{"id":"70b62c9f-6093-49b6-b031-b10899d16803","arxiv_id":"2509.00517","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"First real-space MFM images reveal the low-temperature skyrmion lattice in bulk Cu2OSeO3(100), its nucleation from the tilted conical state, and its alignment to the crystal lattice by field cycling.","lead":"Magnetic force microscopy at 10 K produced the first direct images of the low-temperature magnetic phases in bulk Cu2OSeO3(100), including a skyrmion lattice that appears as the field is lowered. The images show the lattice nucleating from a tilted conical state and gradually locking to the crystal axes during magnetic annealing.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"FFT-based identification of the skyrmion lattice is undermined by the 60° angular folding: a single-q helical/tilted-conical domain also folds into one peak, so sixfold symmetry in zoomed FFTs does not uniquely establish a triangular skyrmion lattice.","rationale":"The paper's central claim is the first real-space observation of the low-temperature skyrmion lattice in bulk Cu2OSeO3. The supporting evidence in fig. 3 is an FFT analysis: sixfold-symmetric peaks in near-field FFTs and condensation of the folded angular distribution under field cycling. The authors themselves state that direct threshold-based identification of skyrmions in the MFM images is 'at least challenging', which moves the entire evidential weight onto the FFT pipeline described in Supplementary S3. That pipeline averages the FFT modulus over six 60° sectors. A single-q helical or tilted-conical state produces two opposite FFT peaks, separated by 180°, which coincide after 60° folding; hence the folded single-peak distribution observed in fig. 3E does not discriminate between a hexagonal skyrmion lattice and a single-q modulated state. The zoomed FFTs with six peaks (fig. 3C,D) could also arise from a mosaic of three single-q domains with relative angles of 60° within the window; the 5° angular resolution and the absence of a real-space peak/particle detection leave this degeneracy unresolved. This is not an external-consensus disagreement; it is an internal inference gap: the published data do not rule out a tilted-conical/helical interpretation. The discrepancy with the FMR report of a stretched skyrmion lattice reinforces that the phase identification is subtle, but it is not the main issue. Because the low-temperature skyrmion phase is already known from SANS/FMR, the novelty of the paper is precisely the real-space identification; if the sixfold FFT is not uniquely diagnostic, the first-real-space-observation claim is overreached. The proposed synthetic-image test would settle the degeneracy quantitatively. Given the suggestive but non-unique evidence, the appropriate disposition is acceptance conditional on the discriminating analysis, rather than outright rejection.","tokens_in":11396,"tokens_out":7100,"duration_ms":84286,"concrete_test":"Apply the same 60°-folded FFT analysis (Supplementary S3) to synthetic background-subtracted MFM images with the same noise level and window size, generated for (i) a perfect triangular skyrmion lattice with the observed lattice constant and (ii) a texture composed of three tilted-conical/helical domains with wavevectors 60° apart, with relative areas chosen to mimic the experimental domain pattern. If the folded angular distributions and zoomed FFT peak patterns from (ii) are statistically indistinguishable from those from (i) and from the experimental images, then the sixfold FFT signature cannot establish the skyrmion-lattice claim; conversely, if a clear quantitative difference (e.g., peak shape, relative intensities, or phase information) exists, the identification is supported. As a complementary check, compute the 2D autocorrelation of the raw +80 mT images: a triangular skyrmion","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim—first real-space observation of the low-temperature skyrmion lattice—rests on classifying the +80 mT texture as a triangular skyrmion lattice from the sixfold symmetry of FFT peaks (main text, fig. 3). The paper explicitly states that 'the quite fluctuating MFM-signal makes a direct threshold based identification of the skyrmions and direct analysis of the lattice at least challenging' (fig. 3 discussion), so the classification is delegated entirely to the FFT angular analysis. That analysis (Supplementary S3) azimuthally partitions the FFT into six 60° intervals and averages them. This folding is not selective for hexagonal order: a single-q helical or tilted-conical modulation produces two FFT peaks separated by 180°, which map into the same 60° sector after folding. Therefore the reported condensation of spectral weight into a single peak around ⟨100⟩ after field cycling (fig. 3E) is equally consistent with domain alignment of a 1D-modulated tilted-conical/helical state. The zoomed FFTs in fig. 3(C,D) do show six peaks, but a window containing three 1D helical/tilted-conical domains with wavevectors separated by 60° would also produce six peaks. Without a discriminating real-space criterion—resolved individual skyrmions, hexagonal autocorrelation, or a topological measure—the sixfold FFT signature alone does not rule out a multi-domain single-q texture. Since the low-temperature skyrmion phase has already been identified in bulk by SANS/FMR, the claimed real-space observation specifically requires distinguishing the MFM texture from tilted-conical/helical states; the present evidence is necessary but not sufficient.