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REVIEW 3 major objections 5 minor 61 references

Thermoelectric Fingerprinting of Bloch- and N\'{e}el-type Skyrmions

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A skyrmion's thermoelectric map reveals its Bloch or Néel character.

desk verdict Clean transport model and a suggestive single-skyrmion image, but the experimental fingerprint claim is circular—the same map sets S∥−S⊥ and then uses it to classify the texture. read the letter →

arxiv 2506.21160 v3 pith:5UDSXA7V submitted 2025-06-26 cond-mat.mes-hall

Christopher E. A. Barker , Elias Saugar , Katharina Zeissler , Robert Puttock , Petr Klapetek , Olga Kazakova , Christopher H. Marrows , Oksana Chubykalo-Fesenko
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Craig Barton
This is my paper · ORCID
classification cond-mat.mes-hall PACS 72.20.Pa75.70.-i75.75.-c
keywords scanningthermoelectricmicroscopyskyrmionBlochNéelanomalousNernsteffectplanarspincaloritronicsfingerprinting
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

The paper tries to show that the nanoscale thermoelectric voltage produced when a hot scanning probe touches a magnetic skyrmion carries enough spatial information to tell which kind of skyrmion it is. It combines scanning thermoelectric microscopy of one skyrmion in a platinum/cobalt multilayer with a model that decomposes the signal into anomalous Nernst, planar Nernst, and anisotropic magneto-thermopower contributions. The model predicts that Bloch and Néel skyrmions give different spatial patterns whenever the in-plane Seebeck coefficients are unequal, and the measured pattern is consistent with a Néel-like texture. If true, this turns an ordinary lab-based atomic force microscope into a fast, non-synchrotron tool for characterising skyrmion spin textures and accelerating skyrmion device development.

What carries the argument

The central object is the Seebeck tensor $\mathbf{S}$ that converts a local thermal gradient $\nabla T$ into an electric field $\mathbf{E} = \mathbf{S}\,\nabla T$, built from three thermoelectric effects: the anomalous Nernst effect (transverse field from out-of-plane magnetisation), the planar Nernst effect, and the anisotropic magneto-thermopower, with coefficients $S_N$, $S_\perp$, and $S_\parallel$. The argument works by feeding analytic Bloch and Néel skyrmion spin textures into the voltage integral and comparing the resulting spatial maps. The ratio $S_\perp / S_\parallel$ is the control knob: at $S_\perp / S_\parallel = 1$ the two textures produce identical maps, while away from unity the planar Nernst and anisotropic magneto-thermopower terms create inverted lobe patterns that fingerprint the wall type.

What would settle it

Measure SThEM on a material with independently confirmed Bloch skyrmions, such as a B20 lamella or a two-dimensional ferromagnet, with the wall type verified by Lorentz TEM or MFM, and check whether the measured lobe pattern is inverted relative to a Néel-textured device with the same Seebeck coefficients. If the two look identical even when $S_\perp / S_\parallel \neq 1$, the fingerprinting claim fails.

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Extended reading notes

Core claim

The authors claim that the spatially resolved thermoelectric voltage from a single skyrmion is a convolution of the skyrmion's internal spin texture with the localised thermal gradient from a heated probe, and that this voltage can be used to distinguish Bloch from Néel skyrmions. Through modelling, they show that the anomalous Nernst effect is identical for both textures, while the planar Nernst effect produces an antisymmetric multi-lobe pattern that is inverted between the two types, and the anisotropic magneto-thermopower responds differently because it depends only on the y-component of the in-plane magnetisation. The measured zero-field SThEM image of a single skyrmion shows a Yin–Yang-like response with an additional lower-left lobe, suggesting a Néel-like texture with $S_\parallel - S_\perp \approx 0.25\,\mu\text{V}\,\text{K}^{-1}$, though the authors note that the real skyrmion is not a perfect circle and may deviate from the ideal texture. They also show that the fingerprint disappears when $S_\perp / S_\parallel = 1$, that helicity cannot be determined from SThEM alone because the $m_x m_y$ product is identical for both types, and that combining SThEM with MFM would give both wall type and helicity.

Load-bearing premise

The analytic Bloch and Néel spin textures used in the model are assumed to match the real skyrmion, which in the measurement is not a perfect circle and may be distorted by magnetostatic effects, so the modelled fingerprint might not line up with actual images.

