{"id":"6a47839c-cc24-4c77-9903-bf21f6ab0dbf","arxiv_id":"2501.06865","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Skyrmions are stabilized at remanence in Re/Co/Pt multilayers via a tilted-field protocol at thickness-dependent angles, and broadband FMR resolves distinct stripe and skyrmion resonant modes.","lead":"This paper reports that magnetic skyrmions, small swirling magnetic textures, can be stabilized in Re/Co/Pt multilayer films at zero magnetic field by first applying a tilted field at a particular angle, and that the needed angle changes with the cobalt layer thickness. It also maps the GHz-frequency magnetic resonances of the stripes and skyrmions, which shift with material parameters, useful for designing magnonic devices.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The remanent bubbles are labeled skyrmions without a direct topological measurement, and the paper's own simulations show the MFM-relevant top half of the stack is non-topological (Q>1), so the stabilization claim is not yet supported.","rationale":"The reader's weakest assumption is also the one I would stress. A round MFM domain is called a skyrmion, but the paper never measures topological charge. The manuscript's own simulations (Micromagnetic simulations; Sup. Fig. SM-5) say the texture is depth-dependent: bottom half Q=1, top half Q>1. Since MFM contrast is dominated by the near-surface stray field, the round contrast in Fig. 2 could be the Q>1 top-half bubbles, not the Q=1 skyrmions. If so, the central statement 'skyrmions can be stabilized without an external magnetic field' is not supported by the experimental data. The FMR mode labels (SKGA, SKC, LFB, HFB) are tied to the same texture assignment, so the dynamic claims inherit the uncertainty. This concern is falsifiable: a synthetic MFM computed from the authors' own Amumax remanent states, or a direct Lorentz/STXM measurement, would settle whether the observed contrast corresponds to Q=1. The abstract/body contradiction about the stabilization-angle trend is real and should be fixed, but it is a secondary typo-level issue compared with the topology question. I do not see the paper's mode-frequency narrative as fatally flawed; the qualitative trends are plausible and supported by self-consistent simulations, although gamma is used as a fitting parameter. The appropriate response is to keep the conditional verdict: add a direct topological characterization or soften the skyrmion claim to 'chiral bubble domains' before publication.","tokens_in":18450,"tokens_out":6015,"duration_ms":65657,"concrete_test":"Compute a synthetic MFM image from the authors' own Amumax relaxed remanent states for sample S2 (and S4) by calculating the stray-field gradient above the top surface from the full 3D magnetization, then compare the simulated contrast of the bottom-half Q=1 skyrmions versus the top-half Q>1 bubbles with the experimental Fig. 2 MFM images. If the experimental contrast is reproduced only when the Q>1 top-half bubbles contribute dominantly, the stabilization claim must be weakened to 'chiral bubble domains'; if the Q=1 bottom-half contribution dominates the synthetic MFM signal, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the round remanent domains imaged by MFM (Fig. 2) are skyrmions stabilized at zero field. The load-bearing assumption is that a round bubble observed in MFM has topological charge Q=1. The paper does not provide a direct topological probe (Lorentz TEM, spin-polarized STXM, or topological Hall effect). This is not merely a missing nice-to-have: the manuscript's own micromagnetic 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)' (Micromagnetic simulations section, Sup. Fig. SM-5). MFM senses the stray field with a strong near-surface weighting, so the round features in Fig. 2 could be the Q>1 bubble textures of the upper layers rather than the Q=1 textures of the lower layers. If so, the abstract's claim that angle-dependent imaging 'confirm[s] that skyrmions can be stabilized without an external magnetic field' is not established by the presented data. The frequency-mode assignment in Figs. 4-5 also rests on the same texture identification, so both the static and dynamic central claims inherit this uncertainty. The abstract/body contradiction about the thickness dependence of the stabilization angle is real but secondary; it concerns the direction of a trend, whereas the topological identification concerns whether the stabilized objects are skyrmions at all.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":18771,"tokens_out":5176,"duration_ms":51342,"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":[{"comment":"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.","section":"Abstract vs. Stabilization of skyrmions at remanence / Summary"},{"comment":"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.","section":"Micromagnetic simulations, cf. Sup. Fig. SM-5"},{"comment":"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.","section":"Micromagnetic simulations (Methods)"},{"comment":"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.","section":"Table 1 vs. Micromagnetic simulations (Methods)"}],"minor_comments":[{"comment":"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.","section":"Dynamic properties"},{"comment":"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.","section":"Methods / LLG equation"},{"comment":"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.","section":"Table 1"},{"comment":"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.","section":"Static magnetic properties"},{"comment":"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.","section":"Discussion / iDMI notation"}],"recommendation":"major_revision","confidential_remarks":"The paper is potentially publishable after a major revision, but the abstract/body contradiction on the stabilization-angle trend and the lack of direct topological identification are serious. The Aex discrepancy between the static DMI analysis and the simulations also needs explicit justification. If these points can be resolved, the study would be a useful contribution to the skyrmion-multilayer literature."