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports magnetic force microscopy (MFM) imaging at 10 K of a bulk Cu2OSeO3(100) single crystal as a function of external magnetic field. The authors identify helical, conical, tilted conical, and skyrmion lattice states, and focus on the low-temperature skyrmion phase stabilized by magnetic field cycling. They observe nucleation and coexistence of tilted conical and skyrmion lattice domains, and claim that prolonged magnetic annealing converts a multidomain skyrmion polycrystal into a long-range-ordered skyrmion lattice locked to the ⟨100⟩ crystal axes. The paper also reports a negative result: no stretched skyrmion lattice is found at low fields, in contrast to an FMR-based report.","tokens_in":11773,"tokens_out":4121,"duration_ms":51681,"significance":"If the identification is sound, this is the first real-space observation of the low-temperature skyrmion phase in bulk Cu2OSeO3, which would be a valuable complement to prior SANS, magnetization, specific heat, and FMR studies. The imaging of nucleation dynamics and the annealing-induced ordering of skyrmion lattice domains would add new information on the metastability and anisotropy-controlled orientation of this phase. The study also usefully documents the absence of a stretched skyrmion lattice in the investigated field range. The supplementary wavelength and orientation analysis is careful and demonstrates cross-sample consistency, with no ad-hoc parameters beyond peripheral fits.","major_comments":[{"comment":"The central claim that the +80 mT texture is a triangular skyrmion lattice rests on the sixfold FFT analysis, but that analysis is not selective for a 2D triangular modulation. The angular procedure partitions the FFT into six 60° intervals and averages them. A single-q helical or tilted-conical domain produces two FFT peaks separated by 180°, which fall into the same folded 60° sector. Therefore the condensation of spectral weight into a single peak around ⟨100⟩ in Fig. 3E is equally consistent with alignment of a 1D-modulated state. The zoomed FFTs in Fig. 3C,D show six peaks, but a window containing three 1D domains with wavevectors separated by 60° would also produce six peaks. Since the authors state that \"the quite fluctuating MFM-signal makes a direct threshold based identification of the skyrmions and direct analysis of the lattice at least challenging,\" the phase label cannot be","section":"Main text, Fig. 3 and Supplementary S3"},{"comment":"Figure 2 is used to support the nucleation scenario and coexistence of tilted conical and skyrmion lattice states. However, the panel labels are not backed by the same FFT or real-space analysis described in Fig. 3. For example, Fig. 2(c) is labeled \"First skyrmions appear\" without specifying the criterion that distinguishes these objects from tilted conical domains or from imaging artefacts. Given the admitted difficulty of direct identification, each phase label in the field-cycling sequence needs an explicit criterion, or a statement that the label is inferred from the field history and the later FFT analysis. This is load-bearing for the nucleation dynamics claim.","section":"Main text, Fig. 2"},{"comment":"The claim that magnetic annealing produces a long-range-ordered skyrmion single crystal locked to the crystal lattice is based on the same folded angular distribution. Even setting aside the folding ambiguity, the measurement of the ~21° rotation between FFT patterns in Fig. 3C,D uses an angular resolution that is stated only in Supplementary S4 as about 5°. The main text should state this resolution when interpreting the angular shift, and the annealing result should be supported by a real-space correlation length or an explicit measure of lattice orientational order, rather than only spectral weight in a folded histogram.","section":"Main text, Fig. 3E and Supplementary S4"}],"minor_comments":[{"comment":"Numerous typos and grammatical errors should be corrected: \"proofed\" -> \"proved/proven\", \"skrmion\" -> \"skyrmion\", \"Evenso\" -> \"Even so\", \"intercepted\" -> \"interspersed\", \"suszeptibility\" -> \"susceptibility\", \"appraoch\" -> \"approach\".","section":"Throughout"},{"comment":"The color coding in Fig. 3A is described in the text but the color bar orientation and the meaning of gray/desaturated