Separating Intrinsic and Domain-Mediated Anomalous Hall Conductivity in Co$_3$Sn$_2$S$_2$ via Contact Engineering

Dima Cheskis; Eddy Divin Kenvo Songwa; Hodaya Gabber; Renana Aharonof; Shaday Jesus Nobosse Nguemeta

arxiv: 2505.22183 · v3 · submitted 2025-05-28 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci· cond-mat.str-el

Separating Intrinsic and Domain-Mediated Anomalous Hall Conductivity in Co₃Sn₂S₂ via Contact Engineering

Eddy Divin Kenvo Songwa , Shaday Jesus Nobosse Nguemeta , Hodaya Gabber , Renana Aharonof , Dima Cheskis This is my paper

Pith reviewed 2026-05-19 13:39 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-scicond-mat.str-el

keywords anomalous Hall conductivityBerry curvatureWeyl semimetalCo3Sn2S2domain structurecontact engineeringintrinsic contribution

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The pith

A contact architecture distributing current through the depth of a 670-micrometer Co3Sn2S2 crystal isolates the intrinsic Berry-curvature anomalous Hall conductivity from domain-mediated contributions.

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

Standard Hall measurements on bulk ferromagnetic Weyl semimetals mix momentum-space Berry curvature effects with local domain and texture signals, making clean separation difficult. The authors address this by engineering contacts on a thick single crystal to promote depth-distributed current flow. Above roughly 0.3 tesla the field forces a single- or few-domain state that exposes the pure intrinsic response, while a crossover near 125 kelvin tracks the drop in magnetization and anisotropy. In zero-field-cooled multidomain states at low fields the Hall signal instead reflects domain physics and possible real-space curvature plus modest extrinsic terms. The work presents contact engineering as a non-invasive route to separate these contributions in thick crystals.

Core claim

In a ~670 μm thick Co3Sn2S2 single crystal, a contact architecture promoting depth-distributed current flow shows that anomalous Hall conductivity depends on the field-enforced domain state: above ~0.3 T a single- or few-domain configuration reveals the momentum-space intrinsic Berry-curvature response, with a crossover near ~125 K driven by rapid magnetization decrease and reduced magnetic anisotropy. In low-field zero-field-cooled multidomain states the Hall response is modified by domain physics, possible real-space Berry curvature, and moderate extrinsic contributions.

What carries the argument

The contact architecture that promotes depth-distributed current flow across the thick crystal, averaging over depth to isolate the intrinsic momentum-space response from surface or local domain effects.

If this is right

Above 0.3 T the measured Hall conductivity directly reflects the intrinsic Berry-curvature contribution in bulk samples.
The ~125 K crossover marks the temperature where magnetization drop and lowered anisotropy allow domain effects to reappear.
Low-field zero-field-cooled states incorporate additional real-space Berry curvature and extrinsic scattering terms.
The same contact approach can be applied to other thick ferromagnetic Weyl semimetal crystals without thin-film processing.

Where Pith is reading between the lines

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

The technique may extend to thermal or spin Hall measurements in bulk crystals where domain averaging is also desirable.
Mapping the exact field scale for single-domain formation could guide device geometries that favor intrinsic response.
Temperature-tuned anisotropy changes near 125 K suggest a route to test similar crossovers in related magnetic topological materials.

Load-bearing premise

The chosen contact geometry produces depth-distributed current that isolates the intrinsic anomalous Hall conductivity without introducing artifacts or changing the underlying domain physics.

What would settle it

If repeating the measurements with conventional surface contacts on the same thick crystal yields the same field-dependent separation or if the extracted high-field AHC still varies strongly with visible surface domain patterns, the isolation claim would fail.

read the original abstract

Decoupling the global Berry-curvature contribution to the anomalous Hall conductivity (AHC) from local domain- and texture-related contributions in bulk ferromagnetic Weyl semimetals is difficult in standard measurements. We address this in a $\sim$670$\mu$m-thick Co$_3$Sn$_2$S$_2$ single crystal using a contact architecture that promotes depth-distributed current flow. We find that the AHC depends on the field-enforced domain state: above $\sim$0.3\,T, a single- or few-domain configuration reveals a momentum-space intrinsic Berry-curvature response, with a crossover near $\sim$125\,K driven by rapid magnetization decrease and reduced magnetic anisotropy. In low-field zero-field-cooled (ZFC) multidomain states, the Hall response is modified by domain physics, with possible real-space Berry curvature and moderate extrinsic contributions. These results demonstrate contact engineering as a practical, non-invasive strategy for separating the momentum-space intrinsic AHC from domain-mediated and extrinsic contributions in thick Weyl semimetal crystals.

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

Contact engineering on thick Co3Sn2S2 crystals isolates intrinsic Berry-curvature AHC from domain effects, but the current distribution assumption needs quantitative checks.

