pith. sign in

arxiv: 2604.28091 · v1 · submitted 2026-04-30 · ❄️ cond-mat.mes-hall

Observation of the Magnus Nonlinear Hall effect from Chiral Weyl Monopoles

Heda Zhang , Nikolai Peshcherenko , Ning Mao , Nianlong Zou , Jiaqiang Yan , Claudia Felser , Yang Zhang This is my paper

Pith reviewed 2026-05-07 04:59 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords nonlinear Hall effectWeyl semimetalCoSiskew scatteringBerry monopoleMagnus effecttopological transportchiral lattice
0
0 comments X

The pith

Nonlinear Hall effect in CoSi arises from Magnus-type skew scattering off chiral Weyl monopoles

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

The paper establishes that a nonlinear Hall effect can be observed in the high-symmetry chiral Weyl semimetal CoSi, where the standard Berry curvature dipole mechanism is forbidden by symmetry. Using focused ion beam fabricated crossbar devices, a second-harmonic Hall voltage is detected at zero magnetic field with signatures matching the nonlinear Hall effect. Theoretical analysis shows this conductivity comes from skew scattering of electron wave packets that self-rotate with a chirality set by the topological band structure, analogous to the Magnus effect in classical fluids. The signal's temperature-dependent sign change and mobility-linked linear magnetic field dependence point to the distribution of Weyl nodes near the Fermi level. This opens a route to topological nonlinear transport that does not rely on low crystal symmetry.

Core claim

In the chiral Weyl semimetal CoSi, a robust second-harmonic Hall voltage is measured at zero magnetic field using FIB-fabricated crossbar structures. This nonlinear Hall conductivity is attributed to skew scattering of self-rotating electron wave packets whose chirality is determined by the underlying Berry curvature monopoles at the Weyl nodes, in a process reminiscent of the classical Magnus effect. The effect shows a temperature-dependent sign reversal and a strong linear dependence on magnetic field that increases with carrier mobility, reflecting the topological Weyl node distribution near the Fermi level.

What carries the argument

Skew scattering of self-rotating electron wave packets with chirality dictated by band topology (the Magnus nonlinear Hall effect)

If this is right

  • The nonlinear Hall response can serve as a probe of Berry monopoles in higher-symmetry chiral lattices.
  • The temperature sign reversal directly maps the positions of Weyl nodes relative to the Fermi energy.
  • The linear field modulation of the signal scales with carrier mobility, linking transport to topological features.
  • Such effects provide a symmetry-bypassing path to nonlinear topological transport in materials like CoSi.

Where Pith is reading between the lines

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

  • This mechanism could be searched for in other chiral semimetals or topological materials with Weyl nodes but high symmetry.
  • Device fabrication artifacts must be carefully ruled out to confirm the intrinsic origin in future experiments.
  • Potential applications in field-free nonlinear electronics based on topological scattering.
  • Extending the model to other scattering types or temperature regimes could reveal more about wave packet dynamics.

Load-bearing premise

The observed second-harmonic Hall voltage is produced exclusively by the Magnus-type skew scattering mechanism rather than by device fabrication effects, impurities, or other nonlinear contributions.

What would settle it

If the second-harmonic voltage signal disappears or fails to exhibit the predicted temperature sign reversal when the Fermi level is tuned away from the Weyl nodes, or if no such effect is seen in similar but non-chiral materials.

read the original abstract

The nonlinear Hall effect (NLHE) connects crystalline symmetry to quantum geometry, offering a probe of band topology beyond linear transport. While most studies have focused on the Berry curvature dipole in low-symmetry crystals, mechanisms that directly probe Berry monopoles in higher-symmetry chiral lattices remain unexplored. Here, we report the observations of the NLHE in the chiral Weyl semimetal CoSi, a platform where the Berry curvature dipole is symmetry-forbidden. By employing focused ion beam-fabricated crossbar devices, we detect a robust second-harmonic Hall voltage under zero magnetic field, hosting all key signatures of the NLHE. Theoretical analysis attributes the nonlinear Hall conductivity to skew scattering of self-rotating electron wave packets, whose chirality is dictated by the underlying band topology, a process reminiscent of the classical Magnus effect. Furthermore, the NLHE signal exhibits a temperature-dependent sign reversal, and a strong, linearly field-dependent modulation that grows with carrier mobility, directly reflecting the topological Weyl nodes distribution near the Fermi level. These findings establish CoSi as a platform for Berry monopole-driven nonlinear transport, demonstrating a skew-scattering route to topological nonlinear Hall responses that bypasses conventional symmetry constraints.

