{zyyy} B_y^3$, and the dipolar component $o_{zz}$ in $\rho_z = o_{zz} B_z$. The trigonal point group of EuCd2Sb2 forbids the linear off-diagonal coupling in the high-symmetry phase, making the cubic term the leading one; the antiferromagnetic ordering breaks $C_3$ only weakly, so the cubic term survives below $T_N$. Above $T_N$ the paper connects $o_{zyyy}$ to the induced magnetization through a Curie-Weiss form, giving the approximate $T^{-3}$ decay. In the forced ferromagnetic phase the symmetry breaking is strong enough that the linear term becomes leading, and the invoked mechanism is field-induced separation of Weyl points under the spin-orbit cross term $k_y^n \sigma_z$.

What would settle it

Re-measure the same film's transverse voltage after antisymmetrizing over field and current reversal and examine the residual of the cubic fit; if a term linear in $B_y$ or even in $B_y$ survives near zero field, the claimed cubic-leading dependence is not established. In the forced ferromagnetic phase, the persistence claim would fail if the slope $d\rho_{yx,\mathrm{AHE}}/dB_y$ plateaued before 24 T in a sample with cleaner contact alignment.

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Extended reading notes

Core claim

The paper's central claim is that the in-plane anomalous Hall resistivity in EuCd2Sb2 is cubic in the in-plane field around zero field in both the paramagnetic phase and the A-type antiferromagnetic phase, even though the antiferromagnetic ordering breaks the $C_3$ symmetry that would permit a linear term. Around zero field the data are fit by $\rho_z = -\rho_{yx,\mathrm{AHE}} = o_{zyyy} B_y^3$, with $o_{zyyy}$ the off-diagonal octupolar response coefficient; above $T_N$, $o_{zyyy}$ falls roughly as $T^{-3}$, in contrast to the out-of-plane coefficient $o_{zz}$, which falls roughly as $T^{-1}$. In the forced ferromagnetic phase above the in-plane saturation field, the leading term becomes $\rho_z \propto B_y$, and the response remains linear up to the 24 T measurement limit. The paper interprets the continuing linear growth as continuing separation of Weyl points along both in-plane and out-of-plane momentum directions, so the Hall response is controlled by field-driven band geometry rather than by saturated spin magnetization.

Load-bearing premise

The cubic extraction assumes that the measured transverse voltage around zero field is an odd, intrinsic Hall response, free of any linear or even-in-field contribution from contact misalignment, planar Hall effect, or anisotropic magnetoresistance; the paper reports a standard four-probe measurement without showing antisymmetrization or subtraction of longitudinal components.

Editorial extensions

If this is right

  • The $B_y^3$ term must be included in zero-field analyses of in-plane Hall data on EuCd2Sb2; a linear-only fit would misidentify the intrinsic response.
  • The $T^{-3}$ decay of $o_{zyyy}$ provides a temperature-resolved fingerprint that distinguishes cubic in-plane Hall response from the $T^{-1}$ behavior of the out-of-plane coefficient in the same crystal.
  • Above saturation, the linear rise persisting to 24 T implies that in-plane Hall measurements can track field-driven Weyl-point separation even after the spin magnetization has saturated.
  • The phase-by-phase switch from cubic to linear leading order gives a template for identifying the multipolar order of Hall coupling in other trigonal semimetals with the same symmetry.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Going beyond the paper, the same symmetry argument predicts cubic in-plane Hall response in other trigonal and (111)-oriented cubic semimetals, so the $B^3$ behavior could serve as a material-independent signature rather than a EuCd2Sb2-specific accident.
  • A testable extension is to antisymmetrize the transverse voltage over current and field reversal; because the paper does not describe such antisymmetrization, the reported $o_{zyyy}$ values are only as clean as the contact alignment and subtraction of longitudinal components.
  • The $T^{-3}$ decay follows from cubing a Curie-Weiss magnetization; comparing $o_{zyyy}$ with the cube of the measured magnetization over the same temperature range would separate the intrinsic octupolar contribution from a trivial magnetization-cube background.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reports magnetotransport measurements of the in-plane anomalous Hall effect (AHE) on trigonal EuCd2Sb2 thin films, with fields up to 24 T. The authors claim that around zero field the in-plane anomalous Hall resistivity follows a cubic function of the in-plane field in both the paramagnetic and antiferromagnetic phases, that the extracted octupolar coefficient ozyyy decays approximately as T^-3 above the Néel temperature, and that in the forced ferromagnetic phase the response becomes linear in field and persists up to the highest measured field. The interpretation is framed through symmetry analysis and the orbital magnetization model, and the authors note a concurrent related paper by J. Chen et al.