areas should be clarified directly in the caption.","section":"Fig. 3"},{"comment":"The two fits for λ′(B) yield B* values of (138±2) mT and (135±2) mT. It would be helpful to state explicitly that these fits are not used to define the magnetic phases and that the ambiguity between rotation and stretching of the helix does not affect the main conclusions.","section":"Supplementary S2"},{"comment":"\"CieCAM\" should be \"CIECAM02\". Also, the sentence \"the resulting color map... by linearly interpolating between the latter and a middle gray in the CieCAM color space\" is unclear and should be rephrased.","section":"Supplementary S4"}],"recommendation":"major_revision","confidential_remarks":"The paper describes a plausible and potentially important result, but the main phase identification needs to be made robust. The FFT folding issue is the key technical concern; if the authors can supply a real-space criterion (autocorrelation or resolved skyrmion cores) or otherwise rule out a multi-domain single-q texture, the paper would likely be acceptable. The current evidence, as written, does not uniquely establish the skyrmion lattice label."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: this is a solid experimental paper, and the central observation is genuinely new. It gives the first real-space MFM images of the low-temperature skyrmion lattice in bulk Cu2OSeO3, along with the nucleation dynamics under field cycling and the annealing of a skyrmion polycrystal into a lattice locked to the crystal axes. Those are valuable confirming measurements, and the field sequence in Fig. 1 (conical → tilted conical → skyrmion lattice → helical) is coherent and consistent with the SANS-derived phase diagram.\n\nThe strength of the paper is that it does real-space imaging where previous work relied on SANS, magnetization, and FMR. The coexistence of tilted conical and skyrmion domains during the transition (Fig. 2) is a concrete observation, not an inference. The annealing result in Fig. 3, showing spectral weight condensing around ⟨100⟩ as a function of cycling count, is also a nice demonstration of orientational locking.\n\nThe soft spot is exactly where the stress-test note points: the phase identification at +80 mT rests on the sixfold FFT pattern rather than on resolved individual skyrmions. The authors themselves say direct threshold-based identification is \"at least challenging.\" The 60° folding in the angular analysis (Supplementary S3) does reduce the selectivity of the averaged distribution—single-q helical or tilted-conical domains also fold into a single peak per sector. But in the raw FFTs of the zoomed areas (Figs. 3C,D), six peaks are visible without folding, and the corresponding real-space patches are locally uniform color domains, not obviously multi-domain. That, combined with the known SANS phase at this field, makes the skyrmion assignment credible. Still, a referee should ask for a real-space criterion—say, resolved skyrmion cores, a hexagonal autocorrelation, or a comparison of the measured wavelength with the skyrmion lattice spacing—to exclude a textured single-q state. This is a fixable deficiency, not a fatal one.\n\nMinor points: the supplementary wavelength fits give two indistinguishable B* values and the authors honestly say they cannot distinguish helix rotation from stretching; that's peripheral. The absence of the FMR-stretched skyrmion lattice in their images is noted as a discrepancy for future work, and that seems fair.\n\nThis paper deserves a serious referee. It's an important confirming measurement for the skyrmion community, and the methodological tension between FFT symmetry and real-space identification is worth airing in peer review. Send it out, with a request that the authors strengthen the real-space discrimination and soften the \"clearly identify\" phrasing in the abstract.\n\nBest, [You]","headline":"First real-space MFM of the low-temperature skyrmion lattice in bulk Cu2OSeO3; the evidence is convincing but the FFT-based phase identification needs a real-space discriminator to fully rule out multi-domain single-q textures.","tokens_in":12275,"tokens_out":3350,"would_cite":true,"duration_ms":44109,"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":"Magnetic force microscopy images the low-temperature skyrmion lattice in a bulk Cu2OSeO3 crystal for the first time, and shows that repeated field cycling can anneal it into a single crystal locked to the lattice axes.","keywords":["skyrmion lattice","Cu2OSeO3","magnetic force microscopy","low-temperature skyrmion phase","magnetic annealing","domain orientation","cubic anisotropy","helical phase"],"falsifier":"Observe the same sample at 80 mT and 10 K with a probe that resolves individual skyrmion cores, for example spin-polarized scanning tunneling microscopy on a cleaved surface or Lorentz transmission electron microscopy on a thin lamella of identical material. If the pattern is a