Editorial extensions

If this is right

  • A standard scanning probe microscope can fingerprint individual skyrmions as Bloch or Néel without needing synchrotron or neutron facilities.
  • The same measurement can estimate the relative size of the in-plane Seebeck coefficients from the skyrmion's cross-sectional profile.
  • Combining SThEM with MFM would give both skyrmion type and helicity, enabling fast material screening.
  • The modelled distinguishability sets a material requirement: candidate devices should show a significant $S_\parallel - S_\perp$ difference to make the two textures separable.
  • The technique's roughly 15 nV noise floor means the predicted signals are measurable in realistic multilayer stacks.

Reading between the lines

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

  • Because the planar Nernst lobe pattern is antisymmetric and simply changes sign between Bloch and Néel walls, a reader could train an automated classifier on the model maps to label skyrmion type from raw SThEM images, which the paper does not do.
  • The same Seebeck-tensor framework should extend to other chiral textures such as antiskyrmions, merons, or hybrid Bloch-Néel walls, where the in-plane spin winding differs in predictable ways.
  • The authors' observation that vertical temperature gradients and the spin Seebeck effect were left out suggests insulating skyrmion hosts could give additional texture contrast, since those systems suppress charge currents but not magnon heat transport.
  • If the technique matures, it could serve as an inline metrology step in the skyrmion-device fabrication cycle, replacing destructive or slow magnetic imaging for routine checks.
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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 / 5 minor

Summary. The manuscript reports a scanning thermoelectric microscopy (SThEM) measurement of the local thermoelectric voltage from a single skyrmion in a Pt/Co/Ir multilayer, together with a semi-analytical thermoelectric model. The model decomposes the signal into anomalous Nernst, planar Nernst, and anisotropic magneto-thermopower contributions (Eqs. 1-3), and uses analytic Bloch- and Néel-type spin textures as inputs. Simulated images for the two texture types are shown to differ when the in-plane Seebeck anisotropy S∥ - S⊥ is nonzero, and the measured SThEM image is compared qualitatively with the simulations. The paper concludes that SThEM can fingerprint Bloch and Néel skyrmions. The experimental support consists of a single skyrmion image, an inferred value S∥ - S⊥ ≈ 0.25 µV/K, and a visual match to a Néel-type simulation; no Bloch-type skyrmion was measured.

Significance. If the claimed capability is established, SThEM would be a valuable, lab-based addition to the suite of nanoscale spin-texture probes, particularly because the signal decomposition is physically clean: the texture-discriminating contribution is explicitly traced to the m_x m_y term in Eq. (3b), and the model makes a falsifiable prediction that Bloch and Néel responses become identical when S∥ = S⊥. The stated noise floor of ≈15 nV indicates useful sensitivity. However, the central claim currently rests on a single qualitative comparison and on a Seebeck-anisotropy value inferred from the same image used for classification. The distinction between a model prediction and a demonstrated experimental capability is not yet resolved, so the significance is conditional pending a proper positive control or independent parameter determination.

