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REVIEW 4 major objections 5 minor 3 references

Angle-dependent resonant dynamics of stripes and skyrmions in Re/Co/Pt multilayers

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A tilted-field saturation protocol stabilizes zero-field skyrmion lattices in Re/Co/Pt multilayers, with the stabilization angle set by Co thickness and the resonant spectrum tied to interfacial Dzyaloshinskii-Moriya interaction.

desk verdict Solid experimental core—systematic remanence-stabilization angles and FMR modes in Re/Co/Pt—but the skyrmion claim lacks direct topological support and the abstract contradicts the body on the thickness trend. read the letter →

arxiv 2501.06865 v1 pith:JHIFKAFF submitted 2025-01-12 cond-mat.mtrl-sci

Sukanta Kumar Jena , Kilian Lenz , Mateusz Zelent , Mathieu Moalic , Artem Lynnyk , Aleksiej Pietruczik , Pawe{l} Aleszkiewicz , Ewelina Milińska
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Jürgen Lindner Andrzej Wawro
This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords skyrmionsRe/Co/PtmultilayersinterfacialDzyaloshinskii-Moriyainteractionferromagneticresonancemagnonicsmagneticforcemicroscopyspin-reorientationtransitionremanence
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 reports a recipe for holding skyrmion lattices in [Re/Co/Pt]20 multilayers with no external magnetic field: saturate the sample under a static field tilted at a particular polar angle, then lower the field to zero, and the material remains in a dense pattern of circular magnetic bubbles. The angle required for this zero-field stabilization, according to the body text, starts near 86° for the 8 Å Co sample and moves toward 0° as Co thickness grows to 24 Å, tracking the spin-reorientation transition from out-of-plane to in-plane anisotropy. The paper also maps the dynamics of these textures with broadband ferromagnetic resonance, resolving up to four resonant modes whose frequency ranges narrow as the interfacial Dzyaloshinskii-Moriya interaction weakens with increasing Co thickness, and it reports that the effective Gilbert damping falls as Co thickens. These results matter because zero-field skyrmion stability and tunable GHz-frequency resonances are the two ingredients needed for racetrack memory and magnonic devices, where a bias magnet or continuous energy input would otherwise be required.

What carries the argument

The central mechanism is the tilted-field remanence protocol: the sample is saturated along a chosen polar angle, and when the field is reduced to zero the balance between the perpendicular field component, the demagnetizing energy, and the effective anisotropy leaves bubble textures frozen in place. The knob that tunes this balance is the Co thickness, which drives the effective anisotropy through zero and simultaneously lowers the effective interfacial Dzyaloshinskii-Moriya interaction (iDMI), the interface-induced antisymmetric exchange that gives the bubbles their chirality. The dynamic analysis rests on named resonant modes resolved by broadband ferromagnetic resonance and reproduced in micromagnetic simulations of the complete multilayer stack: the Kittel uniform mode (KM), low-, intermediate-, and high-frequency modes (LF, IF, HF), and a zero-field mode (ZF), with simulation counterparts SKGA (skyrmion edge), LFB/HFB (bulk around and between bubbles), H0DE (zero-field domain edge), and LFDV/HFDV (domain-wall and domain-volume modes). The decisive step is matching each measured resonance branch to a specific magnetic texture and its amplitude profile across the 20 magnetic layers.

What would settle it

Image the remanent bubble states produced by the tilted-field protocol (for example 86° for 8 Å Co and 30° for 16 Å Co) with spin-polarized scanning transmission X-ray microscopy and compute the topological charge of individual bubbles; if most imaged bubbles do not carry charge $\pm 1$, the zero-field skyrmion stabilization claim fails.

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Extended reading notes

Core claim

The paper claims that angle-dependent saturation plus relaxation to remanence can stabilize skyrmion lattices in epitaxial [Re(10 Å)/Co(dCo)/Pt(10 Å)]20 multilayers across a wide range of effective anisotropy, from out-of-plane easy axis at dCo = 8 Å to in-plane easy axis at 24 Å. The stabilization angle decreases with Co thickness: roughly 86° for 8 Å, 78° for 10 Å, 30° for 16 Å, and close to 0° for 20–24 Å, with the highest skyrmion density observed in the thinnest Co sample. Ferromagnetic resonance from 0.1 to 35 GHz reveals a Kittel uniform mode plus up to three texture-induced modes, and micromagnetic simulations of the full 20-layer stack reproduce the measured spectra and assign each branch to a layer-resolved excitation of skyrmions, chiral bubbles, or stripe domains. The paper concludes from these data that the frequency span of the resonant modes narrows as the effective iDMI decreases with Co thickness, and that the effective damping is lower for thicker Co layers, linking the static stabilization angle, the dynamic mode spectrum, and the material parameters in a single system.

