Visualizing Microwave-Driven Dynamics of Antiskyrmions and Surface Skyrmions

Chuhang Liu; Daisuke Nakamura; Kosuke Karube; Myung-Geun Han; Naoto Nagaosa; Spencer Reisbick; Wataru Koshibae; Xiuzhen Yu; Yasujiro Taguchi; Yimei Zhu

REVIEW 4 major objections 4 minor 1 references

Visualizing Microwave-Driven Dynamics of Antiskyrmions and Surface Skyrmions

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Microwave-driven antiskyrmion motion can be imaged in real space with picosecond resolution.

desk verdict A solid method demonstration of ultrafast Lorentz TEM for gigahertz spin-texture dynamics, with a believable but under-quantified rotational-sense claim. read the letter →

arxiv 2607.20904 v1 pith:5T7RM73D submitted 2026-07-23 cond-mat.mtrl-sci

Zhuolin Li , Daisuke Nakamura , Spencer Reisbick , Chuhang Liu , Myung-Geun Han , Kosuke Karube , Wataru Koshibae , Naoto Nagaosa

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Yasujiro Taguchi Yimei Zhu Yoshinori Tokura Xiuzhen Yu

This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords antiskyrmionssurfaceskyrmionshybridtopologicalspintexturesultrafastelectronmicroscopyLorentztransmissionmicrowave-drivendynamicsstroboscopicpump-probesecond-harmonicnonlinearresponse

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

This paper aims to show that microwave-driven motion of a topological spin texture can be watched directly in real space rather than inferred only from spectra. Using phase-locked pulses of electrons in a Lorentz transmission electron microscope, the authors image a hybrid antiskyrmion—a central antiskyrmion capped by skyrmions at the surfaces—while a 4 GHz field deforms it. The images reveal that the antiskyrmion area oscillates at the drive frequency and at a second-harmonic component, a sign of nonlinear response, and that the two kinds of core follow different trajectories but rotate in the same counterclockwise sense. Micromagnetic simulations reproduce these features and tie the counterclockwise rotation to the bending of the three-dimensional core along the thickness. If the paper is right, ultrafast electron microscopy becomes a general real-space probe for high-frequency spin dynamics, and core geometry, not topological charge, shapes the rotation.

What carries the argument

The central object is the hybrid antiskyrmion texture: a single spin structure whose interior is an antiskyrmion while the top and bottom surfaces host skyrmions, so that the projected Lorentz image shows a square antiskyrmion boundary plus an inner vortex-like dot. The argument is carried by the phase-locked, laser-free stroboscopic ultrafast electron microscopy measurement, in which the same radio-frequency source both chops the electron beam into 4 GHz (or 5.25 GHz) pulses and drives the sample through a phase shifter and frequency doubler; stepping the phase yields delay-time snapshots with roughly 2.7 ps per degree. The quantitative diagnostic is the signed area $\chi = \frac{1}{2}\oint(x\,dy - y\,dx)$ of each core trajectory, which separates the motion into counterclockwise and clockwise circular components and fixes the net rotational sense. In the layer-resolved simulations, $\chi(z)$ is compared with the topological charge $Q$ and the second derivative of the core cross-section area $d^2S_{\mathrm{core}}/dz^2$; the curvature quantity, not $Q$, marks where the counterclockwise response is enhanced.

What would settle it

Re-run the micromagnetic simulation of the hybrid texture with the surface-skyrmion caps removed, keeping the central antiskyrmion, and compute the Lorentz projection under the same 4 GHz drive; if a comparable inner vortex-like feature still appears and its centroid traces a counterclockwise loop, the paper's identification of that feature with the surface-skyrmion cores is falsified.

