arxiv: 2604.21293 · v1 · submitted 2026-04-23 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Recognition: unknown

Higher odd-order nonlinear Hall effect in magnetic topological insulator Mn(Bi1-xSbx)2Te4

Xiubing Li , Zheng Dai , Shuai Zhang , Heng Zhang , Congcong Li , Boyuan Wei , Fengyi Guo , Chunfeng Li

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Fucong Fei Minhao Zhang Xuefeng Wang Huaiqiang Wang Fengqi Song

Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:21 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci

keywords nonlinear Hall effectmagnetic topological insulatorBerry curvature multipolesMn(Bi1-xSbx)2Te4higher-order transportquantum geometryantiferromagnetic order

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The pith

Higher odd-order nonlinear Hall effects arise from Berry curvature multipoles in the magnetic topological insulator Mn(Bi1-xSbx)2Te4.

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

This paper reports the experimental observation of third-, fifth-, and seventh-order nonlinear Hall effects in thin flakes of the magnetic topological insulator Mn(Bi1-xSbx)2Te4. These higher-order voltages display a characteristic twofold angular dependence and appear only when the material is magnetically ordered below its Néel temperature. The response strength is greatest near the charge-neutral doping level and falls off exponentially with increasing order. Comparable signals occur in both odd and even layer thicknesses. The authors attribute the phenomenon to multipole moments of the Berry curvature in the material's band structure.

Core claim

In thin flakes of Mn(Bi1-xSbx)2Te4 the nonlinear Hall response is measured at the third, fifth, and seventh orders. These voltages exhibit twofold symmetry with respect to the angle between current and magnetic field or crystal axes. The effect vanishes above the Néel temperature, maximizes near charge neutrality, and decreases exponentially with order number. It occurs with similar strength regardless of whether the number of layers is odd or even. Analysis shows that the higher-order terms can be generated by Berry curvature multipoles, which are higher moments of the geometric phase distribution across the Brillouin zone.

What carries the argument

Berry curvature multipoles, the higher-order moments of the Berry curvature distribution that generate nonlinear Hall responses beyond the dipole term.

If this is right

The nonlinear Hall effect extends to high odd orders when Berry curvature possesses significant multipole structure.
Magnetic ordering is required to activate these higher-order contributions.
Charge neutrality optimizes the visibility of the effect.
The exponential decay with order indicates a characteristic scale set by the electronic structure.
The effect appears independently of layer parity, showing it does not rely on net magnetization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar higher-order nonlinear Hall signals may be detectable in other antiferromagnetic or ferromagnetic topological materials with strong spin-orbit coupling.
Transport measurements at multiple orders could serve as a probe of the full quantum geometric tensor beyond the usual dipole approximation.
The exponential suppression with order sets a practical limit on which higher-order terms remain observable in typical samples.

Load-bearing premise

The detected higher-order voltages truly reflect intrinsic nonlinear Hall responses from Berry curvature multipoles and are not caused by Joule heating, thermoelectric effects, or measurement artifacts.

What would settle it

If the higher-order voltages persist with the same magnitude and twofold angular dependence above the Néel temperature, the claim that they require magnetic order and arise from Berry curvature multipoles would be falsified.

read the original abstract

The nonlinear Hall effect is a new member of the Hall effect family, which attracts intense research interests, and it is closely related to the quantum geometry of quantum materials. The previous studies primarily concentrate on the second-order and third-order nonlinear Hall effect. However, the experimental study of higher-order nonlinear Hall effect is scarce at present. In this work, we report the observations of the higher odd-order (third-, fifth-, seventh-order) nonlinear Hall effect in magnetic topological insulator Mn(Bi1-xSbx)2Te4 thin flakes. The higher odd-order nonlinear Hall voltage exhibits a twofold angular dependence and exists only below the N\'eel temperature. It reaches its maximum near the charge neutral point and decays exponentially as the order of the nonlinear Hall effect increases. Furthermore, such higher odd-order nonlinear Hall effect is observed in both odd- and even-layer samples with comparable magnitudes. Theoretical analysis indicates that the higher odd-order nonlinear Hall effect responses may arise from the Berry curvature multipoles. Our work paves the way for the study of the higher-order nonlinear transport phenomena.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper reports experimental signals for fifth- and seventh-order nonlinear Hall effects in Mn(Bi1-xSbx)2Te4 that follow the expected temperature, angular, and doping patterns for Berry curvature multipoles.

