{"id":"c88a514a-8e4c-4b80-b993-f12c8d212f64","arxiv_id":"2605.26044","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Neutron diffraction reveals a partial long-range ordered noncoplanar multi-k state of Ising Tb moments on corner-sharing octahedra in Cd6Tb, with the remaining moments showing persistent dynamics, proposed as a candidate for octahedral spin-ice physics and magnetic fragmentation.","lead":"The paper reports neutron diffraction and muon spin rotation data on the quasicrystal approximant Cd6Tb showing a noncoplanar multi-k magnetic structure where only one-third of the Tb moments order long-range on a corner-sharing octahedral network while the rest fluctuate on microsecond scales. A smart generalist might read it to see how a periodic material can serve as a testable proxy for exotic magnetism expected in aperiodic quasicrystals.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Muon relaxation interpretation as intrinsic fragmentation dynamics rests on untested assumption that it is not due to static disorder or site-dependent effects.","rationale":"The reader's weakest assumption correctly isolates the interpretive step that converts raw diffraction + μSR observables into a realization of octahedral spin-ice fragmentation. No stronger internal inconsistency (e.g., in the reported multi-k structure itself) is apparent from the supplied abstract and claim wording; the geometry match and fluctuation origin remain the least secured links.","tokens_in":1814,"tokens_out":356,"duration_ms":16534,"concrete_test":"Re-analyze the μSR spectra (Fig. 4 or equivalent) with a two-component model that includes a static Gaussian Kubo-Toyabe term plus dynamic Lorentzian; if the dynamic fraction required to fit the data drops below 60% of the non-ordered Tb sites when the static width is allowed to vary, the claim of persistent intrinsic dynamics weakens.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim equates the observed 1/3 long-range order plus reduced static moments with muon-detected microsecond dynamics to magnetic fragmentation predicted for octahedral spin ice. This requires (i) the corner-sharing octahedra network in the Cd6Tb approximant to reproduce the exact connectivity and degeneracy of the quasicrystal case, and (ii) the μSR relaxation rate arising solely from fluctuating Tb moments rather than from static inhomogeneity, multiple muon stopping sites, or weak disorder. The abstract and structure description do not supply a quantitative check that alternative static channels are excluded (e.g., via temperature-dependent line-shape analysis or comparison to a non-magnetic reference). If either condition fails, the fragmentation interpretation does not follow from the data.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript reports neutron diffraction and muon spin rotation measurements on the Tsai-type quasicrystal approximant Cd6Tb. It identifies a noncoplanar multi-k magnetic ground state consisting of Ising-like Tb moments arranged on a network of corner-sharing octahedra. Only one third of the Tb moments develop long-range order while the remainder exhibit strongly reduced static order accompanied by persistent spin dynamics on microsecond timescales; this coexistence is interpreted as a realization of magnetic fragmentation, a key prediction of octahedral spin-ice physics.","tokens_in":1970,"tokens_out":379,"duration_ms":16742,"significance":"If the fragmentation interpretation is robust, the work supplies an experimental platform for octahedral spin-ice physics in a periodic approximant that preserves the local connectivity of icosahedral quasicrystals. The combination of diffraction-derived structure and μSR dynamics offers a concrete test of fragmentation predictions outside the canonical pyrochlore setting.","major_comments":[{"comment":"Abstract (final paragraph) and μSR results section: the claim that the observed 1/3 long-range order plus reduced static moments and microsecond dynamics directly realizes magnetic fragmentation requires that the μSR relaxation arises solely from intrinsic Tb-moment fluctuations. No temperature-dependent line-shape analysis, comparison to a non-magnetic isostructural reference, or quantitative exclusion of static inhomogeneity or multiple muon sites is described; without these checks the fragmentation assignment remains an untested interpretation rather than a data-driven conclusion.","section":"Abstract"}],"minor_comments":[{"comment":"Abstract: the statement that neutron diffraction and μSR 'support' the claims would be strengthened by explicit mention of error bars, refinement R-factors, or data tables for the magnetic structure solution.