Load-bearing premise

The load-bearing assumption is that the circular domains seen in the magnetic force microscopy at remanence are topologically nontrivial skyrmions; the paper's own simulations (Supplementary Fig. SM-5) find that only the bottom half of the stack has winding number 1 while the top half consists of non-topological bubbles with chiral kinks, and no direct measurement of the topological charge is offered, so if the imaged bubbles are not $Q=1$ skyrmions the central stabilization claim fails.

Editorial extensions

If this is right

  • Zero-field skyrmion lattices can be produced at room temperature in a heavy-metal/Co multilayer by saturating along the correct polar angle first, without needing current pulses or a simultaneous in-plane plus out-of-plane bias.
  • The same protocol works on both sides of the spin-reorientation transition: samples with out-of-plane anisotropy need a nearly in-plane saturation field, while samples with in-plane anisotropy need a nearly perpendicular one.
  • Choosing the Co thickness sets the operating band of a magnonic device because thicker Co lowers the effective iDMI and narrows the frequency range of the texture modes.
  • Thicker Co layers also give lower effective Gilbert damping, meaning faster and less dissipative magnetization dynamics in an otherwise identical stack.
  • The zero-field mode and the frequency band gap between domain-wall and domain-volume modes provide a measurable route to the magnon group velocity in stripe-based waveguides.

Reading between the lines

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

  • If the imaged bubbles are indeed skyrmions, the stabilization recipe should transfer to other heavy-metal/ferromagnet multilayers whenever the effective anisotropy and iDMI are known, so the stabilization angle could be predicted rather than scanned; the paper's own density maps suggest the yield is largest near the saturation field, which could become a design heuristic.
  • The abstract and the body disagree on the direction of the thickness trend for the stabilization angle (abstract says it increases with Co thickness, the body and Fig. 3 show it decreasing from 86° to near 0°), an inconsistency that should be resolved before the trend is used quantitatively.
  • The paper does not directly measure the topological charge of the remanent bubbles; if the non-topological top-half textures dominate the MFM signal, the stabilized objects would still be useful zero-field bubble lattices but would not support skyrmion-specific topological protection.
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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

4 major / 5 minor

Summary. The manuscript reports static and dynamic studies of epitaxial [Re(10 Å)/Co(dCo)/Pt(10 Å)]20 multilayers with Co thicknesses from 8 to 24 Å. SQUID magnetometry characterizes the anisotropy crossover; MFM shows field-driven evolution from labyrinth domains to bubble/skyrmion states and remanent bubble states after cycling tilted magnetic fields; and VNA-FMR reveals multiple resonant modes in out-of-plane, in-plane, and tilted configurations. Micromagnetic simulations with the authors' Amumax code reproduce hysteresis loops, skyrmion density maps, and mode profiles for samples S2 and S4. The central claims are that zero-field skyrmion stabilization is achieved at specific polar angles, that the stabilization angle varies with Co thickness, that the mode frequencies and iDMI strength decrease with increasing Co thickness, and that Gilbert damping decreases with Co thickness.

Significance. If the central claims hold, the paper offers a useful materials-level demonstration of remanent skyrmion stabilization in Re/Co/Pt multilayers and a systematic FMR mode map across a spin-reorientation transition. The direct MFM and VNA-FMR data over six thicknesses are valuable, and the full-stack simulations with periodic boundary conditions, plus the publicly cited Amumax code, are a real strength. However, the significance is currently tempered by two load-bearing issues: the abstract/body contradiction on the thickness trend of the stabilization angle, and the absence of direct topological evidence that the imaged remanent bubbles are Q=1 skyrmions. The quantitative dynamic interpretation also depends on simulation parameters that are fitted to the same experimental data, so the simulated mode assignments should be presented as supportive rather than as independent confirmation.

