{"id":"5bd0a92b-ff5d-4631-94f6-9b93c81b59b0","arxiv_id":"2412.14069","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Fractional Bloch skyrmion tubes form at zero field in double-helix cobalt nanowires when two regions of opposite geometric chirality are interfaced and a minor magnetic field loop is applied.","lead":"This paper shows that 3D-printed cobalt nanowires shaped like double helices can host fractional skyrmion tubes at room temperature and zero magnetic field. The effect comes from joining two helix regions with opposite handedness, which allows the magnetization to break its usual coupling to the geometry.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Experimental inference of χ_M≠χ_G rests on a two-parameter vortex fit that cannot represent the claimed skyrmion's oppositely magnetized shell; a synthetic forward-model test is needed to rule out a fitting artifact.","rationale":"The reader's weakest assumption correctly identifies the two-parameter vortex model as the load-bearing link between the XMCD images and the claim that the bottom region has χ_M≠χ_G. My reading sharpens this: the claimed skyrmion state is not a small perturbation of a vortex tube but has the defining feature of an oppositely magnetized outer shell. Because the XMCD asymmetry in the tilted geometry couples axial magnetization to the left-right signal, a uniform-polarity vortex fit is structurally unable to describe the very state it is used to prove. The synthetic-fit test I propose directly probes whether the inverse procedure recovers the known true parameters from the authors' own simulated state; this is the minimal check that would settle whether the experimental inference is an artifact. I do not think this concern requires changing the reader's CONDITIONAL verdict—the concern is exactly why 'conditional' is the right level of confidence. The paper has genuine independent support: the micromagnetic simulations are parameter-based (not fit to the specific line profiles), the simulated and experimental XMCD contrasts agree well, and the topological-charge analysis is an internally consistent prediction. Those strengths make the central claim plausible, but they do not remove the need to validate the model-dependent experimental extraction. If the synthetic-fit test fails, the experimental half of the central claim would need to be downgraded; if it passes, the claim is substantially strengthened. The absence of deposited code, data, and the referenced supplementary sections makes the test impossible for an independent reader to run today, which further justifies maintaining a CONDITIONAL rather than ACCEPT verdict.","tokens_in":12702,"tokens_out":8139,"duration_ms":78806,"concrete_test":"Take the remanent skyrmion state from the authors' micromagnetic simulation of Fig. 3c(vii), compute its XMCD projection along the experimental beam direction with the stated 15–20° tilt and 8 nm/pixel resolution, then apply the same two-parameter vortex fitting routine (Supplemental Section 1) to this synthetic image. If the fitted C and P for the bottom RH region recover the true simulated texture (i.e., indicate χ_M≠χ_G with the correct sign), the experimental inference is supported. If the fit instead yields χ_M=χ_G, or if the residuals are comparable to noise, the line-profile evidence for a fractional skyrmion tube is invalidated. If the fit is ambiguous, repeat with a Bayesian model comparison between the two-parameter vortex forward model and the full simulated skyrmion forward model to see which one actually explains the measured profile.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central new result is the experimental observation of a remanent zero-field state in which the bottom (right-handed) chiral region has magnetochirality opposite to its geometry, χ_M≠χ_G, forming a fractional Bloch skyrmion tube. The experimental evidence for this is the XMCD line-profile asymmetry in state vii (Fig. 3b, left): both regions show larger intensity on the left, interpreted as a uniform left-handed magnetochirality throughout the nanowire. This interpretation is made by fitting the profiles to a 'vortex tube state in both regions' with two parameters per region, circulation C and polarity P (Supplemental Section 1). The load-bearing problem is that the claimed skyrmion state is precisely not a uniform vortex tube: micromagnetic simulations (Fig. 3c, vii; Fig. 4h) show a +M_z core surrounded by an outer shell with substantial −M_z. In the tilted imaging geometry (~15–20°), the axial M_z component projects onto the X-ray beam and contributes to the left-right asymmetry that the two-parameter model attributes to C and P. A model that assumes a uniform polarity cannot represent an oppositely magnetized shell; the effective C and P extracted for the bottom region could therefore be biased, and the inferred χ_M≠χ_G could be a fitting artifact. If that inference is invalid, the experimental support for the fractional skyrmion tube collapses to a consistency check with simulations, and the claim that the state is experimentally demonstrated is not justified. The manuscript does not show the fits, residuals, or error bars, and the referenced Supplementary Section 1 was not available, so this model dependence is unquantified.