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading of the manuscript and for identifying an important point regarding the robustness of the magnetic fragmentation interpretation. We address the major comment below.","responses":[{"response":"We agree that the fragmentation interpretation would be strengthened by the additional controls noted. The current manuscript combines neutron diffraction (establishing the 1/3 ordered multi-k structure on the octahedral network) with μSR (showing reduced static fields and persistent dynamics below the ordering temperature) to motivate the fragmentation scenario, but does not include an explicit non-magnetic reference comparison or a dedicated line-shape study. In the revised manuscript we will add μSR data on the isostructural non-magnetic compound Cd6Y to demonstrate that the observed relaxation is Tb-moment specific. We will also expand the μSR section with a temperature-dependent line-shape analysis and a brief discussion of why multiple muon sites or static inhomogeneity are inconsistent with the known crystal structure and the sharp magnetic transition seen in diffraction. These additions will make the assignment more data-driven while preserving the original scientific narrative.","revision_made":"yes","referee_comment":"[Abstract] Abstract (final paragraph) and μSR results section: the claim that the observed 1/3 long-range order plus reduced static moments and microsecond dynamics directly realizes magnetic fragmentation requires that the μSR relaxation arises solely from intrinsic Tb-moment fluctuations. No temperature-dependent line-shape analysis, comparison to a non-magnetic isostructural reference, or quantitative exclusion of static inhomogeneity or multiple muon sites is described; without these checks the fragmentation assignment remains an untested interpretation rather than a data-driven conclusion."}],"tokens_in":1326,"tokens_out":348,"duration_ms":22331,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that this paper reports neutron diffraction on Cd6Tb revealing a noncoplanar multi-k magnetic ground state on corner-sharing octahedra, with only one third of the Tb moments developing long-range order while the rest show reduced static moments and microsecond-scale dynamics from muon spin rotation. They interpret the coexistence as a possible realization of magnetic fragmentation in an octahedral spin-ice setting, using a periodic approximant that keeps the local geometry of quasicrystals.\n\nThe work is new in tying the specific multi-k arrangement and the partial-order fraction directly to the fragmentation idea in this material. Earlier approximant studies existed, but the combination of the structure details with the dynamic evidence here is not already in the literature.\n\nIt does well by giving experimenters a periodic system where full characterization is feasible, which is a practical step beyond purely aperiodic quasicrystals. Neutron data for the moment directions and muon data for the time scales are the right tools for this question.\n\nThe soft spot is the fragmentation interpretation. It assumes the observed dynamics come from intrinsic spin fluctuations tied to the octahedral connectivity rather than static disorder, multiple muon sites, or weak inhomogeneity. The abstract gives no error bars, refinement tables, or explicit tests that rule out those alternatives, so the link to theory stays suggestive until the full analysis is checked. The stress-test note on untested muon assumptions matches what is visible here.\n\nThis is for researchers in frustrated magnetism who want experimental test cases for spin-ice variants and fragmentation. A reader focused on new materials for quantitative checks will find value, even if the interpretation needs tightening.\n\nIt deserves a serious referee because the experimental approach is appropriate and the material is relevant, though revisions on the dynamic data analysis are likely needed.","headline":"Cd6Tb shows a multi-k structure with 1/3 ordered moments and muon-detected dynamics that could fit octahedral spin-ice fragmentation, but the muon part needs tighter checks against disorder.","tokens_in":2501,"tokens_out":444,"would_cite":false,"duration_ms":23921,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Neutron diffraction in Cd6Tb reveals a noncoplanar multi-k order of Ising-like moments on corner-sharing octahedra with only one third fully ordered.","keywords":["quasicrystal approximant","octahedral spin ice","magnetic fragmentation","neutron diffraction","muon spin rotation","Cd6Tb","multi-k magnetic order","Ising moments"],"falsifier":"A measurement showing that all Tb moments develop full long-range order below the transition temperature, or that the muon relaxation rate vanishes at low temperature without applied field, would