{"id":"c4e9ca98-264f-4e55-8075-f79a3c2881c5","arxiv_id":"2608.00871","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Fe1+δSb is established as a non-collinear antiferromagnet with predicted momentum-dependent spin splitting, and chromium doping introduces a cluster spin-glass state.","lead":"This paper shows that the iron antimonide compound Fe1+δSb is a new member of a recently discovered family of magnets that combine zero net magnetization with useful spin-dependent electronic behavior. It also shows that substituting chromium tunes the magnetism into a glassy state, pointing to practical tuning strategies for spintronic materials.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The f-wave Sz-dominated splitting is computed for clean stoichiometric FeSb, leaving the defining interstitial Fe and the paper's own local Amm2 distortion untested; the central claim requires that this model link survives.","rationale":"The reader identified the same weakest assumption: the DFT calculation is performed on a clean stoichiometric FeSb cell while the actual material contains 17–30% interstitial Fe. I sharpen this by noting that the manuscript's own PDF refinement finds a local Amm2 distortion that grows with δ, providing a concrete symmetry-lowering mechanism that the calculation ignores. The neutron diffraction and the τT/PT symmetry analysis for the magnetic order are credible, so the empirical magnetic structure is not the problem. The claim that Fe1+δSb is a non-collinear NRSS AFM could still survive if the f-wave pattern persists in a supercell including interstitial Fe; the paper's conclusion is therefore not falsified, but the link from idealized FeSb to real Fe1+δSb is unverified. A single supercell calculation would settle whether the stoichiometric approximation changes the qualitative spin texture. Direct spin-resolved ARPES is not provided, but that is a higher bar than the field typically uses for NRSS predictions; the missing supercell calculation is the more specific and decisive gap. I therefore keep the reader's CONDITIONAL verdict unchanged.","tokens_in":12919,"tokens_out":7923,"duration_ms":73532,"concrete_test":"Recompute the DFT+U spin-resolved band structure of Fig. 7 using the same √3×√3 magnetic supercell but with one Fe atom added at a 2d interstitial site (composition Fe1.17Sb), using the experimental lattice parameters and the refined 120° in-plane spin configuration; compare the Sz and Sx/Sy projections along Γ–M and Γ–K around E_F. If the six-lobed Sz-dominated f-wave pattern does not persist, the central prediction is an artifact of the stoichiometric model rather than a property of Fe1+δSb.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing link is the move from an idealized stoichiometric DFT cell to the real Fe1+δSb samples. The band structures in Figs. 6–7 are calculated for FeSb with empty 2d interstitial sites, whereas the refined compositions place 17–30% Fe on those sites. The manuscript's own PDF analysis (Table S3) shows that at δ=0.30 the locally disordered structure is better described by an orthorhombic Amm2 model (Rw drops from 9.98% to 6.24%), i.e., the symmetry that the f-wave classification uses is already locally broken in the very material being claimed as a platform. Interstitial Fe is not electronically inert: it adds d states near E_F, changes the electron count, and the paper associates it with cluster-spin-glass behavior, so it can plausibly alter the low-energy spin texture. The paper neither tests this supercell nor flags it as a limitation. Consequently, the neutron-diffraction result establishes a compensated 120° order, and the symmetry analysis establishes that some spin splitting is allowed, but the specific, novel prediction—Sz-dominated, odd-parity f-wave-like splitting—is not demonstrated for Fe1+δSb as synthesized.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a combined experimental and computational study of the NiAs-type metal-excess antiferromagnet Fe1+δSb (δ ≈ 0.17–0.30). Neutron diffraction establishes a 120° coplanar compensated magnetic order with propagation vector k = (1/3, 1/3, 0) that persists across the composition range, with the ordered moment decreasing from 1.74 to 0.96 μB/Fe as interstitial Fe content increases. PDF refinements show growing local orthorhombic (Amm2) distortions with increasing δ. DFT+U band-structure calculations on stoichiometric FeSb with this magnetic order predict momentum-dependent spin splitting dominated by the out-of-plane Sz component with an odd-parity f-wave-like symmetry, which the authors interpret as non-relativistic spin splitting (NRSS) characteristic of a non-collinear altermagnet. The paper also examines the Cr-substituted series Fe1.2xCr1.2−1.2xSb and reports enhanced low-temperature magnetization and cluster spin-glass behavior at intermediate Cr content.","tokens_in":13124,"tokens_out":9676,"duration_ms":83028,"significance":"The experimental determination of the magnetic structure and the