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports the formation of room-temperature fractional Bloch skyrmion tubes in 3D-printed cobalt double-helix nanowires with two regions of opposite geometric chirality. Using X-ray magnetic circular dichroism (XMCD) ptychography and micromagnetic simulations, the authors identify a remanent zero-field state in which the bottom (right-handed) chiral region acquires a magnetochirality opposite to its geometric chirality, resulting in a hybrid vortex/skyrmion texture. The interpretation is supported by line-profile analysis of XMCD images (interpreted as showing a uniform left-handed magnetochirality in both regions) and by simulations that compute local topological charge Q from 0.4 to 0.8. The paper also presents a phase diagram for vortex versus anti-parallel states and demonstrates field-driven reconfigurability between pure vortex and mixed skyrmion-vortex states.","tokens_in":12921,"tokens_out":3185,"duration_ms":30274,"significance":"If the experimental inference is correct, this work provides a new and potentially important mechanism for stabilizing fractional skyrmion tubes at room temperature in three-dimensional nanostructures without Dzyaloshinskii-Moriya interactions, using purely geometric chirality. The simulations use material parameters taken from prior FEBID cobalt literature and are not fitted to the XMCD data, which is a strength. The experimental images are of high quality and the qualitative agreement between experimental and simulated XMCD projections is compelling. The paper also contributes a useful phase diagram and a demonstration of field-driven reconfigurability, which are of interest to the 3D nanomagnetism community.","major_comments":[{"comment":"The central experimental claim that χ_M ≠ χ_G in the bottom region rests on the fitting of XMCD line profiles to a two-parameter vortex tube model (circulation C and polarity P per region). However, the state claimed to be a skyrmion tube (Fig. 3c, vii) is explicitly not a uniform vortex tube: micromagnetic simulations show a +M_z core surrounded by a shell with substantial −M_z. In the tilted imaging geometry (~15–20°), the axial M_z component of the shell projects onto the X-ray beam and contributes to the left-right asymmetry that the two-parameter model attributes to C and P. A model assuming a uniform polarity per region cannot represent an oppositely magnetized shell, so the extracted C and P for the bottom region may be biased. The authors should perform a synthetic forward-model test: take the simulated skyrmion texture, compute its XMCD projection under the experimental tilt, add realistic noise, and run the same fitting routine to verify that it recovers the known C and P (or, if it does not, quantify the bias). Alternatively, the experimental line profiles should be compared directly with full micromagnetic forward models of the skyrmion state, rather than through the two-parameter vortex fit. Without such a test, the experimental evidence for χ_M ≠ χ_G is model-dependent and the statement in the abstract that the formation of fractional skyrmion tubes is 'demonstrated' is not fully supported.","section":"Results, Fig. 3b and Supplemental Section 1"},{"comment":"The statement that 'the skyrmion state observed is a fractional skyrmion, with Q values always smaller than 1' is based entirely on micromagnetic simulations; the experimental XMCD images do not directly measure the topological charge. The text should clarify that Q is a simulated quantity, not extracted from experiment, to avoid implying that the experimental data alone establish the fractional topological charge. If the authors wish to claim experimental demonstration of fractional skyrmions, they should either provide an observable proxy for Q or soften the language to 'simulations predict a fractional skyrmion with Q up to 0.8'.","section":"Results, Fig. 4f and Discussion"}],"minor_comments":[{"comment":"Reference [9] misspells 'Nagaosa' as 'Nagosa'; reference [39] has 'deicated' instead of 'dedicated'; reference [37] has 'ASC Appl. Nanomater' instead of 'ACS