read the letter

The punchline is that contact engineering on a thick crystal of Co3Sn2S2 lets them isolate the intrinsic Berry-curvature anomalous Hall conductivity from domain-mediated contributions. They do this by using a contact architecture that promotes current flow distributed through the depth of the 670 micrometer sample. In the single or few-domain state enforced above 0.3 T, the anomalous Hall conductivity shows the expected momentum-space response. They also report a crossover near 125 K tied to a rapid decrease in magnetization and reduced magnetic anisotropy. In contrast, the low-field zero-field-cooled multidomain state shows modifications from domain physics, possibly including real-space Berry curvature and some extrinsic terms. What the paper does well is demonstrate a non-invasive method to separate these contributions in bulk crystals. This is a step beyond standard measurements where domain effects often mix in. The approach seems straightforward and could be adapted to other materials. The soft spots are around the current distribution assumption. The claim depends on the contacts creating a depth-averaged current that suppresses domain and texture effects without artifacts. However, things like current crowding near the surface contacts or temperature-dependent changes in resistivity anisotropy might produce similar field and temperature dependencies. No finite-element simulations, potential mapping, or thickness variation experiments are described to confirm uniformity or rule out mimics. This part of the argument is the least secure. The rest of the experimental details, from the abstract, appear consistent with their domain-state interpretations, and the circularity burden is low since domains are controlled externally. This paper is for researchers in quantum materials and spintronics who deal with anomalous Hall transport in Weyl semimetals. A reader looking for new experimental techniques to probe intrinsic topological responses would find it relevant. It deserves serious referee attention because the idea has practical value and the observations are specific, even though the current flow modeling could use more work. I would recommend sending this to peer review.

Referee Report

1 major / 1 minor

Summary. The manuscript reports an experimental transport study on a ~670 μm thick Co₃Sn₂S₂ single crystal in which a specific contact architecture is used to promote depth-distributed current flow. The central claim is that this geometry allows separation of the momentum-space intrinsic Berry-curvature anomalous Hall conductivity (AHC) from domain- and texture-mediated contributions: above ~0.3 T the field-enforced single- or few-domain state reveals the intrinsic response, while a crossover near ~125 K is attributed to rapid magnetization decrease and reduced anisotropy; in low-field zero-field-cooled multidomain states the Hall response is modified by domain physics and possible real-space Berry curvature.

Significance. If the geometry-dependent isolation of the intrinsic AHC is robustly demonstrated, the work offers a practical, non-invasive contact-engineering route to disentangle intrinsic and extrinsic/domain contributions in thick bulk Weyl semimetals. The external control of domain state via applied field and the temperature-dependent crossover provide falsifiable signatures that could be tested in other materials. The study is grounded in standard transport measurements rather than post-hoc fitting.

major comments (1)

[Experimental methods / contact geometry description] The central claim rests on the assertion that the chosen contact geometry on the 670 μm crystal produces a depth-averaged current density that suppresses domain-wall and texture contributions above ~0.3 T while preserving the momentum-space intrinsic term. No finite-element current-flow simulation, potential mapping, or thickness-variation control experiment is described to quantify the current uniformity or to rule out artifacts from surface current crowding or temperature-dependent resistivity anisotropy. This assumption is load-bearing for the interpretation of both the field and temperature crossovers.

minor comments (1)

[Abstract and sample characterization] The abstract states the crystal thickness as ~670 μm; the corresponding value and its uncertainty should be stated explicitly in the main text with a reference to the sample-preparation section.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for their positive assessment of its potential significance. We address the major comment below and describe the revisions we will implement to strengthen the presentation of the contact-geometry results.

read point-by-point responses

Referee: [Experimental methods / contact geometry description] The central claim rests on the assertion that the chosen contact geometry on the 670 μm crystal produces a depth-averaged current density that suppresses domain-wall and texture contributions above ~0.3 T while preserving the momentum-space intrinsic term. No finite-element current-flow simulation, potential mapping, or thickness-variation control experiment is described to quantify the current uniformity or to rule out artifacts from surface current crowding or temperature-dependent resistivity anisotropy. This assumption is load-bearing for the interpretation of both the field and temperature crossovers.

Authors: We agree that quantitative validation of the current distribution is important for supporting the central interpretation. The contact architecture was chosen specifically to promote depth-distributed flow in the thick crystal, as described in the Methods. In the revised manuscript we will add finite-element simulations of the current density using the exact sample thickness (~670 μm) and contact positions employed in the experiment. These simulations will quantify the degree of depth averaging, assess possible surface current crowding, and examine the influence of any temperature-dependent resistivity anisotropy. Potential mapping was not performed experimentally, but the simulations will provide a direct computational check on uniformity. Thickness-variation control experiments would require additional high-quality crystals of different thicknesses, which is experimentally demanding and not feasible with the crystals currently available; we will note this limitation explicitly while emphasizing that the observed, reproducible crossovers at ~0.3 T and ~125 K provide internal consistency supporting the separation of intrinsic and domain-mediated contributions. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental interpretation stands on independent measurements

full rationale

This is a purely experimental transport study on a thick Co3Sn2S2 crystal. The central claim—that a specific contact geometry promotes depth-distributed current flow and thereby isolates the momentum-space intrinsic AHC above ~0.3 T—rests on direct Hall resistivity measurements under controlled field and temperature, not on any equation or parameter that is fitted to the same dataset and then re-labeled as a prediction. No self-definitional loops, fitted-input predictions, or load-bearing self-citations appear in the reported chain; domain states are set externally by applied field, and the contact architecture is presented as an empirical design choice rather than a derived necessity. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard condensed-matter assumptions about decomposing AHC into intrinsic and domain contributions plus the experimental premise that depth-distributed current isolates the intrinsic part.

axioms (1)

domain assumption Anomalous Hall conductivity can be separated into momentum-space intrinsic Berry curvature and real-space/domain-mediated contributions.
This decomposition is used to interpret the difference between high-field single-domain and low-field multidomain states.

pith-pipeline@v0.9.0 · 5759 in / 1294 out tokens · 88461 ms · 2026-05-19T13:39:57.155580+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

contact architecture that promotes depth-distributed current flow... above ~0.3 T, a single- or few-domain configuration reveals a momentum-space intrinsic Berry-curvature response

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