falsify the fragmentation claim.","tokens_in":2725,"feed_emoji":"","tokens_out":727,"duration_ms":19018,"temperature":0.7,"pith_summary":"The paper establishes that the magnetic ground state of the quasicrystal approximant Cd6Tb consists of Ising-like Tb moments arranged on a network of corner-sharing octahedra in a noncoplanar multi-k configuration. Neutron diffraction identifies this structure while muon spin rotation shows that two-thirds of the moments exhibit strongly reduced static order and persistent dynamics on microsecond timescales. A sympathetic reader would care because this partial ordering matches the predicted magnetic fragmentation of octahedral spin-ice physics and occurs in a periodic material that retains the local geometry of icosahedral quasicrystals.","feed_headline":"Cd6Tb shows one-third ordering consistent with octahedral spin-ice fragmentation","feed_subtitle":"Neutron diffraction and muon data find noncoplanar order on octahedra with persistent dynamics in the remaining moments.","key_machinery":"The network of corner-sharing octahedra formed by the Tb sites, which supplies the local connectivity and Ising anisotropy needed for octahedral spin-ice rules and the resulting fragmentation into ordered and fluctuating moment components.","core_discovery":"Using neutron diffraction measurements, we find a noncoplanar multi-k magnetic ground state composed of Ising-like Tb moments arranged on a network of corner-sharing octahedra, the ingredients required to host octahedral spin-ice physics. Remarkably, only one third of the Tb moments develop long-range magnetic order, whereas the remaining moments display strongly reduced static order accompanied by persistent spin dynamics on microsecond timescales, as evidenced by muon spin rotation. This coexistence of ordered and fluctuating moments constitutes a potential realization of magnetic fragmentation - a key prediction of octahedral spin-ice physics - in a quasicrystal-related material.","pith_inferences":["If the octahedral network in Cd6Tb faithfully reproduces the relevant connectivity of quasicrystals, similar partial ordering should be searchable in other Tsai-type approximants with different rare-earth ions.","Temperature- or field-dependent muon measurements could distinguish intrinsic fragmentation dynamics from disorder-induced relaxation.","Single-crystal neutron studies under applied field would test whether the fluctuating component can be polarized without destroying the ordered fraction."],"forward_implications":["The multi-k noncoplanar structure satisfies the local ice-rule constraints on each octahedron while leaving a fluctuating sublattice.","The one-third ordered fraction matches the expected fragmentation pattern in which some moments freeze and others remain dynamic.","The same local octahedral connectivity is preserved in true quasicrystals, implying that fragmentation may appear there as well.","The microsecond dynamics detected by muons set a lower bound on the fluctuation timescale inside the fragmented state."],"fun_headline_variants":["Cd6Tb shows multi-k order on corner-sharing octahedra","One third Tb moments order in Cd6Tb with dynamics in rest","Octahedral spin ice physics in periodic Cd6Tb approximant","Noncoplanar Ising order fragments magnetically in Cd6Tb","Partial order and persistent dynamics coexist in Cd6Tb"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"That the observed partial ordering and muon relaxation arise directly from the octahedral geometry and spin-ice fragmentation rather than from sample disorder or extrinsic relaxation channels.","fun_headline_variants_meta":{"raw":{"variants":["Cd6Tb shows multi-k order on corner-sharing octahedra","One third Tb moments order in Cd6Tb with dynamics in rest","Octahedral spin ice physics in periodic Cd6Tb approximant","Noncoplanar Ising order fragments magnetically in Cd6Tb","Partial order and persistent dynamics coexist in Cd6Tb"]},"model":"grok-4.3","cost_usd":0.005385,"raw_usage":{"total_tokens":2609,"prompt_tokens":695,"num_sources_used":0,"completion_tokens":84,"cost_in_usd_ticks":53849500,"prompt_tokens_details":{"text_tokens":695,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1830,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":695,"tokens_out":84,"duration_ms":14808,"temperature":1.0,"reasoning_tokens":1830,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-29T20:33:29.700437+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A measurement showing that all Tb moments develop full long-range order below the transition temperature, or that the muon relaxation rate vanishes at low temperature without applied field, would falsify the fragmentation claim.","supporting_citations":[],"review_version":1}