Appl. Nano Mater.'; reference [46] has 'effe5cts' instead of 'effects'.","section":"References"},{"comment":"In the caption for Fig. 2j, the color/line labels for LH and RH regions should be double-checked: the text says 'green: LH, black: RH' but the figure appears to show green and black lines with opposite signs; ensure the colors and symbols are clearly distinguishable in print.","section":"Figure 2 caption"},{"comment":"The topological charge formula should define the integration domain (an xy plane) and the notation for the magnetization unit vector; currently M is used for both the magnetization vector and its normalized version.","section":"Introduction, Eq. (1)"},{"comment":"In the caption, the minor loop sequence is described as '(iii, vii-x)' but the text in the main body refers to a second remanent state as 'vi'; please ensure the state numbering is consistent between the text and figure.","section":"Results, Fig. 3a"}],"recommendation":"major_revision","confidential_remarks":"The novelty of the work is substantial and the simulations are thorough, but the experimental inference of the key claim (χ_M ≠ χ_G and thus skyrmion formation) is not robust to the model assumption of a two-parameter vortex tube. A synthetic forward-model test is a reasonable and feasible request that would strengthen the paper considerably. If the authors can show the fitting routine correctly extracts C and P from simulated skyrmion textures, the paper would be suitable for publication. If not, the experimental support would collapse to a qualitative match with simulations, which would reduce the significance to a simulation-backed prediction rather than a demonstration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear Colleague,\n\nThe headline: this paper reports a new and plausible mechanism for producing fractional skyrmion tubes at zero field, by interfacing two regions of opposite geometric chirality in a 3D-printed cobalt double-helix nanowire. It is a credible combination of ptychographic XMCD imaging and micromagnetic simulations, and it makes a genuine advance over the authors' earlier single-chirality helix work.\n\nWhat's actually new: the demonstration (if correct) of a remanent state where the magnetochirality opposes the geometric chirality in one region, χ_M ≠ χ_G, leading to an enhanced local topological charge up to Q≈0.8. The geometry-based route avoids DMI or heavy metals, which is interesting for 3D nanomagnetism. The paper also does several things well: the phase diagram in Fig. 1d gives a clear rationale for choosing helix parameters to favor vortex/AP coexistence, and the simulation-to-experiment comparison for the major-loop states is convincing.\n\nThe soft spots are real but not fatal. The most significant is the one the stress-test flagged: the experimental inference that the bottom region has χ_M ≠ χ_G rests on interpreting an XMCD line-profile asymmetry through a two-parameter vortex model. That model cannot represent a skyrmion tube with an oppositely magnetized shell, so the extracted C and P for that region could in principle be biased by the axial M_z projection. However, note that for the key remanent state (Fig. 3b) the paper does not actually fit C and P; it shows the raw profile asymmetry and compares it to the simulated XMCD from the skyrmion state, which matches. So the claim is supported by simulation-consistency rather than by the vortex fit alone. Still, the lack of a synthetic test (take the simulated skyrmion, project it, fit it with the vortex model) leaves the concern open. The paper also gives no error bars on the line profiles or fits, and the supplementary material was not available for review.\n\nThe simulation parameters are from prior FEBID cobalt literature and the sample geometry, not fitted to the data; that is a strength. The absence of deposited code/data is a minor weakness, not unusual for this field.\n\nWho should read it: anyone working on 3D nanomagnetism, topological spin textures, or geometry-driven spintronics. The paper deserves a serious referee. My recommendation: send it to review, but the authors should add a forward-model check of their fitting procedure and provide fitting residuals/error bars to close the stress-test gap.