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Extended reading notes

Core claim

On its own terms, the paper establishes that a hybrid antiskyrmion texture in (Fe0.63Ni0.3Pd0.07)3P responds to 4 GHz and 5.25 GHz microwaves with measurable, picosecond-scale real-space motion. The enclosed area of the antiskyrmion oscillates at the drive frequency and at its second harmonic, with the fundamental area change carried mainly by the height modulation and the second-harmonic change carried mainly by the width modulation. Tracking the two core features separately, the authors find that the central antiskyrmion core and the surface-skyrmion core trace different orbital shapes yet both rotate counterclockwise. Micromagnetic simulations reproduce the area oscillation, the common rotational sense, and the larger orbital amplitude at 5.25 GHz, and attribute the enhanced counterclockwise response to the local bending of the three-dimensional core iso-surface along the thickness rather than to the topological charge.

Load-bearing premise

The result depends on the assumption that the inner vortex-like contrast seen in Lorentz images is produced by the surface-skyrmion cores and that its centroid follows their motion; if that contrast also contains contributions from the antiskyrmion boundary or from other depths, the claimed surface-skyrmion trajectory would be contaminated.

Editorial extensions

If this is right

The same microwave tone makes the central antiskyrmion and the surface-skyrmion cores rotate counterclockwise, so in a hybrid texture the mutual coupling, not the individual topological charge, sets the rotational sense.
The measured 8 GHz second-harmonic component means a single 4 GHz tone produces frequency-doubled deformation, a nonlinear response that could be used for frequency conversion.
Simulations place resonances near 4.70 and 5.13 GHz, close to the two experimental drive frequencies, so sweeping the drive should expose discrete modes of the individual hybrid texture rather than the higher-frequency crystal modes reported for antiskyrmion arrays.
The layer-resolved signed area tracks $d^2S_{\mathrm{core}}/dz^2$ rather than $Q$, so core-geometry curvature along the thickness is the quantity that controls where strong counterclockwise rotation is generated.

Reading between the lines

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

The authors do not test whether the synchronized counterclockwise sense persists as sample thickness changes; if it does, the common rotation would be a generic property of vertically connected hybrid textures rather than a feature of this specific material.
If three-dimensional imaging with picosecond resolution becomes possible, it should reveal a depth-dependent rotational sense, because the simulations show clockwise components that dephase and partially cancel in projection.
The link between the second-harmonic area response and the width modulation suggests a practical readout: the axis with weaker confinement could be identified by which dimension dominates the frequency-doubled signal.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

What you should know first: this paper's real advance is methodological. It shows that a laser-free, RF-stroboscopic UEM can image microwave-driven magnetic texture dynamics in real space with picosecond time steps. The specific observations for a hybrid antiskyrmion/surface-skyrmion texture — anisotropic area breathing, a second-harmonic response, and distinct core trajectories — are plausible and clearly presented. The simulations are a genuine strength: they use literature parameters, are not fitted to the measured dynamics, and reproduce the key experimental features, including the counterclockwise rotation and the larger response at 5.25 GHz. That is real evidence, not just a story.

The paper does what it claims. The picosecond area changes, the 4 GHz plus 8 GHz structure in the filtered traces, and the qualitative difference between the two core trajectories are all supported by the figures. The second-harmonic component is the most original physical observation, and the correlation with anisotropic confinement is reasonable. The writing is clean, the figures are legible, and the methods section is detailed enough to reproduce the analysis if the data were available.

The soft spots are real but not fatal. The central rotational-sense claim rests entirely on the signed-area metric chi, and there are no error bars, bootstrap intervals, or sensitivity checks on the sign. The stress-test note is fair: with only 2.5 cycles and a bandpass filter, residual noise or filter choice could change the small-amplitude components and potentially flip the sign of chi. The analysis is also performed on a single texture, so there is no demonstration of shot-to-shot or texture-to-texture reproducibility. Separately, the inner vortex-like contrast is identified as the surface-skyrmion projection based on prior work, not re-established here; that identification is reasonable but not airtight. Two smaller issues: the simulation uses a 150 mT static field while the experiment uses 100 mT, and the paper does not comment on the discrepancy; and the raw image series are not deposited, only the custom scripts, which limits independent verification. None of these undermines the qualitative conclusions, but they do mean the rotational-sense claim is conditional rather than settled.