major comments (4)
  1. [Abstract vs. Stabilization of skyrmions at remanence / Summary] The abstract states that skyrmions are stabilized 'with the stabilization angle increasing alongside Co thickness,' but the body states the opposite: 'with increasing the Co thickness, the angle for skyrmion stabilization decreases from θ=86° to θ=0° for sample S5,' and the Summary says the stabilization angle 'shifts towards the lower angle (θ ≈ 0°).' Since the thickness dependence of the stabilization angle is a central quantitative claim of the paper, this contradiction must be resolved in revision; the abstract should be corrected to agree with the figures and body text.
  2. [Micromagnetic simulations, cf. Sup. Fig. SM-5] The identification of the remanent MFM bubbles as skyrmions is not directly established. The manuscript's own simulations state that in the relaxed remanent states 'the skyrmions in the bottom half of the stack remain topological (Q=1), while the top half comprises largely non-topological bubbles, with multiple chiral kinks (Q>1).' Because MFM senses the stray field with a strong near-surface weighting, the round features in Fig. 2 may correspond to the Q>1 upper-layer textures rather than the Q=1 lower-layer textures. The central claim that angle-dependent imaging confirms zero-field skyrmion stabilization therefore requires direct topological evidence (e.g., Lorentz TEM or spin-polarized STXM), or the claim must be substantially softened to refer to chiral bubble states.
  3. [Micromagnetic simulations (Methods)] The dynamic simulations use the gyromagnetic ratio as a fitting parameter 'reproducing closely the KM mode frequencies,' and the parameters Ms, Ku, Aex, and DMI are fine-tuned to reproduce the experimental hysteresis loops. Consequently, the simulated mode frequencies and mode assignments are not independent validation of the experimental mode identification. The manuscript should state which parameters were fixed a priori and which were adjusted, and should quantify how sensitive the simulated spectra are to the fitted parameters, particularly γ.
  4. [Table 1 vs. Micromagnetic simulations (Methods)] There is an unexplained order-of-magnitude discrepancy in the exchange constant: the DMI extraction in the static section uses Aex = 22, 24, and 28 pJ/m for Co thicknesses of 8, 10, and 12 Å, while the simulations for S2 and S4 use Aex = 2 pJ/m and 2.5 pJ/m, respectively. Because both the reported iDMI values and the simulated mode spectra depend on Aex, the authors must justify the two sets of values and explain how they can both be appropriate for the same samples.
minor comments (5)
  1. [Dynamic properties] The text refers to 'Fig. 1(d)' and 'Figs. 2(g)-2(i)' where the FMR plots are actually in Fig. 4; the cross-references should be corrected.
  2. [Methods / LLG equation] The Landau-Lifshitz-Gilbert equation in the Methods section is corrupted by text-conversion artifacts ('d𝑚d𝑡=γµ*1+α-x...'); it must be retyped correctly, and the definition of the topological charge Q used in the simulations should be given explicitly in the main text or Methods.
  3. [Table 1] Table 1 has irregular and incomplete entries (e.g., missing domain-width values for S2 and S3, garbled header text), and the sentence 'Magnetic properties of of the [Re(10 Å)/Co(dCo)/Pt(10 Å)]20 multilayers' contains typos; the table and caption need careful editing.
  4. [Static magnetic properties] The statement that 'the skyrmion bubble density increases significantly with decreasing uniaxial anisotropy energy from 1.69 MJ/m3 to 1.37 MJ/m3' should specify whether effective anisotropy is meant and should clarify the comparison because the applied fields also differ between samples.
  5. [Discussion / iDMI notation] The units and notation for DMI are inconsistent between D_eff (mJ/m2), D_s (pJ/m), and the Discussion quote 'Ds = 2.98 pJ/m'; please harmonize the notation and clearly distinguish effective from surface DMI throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the static and dynamic claims rest on direct MFM/FMR measurements, and the calibrated micromagnetic simulations are used only for qualitative mode assignment.

full rationale

The paper's central results—zero-field remanent bubble stabilization versus polar angle and the FMR mode structure—are direct experimental observations, not outputs of a fitted model. The micromagnetic simulations are explicitly calibrated: parameters are fine-tuned to reproduce the measured hysteresis loops, and the gyromagnetic ratio is fitted to the Kittel mode ('We used the gyromagnetic ratio as a fitting parameter to simulate the spin wave dynamics yielding γ=1.3095 Mrad/Ts reproducing closely the KM mode frequencies'), and the authors concede quantitative frequency shifts relative to experiment. No resonant mode or stabilization angle is claimed to be a prediction forced by that calibration; the simulated spectra are used qualitatively to label experimentally observed modes (SKGA/LFB/HFB, H0DE/LFDV/HFDV). The one potentially relevant self-citation, Salikhov et al. (Ref. 16) for the tilted-field stabilization protocol, is not load-bearing: the present paper supplies its own angle-dependent MFM data. There is, however, a genuine evidence gap rather than circularity: the paper's own simulations state that 'the skyrmions in the bottom half of the stack remain topological (Q=1), while the top half comprises largely non-topological bubbles, with multiple chiral kinks (Q>1)', and MFM's near-surface sensitivity means the remanent bubbles are not directly shown to be Q=1 skyrmions; this weakens the skyrmion claim but is not a reduction of a derivation to its inputs. The abstract/body contradiction about the direction of the thickness dependence of the stabilization angle is likewise a consistency issue, not circularity.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The core experimental observations (MFM images, FMR spectra) are direct measurements. The quantitative extraction of DMI and the mode assignment rest on model assumptions and on simulation parameters fitted to the same experimental data, so the independent evidentiary weight of those derived numbers is limited.

