{"id":"fc15baf7-d762-4cb6-92c2-c8c6eff0076e","arxiv_id":"2411.16395","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Stable skyrmion and antiskyrmion tubes with topological charge plus or minus one are predicted in rhombohedral barium titanate, and electric-field switching between them is demonstrated in simulations.","lead":"This paper uses quantum-mechanical simulations to show that tiny swirling polarization tubes, skyrmions and antiskyrmions, can be stabilized in rhombohedral barium titanate and switched by electric fields. If these predictions hold, they offer a new route to topological nanoelectronic devices in a common and well-studied ferroelectric material.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central stability claim rests on a revised second-principles model whose error bar is comparable to the ~0.07 meV/f.u stabilization margin, with no DFT cross-validation on the skyrmion textures shown.","rationale":"The reader's weakest assumption correctly identifies second-principles fidelity as the key risk. My attack sharpens it by quantifying the stabilization margin (~0.07 meV/f.u) and by noting that the revised model's added sixth- and eighth-order terms are not cross-validated on the relevant vortex/antivortex textures. The direct 7x7x1 DFT relaxations are positive evidence for a small-cell metastable state, so the central 0 K stabilization claim is plausible; the main unresolved question is whether the thermodynamic-limit extrapolation is trustworthy. The secondary red flags (Tc inconsistency and 1-u.c.-z switching) reinforce the same conditional posture rather than overturning the stabilization claim. I therefore agree with the CONDITIONAL verdict and recommend no change.","tokens_in":13763,"tokens_out":8275,"duration_ms":82950,"concrete_test":"Relax the Ti-centered skyrmion tube with the same DFT settings (PBEsol, 40 Ha cutoff, adapted k-point mesh) in an 11x11x1 supercell, starting from the second-principles relaxed structure, and compare the relaxed energy against the R3m monodomain in the same supercell. If the tube collapses to the monodomain, or if its energy is more than ~0.1 meV/f.u above R3m, the infinite-supercell metastability claim is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The infinite-supercell metastability argument hinges on the asymptotic defect energy Ed = -24.87 ± 0.01 meV/f.u, only ~0.07 meV/f.u above the rhombohedral R3m ground state, and on size/orientation energy differences of 0.1-1.2 meV/f.u. These are the energy scales that decide whether the skyrmion and antiskyrmion tubes are local minima at all. The second-principles model used for the extrapolation is described as 'a slight revision' of Ref. [40] with refitted anharmonic terms and additional sixth- and eighth-order terms, but the manuscript does not show a cross-validation of this revised model against DFT for the vortex/antivortex textures themselves; only 7x7x1 DFT relaxations are reported. Because the added high-order terms increase fitting flexibility, the near-degeneracy with R3m and the low collapse barrier could be artifacts of the model. The absence of the promised Data Availability section—where the model and its validation were said to be publicly accessible—makes this untestable from the manuscript as submitted. A secondary red flag is the internal inconsistency in thermal stability (main text: 150/80 K; Supplemental: 20/50 K), which suggests the model's finite-temperature predictions are not robust, and the switching simulations use a 1-unit-cell z-supercell that artificially enforces translational invariance along the tube.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports DFT and second-principles calculations of translationally invariant polarization textures along [001]_pc in rhombohedral BaTiO3. The authors construct columnar nanodomains with vortex-like in-plane polarization backgrounds and obtain relaxed skyrmion and antiskyrmion textures with topological charge Q=±1, including Ti- and Ba-centered variants. They analyze the dependence of the defect energy on nanocolumn size, orientation, and supercell size, extrapolating an infinite-supercell defect energy Ed=-24.87±0.01 meV/f.u. that lies only 0.07 meV/f.u. above the R3m ground state. They report finite-temperature stability up to 150 K (Ti-centered) and 80 K (Ba-centered), and propose electric-field protocols, including an AFM-tip Gaussian field, to stabilize and reversibly switch between skyrmion and antiskyrmion states. They also show analogous textures in KNbO3.","tokens_in":14013,"tokens_out":6000,"duration_ms":57337,"significance":"If the model fidelity is established, the paper makes a substantial advance: it is the first prediction of coexisting ferroelectric skyrmions and antiskyrmions in the same material under identical conditions, and the first proposal of reversible electric-field switching of the topological charge in a ferroelectric. The topological charge is measured from the relaxed polarization field, not imposed, and the DFT relaxations provide direct zero-temperature evidence. The helicity calculation offers a concrete experimental observable, and the extension to KNbO3 broadens the relevance. However, the thermal stability numbers are internally inconsistent, and the second-principles model—whose error bar is comparable to the stabilization margin—is not cross-validated against DFT for the defects in the manuscript as submitted.","major_comments":[{"comment":"The finite-temperature stability claim is internally inconsistent: the main text reports critical temperatures of 150 K for Ti-centered and 80 K for Ba-centered defects, while Supplementary Section VIII states that its NEB barriers \"align well with the critical temperatures of T=20 K and T=50 K reported in the main text.