local structural distortions is careful and provides a solid basis for the symmetry-based classification of Fe1+δSb as a candidate non-collinear NRSS antiferromagnet. If the DFT prediction is robust to the inclusion of interstitial Fe, the paper would add a new and tunable platform to the emerging field of non-relativistic spin splitting, with interstitial concentration as a design knob. The spin-space-group symmetry reasoning is consistent with recent theoretical frameworks for odd-parity magnets. However, since the central f-wave splitting is a prediction on an idealized FeSb cell rather than on the actual Fe1+δSb composition, the significance for the synthesized materials is presently conditional.","major_comments":[{"comment":"The band-structure and spin-splitting results are computed for stoichiometric FeSb with empty interstitial 2d sites, whereas the samples studied have refined interstitial occupancies of 0.175–0.302 (Table S1) and, at δ = 0.30, a local structure better described by an orthorhombic Amm2 model (Table S3; Rw decreases from 9.98% to 6.24%). Because interstitial Fe adds d states near EF, alters the electron count, and is associated with the spin-glass behavior noted in the paper, and because the Amm2 distortion lowers the symmetry on which the f-wave classification is based, the calculation as presented does not establish that the predicted Sz-dominated odd-parity spin splitting survives in Fe1+δSb as synthesized. The authors should either test a supercell containing interstitial Fe (e.g., an ordered model with an Amm2-like arrangement) to show the splitting persists, or explicitly identify this as a limitation and soften the claim that the material is a non-collinear NRSS platform. This is the load-bearing gap between the DFT prediction and the paper's central claim.","section":"Methods (DFT) and Figs. 6–7"},{"comment":"The statement that τT symmetry is automatically broken for k = (0,0,0) is not correct in general: a collinear compensated antiferromagnet with sublattices related by a pure translation (e.g., a simple A-type AFM) preserves τT, which is precisely why it does not exhibit NRSS. The subsequent argument for Fe1+δSb—that the 120° arrangement forces any candidate translation to be combined with a rotation—is the correct one and supports the breaking of τT. The erroneous sentence should be removed or corrected, as the symmetry analysis is the foundation of the NRSS classification.","section":"Symmetry analysis (Results and Discussion)"}],"minor_comments":[{"comment":"The matrix equation for the NiAs-to-Amm2 transformation is garbled in the manuscript; it should be typeset properly and the basis transformation should be defined clearly.","section":"Methods/PDF transformation"},{"comment":"Table S5 reports 'Mx (1/2My)' without defining whether the entries are the total moment or a component; the main text states the moment decreases from 1.74 to 0.96 μB/Fe, which appears to be the magnitude derived from the table's components. Please make this relationship explicit.","section":"Table S5 and main text"},{"comment":"The notation for composition is inconsistent: the abstract uses δ = 0.17–0.30, while the text refers to Fe1.17Sb, Fe1.23Sb, and Fe1.30Sb. Unify the notation for clarity.","section":"Throughout"},{"comment":"The Hubbard U and Hund's J parameters are taken from Ref. [27], which deals with hematite and chromia rather than FeSb; a brief justification for these values for FeSb, or a sensitivity test, would strengthen the calculation.","section":"Methods (DFT+U)"},{"comment":"The text states that in-plane spin splittings are negligible, but the figures show small but nonzero Sx and Sy projections; reporting a quantitative scale of the splitting (e.g., in meV) would help the reader assess the physical relevance.","section":"Figs. 6 and 7"}],"recommendation":"major_revision","confidential_remarks":"The experimental core of the paper is sound and the neutron diffraction results are credible. The main issue is the gap between the DFT prediction on idealized FeSb and the actual Fe1+δSb samples that contain 17–30% interstitial Fe and local symmetry lowering. The authors have not acknowledged this limitation, and it should be addressed before publication. I also note that the title and abstract use 'establishing' for a prediction that has not been experimentally verified; this phrasing should be moderated. The reliance on several recent preprints for key symmetry arguments is acceptable in this fast-moving field, but the authors should confirm the final claims against the published versions if they change."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nTwo things you should know up front. First, this paper gives a careful, honest re-examination of a magnetic structure that has been known since 1973—Fe1+δSb's 120° coplanar order—and adds a genuinely new prediction: in the stoichiometric limit, the compound would show f-wave-like, Sz-dominated non-relativistic spin splitting, placing it in the small non-collinear NRSS class. Second, that prediction is made for a crystal that does not match the actual samples, and the paper never confronts the discrepancy.