major comments (3)
  1. [Qualitative comparison paragraph (Fig. 1(d); Fig. 4)] The classification of the measured skyrmion as Néel-like is circular. The text states that the Yin-Yang-like shape and the lower-left lobe suggest a Néel-like texture with S∥ - S⊥ ≈ 0.25 µV/K, but that value is inferred from the same experimental image that is then used to identify the texture. Since Eqs. (3b) and (3c) show that the only texture-discriminating contributions (PNE and AMTP) are proportional to S∥ - S⊥, and Fig. 2(b)(iii)/(d)(iii) shows that the Bloch and Néel simulations coincide when S∥ = S⊥, the experimental image cannot simultaneously determine the anisotropy and validate the discriminator. An independent measurement of S⊥ and S∥ on this stack, or a positive control on a known Bloch-skyrmion host, is required to break this circularity.
  2. [Fig. 4 and final discussion paragraph] The paper has no positive control for the fingerprinting claim: no Bloch-type skyrmion was measured, and Fig. 4 explicitly shows a continuum of mixed Bloch-Néel responses parameterized by x. With only one skyrmion and a qualitative visual match, the 2D voltage map does not uniquely determine the texture without additional input. The final discussion also concedes that helicity cannot be determined from SThEM alone. The claim that SThEM can 'fingerprint skyrmion types, Bloch and Néel' should therefore be reframed as a model prediction with a consistency check, or supported by a measurement on a known Bloch host using the same pipeline.
  3. [Model inputs (analytic spin textures from refs. 28 and 40)] The model's predictive power depends on the analytic spin textures faithfully representing the measured skyrmion. The authors note that the measured skyrmion is not a perfect circle and that magnetostatic contributions in multilayers can distort the texture, yet no quantitative fit metric or uncertainty analysis is provided for the comparison between the simulated and measured voltage maps. Because the PNE/AMTP signatures in Eqs. (3b)-(3c) depend on the local m_x m_y distribution, a distorted texture could plausibly mimic a different wall type, weakening the conclusion that the observed lobe pattern uniquely identifies a Néel-like texture.
minor comments (5)
  1. [Throughout] There are several typographical errors, including 'Dzyaloshinskii–Moryia' (should be Moriya), 'skymrion' in the concluding paragraph, 'optolithogrpahy', 'the the local', and 'such at those found'. A careful proofreading pass is recommended.
  2. [Introduction, first paragraph] The phrase 'Yin–Yangesque' is informal and not precisely defined; consider replacing it with a more quantitative description of the lobe pattern.
  3. [Equation (3a) area] The sentence 'S N it the anomalous Nernst Seebeck coefficient' contains a typo and should read 'S N is the anomalous Nernst Seebeck coefficient'.
  4. [Figure 1 caption] The caption states that line profiles are 'averaged' but does not specify how many profiles were averaged or over what region; adding this detail would improve reproducibility.
  5. [Data Availability statement] The data availability statement ends with an ellipsis and does not provide a working repository link; it should be completed before publication.

Circularity Check

1 steps flagged · score 4.0 of 10

The Bloch/Néel fingerprint model is a physically independent forward calculation, but the experimental 'Néel-like' classification is partially self-consistent: S∥−S⊥ is inferred from the same SThEM image used to assign the texture.

  1. fitted input called prediction [Qualitative comparison of model and experiment, discussion of Fig. 1(d) and Fig. 2, after Eqns. (3a)-(3c) (unnumbered section, pp. 9-10).]
    "TheYin–Yangesque nature of the skyrmion and the lower left (red) lobe in Fig. 1(d) suggests a Néel–like texture where S∥ −S⊥ is≈0.25µV·K−1."

    The same measured image is used both to determine the Seebeck anisotropy (S∥−S⊥ ≈ 0.25 µV/K) and to classify the skyrmion as Néel-like. In the model, the discriminating PNE term (Eq. 3b) is proportional to (S∥−S⊥)mxmy, and the paper notes that when S∥=S⊥ the Bloch and Néel images are identical (Fig. 2(iii)). Thus the visibility and sign of the texture-specific signal are jointly set by the parameter extracted from the very image being classified. The image is therefore not an independent test of the fingerprint; it is consistent with the model by construction. The paper does note the conclusion is uncertain and proposes an alternative anisotropy-based explanation, softening the claim, but the experimental fingerprint is still a fit rather than a validated discrimination.

full rationale

The core forward model (Eqs. 1-3) is not circular: it computes thermoelectric voltages from the Seebeck tensor and specified spin textures, and the Bloch/Néel difference follows from the in-plane magnetization products in Eq. 3b. That is a legitimate model prediction, though it is not empirically validated because no Bloch skyrmion was measured under the same pipeline. The principal circularity is narrower: the only quantitative experimental conclusion about texture type rests on an anisotropy value read from the same SThEM image used to support the Néel assignment, so the agreement between measurement and simulation is partially self-consistent. Self-citations (e.g., ref. 48 for S_N and the thermal profile) are not load-bearing for the Bloch/Néel distinction, which depends on S∥−S⊥, and the paper supports its chosen range with external measurements and ab initio calculations. The manuscript also explicitly acknowledges the difficulty of absolute certainty and the inability to determine helicity, which reduces the force of the fingerprinting claim. Overall, the central derivation has independent content, but one experimental classification is fitted rather than independently predicted, giving a moderate circularity score.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on five free parameters (Seebeck coefficients, tip temperature, and texture profile parameters) and several domain assumptions about the thermal gradient and the fidelity of analytic spin textures. No new physical entities are introduced.