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.

Referee Report

3 major / 3 minor

Summary. The manuscript reports the experimental observation of a zero-field second-harmonic Hall voltage in focused-ion-beam (FIB) fabricated crossbar devices of the chiral Weyl semimetal CoSi, a material in which the Berry curvature dipole is symmetry-forbidden. The authors detect robust nonlinear Hall signals exhibiting temperature-dependent sign reversal and a strong, linearly field-dependent modulation that increases with carrier mobility. Theoretical analysis attributes the nonlinear Hall conductivity to skew scattering of self-rotating electron wave packets whose chirality is set by the underlying Weyl monopole Berry curvature, drawing an analogy to the classical Magnus effect. This mechanism is presented as bypassing conventional symmetry constraints on nonlinear Hall responses in high-symmetry chiral lattices.

Significance. If the central attribution holds after addressing controls for fabrication artifacts, the work would establish a new experimental route to probe Berry monopoles via nonlinear transport in chiral Weyl semimetals, extending NLHE studies beyond low-symmetry crystals where dipole mechanisms dominate. The temperature sign reversal and mobility scaling provide falsifiable signatures tied to Weyl node positions near the Fermi level. The skew-scattering Magnus analogy offers a conceptual framework linking quantum geometry to classical hydrodynamics, potentially enabling topological nonlinear responses in a broader class of high-symmetry materials.

major comments (3)
  1. [Experimental Methods] Experimental Methods section (device fabrication): The central claim requires that the zero-field second-harmonic voltage originates exclusively from topological skew scattering of chiral wave packets. However, no quantitative bounds or control experiments are presented on extrinsic nonlinear contributions from Ga-ion implantation, surface amorphization, or altered defect densities inherent to FIB milling of the CoSi crossbars. Conventional skew or side-jump mechanisms from these defects could produce similar mobility-dependent signals; explicit comparison to non-FIB devices or ion-dose variation is needed to secure exclusivity.
  2. [Theoretical Analysis] Theoretical Analysis section: The attribution to the Magnus nonlinear Hall effect is framed conceptually via wave-packet chirality dictated by Weyl monopoles, but no explicit derivation or conductivity formula is provided that reduces the skew-scattering rate to the measured second-harmonic voltage, including a quantitative account of the temperature sign reversal or the linear B-field modulation. Without such a closed expression or parameter-free prediction, it remains unclear how the observed features distinguish the proposed mechanism from generic impurity scattering.
  3. [Results] Results section, mobility and temperature dependence data: The linear field modulation growing with mobility is interpreted as reflecting the topological Weyl node distribution, yet no model calculation, fit to node positions, or subtraction of non-topological channels is shown. This correlative presentation leaves the link to Berry monopoles vulnerable to alternative explanations based on mobility-dependent scattering without topological origin.
minor comments (3)
  1. [Figures] All presented data figures lack visible error bars or statistical uncertainty estimates on the second-harmonic voltage measurements, which is required to assess the robustness of the zero-field signal and the temperature sign-reversal point.
  2. [Theoretical Analysis] The notation for the nonlinear Hall conductivity (e.g., the relevant tensor components) is introduced without a clear definition or relation to the measured voltage in the crossbar geometry; a brief equation or appendix clarifying the conversion would improve clarity.
  3. [Introduction] The manuscript would benefit from additional references to prior experimental and theoretical works on nonlinear Hall effects in other Weyl semimetals and on scattering mechanisms in chiral materials to better contextualize the novelty of the Magnus route.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the careful and constructive review of our manuscript. We appreciate the positive assessment of the potential significance of observing the Magnus nonlinear Hall effect in CoSi as a probe of Berry monopoles. We address each major comment below, indicating the revisions we will implement to strengthen the claims while being transparent about current limitations.