triangular array of isolated skyrmion cores, the skyrmion-lattice assignment is confirmed; if it is a stripe-like or disordered modulation, the assignment fails. Alternatively, run small-angle neutron scattering on the identical field-cycled crystal: a sixfold scattering pattern rotated to <100> would confirm the lattic","tokens_in":11331,"feed_emoji":"🧲","tokens_out":6251,"duration_ms":68238,"temperature":0.7,"pith_summary":"The paper reports the first real-space magnetic force microscopy images of the low-temperature skyrmion phase in bulk Cu2OSeO3. At 10 K, with the magnetic field along a <100> direction, the authors resolve helical, conical, tilted conical, and skyrmion lattice domains by tuning the external field. They show that repeated small field cycles—a magnetic annealing protocol—nucleate the skyrmion lattice and, with enough cycles, transform a misoriented skyrmion 'polycrystal' into a single crystal whose lattice orientation locks to the underlying Cu2OSeO3 cubic axes. Along the way they observe coexistence of tilted conical and skyrmion states, and they do not find the stretched skyrmion lattice reported in some resonance experiments. If correct, this establishes the low-temperature skyrmion phase as a real, imageable bulk texture and clarifies how it nucleates and orders.","feed_headline":"First real-space look at the low-temperature skyrmion lattice","feed_subtitle":"MFM at 10 K resolves helical, conical, and skyrmion phases in bulk Cu2OSeO3 as field cycling orders the lattice.","key_machinery":"The central object is the skyrmion lattice itself: a triangular array of swirling spin textures whose sixfold Fourier symmetry can be measured even when individual skyrmions are hard to identify in raw images. The key mechanism is magnetic annealing—repeatedly sweeping the external field by 5–10 mT between consecutive images—which drives nucleation of skyrmions from the tilted conical state and then orders a skyrmion polycrystal into a single crystal. The identification of lattice orientation relies on a moving-window fast Fourier transform algorithm that extracts the in-plane rotation angle of the sixfold diffraction pattern, with an angular resolution of about 5 degrees.","core_discovery":"Using magnetic force microscopy at 10 K, the paper reports the first real-space imaging of the low-temperature skyrmion lattice in bulk Cu2OSeO3. As the field is lowered from saturation, the images resolve helical, conical, tilted conical, and skyrmion lattice domains in one crystal. The central discovery is that field cycling acts as magnetic annealing: it first nucleates skyrmions out of the tilted conical state, with both phases coexisting at the transition, then converts a disordered skyrmion polycrystal into a long-range-ordered skyrmion single crystal whose lattice orientation becomes locked to the <100> directions of the Cu2OSeO3 crystal, an effect attributed to cubic anisotropy. The","pith_inferences":["Because the skyrmion lattice orientation locks to <100> directions, strain or electric-field tuning of the cubic anisotropy should rotate or reorient the lattice on demand; the paper does not test this, but it follows directly from the locking mechanism it reports.","The observed coexistence of tilted conical and skyrmion phases under field cycling suggests that bulk hysteresis measurements may include kinetic effects; one testable consequence is that faster cooling or larger field steps should delay or prevent skyrmion nucleation.","MFM is surface-sensitive, so whether the locked single-domain skyrmion lattice seen near the surface matches the bulk spin texture could be checked with a bulk probe such as small-angle neutron scattering on the same annealed crystal.","The discrepancy with the stretched skyrmion lattice reported from ferromagnetic resonance could stem from surface versus bulk sensitivity or from different field protocols; a combined MFM and resonance study on the same sample after identical annealing would settle which picture is correct."],"forward_implications":["At 10 K, sweeping the field from saturation to zero reveals four distinct magnetic textures in one crystal: helical, conical, tilted conical, and skyrmion lattice.","Repeated small field cycles nucleate the skyrmion lattice out of the tilted conical state, with both phases coexisting during the transition.","Longer cycling anneals the skyrmion polycrystal into a single skyrmion lattice whose orientation locks to Cu2OSeO3's <100> axes.","The low-temperature skyrmion phase transition is kinetically slow: thermal activation at 10 K is insufficient to complete it quickly, which accounts for the large hysteresis seen in bulk measurements.","No stretched skyrmion lattice is found in the low-field region; instead a proper helical phase with all three helical domains populated appears, disagreeing with an earlier ferromagnetic resonance report."],"supporting_citations":[{"why":"Identified the low-temperature