free parameters (6)
  • gyromagnetic ratio (simulation) = 1.3095 Mrad/Ts
    Stated in Methods as 'used the gyromagnetic ratio as a fitting parameter to simulate the spin wave dynamics yielding gamma=1.3095 Mrad/Ts reproducing closely the KM mode frequencies'. This scales all simulated mode frequencies, so the KM match is partly by construction.
  • effective saturation magnetization Ms (simulation) = 1.3374 MA/m
    Fine-tuned to reproduce experimental hysteresis loops for samples S2 and S4; the text says 'fine-tuning these parameters to achieve the closest alignment with the experimental observations'.
  • perpendicular anisotropy Ku (simulation) = 1.756 MJ/m3 (S2), 1.169 MJ/m3 (S4)
    Assigned in simulation and fine-tuned to match the OOP hysteresis loop shape; not independently measured for the simulation.
  • exchange constant Aex (simulation) = 2 pJ/m (S2), 2.5 pJ/m (S4)
    Chosen in simulation methods; these values are close to literature values but are effectively fitted to reproduce experimental domain behavior.
  • interfacial DMI constant D (simulation) = 0.003 J/m2 (S2), 0.00218 J/m2 (S4)
    Used in simulation; the values are within the range of the table's D_eff values but are adjusted as part of the fitting process to match hysteresis and skyrmion densities.
  • exchange constants for DMI extraction = Aex = 22, 24, 28 pJ/m for Co thickness 8, 10, 12 Å
    Taken from literature (refs 30-32) and used in the K_eff method to compute D_eff; these are not measured on the present samples, making the DMI estimate model-dependent.
assumptions (4)
  • domain assumption Bubbles imaged by MFM at remanence are topologically nontrivial skyrmions (Q=1).
    No direct topological measurement is performed in the experiment. The identification relies on image morphology and micromagnetic simulations whose parameters were fitted to reproduce the same experimental samples. The paper's own simulations show a mixed structure across the stack (Q=1 in the bottom half, Q>1 in the top half).
  • domain assumption The K_eff method (Ref. 30) provides a valid estimate of the interfacial DMI strength from domain wall width and literature exchange constants.
    Used to compute D_eff and D_s in Table 1. The method assumes a specific domain wall energy model and that the literature Aex values apply to these epitaxial samples.
  • domain assumption 0 K micromagnetic simulations with fitted parameters can reproduce room-temperature MFM/FMR observations.
    Simulations neglect thermal fluctuations except for a short 320 K anneal during hysteresis relaxation. The fits are judged by qualitative agreement with experimental hysteresis loops, and the simulated FMR modes are shifted relative to experiment.
  • domain assumption The experimental FMR modes can be assigned to specific magnetic textures (labyrinth, stripes, skyrmions) based on comparison with simulated spectra.
    Mode assignments in Figs. 4 and 5 are based on simulated spectra, which are calibrated with fitted gamma and other parameters and show frequency/field shifts relative to experiment. No phase-sensitive or spatially resolved measurement confirms mode localization in the experimental samples.

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Cite this review

Pith. "Pith review of Angle-dependent resonant dynamics of stripes and skyrmions in Re/Co/Pt multilayers." pith.science (2026). https://pith.science/paper/JHIFKAFF

@misc{pith2026250106865,
  author       = {Pith},
  title        = {Pith review of: Angle-dependent resonant dynamics of stripes and skyrmions in Re/Co/Pt multilayers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JHIFKAFF}},
  note         = {Machine review of arXiv:2501.06865}
}
abstract

