Modulation of anomalous Hall angle in a magnetic topological semimetal

Baogen Shen; Binbin Wang; Claudia Felser; Enke Liu; Gangqin Liu; Hongxiang Wei; Jinying Yang; Meng Lv; Qingqi Zeng; Shen Zhang

arxiv: 2607.00396 · v1 · pith:IMM5TUGPnew · submitted 2026-07-01 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Modulation of anomalous Hall angle in a magnetic topological semimetal

Jinying Yang , Yanxing Shang , Xingchen Liu , Yibo Wang , Xuebin Dong , Qingqi Zeng , Meng Lv , Shen Zhang

show 9 more authors

Yang Liu Binbin Wang Hongxiang Wei Yizheng Wu Stuart Parkin Gangqin Liu Claudia Felser Enke Liu Baogen Shen

This is my paper

Pith reviewed 2026-07-02 07:36 UTC · model grok-4.3

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

keywords anomalous Hall angleWeyl semimetalCo3Sn2S2Fe dopingHall conductivitymagnetic sensortopological semimetal

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The pith

The anomalous Hall angle reaches around 25 degrees in Fe-doped Co3Sn2S2 by expressing it as a function of resistivity times anomalous Hall conductivity.

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

This paper seeks to establish that the efficiency of converting a longitudinal current into a transverse Hall current can be increased by modulating the anomalous Hall angle in the magnetic Weyl semimetal Co3Sn2S2. The authors propose formulating tan of the angle directly as a function of the product of electrical resistivity and anomalous Hall conductivity, which permits tuning the angle up to a magnitude of 0.46. If correct, this yields devices with substantially higher sensitivity for magnetic field detection than typical magnetic materials allow. Microfabricated devices from Fe-doped single-crystalline nanoflakes reach a Hall sensitivity of 7028 μΩcm/T and detect fields down to 23.5 nT/Hz0.5 at 1 Hz.

Core claim

We propose that tanθA can be formulated as a function of the product of electrical resistivity and anomalous Hall conductivity; applying this relation in Fe-doped Co3Sn2S2 modulates tanθA up to 0.46 (around 25°), producing anomalous Hall devices with Hall sensitivity of 7028 μΩcm/T and magnetic field detectability of 23.5 nT/Hz0.5 at 1 Hz.

What carries the argument

The proposed formulation of tanθA as a function of the product of electrical resistivity and anomalous Hall conductivity.

If this is right

Microfabricated devices achieve a Hall sensitivity of 7028 μΩcm/T.
Magnetic field detectability reaches 23.5 nT/Hz0.5 at 1 Hz.
Anomalous Hall angles become accessible at magnitudes far above the 0.1–3° range typical for magnetic materials.

Where Pith is reading between the lines

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

The same product-based tuning may be testable in other doped Weyl semimetals to check whether the angle modulation generalizes beyond Co3Sn2S2.
If the relation survives temperature changes, it could be checked for sensor operation above cryogenic conditions.

Load-bearing premise

The anomalous Hall angle depends only on the product of resistivity and anomalous Hall conductivity even after Fe doping, without extra scattering or band-structure changes altering the relation.

What would settle it

A set of resistivity, conductivity, and Hall-angle measurements on the same Fe-doped samples showing that the observed tanθA deviates systematically from the value predicted by the resistivity-conductivity product.

Figures

Figures reproduced from arXiv: 2607.00396 by Baogen Shen, Binbin Wang, Claudia Felser, Enke Liu, Gangqin Liu, Hongxiang Wei, Jinying Yang, Meng Lv, Qingqi Zeng, Shen Zhang, Stuart Parkin, Xingchen Liu, Xuebin Dong, Yang Liu, Yanxing Shang, Yibo Wang, Yizheng Wu.

**Figure 1.** Figure 1: Generic formula and scheme for anomalous Hall angle (θ A). a, Relation between tanθ A, longitudinal resistivity (ρxx) and anomalous Hall conductivity (σ A H ). Absolute values of tanθ A and σ A H are adopted here. Two solutions (θ A 1 and θ A 2 ) connect the two regions and the split line is tanθ A = 1. For most materials, tanθ A is usually smaller than 0.05. The dotted lines indicate the first (f 1 ), thi… view at source ↗