\" These two sets of numbers cannot both be correct, and the discrepancy directly affects the claimed robustness of the tubes. Please correct the values and reconcile the NEB barriers with the actual molecular-dynamics critical temperatures.","section":"Section I, 'Stability of the skyrmion tubes'; Supplementary Section VIII"},{"comment":"The central metastability result rests on a second-principles model described as \"a slight revision\" of Ref. [40] with refitted anharmonic terms and added sixth- and eighth-order terms. The manuscript text refers to a Data Availability section for the model and its validation, but no such section appears in the submitted version. Given that the infinite-supercell defect energy Ed = -24.87 ± 0.01 meV/f.u. lies only about 0.07 meV/f.u. above the R3m ground state and that size/orientation energy differences are 0.1–1.2 meV/f.u., the model's error on these subtle textures must be demonstrated. Please provide the validation data and a direct comparison of second-principles and DFT energies for the skyrmion/antiskyrmion configurations at the supercell sizes used for the extrapolation.","section":"Supplementary Methods (Section III); model validation"},{"comment":"The switching simulations use a supercell containing one unit cell along z, which artificially enforces translational invariance along the tube axis. Since the central object is a tube and the claimed reversible switching is between tube states, the protocol should be tested with a longer z-supercell to confirm that z-dependent fluctuations or three-dimensional topological events do not alter the conclusion. At minimum, the text should state why the 1-u.c. cell is sufficient for this claim.","section":"Supplementary Methods (Section III), electric-field simulations"}],"minor_comments":[{"comment":"The phrase \"the expected prohibitive energetic barriers are overcomed\" contains a grammatical error; \"overcomed\" should be \"overcome.\"","section":"Abstract"},{"comment":"The sentence \"characterized by skyrmion numbers of Q = ±1, .\" contains a stray comma before the period.","section":"Section II (Discussion)"},{"comment":"The main text refers to \"see Fig.S2\" for the near-degeneracy between skyrmion and antiskyrmion energies, but the Supplementary figure numbering visible in the extracted material suggests the energy comparison appears in Fig. 5; please reconcile the cross-references.","section":"Section I (Results)"},{"comment":"The sentence \"we extract the harmonic part directly from the DFPT calculations mentioned above and the anharmonic part is fitted to reproduce the DFT data using the same parameters mentioned above\" is vague about which DFT data and which parameters are used; specify the fitting set and the fitted coefficients.","section":"Supplementary Methods (Section III)"},{"comment":"There is a typo, \"disapearance,\" in the first paragraph; also, the sentence reporting T=20 K and T=50 K duplicates the inconsistency already raised in the major comments and should be corrected consistently.","section":"Supplementary Section VIII"}],"recommendation":"major_revision","confidential_remarks":"The paper is appropriate for a condensed-matter journal. The main concern is not the novelty or the zero-temperature DFT evidence but the verifiability and robustness of the second-principles extrapolations and the finite-temperature numbers. The missing Data Availability section and the critical-temperature inconsistency should be fixed before publication; I do not see grounds for outright rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one before trusting any claim that rhombohedral BaTiO3 cannot host Q=±1 skyrmion tubes. The DFT relaxations in a 7x7x1 cell give clean, relaxed skyrmion and antiskyrmion textures, with integer topological charge computed from the relaxed field rather than imposed, and the two are nearly degenerate. That part looks solid and it directly contradicts Refs. [6] and [18]. Showing the same textures in KNbO3 and sketching a plausible electrode/AFM-tip switching protocol is a real step beyond prior work.\n\nWhere I get nervous is the second-principles layer. The model is a revision of Ref. [40] with refitted anharmonic terms and extra sixth- and eighth-order terms. The supplementary does compare model and DFT energies for the 7x7x1 defects, so the stress-test note overshoots when it says there is no cross-validation at all. But the infinite-supercell metastability argument ends up with the defect only ~0.07 meV/f.u above the R3m ground state, and the added high-order flexibility could in principle manufacture that near-degeneracy. I would want the model's energy differences for the larger cells benchmarked against at least one or two DFT points, and I would want the promised Data Availability section to actually appear.\n\nThere is also a plain inconsistency in the thermal stability numbers: the main text says Ti-centered is stable to 150 K and Ba-centered to 80 K, while the supplementary says 20 K and 50 K. Those cannot both be right, and given that Tc is sensitive to the z-supercell size (6 u.c. for Tc, 1 u.c. for the field runs), the finite-temperature claims need a pass before they are quoted.