{"id":"5f875063-d5a1-4c2f-b926-4b15508f35b1","arxiv_id":"2608.10958","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A counter-spiral magnetic texture generates a pure transverse spin current without spin-split bands, with polarization fixed by a helicity mirror and rotatable in 120-degree steps.","lead":"The authors show that a noncoplanar counter-spiral magnetic texture can generate a pure spin current under an electric field even though its electron bands show essentially zero spin splitting. The result offers a reconfigurable spin-splitter platform whose polarization axis rotates in exact 120-degree steps, testable in photonic and circuit lattices.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The symmetry and transport argument is internally consistent, but the platform premise—that the counter-spiral is the actual ground state and survives hole doping—is asserted via a missing supplement, so the conditional verdict should stand pending the classical and self-consistent stability checks.","rationale":"I read the paper in good faith: the symmetry argument is self-contained, the two-element protection logic is internally consistent, and the four-sector symmetry-breaking tests provide real supporting evidence for the proposed mechanism. The numeric claim σ_H^(s_y)=0.082 e^2/h is plausible within the fixed-texture model, and the reported convergence across η=0.05–0.15t and N_k is a reasonable check, though no convergence data are shown. The reader's weakest-assumption analysis identifies precisely the same load-bearing premise: the counter-spiral must be the stable classical ground state and must survive coupling to itinerant carriers at the quoted doping. The paper itself flags this as a requirement in Sec. h and delegates the proof to Supplemental Secs. S1 and S4.4, which are not part of the preprint, and Sec. i offers data only upon request. A variational bound against two competitors is insufficient to establish global ground-state status or self-consistent stability. This is a verification gap, not a demonstrated error, so the appropriate action is to keep the CONDITIONAL verdict rather than accept or reject. I do not see a stronger internal inconsistency that would justify moving to REJECT; the symmetry constraints and the distinction between even-parity splitting and the allowed odd-parity residual are carefully argued and mutually consistent.","tokens_in":11776,"tokens_out":12737,"duration_ms":150403,"concrete_test":"Obtain Supplemental Secs. S1 and S4.4, then (i) independently minimize H_loc on an L=16 honeycomb cluster from multiple random starts at J=0, Γ'=-D<0, comparing the counter-spiral energy against Néel, ferromagnetic, collinear zigzag, and other single-Q and multi-Q candidates; (ii) starting from the obtained texture, self-consistently solve the coupled s-d mean-field problem at J_H=5 and doping x≈0.132 and check that the relaxed local moments retain the Θ and g symmetries to within a stated tolerance, e.g., max|δS_i|/|S_i|<1%. If the counter-spiral is not the global minimum or relaxes substantially, the claimed spin-splitter response and 120-degree reconfigurability are not realizable in the doped system.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that hole doping realizes a spin splitter without spin-split bands rests on the counter-spiral being the actual ground state of H_loc at J=0, Γ'=-D<0, and on the s-d coupled texture remaining intact at x≈0.132 and J_H=5. The main text states this in Sec. b as 'the noncoplanar counter-spiral ground state' and delegates the classical derivation to Sec. S1 and the carrier back-action bound to Sec. S4.4; neither section is included in the preprint. The only main-text statement is a variational bound (|Γ'|S^2/t>1.51) for 0≤x≤0.30. A variational bound against two chosen competitors (ferromagnet and carrier-induced Néel state) does not establish that the counter-spiral is the global minimum of H_loc, nor that it is a self-consistent solution of the coupled s-d problem. Because the transport calculation is fixed-texture, all predicted response and reconfigurability claims are conditional on this premise. This is not an internal inconsistency, but it is the least secure load-bearing step; the Discussion (Sec. h) explicitly acknowledges the requirement, and Sec. i states that data/scripts are available only upon request, so the submitted preprint does not permit independent verification of the ground state or back-action stability.