\n\nBest,\n[Your name]","headline":"A credible, well-illustrated demonstration of a new route to fractional skyrmion tubes via geometric chirality interfaces, with the main soft spot being the indirect, model-dependent experimental identification of the 3D spin texture.","tokens_in":13638,"tokens_out":5907,"would_cite":true,"duration_ms":51169,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In a 3D-printed cobalt double-helix nanowire with two regions of opposite chirality, a minor hysteresis loop creates a zero-field remanent state containing a fractional Bloch skyrmion tube with local topological charge up to about 0.8.","keywords":["fractional skyrmions","skyrmion tubes","3D magnetic nanowires","magnetochirality","geometric chirality","XMCD ptychography","micromagnetic simulation","zero-field remanent state"],"falsifier":"Reconstruct the full three-dimensional magnetization of the nanowire at zero field after the minor loop using X-ray vector nanotomography; if the bottom region does not show a central core of one axial polarity surrounded by a shell of opposite polarity with a radial vortex-like circulation (a Bloch skyrmion tube), the central claim is refuted.","tokens_in":12407,"feed_emoji":"🧲","tokens_out":6316,"duration_ms":48677,"temperature":0.7,"pith_summary":"This paper claims that fractional Bloch skyrmion tubes can be stabilized at room temperature and zero magnetic field by purely geometric means: 3D-printed cobalt double-helix nanowires that contain two regions of opposite geometric chirality. The authors show that when a minor hysteresis loop is applied to such a nanowire, the bottom region can settle into a spin texture whose magnetochirality opposes its geometric chirality, forming a fractional skyrmion tube with local topological charge $Q$ up to about 0.8. The result matters because it provides a route to topological spin textures without heavy-metal layers or Dzyaloshinskii–Moriya interactions, using reconfigurable 3D nanostructures. It also demonstrates control between distinct zero-field states—pure vortex, skyrmion–vortex hybrids—suggesting a platform for 3D topological spintronics.","feed_headline":"3D-printed chiral nanowires make fractional skyrmions at zero field","feed_subtitle":"A minor magnetic loop breaks chirality coupling and leaves a stable skyrmion tube with Q up to 0.8.","key_machinery":"The load-bearing object is the chirality-interfaced double-helix nanowire: a right-handed and a left-handed cobalt double helix joined by a chirality interface, with pitch 200 nm and strand separation 66 nm chosen so the vortex and anti-parallel states are nearly degenerate at zero field. The argument is carried by the vortex-tube analysis, in which each chiral region's magnetization is described by a circulation amplitude $C$ and a polarity amplitude $P$, with magnetochirality defined as $\\chi_M = C \\times P$, and by the topological charge $Q$ computed per $xy$ plane. The key mechanism is the minor hysteresis loop starting from a hybrid vortex/anti-parallel state: as the field is reduced, the chirality interface couples the regions so that the bottom AP domains evolve into a vortex-like state with a large axial magnetization, i.e. a Bloch skyrmion tube that opposes the geometric chirality. The higher $Q$ in the bottom region is directly attributed to the breaking of chirality coupling and the resulting larger solid angle covered by the magnetization.","core_discovery":"The central discovery is a zero-field remanent magnetic state in an interfaced chiral double-helix nanowire, in which the geometric–magnetic chirality coupling is locally broken: the top left-handed region retains its geometrically favoured vortex state ($\\chi_M = \\chi_G$), while the bottom right-handed region adopts a spin configuration with $\\chi_M \\neq \\chi_G$, forming a Bloch-type skyrmion tube. The skyrmion state is fractional, with $Q$ values always below 1 and reaching $Q \\approx 0.8$ close to switching fields, over a continuous range $0.4 < Q < 0.8$. The formation is driven by a hybrid vortex/anti-parallel state that appears during magnetic reversal: when the field is removed, one anti-parallel domain becomes the skyrmion core and the other becomes the circulating shell, minimizing magnetic surface charges. This mechanism is supported by X-ray magnetic circular dichroism ptychography and reproduced by micromagnetic simulations.","pith_inferences":["By analogy with the chirality interface, other 3D-printed geometries that force a competition between geometric and magnetic chirality—e.g., twisted ribbons or interlocked rings—might also host fractional skyrmion tubes, a hypothesis the paper does not test.","If the fractional charge $Q$ is truly set by the helical slope, then varying the local pitch along a single nanowire could create graded topological charge profiles, potentially enabling position-addressable skyrmionics; this is an extrapolation beyond the reported constant-pitch devices.","Direct three-dimensional magnetization tomography of the remanent skyrmion state would verify the vortex-tube assumption underlying the XMCD analysis and could reveal whether the