Significance. If validated, the paper would provide a systematic multipolar characterization of the off-diagonal coupling in the in-plane AHE of a trigonal antiferromagnet, extending previous low-field studies and adding high-field data up to 24 T. The distinction between magneto-cubic and magneto-linear regimes across magnetic phases is potentially important for understanding Berry-curvature and orbital-magnetization contributions to the Hall effect. However, the quantitative claims currently lack the experimental validation needed to distinguish them from trivial contamination, so the significance is contingent on a more careful data-analysis presentation.

major comments (3)
  1. [Materials and Methods, Transport measurement; Fig. 2C] The extraction of rho_yx,AHE from the raw Hall voltage is not described. The Methods state only that a standard four-probe method was used, with no mention of field-reversal antisymmetrization, subtraction of longitudinal or planar Hall components, or correction for contact misalignment. Since Eq. (1) assumes the measured quantity is the intrinsic anomalous Hall response, a linear ordinary-Hall contribution from a small out-of-plane field component or an even-in-field magnetoresistance admixture would directly bias the cubic fit. Please report the full extraction procedure, show residuals and error bars for the cubic fits in Fig. 2C, and compare against linear and linear-plus-cubic models.
  2. [Eq. (4) and Fig. 3C] The claimed T^-3 decay of ozyyy is largely built into the construction of Eq. (4), where ozyyy is defined as the prefactor of B_y^3 and the magnetization is inserted as a Curie-Weiss form, giving ozyyy = ozyyy_tilde (a + bC/(T+theta))^3 by construction. A roughly cubic inverse-temperature decay is therefore anticipated rather than empirically discovered. To make the 'unconventional decay' claim substantive, the temperature dependence should be quantitatively fit to Eq. (4) with reported parameters and compared with alternative forms such as T^-1, T^-2, or exponential decay over the same temperature window. A dashed guide line without residuals is not sufficient.
  3. [Fig. 4A] The high-field linear response in the forced ferromagnetic phase is presented as rho_yx,AHE, but no node-angle control is shown for the 24 T data. If the sample has a small out-of-plane misalignment, an ordinary Hall contribution proportional to B_z ~ epsilon B grows linearly with field and could mimic the observed 'magneto-linear' dependence. The prior work cited for the three-fold symmetry was not performed at 24 T. Please report field sweeps at the symmetry-determined node angles (phi = 0, 60, 120, ... degrees) at high fields and quantify the out-of-plane field alignment uncertainty, and provide a linear fit to the high-field segment rather than relying on visual inspection.
minor comments (4)
  1. [Eq. (3)] The constants a and b in Eq. (3) are introduced without definition or dimensionality; please define them explicitly as conversion factors between applied field, spin magnetization, and the effective field that enters the cubic coupling.
  2. [Figs. 3C and 3D] The dashed lines labeled T^-3 and T^-1 are guides to the eye only; please state the temperature range included in the comparison and how 'roughly' is quantified, since the text does not report a fit.
  3. [Abstract and Discussion] The phrase 'unconventional decay' is used before any quantitative comparison with alternative temperature laws is presented; consider tempering the wording or adding such a comparison to avoid overstating the empirical content.
  4. [Introduction, paragraph 3] The discussion of why magneto-linear coupling is symmetry-forbidden in the trigonal paramagnetic phase but allowed in the antiferromagnetic phase would benefit from a compact symmetry table or explicit decomposition, since the paper's central observation is that the cubic term survives even in the AFM phase.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central field-dependence claims are new measurements, and the T^-3 trend is a model-consistency check rather than a fitted input renamed as a prediction.

full rationale

The core experimental claims are based on new in-plane and out-of-plane field sweeps of the same EuCd2Sb2 film, and the magneto-cubic and magneto-linear dependences are extracted directly from those data rather than being inherited from prior work. The octupolar coefficient ozyyy is defined in Eq. (1) as the coefficient of B_y^3 and is fitted at each temperature from the measured field sweeps; Eq. (4) then derives a Curie-Weiss expectation for the temperature dependence of that same coefficient by inserting M_y = C/(T+|θ|) B_y into the cubic coupling of Eq. (3). This is a model-consistency check, not an independent first-principles prediction, because the cubic field dependence is already the empirical input and the comparison in Fig. 3C is qualitative ('roughly'). However, it is not circular in the prohibited sense: the T^-3 exponent is not used as a fit parameter, no parameter of Eq. (4) is extracted from the ozyyy(T) data that are then shown to follow T^-3, and an observed T^-1 or T^-2 trend would have disagreed with the model. The self-citations to refs. [15], [17], and [20] provide prior observations and the orbital-magnetization interpretation, but the present field- and temperature-dependent data and symmetry arguments are presented independently. The lack of reported antisymmetrization or node controls is an experimental-validation concern about possible ordinary-Hall or planar-Hall contamination, not a circularity of the derivation chain. No load-bearing step equates a predicted quantity to its own input by construction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new particles, forces, or fields are introduced. The octupolar tensor component ozyyy is a response coefficient defined by the B cubed fit, not a new physical entity. The main hidden costs are the unverified Curie-Weiss and symmetry assumptions, plus the unspecified contamination subtraction.

