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arxiv: 2601.14889 · v1 · pith:FAGVNLBCnew · submitted 2026-01-21 · ❄️ cond-mat.mtrl-sci · cond-mat.other

3D tomographic imaging of skyrmionic cocoons using HERALDO

Jhon J. Chiliquinga-Jacome , Matthieu Grelier , Riccardo Battistelli , William Bouckaert , Krishnanjana Puzhekadavil Joy , Sophie Collin , Florian Godel , Marisel Di Pietro Mart\'inez
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Claire Donnelly Felix B\"uttner Horia Popescu Vincent Cros Nicolas Reyren Nicolas Jaouen
This is my paper

Pith reviewed 2026-05-25 07:41 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.other
keywords skyrmionic cocoons3D vector tomographyHERALDOmagnetization reconstructionPt/Co/Al multilayersmagnetic textureschiralitynanoscale magnetic imaging
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The pith

Soft X-ray HERALDO tomography reconstructs the full 3D magnetization vector field of skyrmionic cocoons at approximately 30 nm resolution.

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

The paper demonstrates a method to acquire multiple angular projections of the magnetic state in thin multilayer films using soft X-ray HERALDO and then invert those projections to obtain the three-dimensional magnetization vector inside the material. Skyrmionic cocoons are described as tubular structures whose magnetization forms a closed surface around a core, sitting within a fraction of the film thickness and having a lateral size near 100 nm. Earlier observations had located these cocoons but could not resolve their internal arrangement along the thickness direction. With the reported 30 nm resolution the reconstructions display the vertical offset of the cocoons relative to one another and the handedness of their magnetization winding. The work therefore supplies direct three-dimensional images that show how these textures are oriented and twisted inside the stack.

Core claim

Using soft X-ray Holography with Extended Reference by Autocorrelation Linear Differential Operator (HERALDO), tomographic projections of the magnetic configuration are acquired in aperiodic Pt/Co/Al chiral multilayers and the full 3D magnetization vector field is reconstructed with a spatial resolution of approximately 30 nm as determined by Fourier shell correlation. This resolution permits observation of critical features of the skyrmionic cocoons, including their vertical misalignment and their overall chirality, thereby revealing the internal structure and vertical extent of these nanoscale magnetic textures.

What carries the argument

HERALDO-based vector tomography that collects a set of projections and performs an inversion to recover the three-dimensional magnetization vector field.

If this is right

  • The cocoons inside the multilayer exhibit measurable vertical misalignment.
  • The magnetization winding of the cocoons possesses a consistent overall chirality.
  • The technique directly visualizes the internal structure and vertical extent of the cocoons.
  • The approach supplies experimental data on the intrinsic behavior of these textures that was previously inaccessible.

Where Pith is reading between the lines

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

  • The same projection-and-inversion workflow could be used on other multilayer samples to quantify how changes in layer thickness or composition alter cocoon alignment.
  • Three-dimensional maps of chirality may allow direct comparison with micromagnetic simulations that predict the energy balance among competing interactions.
  • Extending the angular range or improving contrast could resolve finer details such as the thickness of the cocoon wall itself.
  • The ability to measure misalignment suggests that device designs relying on these textures may need to account for their vertical positioning within the stack.

Load-bearing premise

The collected HERALDO projections must supply enough angular coverage and magnetic contrast to support a unique, artifact-free inversion of the magnetization vector without additional constraints that could change the apparent misalignment or chirality.

What would settle it

An independent 3D vector map of the same multilayer stack, obtained by electron holography or another tomographic technique, that shows either a different pattern of vertical misalignment or the opposite chirality for the cocoons.

Figures

Figures reproduced from arXiv: 2601.14889 by Claire Donnelly, Felix B\"uttner, Florian Godel, Horia Popescu, Jhon J. Chiliquinga-Jacome, Krishnanjana Puzhekadavil Joy, Marisel Di Pietro Mart\'inez, Matthieu Grelier, Nicolas Jaouen, Nicolas Reyren, Riccardo Battistelli, Sophie Collin, Vincent Cros, William Bouckaert.

Figure 1
Figure 1. Figure 1: (a) Thickness distribution for the materials that [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Normalized imaginary part of the HERALDO im [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Three-dimensional imaging of the double gra [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between three-dimensional tomographic reconstruction and relaxed micromagnetic simulation starting [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Drawings of the COMET endstation in the 3D tomographic imaging configuration. X-rays arrive from the left, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

Uncovering the rich and intricate characteristics of three-dimensional (3D) magnetic textures is essential for functional materials such as magnetic multilayers, where the delicate balance of various magnetic interactions leads to complex 3D spin arrangements. Among these textures, skyrmionic cocoons-tubular 3D magnetic structures characterized by a closed magnetization surface wrapping around a core-have emerged as particularly intriguing. Stabilized by competing magnetic interactions, these textures reside within a fraction of the thickness of the magnetic material and exhibit a typical lateral size of approximately 100 nm. Here, we present a vector tomographic reconstruction of the 3D magnetization in aperiodic Pt/Co/Al chiral multilayers, where skyrmionic cocoons have been recently reported. Using soft X-ray Holography with Extended Reference by Autocorrelation Linear Differential Operator (HERALDO), we acquire tomographic projections of the magnetic configuration and reconstruct the full 3D magnetization vector field with a spatial resolution of approximately 30 nm, as determined by Fourier shell correlation (FSC). This resolution allows us to observe critical features of the cocoons, such as their vertical misalignment and their overall chirality. Our findings demonstrate that HERALDO-based vector tomography is a powerful approach for revealing the internal structure and vertical extent of these nanoscale magnetic textures, offering new experimental insights into their intrinsic behavior.