\n\nThe switching runs use a 1-unit-cell z-supercell, which enforces translational invariance along the tube. That may be fine because the textures are tubes, but without a thicker check it is an assumption, not a verification.\n\nNet: the core stabilization result is credible and important, and the paper deserves a serious referee. I would ask for the Tc discrepancy to be fixed, a sensitivity statement on the high-order model terms, and at least one DFT check on a larger supercell before publication. Conditional accept, not desk reject.","headline":"DFT evidence for Q=±1 skyrmion/antiskyrmion tubes in rhombohedral BaTiO3 is credible and important; the second-principles finite-temperature and switching claims need revision before they can be trusted.","tokens_in":14636,"tokens_out":3395,"would_cite":true,"duration_ms":31575,"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":"This paper predicts that rhombohedral BaTiO3 can host stable skyrmion and antiskyrmion tubes with topological charge Q = ±1 under identical conditions, switchable by electric fields.","keywords":["ferroelectric skyrmions","antiskyrmion tubes","BaTiO3","rhombohedral ferroelectrics","electric-field switching","topological polarization textures","second-principles calculations","Pontryagin density"],"falsifier":"Run the same electric-field switching protocol in a second-principles supercell with 6 unit cells along the tube direction (the z-size used for the critical-temperature simulations); if the skyrmion and antiskyrmion states no longer persist or the switching becomes irreversible, the central claim fails. Alternatively, an atomic-resolution polarization mapping experiment following the proposed electrode protocol should measure an integrated Pontryagin density of exactly ±1 for the vortex/antivortex states; observing a Q = 0 monodomain result would disprove the prediction.","tokens_in":13506,"feed_emoji":"🌀","tokens_out":5215,"duration_ms":43638,"temperature":0.7,"pith_summary":"The paper predicts that rhombohedral BaTiO3 can host stable, tube-shaped polarization textures with topological charge Q = ±1 — skyrmions and antiskyrmions — in the same material under identical conditions. Earlier work dismissed such [001]-oriented skyrmion tubes because the 180° domain walls they require cost too much energy. The authors show that if the surrounding polarization is allowed to relax into a vortex- or antivortex-like pattern, those energy barriers disappear while the topological charge is preserved. They further argue that the textures can be stabilized and reversibly switched by spatially modulated electric fields, providing a practical route to topological switching in a ferroelectric. This matters because electric-field control of topological charge in a single material is a prerequisite for skyrmion-based nanoelectronic devices.","feed_headline":"Skyrmions and antiskyrmions made switchable in BaTiO3","feed_subtitle":"Theory predicts electric fields can flip a topological texture between Q = +1 and Q = −1 in a bulk ferroelectric.","key_machinery":"The mechanism is the delocalization of the vortex/antivortex distortion: instead of imposing a fixed antiparallel matrix, the polarization field is allowed to form a continuous vortex-like rotation that surrounds the out-of-plane nanocolumn, so the energy cost of 180° walls is avoided and the structure remains topologically nontrivial. The topological character is certified by integrating the Pontryagin density, Q = (1/4π)∫ n·(∂n/∂x × ∂n/∂y) dxdy, using a lattice recipe that is numerically stable for rapidly varying fields. Switching is achieved by applying a cosine-modulated in-plane field plus a Gaussian out-of-plane field (as from an AFM tip), with the Born effective charges converting the electric field into atomic forces.","core_discovery":"The central claim is that translationally invariant polarization nanocolumns along [001]pc in rhombohedral BaTiO3, carrying skyrmion numbers Q = ±1, are metastable and nearly degenerate in energy, contrary to prior expectations. The key novel finding is that the in-plane, Bloch-like component of the polarization extends across the entire matrix rather than being confined to a domain wall, which lets each cell locally approach the R3m ground state and avoids the prohibitive cost of 180° walls. Both Ti-centered and Ba-centered variants are stable (Ba-centered lower by about 1.2 meV per formula unit in a 7x7x1 supercell), and the two textures remain stable under thermal fluctuations up to 150 K and 80 K, respectively. The paper also demonstrates computationally that a sequence of spatially modulated electric fields can nucleate the nanocolumn and reversibly flip it between skyrmion and antiskyrmion states, and that similar textures appear in KNbO3.","pith_inferences":["A direct experimental test could use resonant soft X-ray diffraction circular dichroism to detect the chiral signature of the skyrmion tube, since the paper computes a nonzero helicity.","The authors' critical temperatures depend on the chosen z-supercell size (6 unit cells for the Tc estimate, 1 unit cell for the field-switching simulations); if thicker or thinner samples change the stability window dramatically, the practical operating range may be narrower than the 10 K simulations suggest.","The predicted electric-field switching could be adapted to existing BaTiO3 nanoisland or freestanding-layer geometries, where vortex–antivortex lattices have already been reported, potentially yielding a room-temperature topological