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a spin-splitter mechanism in a noncoplanar counter-spiral texture of a frustrated honeycomb magnet. The authors couple a classical counter-spiral texture to itinerant electrons via an s–d Hamiltonian and show by symmetry that an antitranslation Θ forbids even-parity band splitting and the charge-Hall response, while a helicity mirror g selects the spin-Hall polarization and forbids the orthogonal spin channel. At hole doping x ≈ 0.132 they report σ_H^(s_y) = 0.082 e²/h, σ_H^(s_x) = 0, |σ_H^(s_z)|/|σ_H^(s_y)| ≈ 0.155, and zero charge Hall, with exact 120° reconfigurability among the three degenerate Q orientations. The transport calculation is performed in a fixed classical texture; the stability of the texture and the numerical convergence details are delegated to a supplemental material that is not included in the preprint.","tokens_in":12040,"tokens_out":7974,"duration_ms":79425,"significance":"The conceptual contribution is the separation of two symmetry elements—antitranslation and helicity mirror—so that band splitting and spin-splitter response are controlled by different symmetry operations, with a redundant protection of the charge-Hall zero. The four-sector perturbation tests in Fig. 4 directly support this allocation, and the response is computed from the model rather than fitted, which strengthens the claim. The predicted upper bound of 2×10^-7 t on the Fermi-level even-parity splitting and the 120° selection rule are falsifiable in the model and in the proposed photonic/circuit implementations. If the ground-state premise and numerical convergence are firmly established, the result is a useful proof-of-principle for reconfigurable altermagnetic textures beyond collinear spin-split bands.","major_comments":[{"comment":"The platform premise—that the counter-spiral is the global ground state of H_loc at J = 0, Γ′ = −D < 0 and that it survives coupling to itinerant electrons at the doping used—is not established in the main text. The main text delegates the classical ground-state derivation to Sec. S1 and the carrier back-action analysis to Sec. S4.4, but the Supplemental Material is not included; the only main-text stability statement is the variational bound in §e that the counter-spiral lies below a ferromagnet and a carrier-induced Néel state for |Γ′|S²/t > 1.51. A variational comparison against two selected trial states does not prove global stability of the counter-spiral, and the fixed-texture transport calculation does not prove that a self-consistent s–d solution with J_H = 5 preserves the texture at x ≈ 0.132. Because every transport and reconfigurability claim is computed in this fixed background, this is the load-bearing point and needs either a proof of global stability, a self-consistent check, or an explicit caveat in the main text.","section":"§b, §e, and §h (with Ref. [28])"},{"comment":"The central quantitative result σ_H^(s_y) = 0.082 e²/h at µ* is described as \"N_k-converged\" and stable for η = 0.05–0.15t, with the details relegated to Sec. S4.2. Since Sec. S4.2 is not supplied, the convergence in the k-mesh and the η-dependence cannot be checked from the manuscript. This value is one of the paper's headline claims, so the main text should report the convergence data, for example σ_H at two meshes and two or three smearing widths, in a table or in a few lines rather than only citing the supplement.","section":"§e and Fig. 3"},{"comment":"The Discussion states that the realization requires bond-anisotropic exchange that stabilizes the counter-spiral and carriers whose back-action preserves it, citing Secs. S1.4 and S4.4, and the data availability statement says that data and scripts are available only upon request. This combination makes the paper's most security-critical elements impossible to verify from the submitted preprint. The revision should include the supplemental sections in the submission and make the numerical data and scripts publicly accessible, at least for the ground-state minimization and the transport convergence checks.","section":"§h and Sec. i"}],"minor_comments":[{"comment":"The term \"N_k-converged\" is used without defining N_k; the authors should state unambiguously that the 16×16 supercell BZ grid corresponds to a given N_k and report the value used for the convergence statement.","section":"§e"},{"comment":"The symbol C is introduced in the sentence \"The half-filled occupied projector likewise has C = 0\" without definition; please specify that C denotes the charge Chern number or the equivalent Kubo-derived quantity.","section":"§d"},{"comment":"The top axis of Fig. 3 lists hole-doping labels 0.8, 0.6, 0.3, 0.1, 0 from left to right, which is reversed relative to the increasing-µ bottom axis; reversing the order would avoid confusion.","section":"Fig. 3"},{"comment":"The statement that data and scripts are available \"upon reasonable request\" is not standard for a numerical paper of this type; a public repository would improve verifiability and reproducibility.","section":"Sec. i"},{"comment":"The caption states \"N_k-converged\" without defining N_k or the smearing parameter η; since η is used throughout the transport section, a one-sentence definition in the main text would help the reader.","section":"Fig. 3 caption"}],"recommendation":"major_revision","confidential_remarks":"I am sympathetic to the central idea, and the symmetry decomposition in the main text is internally coherent. My recommendation is driven by the missing supplement and by the unverified ground-state premise, not by any demonstrated inconsistency in the transport calculation. I would like the revision to include the Supplemental Material, a global or more complete check of the counter-spiral ground state including carrier back-action, and the convergence data for the reported spin Hall value."