Who gets value from this: experimentalists working on UEM or Lorentz TEM, and the topological-spin-texture community. The paper deserves a serious referee. I would send it out, with instructions to the authors to add uncertainty on the signed-area metric, analyze more than one texture if possible, address the static-field discrepancy, and make at least a representative raw data sequence available.

My recommendation: engage with it; the method result is likely to be cited, and the physical claims are strengthenable rather than wrong.

Referee Report

4 major / 4 minor

Summary. The paper reports time-resolved Lorentz TEM (UEM) observations of a hybrid antiskyrmion/surface-skyrmion texture in (Fe,Ni,Pd)3P under 4 GHz and 5.25 GHz microwave excitation. Using stroboscopic phase-locked imaging, the authors measure the oscillating area, width, and height of the antiskyrmion and extract fundamental and second-harmonic components. They track the centroid of the antiskyrmion contour and the centroid of the inner vortex-like contrast (attributed to the projected surface-skyrmion cores), and from these trajectories compute a signed area χ (Eq. (2)) to claim that both cores rotate counterclockwise. Micromagnetic simulations (MuMax3) with literature parameters reproduce the area modulation and the counterclockwise rotation, and correlate the z-dependent signed area with the second derivative of the core cross-section area along thickness.

Significance. If the claims hold, this is a significant methodological advance: real-space, picosecond visualization of microwave-driven dynamics of an antiskyrmion and coexisting surface skyrmions, with evidence for a nonlinear (second-harmonic) response and a common rotational sense of distinct topological cores. The combination of experiment and simulation, together with publicly available analysis code, makes the work reproducible. The identification of a geometry-dependent rotational response (correlation with d2S_core/dz^2) provides a concrete, falsifiable hypothesis for future studies. The manuscript also demonstrates the capability of RF-controlled stroboscopic UEM for direct imaging of programmable spin-texture dynamics.

major comments (4)

[Experimental setup / Fig. 2a caption] The stated time calibration is internally inconsistent. For 4 GHz excitation the period is 250 ps, so a phase increment of Δφ = 5° corresponds to 3.47 ps, not 13.9 ps; conversely, 13.9 ps corresponds to 20° at 4 GHz. The text also states 'Δφ = 1° ~ 2.7 ps', which would imply a ~1 GHz reference. Since all time axes, the 4/8 GHz bandpass filter, and the '2.5 cycles' window depend on this calibration, please clarify the reference frequency of the phase shifter, give the correct phase-to-time conversion, and reconcile the number of frames with the claimed 2.5 microwave cycles.
[The core dynamics / Eq. (2) / Fig. 3f] The central claim that both cores rotate counterclockwise rests entirely on the sign of χ computed from bandpass-filtered trajectories containing only the 4 GHz and 8 GHz components, with no uncertainty or sensitivity analysis. The residual covariance envelopes in Fig. 3c-d are not propagated to χ, and only a single texture is analyzed. I request a bootstrap of the raw centroid measurements (or an equivalent resampling) and a stability test of the sign under variations of the filter bandwidth or the number of retained harmonics; if the sign is not robust, the claim should be weakened or presented as tentative.
[The core dynamics / Figs. 3a-b] The inner vortex-like L-TEM contrast is identified as the projected superposition of the surface-skyrmion cores on the basis of refs 28, 40, 41, and its centroid is used to track the surface-skyrmion core. This identification is the experimental basis for the surface-skyrmion trajectory and the common-rotation claim. I ask the authors to re-validate it in this context, for example by quantifying the sensitivity of the white-dot centroid to the segmentation threshold and by comparing the tracked trajectory with the projected surface-skyrmion core position in the simulated L-TEM images.
[Micromagnetic simulation / Fig. 4f] The claim that the z-dependent signed-area profile 'correlates more closely' with d2S_core/dz^2 than with Q is made by visual inspection of a single simulation. I request a quantitative correlation measure (e.g., Pearson or Spearman coefficient over z) and a discussion of how the comparison would be affected by the static-field mismatch (Bs=150 mT in the simulation vs 100 mT in the experiment) and by the simplified isolated-texture geometry.