read the original abstract

The anomalous Hall angle ({\theta}A) is a measure of the efficiency of converting a longitudinal driving current to a transverse spin-polarized Hall current. For anomalous Hall sensing, a large anomalous Hall angle can improve the sensitivity of magnetic field detection. However, modulation of this angle is challenging and magnetic materials typically have low angles of 0.1 to 3{\deg}. Here, we report modulation of the anomalous Hall angle in the magnetic Weyl semimetal Co3Sn2S2. We propose that the angle parameter tan{\theta}A can be formulated as a function of the product of electrical resistivity and anomalous Hall conductivity. Our scheme was utilized to demonstrate the modulation of tan{\theta}A up to a magnitude of 0.46, corresponding to an angle of around 25{\deg}. Microfabricated anomalous Hall devices using Fe-doped Co3Sn2S2 single-crystalline nanoflakes exhibit a high Hall sensitivity of 7028 {\mu}{\Omega}ucm/T and a magnetic field detectability of 23.5 nT/Hz0.5 at 1 Hz.

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

Fe-doped Co3Sn2S2 reaches ~25° anomalous Hall angle with reported device metrics, but the tanθA formulation is just the standard definition.

read the letter

The main takeaway is that Fe-doped Co3Sn2S2 nanoflakes reach an anomalous Hall angle of around 25 degrees, with fabricated devices showing a sensitivity of 7028 μΩcm/T and detectability of 23.5 nT/Hz0.5 at 1 Hz.

The paper does the experimental part competently. They work with single-crystalline nanoflakes, apply Fe doping, and build microfabricated Hall devices. Reporting those specific metrics is useful for anyone comparing sensor performance in topological materials.

The softer part is the conceptual framing. They say they propose that tanθA can be formulated as the product of resistivity and anomalous Hall conductivity. That relation is standard; it is how the angle is defined from the conductivity tensor. The abstract treats it as a scheme for modulation, but the modulation comes from changing the material properties through doping, not from the formula itself. The stress-test concern holds: doping can alter scattering rates and the position relative to Weyl nodes, so the product approximation needs checking against the actual measured ρ_xy/ρ_xx. If the paper shows that check with error bars, fine; if not, the attribution is loose.

The central experimental claims look plausible on their face, but the novelty is in the numbers and the device work rather than a new way to think about the angle.

This paper is aimed at people working on magnetic sensors or Weyl semimetal devices. Someone in that niche would get value from the reported performance.

I would recommend sending it for peer review. The experimental results are concrete enough to be worth referee scrutiny.

Referee Report

2 major / 1 minor

Summary. The manuscript claims modulation of the anomalous Hall angle θ_A in Fe-doped Co3Sn2S2 magnetic Weyl semimetal nanoflakes by formulating tan θ_A as the product of longitudinal resistivity ρ_xx and anomalous Hall conductivity σ_AH, achieving values up to 0.46 (corresponding to ~25°). It further reports microfabricated anomalous Hall devices with Hall sensitivity of 7028 μΩ cm/T and magnetic field detectability of 23.5 nT/Hz^{0.5} at 1 Hz.

Significance. If the experimental data confirm that large modulation of tan θ_A is achieved specifically through control of the ρ_xx σ_AH product in the doped topological semimetal without confounding changes to the conductivity tensor, the work could advance high-sensitivity anomalous Hall sensors. The underlying relation is standard rather than derived, so significance depends on whether the manuscript demonstrates new control mechanisms or device performance beyond existing AHE materials.

major comments (2)

[Abstract] Abstract: the claim that tan θ_A 'can be formulated as a function of the product of electrical resistivity and anomalous Hall conductivity' presents the standard relation tan θ_A ≈ σ_AH ρ_xx (valid when |ρ_AH| ≪ ρ_xx) as a proposal. The manuscript must explicitly verify in the results that the independently measured tan θ_A (from ρ_AH/ρ_xx) equals the product ρ_xx σ_AH within experimental uncertainty for the Fe-doped nanoflakes, because Fe substitution can shift the chemical potential, alter Berry curvature, and introduce momentum-dependent scattering that violates the simple product form.
[Abstract] Abstract: the headline modulation (tan θ_A reaching 0.46) and device metrics are stated without reference to figures, tables, error bars, or comparison to the undoped case. The central claim that modulation is enabled by the proposed scheme is load-bearing on these data; the full manuscript must include quantitative checks that the equality holds and that performance gains are attributable to the modulation rather than generic doping effects.

minor comments (1)

[Abstract] Notation in the abstract uses inconsistent LaTeX (e.g., {\theta}A, {\mu}{\Omega}ucm) that should be standardized to θ_A and μΩ cm throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the major comments point-by-point below and will revise the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that tan θ_A 'can be formulated as a function of the product of electrical resistivity and anomalous Hall conductivity' presents the standard relation tan θ_A ≈ σ_AH ρ_xx (valid when |ρ_AH| ≪ ρ_xx) as a proposal. The manuscript must explicitly verify in the results that the independently measured tan θ_A (from ρ_AH/ρ_xx) equals the product ρ_xx σ_AH within experimental uncertainty for the Fe-doped nanoflakes, because Fe substitution can shift the chemical potential, alter Berry curvature, and introduce momentum-dependent scattering that violates the simple product form.