The dynamic behavior and stabilization of skyrmions in magnetic multilayers are critical for advancing spintronic and magnonic technologies. In our study, we investigate the static and dynamic properties of $[Re/Co(d_{Co})/Pt]_{20}$ multilayers with varying Co thicknesses $(6\text{-}24 \, \text{\r{A}})$, showcasing a transition from out-of-plane to in-plane magnetic anisotropy. Magnetization reversal leads to a transformation from labyrinth domains to skyrmion bubbles due to the interfacial Dzyaloshinskii-Moriya interaction (iDMI). Using angle-dependent imaging at remanence, we confirm that skyrmions can be stabilized without an external magnetic field at specific polar angles, with the stabilization angle increasing alongside Co thickness. Ferromagnetic resonance spectroscopy reveals four distinct resonant modes, including low-frequency $(2\text{-}18\text{GHz})$, high-frequency $(20\text{-}35 \, \text{GHz})$ modes, depending on the magnetization texture. The frequency range of these modes narrows with decreasing effective anisotropy and iDMI strength decreases in thicker Co layers in perpendicular configurations. Moreover, we observe a decrease in effective Gilbert damping with increasing Co thickness, highlighting the potential for efficient energy dissipation. These findings link between material properties and skyrmion dynamics directly and demonstrate tunable resonant modes for magnonic devices. By addressing both static and dynamic aspects, our work advances the development of next-generation spintronic and magnonic applications.

Figures

Figures reproduced from arXiv: 2501.06865 by the authors.

Figure 1
Figure 1. Figure1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 4
Figure 4. (a,-c and g-i) The field-frequency-dependence of the FMR signal (color￾coded) in out-of-plane configuration (𝜃\ = 0°) of samples S1 to S6, respectively. (d-f and j-l) same for the in-plane configuration (𝜃\ = 90°). For the lowest Co thickness of 8 Å (sample S1), we find the KM starting at higher frequencies around f = 25 GHz for the OOP configuration and f = 15 GHz for the IP configuration. Additionally, a high-freq… view at source ↗
Figure 5
Figure 5. (a,b,c) False-color plots of the FMR signals of sample S2 vs. field and frequency for angles 𝜃\ of 0°, 78°, and 90°, respectively. (d,e,f) Corresponding MFM images taken at remanence . (g,h,i) FMR spectra at angles 𝜃\=0°, 30°, and 90° for sample S4, which possesses in-plane anisotropy. (j,k,l) Corresponding MFM images at remanence. Note that the FMR spectra of samples S2 and S4 at 0° and 90°are repeated from [PITH_… view at source ↗
Figures from the paper (3 more)
Figure 6
Figure 6. Figure 6: Hysteresis loops comparing simulation results and experimental measurements (a,b) sample S2 for out-of-plane and in-plane field, respectively. (c,d) same for sample S4 Each panel shows the normalized magnetization (M/Ms) as a function of the applied magnetic field. Pan…
Figure 8
Figure 8. Figure 8: (a-d) Simulated FMR spectra of samples S2 (a,b) and S4 (c,d) as a function of external magnetic field for out-of-plane and in-plane configurations. Green markers indicate the specific field and frequency values corresponding to the visualized magnetization modes shown …
Figure 9
Figure 9. Figure 9: Amplitude distribution across each layer for different Co thicknesses (dCo= 10 Å and 16 Å) and magnetic field orientations, highlighting two selected modes, i.e. the low￾frequency (LF) and high-frequency (HF) mode. Simulations of the S4 system for the IP field configur…

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Works this paper leans on

3 extracted references · 3 canonical work pages

  1. [4]

    Anisotropic Superexchange Interaction and Weak Ferromagnetism

    Moriya, T. Anisotropic Superexchange Interaction and Weak Ferromagnetism. Physical Review 120, 91–98 (1960). 5. Soumyanarayanan, A., Reyren, N., Fert, A. & Panagopoulos, C. Emergent phenomena induced by spin-orbit coupling at surfaces and interfaces. Nature 539, 509–517 (2016). 6. Fert, A., Reyren, N. & Cros, V. Magnetic skyrmions: Advances in physics and...

    work page 1960

  2. [19]

    & Weiler, M

    Flacke, L., Ahrens, V., Mendisch, S., Körber, L., Böttcher, T., Meidinger, E., Yaqoob, M., Müller, M., Liensberger, L., Kákay, A., Becherer, M., Pirro, P., Althammer, M., Geprägs, S., Huebl, H., Gross, R. & Weiler, M. Robust formation of nanoscale magnetic skyrmions in easy-plane anisotropy thin film multilayers with low damping. Physical Review B 104, 15...

    work page 2021

  3. [28]

    M., Choi, Y., Ortega, C

    Lu, Y. M., Choi, Y., Ortega, C. M., Cheng, X. M., Cai, J. W., Huang, S. Y., Sun, L. & Chien, C. L. Pt magnetic polarization on Y3Fe5O12 and magnetotransport characteristics. Physical Review Letters 110, 1–5 (2013). 29. Zhu, L. J., Ralph, D. C. & Buhrman, R. A. Irrelevance of magnetic proximity effect to spin-orbit torques in heavy-metal/ferromagnet bilaye...

    work page 2013

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Reviewed August 10, 2026 · model on record in the stance chip above.