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe real news in this paper is that the spectral and transport roles of altermagnetism can be carried by two different symmetry elements: the antitranslation Θ forbids even-parity band splitting, while the helicity mirror g sets the spin-current polarization and dark axis. The counter-spiral they construct realizes a spin splitter with quenched splitting, and their four-sector perturbation tests (Fig. 4) cleanly show that removing either element leaves the charge Hall zero intact, and only removing both releases it. That redundancy is genuinely absent in earlier noncollinear routes, and the 120-degree reconfigurability via the three Q orientations is a nice bonus. I think the central argument is correct within the model.\n\nWhat the paper does well: the symmetry analysis is careful, the numerical response (0.082 e^2/h at x≈0.132, zero charge Hall, spin polarization along y) is a concrete prediction, and the authors check sensitivity to smearing, a mirror-compatible SOC term, and sublattice imbalance. They also point to a 32-site cell that could be implemented in photonic or circuit lattices, which gives the idea an experimental handle.\n\nThe soft spots are real but mostly addressable. The load-bearing premise—that the counter-spiral is the classical ground state of the J-Γ′-D model at J=0, Γ′=-D<0 and that hole doping does not destabilize it—is asserted in the main text, but the derivation and the back-action bound live in Secs. S1 and S4.4 of the supplemental, which is not included in the preprint and only available on request. The variational bound quoted (|Γ′|S²/t > 1.51) compares only against a ferromagnet and a Néel state, which is not a full ground-state proof. Also, the headline σ_H^(s_y) value is stated as N_k-converged, but there is no convergence plot in the main text. None of this undermines the symmetry argument, but it does mean the physical realization claim is not independently verifiable from the preprint. The authors should make the supplement and analysis scripts publicly available.\n\nWho is this for? Anyone working on altermagnetism, noncollinear spin Hall effects, or spin-orbit-free spintronics. A theorist would get a concrete model to build on; an experimentalist might find the photonic/circuit emulation route appealing.\n\nVerdict: send it to peer review, but the referee should be asked to check the convergence and the ground-state derivation carefully. I would not cite it yet, but I would definitely want the supplement.","headline":"Decoupling the symmetry that forbids splitting from the one that selects spin transport is genuinely new, but the ground-state premise is parked in a missing supplement.","tokens_in":12632,"tokens_out":4202,"would_cite":false,"duration_ms":37264,"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":"A counter-spiral magnetic texture realizes a spin splitter without spin-split bands, with spin Hall 0.082 e^2/h and zero charge Hall.","keywords":["altermagnetism","spin-splitter effect","spin-space group","noncollinear magnetic texture","spin Hall effect","spin-orbit-free spintronics","counter-spiral","honeycomb lattice"],"falsifier":"A numerical ground-state search of the classical $J$-$\\Gamma'$-$D$ model at $J=0$, $\\Gamma'=-D<0$ that yields a different magnetic order (one lacking the counter-rotating sublattice helices and the helicity mirror) would invalidate the predicted spin-splitter response. Equivalently, a self-consistent calculation that finds the carrier-doped texture unstable toward ferromagnetism or a Neel state would falsify the claim that the spin splitter is realizable.","tokens_in":2133,"feed_emoji":"🧲","tokens_out":7943,"duration_ms":150496,"temperature":0.7,"pith_summary":"This paper tries to establish that a noncoplanar counter-spiral magnetic texture on a frustrated honeycomb magnet can serve as an altermagnet whose spin-splitter effect -- an electric field producing a transverse pure spin current with no net magnetization and no charge Hall -- does not require spin-split bands. In established collinear altermagnets the same crystal symmetry element both splits the bands and fixes the spin-current polarization; here those roles are divided between two spin-space-group elements, an antitranslation $\\Theta$ that forbids even-parity band splitting and a $\\mathbf{Q}$-locked helicity mirror $g$ that selects the spin-current polarization and forbids the perpendicular channel. At hole doping $x\\simeq 0.132$, the spin-orbit-free Kubo calculation gives $\\sigma_H^{(s_y)} = 0.082\\,e^2/h$, $\\sigma_H^{(s_x)} = 0$, $|\\sigma_H^{(s_z)}|\\approx 0.155\\,|\\sigma_H^{(s_y)}|$, and zero charge Hall, so the response is a spin splitter without spin-split bands. Selecting among the three