minor comments (4)

[Eq. (2) and Eq. (3)] The subscripts for the circular components are garbled (e.g., 'Cେେ୛,௡' and 'Cେ୛,௡'); please use 'C_CCW,n' and 'C_CW,n' throughout, and check that the definition of χ_n uses the correct absolute squares.
[Fig. 2e-g] The caption states that the ribbon represents the residual standard-deviation envelope of the amplitudes and phases, but the bar charts show point estimates without explicit error bars; please clarify whether the residual envelope corresponds to a confidence interval for the extracted amplitude and phase values.
[Methods / UEM Data Processing] For the 5.25 GHz dataset, the sentence describing the ~69 nm displacement subtraction should clarify whether this is a constant offset or a time-dependent drift, and how the correction affects the computed χ.
[Fig. 1a caption] The statement 'Δφ = 1° ~ 2.7 ps' conflicts with the 4 GHz excitation; please correct or specify the reference frequency at which this conversion applies (see major comment).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: direct UEM observations, literature-based simulation parameters, and independent prior tomography for the hybrid-structure premise.

full rationale

The experimental derivation chain is self-contained: UEM frames are processed with a custom Python workflow, bandpass-filtered to the 4 GHz fundamental and 8 GHz second harmonic, and the rotational sense is read off from the sign of the signed area chi defined in Eq. (2), which is a measurement reduction rather than a fitted prediction. The micromagnetic simulations use MuMax3 with material parameters taken from prior experimental and theoretical studies (refs 28, 39, 49) and are not fitted to the measured dynamics; the sinc-pulse spectra and ac-field responses are emergent Landau-Lifshitz-Gilbert solutions, so the simulated CCW rotation is not equivalent by construction to the input. The one inherited premise, that the inner vortex-like L-TEM contrast tracks the projected surface-skyrmion cores, is taken from refs 28, 40 and 41, including prior electron-holographic tomography; although some of these references share authors with the present paper, they are externally falsifiable experimental evidence rather than an unverified self-citation, and the paper does not claim to re-derive that structural assignment from its own dynamics. The simulation-validation passage ('The agreement between the simulated and experimental contrast supports the validity of this hybrid structure') is a consistency check, not the load-bearing derivation, because the hybrid structure is independently established by ref. 41. No equation or fitted parameter reduces to the claimed observations, so there is no circular step to report.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The experimental observation rests on the accepted hybrid-structure interpretation of the L-TEM contrast and on the assumption of phase-locked periodic dynamics. The supporting simulations use material parameters from prior literature, a static field of 150 mT that differs from the experimental 100 mT, and a drive amplitude chosen rather than measured. These are stated or visible in the text but are assumptions the reader should weigh.

free parameters (3)

Micromagnetic material parameters (A, Ku, Ms, D, alpha) = A=8.1 pJ/m, Ku=31 kJ/m^3, Ms=417 kA/m, D=0.2 mJ/m^2, alpha=0.03
Taken from prior experimental and theoretical studies; the simulated spectra and dynamics depend on these values, and they are not fitted to the present microwave data.
Static magnetic field Bs in simulation = 150 mT
Chosen to stabilize the hybrid texture in the simulation, whereas the experimental imaging in Fig. 1b was performed at 100 mT. The mismatch is not discussed and may affect the resonance frequency comparison.
AC field amplitude B0 in simulation = 7 mT
Selected for the sinc-pulse and ac-field simulations; it is not derived from the experimental 20 dBm microwave power, so the drive strength is not mapped to the experiment.