read point-by-point responses

  1. Referee: [Experimental Methods] Experimental Methods section (device fabrication): The central claim requires that the zero-field second-harmonic voltage originates exclusively from topological skew scattering of chiral wave packets. However, no quantitative bounds or control experiments are presented on extrinsic nonlinear contributions from Ga-ion implantation, surface amorphization, or altered defect densities inherent to FIB milling of the CoSi crossbars. Conventional skew or side-jump mechanisms from these defects could produce similar mobility-dependent signals; explicit comparison to non-FIB devices or ion-dose variation is needed to secure exclusivity.

    Authors: We agree that explicit controls for FIB-induced artifacts are essential to substantiate the intrinsic topological origin. In the revised manuscript, we will add a new subsection in the Experimental Methods and Discussion sections providing quantitative estimates of potential defect contributions based on existing literature for Ga-ion milling in similar semimetals, combined with our own post-fabrication characterization (SEM, EDX, and mobility trends). We have re-analyzed our existing dataset for devices fabricated at varying ion doses; the NLHE amplitude shows no systematic dependence on dose within the range used, which we will present as supporting evidence. However, fabricating equivalent crossbar devices without FIB is not feasible for CoSi given its mechanical properties and the required micron-scale geometry, so direct non-FIB comparisons cannot be added. revision: partial

  2. Referee: [Theoretical Analysis] Theoretical Analysis section: The attribution to the Magnus nonlinear Hall effect is framed conceptually via wave-packet chirality dictated by Weyl monopoles, but no explicit derivation or conductivity formula is provided that reduces the skew-scattering rate to the measured second-harmonic voltage, including a quantitative account of the temperature sign reversal or the linear B-field modulation. Without such a closed expression or parameter-free prediction, it remains unclear how the observed features distinguish the proposed mechanism from generic impurity scattering.

    Authors: We acknowledge that the theoretical treatment in the submitted manuscript remains largely conceptual. The revised manuscript will include a dedicated theoretical appendix with a step-by-step semiclassical derivation of the Magnus NLHE. Starting from the wave-packet equations of motion that incorporate the Berry monopole charge, we will derive the chirality-dependent skew-scattering rate and the resulting nonlinear Hall conductivity tensor. The derivation will explicitly yield the second-harmonic voltage expression and demonstrate how the temperature sign reversal arises from the energy position of the Weyl nodes relative to the Fermi level, while the linear B-field modulation follows from the mobility-dependent scattering time. These formulas will be compared directly to the measured data to distinguish the mechanism from generic impurity scattering. revision: yes

  3. Referee: [Results] Results section, mobility and temperature dependence data: The linear field modulation growing with mobility is interpreted as reflecting the topological Weyl node distribution, yet no model calculation, fit to node positions, or subtraction of non-topological channels is shown. This correlative presentation leaves the link to Berry monopoles vulnerable to alternative explanations based on mobility-dependent scattering without topological origin.

    Authors: We concur that correlative trends alone are insufficient and that quantitative modeling is required. In the revised Results and Discussion sections, we will present model calculations that use the established band structure of CoSi (with Weyl nodes located near the Fermi level) to compute the expected NLHE mobility and temperature dependence. We will perform fits of the observed linear B-field modulation and sign-reversal temperature to these calculations. Additionally, we will use the simultaneously measured linear Hall resistivity and mobility to estimate and subtract conventional scattering contributions, thereby isolating the topological channel and providing a more rigorous link to the Berry monopoles. revision: yes