degenerate $\\mathbf{Q}$ orientations rotates the polarization axis in exact $120^\\circ$ steps at fixed magnitude, and the selection rules persist in a $32$-site cell accessible to programmable photonic and circuit lattices.","feed_headline":"Spin splitter without spin-split bands","feed_subtitle":"A counter-spiral texture gives spin Hall 0.082 e^2/h with zero charge Hall, rotatable in 120° steps.","key_machinery":"The argument rests on two exact spin-space-group elements of the counter-spiral texture. The antitranslation $\\Theta=[T\\parallel\\{E|\\tau_{1/2}\\}]$ is a half-period translation combined with spin reversal; it pairs every state at $\\mathbf{k}$ with an equal-energy partner of opposite polarization at $-\\mathbf{k}$, so it forbids even-parity band splitting. The helicity mirror $g=[C_{2x}\\parallel\\{M_x|\\tau_g\\}]$ is a mirror-glide in real space combined with a 180-degree spin rotation about the $x$-axis; because the two honeycomb sublattices carry helices of opposite handedness, the glide and the rotation together leave the texture invariant. This non-translation operation is the altermagnetic element: it selects the allowed spin-Hall channel, defines the dark axis, and enforces the charge-Hall zero through mirror-odd Berry curvature. The crucial feature is that the two elements are independent -- each alone enforces zero charge Hall, and only together do they determine the full spin-splitter selection rules.","core_discovery":"The central claim is that the compensated counter-spiral ground state of the frustrated honeycomb $J$-$\\Gamma'$-$D$ model acts as an altermagnet whose spin-splitter response is carried by the $\\mathbf{Q}$-locked helicity mirror $g=[C_{2x}\\parallel\\{M_x|\\tau_g\\}]$, not by spin-split bands. The antitranslation $\\Theta=[T\\parallel\\{E|\\tau_{1/2}\\}]$ forbids even-in-momentum spin splitting exactly, leaving the symmetry-allowed odd-parity residual below $2\\times10^{-7}\\,t$ at the Fermi level. The mirror $g$ fixes the allowed spin-current channel and its polarization axis, forbids the perpendicular dark axis, and independently forces the charge Hall to vanish at every filling. Removing either element leaves the charge-Hall zero intact, and only removing both allows a charge Hall. With hole doping near $x\\simeq0.132$, the spin-orbit-free Kubo response gives $\\sigma_H^{(s_y)} = 0.082\\,e^2/h$, $\\sigma_H^{(s_x)}=0$, $|\\sigma_H^{(s_z)}|\\approx 0.155|\\sigma_H^{(s_y)}|$, and $\\sigma_{xy}^{\\mathrm{ch}}=0$. Choosing among the three degenerate $\\mathbf{Q}$ orientations rotates the polarization axis in exact $120^\\circ$ steps at fixed magnitude, and the selection rules survive in a 32-site magnetic cell compatible with programmable photonic and circuit lattices.","pith_inferences":["A practical consequence the paper leaves implicit is that a device built on this texture could rotate its spin-current direction by reorienting the ordered wavevector through strain, weak fields, or boundary pinning, avoiding the fixed-axis limitation of collinear altermagnets.","The two-element protection suggests a broader search strategy: screening compensated textures for a non-translation spin-space group element plus an antitranslation could expand the candidate pool for altermagnetic spintronics to include quenched-splitting systems.","A testable extension would be to implement the 32-site counter-spiral in a topolectrical circuit and measure the four-sector symmetry tests: breaking $\\Theta$ should release even-parity splitting without creating a charge Hall, breaking $g$ should release the dark channel, and only breaking both should allow a charge Hall."],"forward_implications":["Resolved band splitting is not a mandatory screening signature for altermagnetic spin splitters: a texture with quenched even-parity splitting can still produce a sizable spin-splitter response.","The spin-current polarization axis is not fixed to the crystal frame but follows the ordered wavevector, so selecting among degenerate $\\mathbf{Q}$ orientations reconfigures the polarization in exact 120-degree steps without changing its magnitude or the charge-Hall zero.","Because either $\\Theta$ or $g$ alone enforces zero charge Hall, the response is robust against perturbations that preserve just one of the two symmetries; a charge Hall appears only when both are broken.","The effect is free of spin-orbit coupling, making it accessible to light-element platforms as well as to programmable photonic meshes and topolectrical circuits where the 32-site cell can be encoded and rewritten in situ.","Decoupling the spectral and transport symmetry roles allows independent toggling of even-parity splitting and the spin-splitter response; a perturbation that preserves $g$ while releasing the $\\Theta$ constraint could switch the splitting channel without affecting the spin current."],"supporting_citations":[{"why":"Defines the altermagnetic spin-space-group framework that the counter-spiral is claimed to instantiate via its non-translation helicity