read the letter

The main takeaway is that the authors have measured these higher odd-order nonlinear Hall voltages in the magnetic topological insulator and shown they only exist below the Néel temperature with the right angular and doping dependence. They use AC current and harmonic detection to isolate the third-, fifth-, and seventh-order terms. The signals decay exponentially with order, peak at charge neutrality, and appear in both odd- and even-layer flakes after resistance normalization. This last point is useful because it suggests the effect is not limited to surfaces. What is new here is the push beyond third order, where most prior experimental work stopped. The temperature cutoff at the magnetic transition and the twofold angular pattern match what one would expect for odd-order responses tied to broken time-reversal symmetry. The paper handles the experimental aspects well with multiple checks. The theoretical link to Berry curvature multipoles is reasonable but stays qualitative, without quantitative predictions for the observed amplitudes. Soft spots are minor. One could ask for more detail on how they subtracted background or estimated heating contributions, but the provided controls seem to address the main concerns. No obvious contradictions in the data description. This is for researchers in topological materials and nonlinear transport. It adds useful data points to the quantum geometry toolkit. I would recommend sending it for peer review. The results are novel enough and the evidence looks solid to warrant referee input.

Referee Report

1 major / 3 minor

Summary. The paper reports experimental observations of third-, fifth-, and seventh-order nonlinear Hall voltages in thin flakes of the magnetic topological insulator Mn(Bi_{1-x}Sb_x)_2Te_4. These signals display a twofold angular dependence, appear exclusively below the Néel temperature, reach maximum amplitude near the charge-neutral point, and decrease exponentially with increasing order. Comparable magnitudes are found in both odd- and even-layer devices after normalization, and the responses are attributed to Berry curvature multipoles on the basis of a theoretical analysis.

Significance. If the reported signals are confirmed as genuine higher-order nonlinear Hall responses, the work extends the nonlinear Hall family beyond second- and third-order effects and supplies direct experimental access to Berry curvature multipoles in a magnetic topological insulator. The use of AC excitation with harmonic lock-in detection, explicit vanishing above T_N, power-law scaling checks, and normalization across layer parities are positive features that strengthen the central claim.

major comments (1)

[data analysis and supplementary figures] § on data analysis and supplementary figures: the power-law scaling of the extracted voltages with current amplitude is stated to confirm the order n, but the manuscript does not report the fitted exponents with uncertainties or show that they remain consistent across the full doping and temperature range; this check is load-bearing for excluding heating or other even-order artifacts.

minor comments (3)

[Figure 2] Figure 2 (angular dependence): the twofold symmetry is clear, but the polar plots would benefit from explicit overlay of the expected cos(2θ) or sin(2θ) functional form with fit residuals.
[Theoretical section] Theoretical section: the statement that responses 'may arise from the Berry curvature multipoles' remains qualitative; a short expansion or reference to the relevant multipole tensor components would clarify how odd orders beyond third are generated.
[Abstract and main text] Abstract and main text: the exponential decay with order is reported but no numerical decay constant or fit to the amplitude vs. order is given; adding this would make the claim more quantitative.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive overall assessment, including the recommendation for minor revision. We address the major comment point by point below.

read point-by-point responses

Referee: the power-law scaling of the extracted voltages with current amplitude is stated to confirm the order n, but the manuscript does not report the fitted exponents with uncertainties or show that they remain consistent across the full doping and temperature range; this check is load-bearing for excluding heating or other even-order artifacts.

Authors: We agree that explicitly reporting the fitted power-law exponents with uncertainties, together with checks of their consistency across doping and temperature, would strengthen the identification of the nonlinear order and help exclude artifacts such as Joule heating. In the submitted manuscript we performed these power-law fits to extract the voltages at each harmonic but did not tabulate the exponents or demonstrate their stability in the main text or SI. In the revised version we will add the fitted exponents (with uncertainties) for representative data sets and include supplementary figures showing the scaling behavior at multiple doping levels and temperatures below T_N. These additions will confirm that the exponents remain close to the expected integer values (n = 3, 5, 7) throughout the relevant parameter range. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The manuscript is an experimental report of observed higher odd-order nonlinear Hall voltages in Mn(Bi1-xSbx)2Te4 flakes, supported by angular, temperature, and doping dependence data plus controls (AC excitation, harmonic detection, TN cutoff, power-law scaling). The brief theoretical statement that responses 'may arise from the Berry curvature multipoles' is interpretive and does not constitute a derivation whose outputs are forced by its own inputs or by self-citation chains. No equations reduce claimed predictions to fitted parameters by construction, and the central results rest on direct measurements rather than self-referential definitions. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that Berry curvature multipoles generate observable higher odd-order nonlinear Hall voltages with the reported angular and temperature dependence; no free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption Berry curvature multipoles produce higher odd-order nonlinear Hall responses that exhibit twofold angular dependence and vanish above the Néel temperature.
Invoked in the final sentence of the abstract as the theoretical explanation for the observed signals.

pith-pipeline@v0.9.0 · 5539 in / 1519 out tokens · 37051 ms · 2026-05-09T21:21:20.919124+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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