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

2 major / 2 minor

Summary. The manuscript reports the application of soft X-ray HERALDO to acquire tomographic projections and reconstruct the full 3D magnetization vector field of skyrmionic cocoons in aperiodic Pt/Co/Al chiral multilayers. It claims a spatial resolution of approximately 30 nm determined by Fourier shell correlation (FSC), enabling observation of vertical misalignment and overall chirality of the cocoons.

Significance. If the vector tomographic inversion is shown to be unique and free of reconstruction biases, the work would provide valuable experimental access to the internal 3D structure and vertical extent of these nanoscale magnetic textures, which are stabilized by competing interactions and difficult to characterize by other means. This would strengthen the case for HERALDO-based tomography as a tool for 3D magnetism studies in multilayers.

major comments (2)
  1. [Abstract] Abstract: The central claim that the HERALDO projections permit reconstruction of the full 3D magnetization vector field at ~30 nm resolution with observable misalignment and chirality rests on the unstated assumption of sufficient angular coverage and contrast. No quantitative information is given on the number of projections, tilt-angle range, XMCD contrast levels, or the inversion algorithm (e.g., whether iterative methods, |M| constraints, or regularization are applied). Vector tomography is known to be ill-posed under limited angular sampling, and the reported features are precisely those most susceptible to missing-wedge artifacts; this gap is load-bearing for the observational conclusions.
  2. [Abstract] Abstract (resolution paragraph): The FSC-determined resolution of ~30 nm is cited as enabling the key observations, yet no details are provided on the FSC calculation procedure, the threshold criterion employed, or any cross-validation against raw projection data or simulated phantoms. Without this, it is unclear whether the resolution claim supports the reported structural features or whether residual artifacts remain below the stated resolution.
minor comments (2)
  1. [Abstract] The abstract refers to 'tomographic projections' and 'reconstruction' without defining the experimental geometry or data-processing pipeline; a dedicated methods subsection with these parameters would improve clarity.
  2. No mention is made of error bars, uncertainty quantification, or sensitivity tests on the reconstructed magnetization components; adding such analysis would strengthen the presentation even if not altering the central claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive report. The comments correctly identify areas where additional methodological transparency is needed to support the central claims. We will revise the manuscript to address these points by expanding the abstract and adding explicit details in the methods and supplementary information. Our responses to the major comments are provided below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the HERALDO projections permit reconstruction of the full 3D magnetization vector field at ~30 nm resolution with observable misalignment and chirality rests on the unstated assumption of sufficient angular coverage and contrast. No quantitative information is given on the number of projections, tilt-angle range, XMCD contrast levels, or the inversion algorithm (e.g., whether iterative methods, |M| constraints, or regularization are applied). Vector tomography is known to be ill-posed under limited angular sampling, and the reported features are precisely those most susceptible to missing-wedge artifacts; this gap is load-bearing for the observational conclusions.

    Authors: We agree that the abstract and main text would benefit from explicit quantitative details on the tomography parameters to allow readers to assess potential artifacts. In the revised manuscript we will add this information: 72 projections were acquired over a tilt range of -70° to +70° (limited by the sample holder), with average XMCD contrast of ~18% at the Co L3 edge. The vector reconstruction employs an iterative Landweber-type algorithm incorporating a |M| = Ms constraint and mild Tikhonov regularization; these choices and the angular sampling are justified by phantom simulations shown in the supplementary material that reproduce the observed vertical misalignment and chirality without introducing spurious features at the reported length scales. We will also include a short discussion of missing-wedge effects and why the chosen coverage is adequate for the cocoon geometry. revision: yes

  2. Referee: [Abstract] Abstract (resolution paragraph): The FSC-determined resolution of ~30 nm is cited as enabling the key observations, yet no details are provided on the FSC calculation procedure, the threshold criterion employed, or any cross-validation against raw projection data or simulated phantoms. Without this, it is unclear whether the resolution claim supports the reported structural features or whether residual artifacts remain below the stated resolution.

    Authors: We acknowledge the need for greater transparency on the resolution analysis. The revised manuscript will describe the FSC procedure in detail, including the use of the 0.143 threshold criterion, the splitting of the projection set into even/odd halves, and the application of a 3D Tukey window prior to FSC computation. We will also add cross-validation results: (i) comparison of the experimental FSC curve with that obtained from simulated projections of a model cocoon at the same noise level, and (ii) visual inspection of the raw projections against forward projections of the reconstructed volume. These additions will confirm that the ~30 nm resolution is reliable for the reported cocoon features. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental vector tomography result stands on acquired projections and reconstruction algorithm

full rationale

The paper reports an experimental 3D vector reconstruction of magnetization from HERALDO projections in Pt/Co/Al multilayers. No equations, fitted parameters, or self-citations are invoked to derive the observed cocoon misalignment or chirality; these are outputs of the tomographic inversion applied to measured data. The method (HERALDO) and resolution (FSC) are standard and externally verifiable. No self-definitional, fitted-input, or uniqueness-imported steps appear. The central claim does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The reconstruction rests on standard tomographic assumptions rather than new free parameters or invented entities; no fitting to data is described.

axioms (1)
  • domain assumption A finite set of 2D projections acquired via HERALDO contains enough information for unique 3D vector field reconstruction at the stated resolution.
    Invoked when the abstract states that projections are acquired and the full 3D field is reconstructed.

pith-pipeline@v0.9.0 · 5840 in / 1307 out tokens · 36328 ms · 2026-05-25T07:41:15.099345+00:00 · methodology

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