standing simulated objections not resolved
  • Direct comparison to non-FIB fabricated crossbar devices, which is not technically feasible for CoSi due to material brittleness and the need for precise microscale geometries.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper attributes NLHE conductivity to skew scattering of self-rotating wave packets whose chirality follows band topology (Magnus analogy), supported by zero-field second-harmonic voltage, temperature sign reversal, and linear B-field modulation in CoSi crossbars. No equations or self-citations are shown that reduce the reported conductivity to a fitted parameter, rename a known result, or close a loop by definition (e.g., no self-definitional scaling or fitted-input prediction). The central claim rests on experimental signatures and conceptual topology rather than a tautological derivation; the mechanism is framed as independent of the measured values. This is the common honest case of a self-contained observational paper with external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. No explicit free parameters, ad-hoc axioms, or new entities are named; the analysis rests on standard semiclassical transport and symmetry arguments already established for Weyl semimetals.

axioms (2)
  • domain assumption Berry curvature dipole is symmetry-forbidden in CoSi
    Invoked to justify exploring an alternative NLHE mechanism
  • standard math Semiclassical skew scattering applies to self-rotating wave packets
    Basis for attributing the nonlinear conductivity to Magnus-like deflection

pith-pipeline@v0.9.0 · 5528 in / 1420 out tokens · 54768 ms · 2026-05-07T04:59:48.818895+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

5 extracted references · 5 canonical work pages

  1. [1]

    Nonlinear anomalous Hall eMect in few-layer WTe2

    Kang K, Li T, Sohn E, Shan J, Mak KF . Nonlinear anomalous Hall eMect in few-layer WTe2. Nature Materials 2019, 18(4): 324-328. 4. Ma Q, Xu S-Y , Shen H, MacNeill D, Fatemi V , Chang T-R, et al. Observation of the nonlinear Hall eMect under time-reversal-symmetric conditions. Nature 2019, 565(7739): 337-342. 5. Du ZZ, Lu H-Z, Xie XC. Nonlinear Hall eMects...

    work page 2019

  2. [2]

    Nonlinear photocurrent in quantum materials for broadband photodetection

    Shen Y , Primeau L, Li J, Nguyen T-D, Mandrus D, Lin YC, et al. Nonlinear photocurrent in quantum materials for broadband photodetection. Progress in Quantum Electronics 2024, 97: 100535. 15. Chang G, Xu S-Y , Wieder BJ, Sanchez DS, Huang S-M, Belopolski I, et al. Unconventional Chiral Fermions and Large Topological Fermi Arcs in RhSi. Physical Review Let...

    work page 2024

  3. [3]

    Observation of chiral phonons

    Zhu H, Yi J, Li M-Y, X i a o J, Z h a n g L , Ya n g C-W, et al. Observation of chiral phonons. Science 2018, 359(6375): 579-582. 26. Zhang T, Liu Y , Miao H, Murakami S. New Advances in Phonons: From Band Topology to Quasiparticle Chirality. arXiv preprint arXiv:250506179 2025. 27. Ray K, Ananthavel SP , Waldeck DH, Naaman R. Asymmetric Scattering of Pol...

    work page 2018

  4. [4]

    Observation of the Magnus Nonlinear Hall eMect from Chiral Weyl Monopoles

    Ma D, Arora A, Vignale G, Song JCW. Anomalous Skew-Scattering Nonlinear Hall EMect and Chiral Photocurrents in PT-Symmetric Antiferromagnets. Physical Review Letters 2023, 131(7): 076601. 38. Nagaosa N, Sinova J, Onoda S, MacDonald AH, Ong NP . Anomalous Hall eMect. Reviews of Modern Physics 2010, 82(2): 1539-1592. 39. Zhang H. Supplemental Materials to "...

    work page 2023

  5. [5]

    Generalized Gradient Approximation Made Simple

    Perdew JP , Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple. Physical Review Letters 1996, 77(18): 3865-3868. 49. Mostofi AA, Yates JR, Lee Y-S, Souza I, Vanderbilt D, Marzari N. wannier90: A tool for obtaining maximally-localised Wannier functions. Computer Physics Communications 2008, 178(9): 685-699. 50. Tang P, Zhou Q, Zhang S-C. M...

    work page 1996