free parameters (3)
  • ozyyy, cubic response coefficient
    Obtained by least-squares fitting rho_yx,AHE = ozyyy * B_y^3 in a low-field window at each temperature; its temperature trend is then used to claim T to the minus three decay. The fit window, residuals, and uncertainties are not given.
  • ozz, linear out-of-plane response coefficient
    Obtained by fitting rho_yx,AHE = ozz * B_z; used as the comparison showing ozz roughly proportional to T to the minus one.
  • a, b, C, theta in Eqs. (3) and (4)
    Constants in the model rho = (a B + b M)^3 and the Curie-Weiss magnetization M = C B / (T + |theta|). They are not fitted or independently measured here, so the predicted T to the minus three behavior is only qualitative.
assumptions (4)
  • domain assumption The magnetic point group determines that magneto-linear coupling is prohibited in the trigonal paramagnetic phase and that magneto-cubic coupling is the leading term; in the antiferromagnetic phase the point group 2/m1' permits linear coupling.
    Invoked in the introduction and results to identify B cubed as the expected leading term; this is a symmetry classification from Ref. [21] and is not re-derived in this paper.
  • domain assumption Above the Neel temperature, the Eu2+ magnetization follows Curie-Weiss behavior with temperature-independent constants C and theta.
    Used in Eq. (4) to convert the model (a B + b M)^3 into an explicit T to the minus three temperature dependence; no magnetization data for this film are shown to validate the Curie-Weiss form.
  • domain assumption The measured rho_yx,AHE is the intrinsic Hall signal after eliminating longitudinal and ordinary Hall contamination.
    The Methods section describes only a standard four-probe method; no antisymmetrization, contact-misalignment correction, or subtraction of planar Hall is described, yet the fitted cubic and linear laws assign the entire signal to the anomalous Hall channel.
  • domain assumption The orbital-magnetization model with Weyl-point splitting from Ref. [15] explains the linear high-field term in the forced ferromagnetic phase.
    Adopted in the Discussion to interpret the 24 T linear behavior; it is not tested quantitatively against the new high-field data.

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Cite this review

Pith. "Pith review of Magneto-cubic and magneto-linear dependence observed in an in-plane anomalous Hall magnet." pith.science (2026). https://pith.science/paper/O5O4LLS7

@misc{pith2026250721458,
  author       = {Pith},
  title        = {Pith review of: Magneto-cubic and magneto-linear dependence observed in an in-plane anomalous Hall magnet},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O5O4LLS7}},
  note         = {Machine review of arXiv:2507.21458}
}
read the original abstract

The Hall effect, particularly that arising from in-plane magnetic field, has recently emerged as a sensitive probe of quantum geometric properties in solids. Especially in trigonal systems, in-plane anomalous Hall effect (AHE) can be explicitly induced by nontrivial off-diagonal coupling between the magnetic field and the Hall vector on the principal plane. Here we elucidate multipolar dependence of the off-diagonal coupling in the in-plane AHE, by systematically measuring on the (001) principal plane of trigonal antiferromagnet EuCd2Sb2 thin films for each magnetic phase. Around zero field, magneto-cubic dependence of anomalous Hall resistivity is clearly observed not only in the paramagnetic phase but also even in the antiferromagnetic phase. An off-diagonal component of the octupolar tensor also exhibits unconventional decay above the magnetic ordering temperature, roughly depending on the inverse temperature to the third power. In the forced ferromagnetic phase, on the other hand, magneto-linear dependence dominantly appears and notably persists up to very high fields. Our findings clarify key aspects of the off-diagonal coupling in the in-plane AHE, paving the way for its future investigations and potential applications beyond conventional expectations about the Hall effect.

Figures

Figures reproduced from arXiv: 2507.21458 by the authors.

Figure 1
Figure 1. FIG. 1: In-plane AHE and its emergence in EuCd [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Contrasting temperature evolution and field depende [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Cubic and linear trends in the detailed temperature d [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Continuing linear change of in-plane AHE in the force [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]

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Reviewed August 6, 2026 · model on record in the stance chip above.