skyrmion phase in Cu2OSeO3 through neutron scattering, magnetization, and specific heat measurements; this is the phase the paper images.","marker":"[18]"},{"why":"Provides additional thermodynamic characterization of the low-temperature skyrmion phase and its stability window.","marker":"[19]"},{"why":"Proposed the rupture-formation mechanism for skyrmion nucleation from metastable spiral states, which the paper's observations support.","marker":"[20]"},{"why":"Reported a stretched skyrmion lattice in the low-field region from ferromagnetic resonance; the paper's real-space images do not reproduce this.","marker":"[21]"},{"why":"Supplies broadband ferromagnetic resonance evidence for the second low-temperature skyrmion phase in the same material.","marker":"[22]"},{"why":"Theoretical prediction that isolated skyrmions and clusters are stable only when surrounded by the conical state, framing the observed coexistence of skyrmion and tilted conical phases.","marker":"[24]"},{"why":"Demonstrated magnetic force microscopy imaging of helices and skyrmions in Cu2OSeO3, establishing the technique used here.","marker":"[25]"},{"why":"Proposed toron-mediated nucleation of skyrmions; the paper's imaging weighs this alternative mechanism against the rupture-formation picture.","marker":"[31]"}],"fun_headline_variants":["First real-space view of low-T skyrmion lattice","Field cycling orders skyrmion lattice in Cu2OSeO3","MFM resolves coexisting skyrmion and conical phases","Skyrmion single crystal via magnetic field cycling","Direct imaging of skyrmion lattice at 10 K"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The claim that the pattern at +80 mT is a triangular skyrmion lattice rests on the sixfold symmetry of the Fourier transform of a background-subtracted MFM image, because the raw MFM signal fluctuates too much to identify individual skyrmions directly.","fun_headline_variants_meta":{"raw":{"variants":["First real-space view of low-T skyrmion lattice","Field cycling orders skyrmion lattice in Cu2OSeO3","MFM resolves coexisting skyrmion and conical phases","Skyrmion single crystal via magnetic field cycling","Direct imaging of skyrmion lattice at 10 K"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000226,"raw_usage":{"total_tokens":1242,"prompt_tokens":619,"completion_tokens":623,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":363,"completion_tokens_details":{"reasoning_tokens":541}},"tokens_in":363,"tokens_out":623,"duration_ms":7461,"temperature":1.0,"reasoning_tokens":541,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T13:29:23.564355+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Observe the same sample at 80 mT and 10 K with a probe that resolves individual skyrmion cores, for example spin-polarized scanning tunneling microscopy on a cleaved surface or Lorentz transmission electron microscopy on a thin lamella of identical material. If the pattern is a triangular array of isolated skyrmion cores, the skyrmion-lattice assignment is confirmed; if it is a stripe-like or disordered modulation, the assignment fails. Alternatively, run small-angle neutron scattering on the identical field-cycled crystal: a sixfold scattering pattern rotated to <100> would confirm the lattic","supporting_citations":[{"cited_title":"Chacon , author L","cited_arxiv_id":null,"evidence_quote":"Identified the low-temperature skyrmion phase in Cu2OSeO3 through neutron scattering, magnetization, and specific heat measurements; this is the phase the paper images."},{"cited_title":"Halder , author A","cited_arxiv_id":null,"evidence_quote":"Provides additional thermodynamic characterization of the low-temperature skyrmion phase and its stability window."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proposed the rupture-formation mechanism for skyrmion nucleation from metastable spiral states, which the paper's observations support."},{"cited_title":"Aqeel , author J","cited_arxiv_id":null,"evidence_quote":"Reported a stretched skyrmion lattice in the low-field region from ferromagnetic resonance; the paper's real-space images do not reproduce this."},{"cited_title":"Lee , author J","cited_arxiv_id":null,"evidence_quote":"Supplies broadband ferromagnetic resonance evidence for the second low-temperature skyrmion phase in the same material."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Theoretical prediction that isolated skyrmions and clusters are stable only when surrounded by the conical state, framing the observed coexistence of skyrmion and tilted conical phases."},{"cited_title":"Milde , author E","cited_arxiv_id":null,"evidence_quote":"Demonstrated magnetic force microscopy imaging of helices and skyrmions in Cu2OSeO3, establishing the technique used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proposed toron-mediated nucleation of skyrmions; the paper's imaging weighs this alternative mechanism against the rupture-formation picture."}],"review_version":1}