fractional charge is robust to local geometric disorder."],"forward_implications":["Room-temperature, zero-field fractional skyrmion tubes can be formed in 3D-printed ferromagnetic nanowires without heavy metals or Dzyaloshinskii–Moriya interactions.","The zero-field state of an interfaced chiral nanowire is reconfigurable: pure vortex, hybrid vortex/anti-parallel, and vortex/skyrmion states can be selected by the field history.","Geometric chirality, through the pitch and strand separation, tunes whether vortex or anti-parallel states are favoured, providing a design parameter for topological state formation.","The coexistence of vortex and fractional skyrmion tubes in the same nanowire could serve as a building block for 3D spintronic devices and reservoir computing schemes."],"supporting_citations":[{"why":"Establishes the vortex and anti-parallel remanent states in cobalt double-helix nanowires and the coupling $\\chi_M = \\chi_G$, the baseline this work modifies.","marker":"[28]"},{"why":"Provides the FEBID layer-by-layer growth method used to fabricate the chiral-interfaced nanowires.","marker":"[33]"},{"why":"Supplies the ptychographic XMCD imaging technique and its resolution, the experimental window into the spin textures.","marker":"[38-42]"},{"why":"Defines confined magnetic skyrmion tubes, the 3D object whose fractional version is claimed here.","marker":"[48]"},{"why":"Documents fractional spin textures with non-integer $Q$, providing the concept that the observed $Q<1$ states are legitimate skyrmionic textures.","marker":"[50]"},{"why":"MuMax3 micromagnetics is the simulation engine behind the phase diagram, hysteresis loops, and $Q$ calculations.","marker":"[59]"}],"fun_headline_variants":["Zero-field fractional skyrmions from 3D-printed chiral nanowires","Chiral double-helix yields fractional skyrmion tubes at zero field","3D-printed chiral nanowires host stable fractional skyrmion tubes","Fractional skyrmion tubes at zero field in chiral nanowires"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The experimental conclusion that the bottom region has the same magnetochirality as the top region at remanence assumes that the magnetization in each chiral region is well described by a two-parameter vortex-tube model (circulation and polarity) and that the nanowire's tilt is known to about 15–20 degrees; a spin texture deviating from that model would invalidate the inferred skyrmion tube.","fun_headline_variants_meta":{"raw":{"variants":["Zero-field fractional skyrmions from 3D-printed chiral nanowires","Chiral double-helix yields fractional skyrmion tubes at zero field","3D-printed chiral nanowires host stable fractional skyrmion tubes","Fractional skyrmion tubes at zero field in chiral nanowires"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000498,"raw_usage":{"total_tokens":2429,"prompt_tokens":924,"completion_tokens":1505,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":540,"completion_tokens_details":{"reasoning_tokens":1425}},"tokens_in":540,"tokens_out":1505,"duration_ms":9138,"temperature":1.0,"reasoning_tokens":1425,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:30:37.147500+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Reconstruct the full three-dimensional magnetization of the nanowire at zero field after the minor loop using X-ray vector nanotomography; if the bottom region does not show a central core of one axial polarity surrounded by a shell of opposite polarity with a radial vortex-like circulation (a Bloch skyrmion tube), the central claim is refuted.","supporting_citations":[{"cited_title":"D., et al., Artificial double-helix for geometrical control of magnetic chirality, ACS Nano, 14, 8084-8092 (2020)","cited_arxiv_id":null,"evidence_quote":"Establishes the vortex and anti-parallel remanent states in cobalt double-helix nanowires and the coupling $\\chi_M = \\chi_G$, the baseline this work modifies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the FEBID layer-by-layer growth method used to fabricate the chiral-interfaced nanowires."},{"cited_title":"T., et al., Real-space imaging of confined magnetic skyrmion tubes, Nat","cited_arxiv_id":null,"evidence_quote":"Defines confined magnetic skyrmion tubes, the 3D object whose fractional version is claimed here."},{"cited_title":"Commun., 13, 2348 (2022)","cited_arxiv_id":null,"evidence_quote":"Documents fractional spin textures with non-integer $Q$, providing the concept that the observed $Q<1$ states are legitimate skyrmionic textures."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"MuMax3 micromagnetics is the simulation engine behind the phase diagram, hysteresis loops, and $Q$ calculations."}],"review_version":1}