assumptions (4)

domain assumption The FNPP lamella hosts a hybrid texture consisting of a central antiskyrmion with Neel-type skyrmions near the top and bottom surfaces, as established by prior electron-holographic tomography and micromagnetic studies.
The interpretation of the inner vortex-like L-TEM contrast as the surface-skyrmion projection relies on this prior structure identification, cited in the introduction and used for core tracking.
domain assumption The phase-locked stroboscopic UEM measurement assumes the microwave-driven dynamics are periodic and repeatable, so that images accumulated over 120 seconds correspond to a fixed phase of the 4 GHz drive.
The method in Fig. 1a and Extended Data Fig. 3 depends on this periodicity; any drift or cycle-to-cycle variation would blur the snapshots and alter the extracted amplitudes.
domain assumption The alternating magnetic field at the sample has both in-plane and out-of-plane components because the lamella is tilted by a few degrees relative to the chip plane.
This justifies the claim that both breathing and gyrotropic modes are accessible; the tilt angle is not precisely characterized.
domain assumption The bandpass filter that retains only the 4 GHz and 8 GHz components is sufficient to represent the true synchronized dynamics; all other components are treated as noise.
The raw traces are filtered to the fundamental and second harmonic before amplitudes, phases, and signed areas are extracted; this assumes no significant higher harmonics or non-synchronized spectral content.

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Cite this review

Pith. "Pith review of Visualizing Microwave-Driven Dynamics of Antiskyrmions and Surface Skyrmions." pith.science (2026). https://pith.science/paper/5T7RM73D

@misc{pith2026260720904,
  author       = {Pith},
  title        = {Pith review of: Visualizing Microwave-Driven Dynamics of Antiskyrmions and Surface Skyrmions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5T7RM73D}},
  note         = {Machine review of arXiv:2607.20904}
}

read the original abstract

Microwaves provide coherent access to low-energy excitations and serve as effective probes of high-frequency spin dynamics in quantum and magnetic systems. For topological spin textures, microwave excitation is expected to generate rich collective responses, yet direct real-space observation of ultrafast dynamics remains limited. Here we use time-resolved Lorentz transmission electron microscopy to visualize microwave-driven dynamics in a hybrid antiskyrmion structure composed of a central antiskyrmion and surface skyrmions. We resolve the picosecond evolution of antiskyrmion area and second-harmonic signals, evidencing nonlinear responses of spin textures under microwave excitations. We track the core motions of the antiskyrmion and surface skyrmions, which follow distinct trajectories while sharing the same rotational sense. Micromagnetic simulations reproduce the key observations and associate the dynamic modes with the spatial modulation of the core profile along the thickness. These achievements establish ultrafast electron microscopy as a powerful real-space approach for probing high-frequency microwave-driven dynamics of topological magnetic solitons.

Figures

Figures reproduced from arXiv: 2607.20904 by the authors.

**Figure 7.** Multiple response peaks are observed, including peaks at 4.7 and 5.13 GHz (details described in Supplementary Note 3), which are close to the experimentally applied frequencies of 4 and 5.25 GHz. For direct comparison with the experimental measurements, sinusoidal ac magnetic fields at 4 GHz and 5.25 GHz were applied to the system with both in-plane and out-of-plane components (see Methods). The time evolution of th… view at source ↗

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Works this paper leans on

1 extracted references · 1 canonical work pages

[1]

1 Zuo, X. et al. Cavity magnomechanics: From classical to quantum. New J. Phys. 26, 031201 (2024). 2 Yao, J. Microwave photonics. J. Lightwave Technol. 27, 314–335 (2009). 3 Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021). 4 Schoelkopf, R. J. & Girvin, S. M. Wiring up quantum syste...

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Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

1 Zuo, X. et al. Cavity magnomechanics: From classical to quantum. New J. Phys. 26, 031201 (2024). 2 Yao, J. Microwave photonics. J. Lightwave Technol. 27, 314–335 (2009). 3 Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021). 4 Schoelkopf, R. J. & Girvin, S. M. Wiring up quantum syste...

work page 2024