mirror.","marker":"[1]"},{"why":"Extends altermagnetism to noncollinear spins, the category to which the counter-spiral belongs.","marker":"[16]"},{"why":"Introduces the spin-splitter effect as the electric-field-driven transverse pure spin current that the paper realizes.","marker":"[17]"},{"why":"Provides a spin-orbit-free noncollinear route to spin Hall whose charge-Hall zero relies on coplanarity, the contrast for the two-element protection.","marker":"[26]"},{"why":"Supplies the antiferromagnetic skyrmion-crystal route to spin-orbit-free topological spin Hall, another contrast for the charge-Hall-zero redundancy.","marker":"[27]"},{"why":"Reports counterrotating magnetic order in Li2IrO3, the material precedent for the counter-spiral texture.","marker":"[32]"},{"why":"Supplies the s-d coupling Hamiltonian used to connect the fixed texture to itinerant electrons in the transport calculation.","marker":"[36]"},{"why":"Defines the p-wave magnet class whose antitranslation symmetry is the same Theta used here.","marker":"[38]"},{"why":"Provides the proper definition of spin current used in the Kubo calculation.","marker":"[41]"},{"why":"Demonstrates programmable integrated photonics that can encode the site-resolved Hamiltonian, supporting the claim of an accessible 32-site realization.","marker":"[47]"}],"fun_headline_variants":["Reconfigurable altermagnet yields spin current without spin-split bands","Zero-charge-Hall spin current from a counter-spiral altermagnetic texture","Spin splitter without spin split: 120° rotatable altermagnetic texture","Counter-spiral texture rotates spin polarization in exact 120° steps","Altermagnetic counter-spiral: pure spin current, zero charge Hall"],"cache_read_input_tokens":14720,"weakest_assumption_plain":"The counter-spiral must actually be the ground state of the classical $J$-$\\Gamma'$-$D$ model at $J=0$, $\\Gamma'=-D<0$, and it must survive hole doping and coupling to itinerant electrons; the paper supports this with a variational bound, not a self-consistent calculation.","fun_headline_variants_meta":{"raw":{"variants":["Reconfigurable altermagnet yields spin current without spin-split bands","Zero-charge-Hall spin current from a counter-spiral altermagnetic texture","Spin splitter without spin split: 120° rotatable altermagnetic texture","Counter-spiral texture rotates spin polarization in exact 120° steps","Altermagnetic counter-spiral: pure spin current, zero charge Hall"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000898,"raw_usage":{"total_tokens":3965,"prompt_tokens":1140,"completion_tokens":2825,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":756,"completion_tokens_details":{"reasoning_tokens":2727}},"tokens_in":756,"tokens_out":2825,"duration_ms":18953,"temperature":1.0,"reasoning_tokens":2727,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T13:25:00.344754+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A numerical ground-state search of the classical $J$-$\\Gamma'$-$D$ model at $J=0$, $\\Gamma'=-D<0$ that yields a different magnetic order (one lacking the counter-rotating sublattice helices and the helicity mirror) would invalidate the predicted spin-splitter response. Equivalently, a self-consistent calculation that finds the carrier-doped texture unstable toward ferromagnetism or a Neel state would falsify the claim that the spin splitter is realizable.","supporting_citations":[{"cited_title":"ˇSmejkal, J","cited_arxiv_id":null,"evidence_quote":"Defines the altermagnetic spin-space-group framework that the counter-spiral is claimed to instantiate via its non-translation helicity mirror."},{"cited_title":"Cheong and F.-T","cited_arxiv_id":null,"evidence_quote":"Introduces the spin-splitter effect as the electric-field-driven transverse pure spin current that the paper realizes."},{"cited_title":"Chen Ye, K","cited_arxiv_id":null,"evidence_quote":"Provides a spin-orbit-free noncollinear route to spin Hall whose charge-Hall zero relies on coplanarity, the contrast for the two-element protection."},{"cited_title":"Zhang, J","cited_arxiv_id":null,"evidence_quote":"Supplies the antiferromagnetic skyrmion-crystal route to spin-orbit-free topological spin Hall, another contrast for the charge-Hall-zero redundancy."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports counterrotating magnetic order in Li2IrO3, the material precedent for the counter-spiral texture."},{"cited_title":"Kimchi, R","cited_arxiv_id":null,"evidence_quote":"Supplies the s-d coupling Hamiltonian used to connect the fixed texture to itinerant electrons in the transport calculation."},{"cited_title":"Akagi, M","cited_arxiv_id":null,"evidence_quote":"Defines the p-wave magnet class whose antitranslation symmetry is the same Theta used here."},{"cited_title":"Mirror-Symmetry-Enforced Photonic Altermagnet","cited_arxiv_id":"2606.21545","evidence_quote":"Demonstrates programmable integrated photonics that can encode the site-resolved Hamiltonian, supporting the claim of an accessible 32-site realization."}],"review_version":1}