Authors: We agree that tan θ_A ≈ ρ_xx σ_AH is a standard relation under the stated approximation. Our manuscript frames the product as the basis for a modulation strategy in the doped Weyl semimetal. To address the concern, we will add explicit verification in the results section by directly comparing the measured tan θ_A (from ρ_AH/ρ_xx) to the product ρ_xx σ_AH across doping levels, with error bars and uncertainty analysis, confirming agreement within experimental limits. This will demonstrate that the relation holds for the Fe-doped nanoflakes despite possible shifts in chemical potential or scattering. revision: yes
Referee: [Abstract] Abstract: the headline modulation (tan θ_A reaching 0.46) and device metrics are stated without reference to figures, tables, error bars, or comparison to the undoped case. The central claim that modulation is enabled by the proposed scheme is load-bearing on these data; the full manuscript must include quantitative checks that the equality holds and that performance gains are attributable to the modulation rather than generic doping effects.

Authors: We will revise the abstract to include references to the relevant figures, tables, and error bars for the tan θ_A = 0.46 value, Hall sensitivity, and detectability. In the main text we will add quantitative comparisons to the undoped Co3Sn2S2 case and other AHE materials, together with checks showing that the performance improvements arise specifically from control of the ρ_xx σ_AH product rather than generic doping. These additions will make the attribution to the modulation scheme explicit. revision: yes

Circularity Check

1 steps flagged

tanθA modulation reduces to ρ_xx ⋅ σ_AH product by the proposed formulation

specific steps

self definitional [Abstract]
"We propose that the angle parameter tanθA can be formulated as a function of the product of electrical resistivity and anomalous Hall conductivity. Our scheme was utilized to demonstrate the modulation of tanθA up to a magnitude of 0.46, corresponding to an angle of around 25°."

The formulation is the standard relation tanθA ≈ ρ_xx ⋅ σ_AH. Demonstrating 'modulation of tanθA' via the scheme is therefore equivalent to modulating the product ρ_xx ⋅ σ_AH, which is the input by construction rather than an independent result of the scheme.

full rationale

The paper's central claim of modulating tanθA to 0.46 rests on proposing and applying the relation tanθA = f(ρ ⋅ σ_AH). This relation is the standard definition (from σ tensor inversion, tanθA ≈ ρ_xy/ρ_xx ≈ σ_AH ⋅ ρ_xx), so the demonstrated modulation is equivalent to modulating the product itself. The abstract presents the relation as a novel 'proposal' and 'scheme' without independent derivation or check that it holds quantitatively under Fe doping. This makes the headline result tautological with the measured inputs rather than a derived outcome.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard condensed matter assumptions about the anomalous Hall effect in magnetic materials. No explicit free parameters, new axioms beyond domain standards, or invented entities are introduced in the abstract.

axioms (1)

domain assumption The relation tanθA = f(ρ × σ_AH) holds and can be used to modulate the angle in the doped material.
Stated as a proposal in the abstract without derivation or independent justification.

pith-pipeline@v0.9.1-grok · 5787 in / 1625 out tokens · 38767 ms · 2026-07-02T07:36:06.791893+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

1 extracted references · 1 canonical work pages

[1]

↑”, “↓” and “→

Nanotechnologies, NV concentration ~ 3 ppm, ND diameter ~ 100 nm) were dropped onto the surface of the Co 3Sn2S2 nanoflakes (Fig. S15c). The sample was then loaded into a closed-cycle optical cryostat (Montana Instruments, S100) for low -temperature measurements. Optically detected magnetic resonance (ODMR) spectra were obtained for each selected NDs by r...

work page arXiv 2010

[1] [1]

↑”, “↓” and “→

Nanotechnologies, NV concentration ~ 3 ppm, ND diameter ~ 100 nm) were dropped onto the surface of the Co 3Sn2S2 nanoflakes (Fig. S15c). The sample was then loaded into a closed-cycle optical cryostat (Montana Instruments, S100) for low -temperature measurements. Optically detected magnetic resonance (ODMR) spectra were obtained for each selected NDs by r...

work page arXiv 2010