\n\nThe experimental core is solid. The neutron diffraction refinements establish the √3×√3 propagation vector and show a monotonic suppression of the ordered Fe moment from 1.74 to 0.96 μB as interstitial Fe content increases from 0.17 to 0.30. The PDF work is a real plus: it shows that at δ = 0.30 the local structure is better described by an orthorhombic Amm2 model, implying that the hexagonal symmetry used in the DFT calculation is already broken locally. The symmetry analysis for NRSS is standard but applied correctly, and the Cr-substitution series—including the cluster spin-glass signature at intermediate concentrations—adds useful phase-diagram information.\n\nThe soft spot is the load-bearing DFT step. The band structures in Figs. 6 and 7 are computed for stoichiometric FeSb with the interstitial 2d sites empty. The actual material is Fe1.17–1.30Sb, with 17–30% of those sites occupied by Fe. Interstitial Fe is not electronically inert: it contributes d states near the Fermi level, changes the electron count, and the paper itself associates it with the cluster-spin-glass freezing. The Amm2 distortion the authors see locally would break the 6-fold rotation that underpins the six-lobed Sz pattern. The paper neither runs a supercell test nor flags this as a limitation. The refined moment for Fe1.30Sb also has about 30% uncertainty, so the concentration trend in moments is less crisp than the text suggests.\n\nNone of this destroys the paper. The neutron data are good, the symmetry reasoning is sound, and the DFT prediction is a forward calculation rather than a fit to a measured splitting. But 'establishing Fe1+δSb as a non-collinear NRSS antiferromagnet' overstates what is demonstrated. The claim is conditional on the idealized model transferring to the real material.\n\nThis paper deserves a serious referee. The right referees will ask for either a supercell calculation with interstitial Fe or an explicit limitation paragraph. I would not cite it as evidence of NRSS in Fe1+δSb until that gap is closed, but I would bring it to a reading group to discuss exactly that tension.\n\nRecommendation: send to peer review, with the interstitial Fe issue as the central required revision.","headline":"A solid neutron-diffraction study of a known magnetic structure with a fresh NRSS classification, but the headline f-wave spin splitting is predicted for a stoichiometric crystal that the real interstitial-doped samples do not match.","tokens_in":13693,"tokens_out":3089,"would_cite":false,"duration_ms":27973,"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":"Neutron and density functional theory establish $\\mathrm{Fe}_{1+\\delta}\\mathrm{Sb}$ as a non-collinear spin-splitting antiferromagnet.","keywords":["non-relativistic spin splitting","altermagnetism","non-collinear antiferromagnet","Fe1+δSb","NiAs-type structure","neutron diffraction","density functional theory","spin glass"],"falsifier":"Compute the bands in a supercell that explicitly includes the experimentally refined interstitial Fe atoms and occupancies, and compare the low-energy $S_z$-projected bands with the predicted six-lobed pattern; if the interstitials erase the $S_z$-dominated splitting or change it qualitatively, the paper's central claim fails. A spin-resolved photoemission experiment on $\\mathrm{Fe}_{1.17}\\mathrm{Sb}$ looking for that same sign-changing pattern in the $k_z=0$ plane would provide the complementary experimental test.","tokens_in":12690,"feed_emoji":"🧲","tokens_out":10733,"duration_ms":92877,"temperature":0.7,"pith_summary":"The paper aims to establish $\\mathrm{Fe}_{1+\\delta}\\mathrm{Sb}$, a metal-rich iron antimonide in the NiAs structure, as a non-collinear non-relativistic spin-splitting (NRSS) antiferromagnet. Neutron diffraction shows that the iron moments form a compensated (zero-net-moment) $120^\\circ$ coplanar triangular order with propagation vector $\\mathbf{k}=(1/3,1/3,0)$, and density functional theory predicts a momentum-dependent spin splitting dominated by the out-of-plane spin component with an odd-parity f-wave-like symmetry. The combination matters because it puts compensated magnetism and spin-splitting electronic bands in one material: in principle, spintronic functions such as spin-polarized currents and spin torques could be obtained without the stray fields of a ferromagnet. The paper also shows that interstitial iron and chromium substitution are experimentally accessible tuning knobs for the magnetic order and its glassy dynamics.","feed_headline":"Fe1+δSb splits spins with zero net magnetic moment","feed_subtitle":"Neutron diffraction pins the 120° triangular order; theory predicts an odd-parity f-wave spin splitting.","key_machinery":"The load-bearing object is the $120^\\circ$ coplanar triangular magnetic order and the symmetry breaking it