free parameters (5)
  • S_N (anomalous Nernst Seebeck coefficient) = 0.2 µV/K
    Fixed from prior work (Puttock et al. 2022, ref 48) rather than measured on this sample; enters the ANE contribution in Eqn. 3a.
  • S_parallel (in-plane Seebeck coefficient parallel to magnetization) = -1.0 µV/K
    Chosen for the simulations; not measured on this sample.
  • S_perpendicular (in-plane Seebeck coefficient perpendicular to magnetization) = varied -0.5, -0.75, -1.0 µV/K; inferred S_parallel - S_perpendicular ≈ 0.25 µV/K
    The simulations scan this value, and the experimental comparison is used to infer S_parallel - S_perpendicular ≈ 0.25 µV/K, so the inference is a fit to the data.
  • Tip-sample contact temperature = ≈327 K
    Assumed from previous work (ref 48); sets the magnitude of the thermal gradient and hence the voltage scale.
  • Skyrmion radius and profile parameters = not specified explicitly
    The analytic spin textures follow refs 28 and 40; parameters such as radius affect the spatial extent of the simulated response but are not listed in the text.
assumptions (6)
  • domain assumption The Seebeck tensor with scalar coefficients S_perp, S_parallel, S_N fully describes the thermoelectric response (Eqn. 1).
    Invoked in Eqn. 1 and 2; assumes no additional effects such as spin Seebeck or vertical-gradient contributions in the analysis.
  • domain assumption Only in-plane thermal gradients contribute; vertical temperature differences are negligible because the film is thin.
    Stated in the text: 'we have included only thermoelectric responses that results from in plane thermal gradients and discounted those occurring from vertical temperature differences due to the small thickness of our sample'.
  • domain assumption The magnetic system is approximated as a single magnetic layer with analytically defined spin textures.
    Stated in the model description; ignores the three-trilayer structure and any interlayer coupling or magnetostatic distortion.
  • domain assumption The measured object is a skyrmion of the assumed type, and the multilayer stack stabilizes Néel-type skyrmions.
    Relies on prior studies (refs 18, 52, 53) that the stack hosts Néel skyrmions; the MFM image confirms a circular feature but not the helicity.
  • domain assumption The tip-sample temperature is ≈327 K as assumed from previous work.
    Used in the thermal modeling; not independently measured here.
  • standard math The PNE and AMTP expressions are valid for arbitrary magnetization direction via rotation operations.
    Standard derivation from the Seebeck tensor rotation; used to obtain Eqns. 2 and 3.

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Cite this review

Pith. "Pith review of Thermoelectric Fingerprinting of Bloch- and N\'{e}el-type Skyrmions." pith.science (2026). https://pith.science/paper/5UDSXA7V

@misc{pith2026250621160,
  author       = {Pith},
  title        = {Pith review of: Thermoelectric Fingerprinting of Bloch- and N\'eel-type Skyrmions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5UDSXA7V}},
  note         = {Machine review of arXiv:2506.21160}
}
read the original abstract

Magnetic skyrmions are nanoscale spin textures that exhibit topological stability, which, along with novel thermal and electrical transport properties, make them the ideal candidates for a variety of novel technological applications. Accessing the skyrmion spin texture at the nanoscale and understanding its interaction with local thermal gradients is essential for engineering skyrmion-based transport phenomena. However, direct experimental insight into the local thermoelectric response of single skyrmions remains limited. To address this, we employ scanning thermoelectric microscopy~(SThEM) to probe the nanoscale thermoelectric response from a single skyrmion. By mapping the local thermoelectric voltage with nanoscale precision, we reveal a unique spatially resolved response that is the convolution of the underlying spin texture of the skyrmion and its interaction with the highly localised thermal gradient originating from the heated probe. We combine this with thermoelectric modelling of a range of skyrmion spin textures to reveal unique thermoelectric responses and allow the possibility of SThEM to be used as a tool to distinguish nanoscale spin textures. These findings provide fundamental insights into the interaction of topologically protected spin textures with local thermal gradients and the resultant spin transport. We demonstrate a novel route to characterise nanoscale spin textures, accelerating the material optimisation cycle, while also opening the possibility to harness skyrmions for spin caloritronics.

Figures

Figures reproduced from arXiv: 2506.21160 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Conceptual overview of scanning thermoelectric microscopy, showing schematic representation [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Shows modelling of the thermoelectric response of a single skyrmion. (a) shows the analytically [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Individual components of the thermoelectric response from (a) Néel and (b) Bloch skyrmion spin [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Combined Bloch and Néel thermoelectric response, showing the normalised sum for a varying ratio [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

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