switch."],"forward_implications":["If the prediction holds, BaTiO3 becomes a single-material platform in which the sign of a topological charge can be toggled by electric fields, something previously possible only across distinct materials or phases.","The near-degeneracy of skyrmion and antiskyrmion states means both textures can be addressed under identical strain and growth conditions, simplifying device design.","Because the in-plane polarization disturbance extends over many unit cells, the required electric-field modulations are coarse, easing experimental implementation of the suggested electrode protocol.","The extension to KNbO3, which is rhombohedral near room temperature, suggests the effect is generic to rhombohedral ferroelectrics and not a special feature of BaTiO3."],"supporting_citations":[{"why":"Supplies the computational experiment of embedding a columnar nanodomain in an antiparallel polarization matrix within PbTiO3, which the authors adapt to rhombohedral BaTiO3.","marker":"[5]"},{"why":"The prior work that concluded [001] skyrmion tubes in BaTiO3 are unfeasible due to the prohibitive 180° domain-wall cost; this is the claim the paper challenges.","marker":"[6]"},{"why":"Predicted only fractional Skyrme lines in rhombohedral BaTiO3 and argued that ordinary skyrmions cannot be stabilized, providing the starting point that the paper overturns.","marker":"[18]"},{"why":"The base second-principles model for BaTiO3 that the authors revise with refitted anharmonic terms and additional sixth- and eighth-order terms.","marker":"[40]"},{"why":"Describes the second-principles methodology used to build the atomistic model from first-principles data.","marker":"[23]"},{"why":"Provides the systematic scheme for constructing the second-principles lattice dynamical model employed here.","marker":"[24]"},{"why":"Supplies the lattice recipe for computing the Pontryagin density integrand, which the paper uses to certify the topological charge Q = ±1.","marker":"[47]"},{"why":"Explains why Ba-centered vortex cores are lower in energy than Ti-centered ones, grounding the paper's finding that Ba-centered skyrmions and antiskyrmions are favored by about 1.2 meV per formula unit.","marker":"[33]"}],"fun_headline_variants":["Electric fields switch skyrmion-antiskyrmion tubes in BaTiO3","BaTiO3 skyrmion tubes flip with applied electric fields","Switchable topological tubes in rhombohedral BaTiO3","Electric-field control of skyrmion and antiskyrmion tubes","Skyrmion-antiskyrmion tubes in BaTiO3 switchable by E-fields"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole stability and switching argument rests on the second-principles model — a slight revision of the model in Ref. [40] with refitted anharmonic and higher-order terms — faithfully reproducing the energetics of textures whose energy differences are only 0.1 to 1.2 meV per formula unit beyond the few configurations validated by DFT.","fun_headline_variants_meta":{"raw":{"variants":["Electric fields switch skyrmion-antiskyrmion tubes in BaTiO3","BaTiO3 skyrmion tubes flip with applied electric fields","Switchable topological tubes in rhombohedral BaTiO3","Electric-field control of skyrmion and antiskyrmion tubes","Skyrmion-antiskyrmion tubes in BaTiO3 switchable by E-fields"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000738,"raw_usage":{"total_tokens":3291,"prompt_tokens":934,"completion_tokens":2357,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":550,"completion_tokens_details":{"reasoning_tokens":2260}},"tokens_in":550,"tokens_out":2357,"duration_ms":15049,"temperature":1.0,"reasoning_tokens":2260,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T13:09:20.773281+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same electric-field switching protocol in a second-principles supercell with 6 unit cells along the tube direction (the z-size used for the critical-temperature simulations); if the skyrmion and antiskyrmion states no longer persist or the switching becomes irreversible, the central claim fails. Alternatively, an atomic-resolution polarization mapping experiment following the proposed electrode protocol should measure an integrated Pontryagin density of exactly ±1 for the vortex/antivortex states; observing a Q = 0 monodomain result would disprove the prediction.","supporting_citations":[{"cited_title":"Nahas, S","cited_arxiv_id":null,"evidence_quote":"Supplies the computational experiment of embedding a columnar nanodomain in an antiparallel polarization matrix within PbTiO3, which the authors adapt to rhombohedral BaTiO3."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The prior work that concluded [001] skyrmion tubes in BaTiO3 are unfeasible due to the prohibitive 180° domain-wall cost; this is the claim the paper challenges."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Describes the second-principles methodology used to build the atomistic model from first-principles data."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the systematic scheme for constructing the second-principles lattice dynamical model employed here."},{"cited_title":"Milnor, Topology from the differentiable viewpoint (The University Press of Virginia, Charlottesville, 1965)","cited_arxiv_id":null,"evidence_quote":"Explains why Ba-centered vortex cores are lower in energy than Ti-centered ones, grounding the paper's finding that Ba-centered skyrmions and antiskyrmions are favored by about 1.2 meV per formula unit."}],"review_version":1}