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Hi X,\n\nQuick take: this is worth engaging with, but the authors have to fix a couple of load-bearing issues before I'd trust the headline claims. The experimental work is real: a clean thickness series of epitaxial Re/Co/Pt multilayers, with MFM imaging of remanent bubble textures after tilted-field saturation, and VNA-FMR up to 35 GHz showing multiple distinct modes. The observation that zero-field bubble lattices can be stabilized at specific polar angles, with the angle shifting with Co thickness, is a useful data point for device people. The simulations model the full 20-layer stack and are transparent about the fitting: gamma is explicitly a fitting parameter, and Ms, Ku, Aex, and DMI are tuned to match hysteresis loops. That's fine for mode assignment but it makes the quantitative frequency claims calibrated rather than predictive.\n\nThe main soft spot is the topology. The paper repeatedly calls the remanent bubbles 'skyrmions' and the abstract says the imaging 'confirm[s] that skyrmions can be stabilized without an external magnetic field.' But there is no direct topological measurement—no Lorentz TEM, no spin-polarized STXM, no topological Hall effect. More importantly, the paper's own micromagnetic simulations state that in the relaxed remanent states only the bottom half of the stack has Q=1, while the top half is largely non-topological bubbles with chiral kinks (Q>1). MFM senses the stray field with strong near-surface weighting, so the round features in the images could be the top-half bubbles, not the Q=1 textures. The authors need to acknowledge this explicitly and either provide a direct topological probe or soften the language to 'bubble textures' rather than 'skyrmions.' This is not a fatal flaw—zero-field bubble stabilization is interesting even without Q=1—but the current claim overreaches.\n\nThere is also a direct contradiction between the abstract and the body. The abstract says the stabilization angle 'increasing alongside Co thickness.' The body and summary say it decreases from 86° to 0° as Co thickness increases. That's a factual inconsistency every reader will trip on.\n\nMinor issues: quantitative results (damping, iDMI) have no error bars; the manuscript has many typos and inconsistent notations (e.g., 'Dzyaloshinskii-Morya', missing entries in Table 1). These are fixable but shouldn't slip through.\n\nBottom line: the experimental dataset is valuable and the core observations are likely correct in qualitative form. Send it to a serious referee, but the authors need to address the topology claim, fix the abstract, and add uncertainties. I'd cite it once the bubble/skyrmion language is made precise.","headline":"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.","tokens_in":19381,"tokens_out":3114,"would_cite":false,"duration_ms":29714,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["skyrmions","Re/Co/Pt multilayers","interfacial Dzyaloshinskii-Moriya interaction","ferromagnetic resonance","magnonics","magnetic force microscopy","spin-reorientation transition","remanence"],"falsifier":"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.","tokens_in":18254,"feed_emoji":"🧲","tokens_out":12708,"duration_ms":111548,"temperature":0.7,"pith_summary":"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.","feed_headline":"Tilted-field sweep locks skyrmion lattices at remanence","feed_subtitle":"Co thickness sets the tilting angle, and ferromagnetic resonance maps four spin modes tied to the chiral coupling.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"supplies the tilted-field saturation and relaxation protocol for stabilizing magnetic bubble states at remanence in multilayers with strong perpendicular anisotropy.","marker":"[16]"},{"why":"provides the low-frequency and high-frequency skyrmion resonance modes in Ir/Fe/Co/Pt that this paper compares against and extends to Re/Co/Pt.","marker":"[17]"},{"why":"gives the three-mode classification (low-, intermediate-, and high-frequency) used to interpret the FMR spectra and attribute modes to skyrmion edges and cores.","marker":"[18]"},{"why":"documents skyrmion formation in easy-plane anisotropy multilayers with low damping, the regime the thicker Co samples approach.","marker":"[19]"},{"why":"supplies the effective-anisotropy-based method for extracting the effective iDMI strength and the exchange constants used for the Re/Co/Pt multilayers.","marker":"[30]"},{"why":"provides the micromagnetic solver that the paper's simulations build on to reproduce hysteresis loops, skyrmion densities, and mode profiles.","marker":"[34]"},{"why":"demonstrates parallel stripe domains as reconfigurable magnonic systems, which the paper invokes for interpreting domain-wall-localized modes and group velocity.","marker":"[27]"}],"fun_headline_variants":["Tilted remanence traps skyrmions at zero field","Co thickness tunes skyrmion stabilization angle","Four spin modes from skyrmions, bubbles, and stripes","Skyrmions locked at remanence by tilted-field sweep","Thickness tunes skyrmion tilt and spin modes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Tilted remanence traps skyrmions at zero field","Co thickness tunes skyrmion stabilization angle","Four spin modes from skyrmions, bubbles, and stripes","Skyrmions locked at remanence by tilted-field sweep","Thickness tunes skyrmion tilt and spin modes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000873,"raw_usage":{"total_tokens":3844,"prompt_tokens":1074,"completion_tokens":2770,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":690,"completion_tokens_details":{"reasoning_tokens":2689}},"tokens_in":690,"tokens_out":2770,"duration_ms":19818,"temperature":1.0,"reasoning_tokens":2689,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:50:09.930183+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"& Weiler, M","cited_arxiv_id":null,"evidence_quote":"documents skyrmion formation in easy-plane anisotropy multilayers with low damping, the regime the thicker Co samples approach."}],"review_version":1}