enforces. In that order each Fe moment points along one of three in-plane directions separated by $120^\\circ$, so the moments cancel while the magnetic cell expands to $\\sqrt{3}\\times\\sqrt{3}$; because adjacent layers along $c$ are aligned, the structure cannot be mapped onto itself by inversion combined with time reversal, and the nonzero propagation vector prevents a pure translation–time-reversal symmetry. The argument then uses a standard criterion for NRSS antiferromagnets: a compensated magnet that breaks both $PT$ and $\\tau T$ can have momentum-dependent spin splitting without spin-orbit coupling. Density functional theory realizes that criterion here as a six-lobed, odd-parity f-wave-like $S_z$-dominated polarization pattern, which survives when spin-orbit coupling is added, and the paper classifies it through spin-group symmetry criteria for odd-parity magnets.","core_discovery":"The central claim, stated on the paper's own terms, is that $\\mathrm{Fe}_{1+\\delta}\\mathrm{Sb}$ ($\\delta = 0.17$–$0.30$) is a non-collinear NRSS antiferromagnet. Neutron powder diffraction shows the regular-lattice Fe moments lie in the $ab$ plane and are rotated $120^\\circ$ from one another, forming a compensated triangular order with a $\\sqrt{3}\\times\\sqrt{3}$ magnetic supercell and $\\mathbf{k}=(1/3,1/3,0)$; the moments stay parallel along $c$. Symmetry analysis says this order breaks both the combined parity–time-reversal ($PT$) and translation–time-reversal ($\\tau T$) symmetries while keeping the net magnetization zero. Density functional theory on the stoichiometric parent then gives momentum-dependent spin splitting even without spin-orbit coupling, with the out-of-plane $S_z$ component dominating and a six-lobed odd-parity f-wave-like pattern in the $k_z=0$ plane. The paper further reports that increasing interstitial Fe suppresses the ordered moment and introduces local orthorhombic distortions, and that intermediate Cr substitution produces a ferromagnetic component and a cluster spin glass.","pith_inferences":["The symmetry criterion is material-blind: any compensated $120^\\circ$ coplanar order with parallel layer stacking and the same propagation vector should show the same f-wave-like out-of-plane NRSS, so the paper's logic could be used to screen other NiAs-type and triangular-lattice antiferromagnets.","The PDF analysis reveals local orthorhombic distortions that are not included in the density functional theory model; testing whether those distortions preserve or modify the six-lobed $S_z$ splitting is a direct next step that the paper does not take.","The small ferromagnetic component at intermediate Cr doping may let an external magnetic field couple to the otherwise field-insensitive compensated order, potentially enabling field control of altermagnetic domains; this is an extension the paper only hints at."],"forward_implications":["The NiAs structure now hosts both collinear altermagnets and a non-collinear NRSS magnet, suggesting the structure type is a repeatable source of spin-splitting compensated magnets.","The predicted sign-changing, momentum-dependent splitting means $\\mathrm{Fe}_{1+\\delta}\\mathrm{Sb}$ should support spin-polarized currents and spin-splitting torques without a net magnetic moment, which is the practical payoff of NRSS antiferromagnets.","Because increasing interstitial Fe monotonically lowers the ordered moment and N\\'eel temperature, stoichiometry offers a continuous experimental dial for the magnetic state that underlies the splitting.","Chromium substitution at intermediate concentrations introduces a ferromagnetic component and cluster spin-glass dynamics, giving a second chemical route to alter the ground state and, potentially, the altermagnetic domain population."],"supporting_citations":[{"why":"Prior neutron study establishing the 120° coplanar magnetic order that this paper re-refines and extends to three compositions.","marker":"[17]"},{"why":"Defines the non-relativistic spin-splitting and altermagnet classification that motivates the study.","marker":"[1]"},{"why":"Theoretical work showing NRSS can appear in non-collinear compensated magnets when PT and τT are broken.","marker":"[13]"},{"why":"Earlier electronic-structure study of a related NiAs-type triangular magnet predicting f-wave-like splitting; the template for the present calculation.","marker":"[16]"},{"why":"Study of off-stoichiometric CrSb showing interstitial metal stabilizes the NiAs structure, supporting the role assigned to excess Fe.","marker":"[18]"},{"why":"Direct observation of altermagnetic band splitting in CrSb, the compound forming the solid solution studied here.","marker":"[10]"},{"why":"Spin-group symmetry criteria used to classify the odd-parity f-wave-like splitting as altermagnetic NRSS.","marker":"[36]"},{"why":"Provides the Mydosh-parameter and Vogel-Fulcher criteria used to identify the Cr-substituted phase as a cluster spin glass.","marker":"[39]"}],"fun_headline_variants":["Fe1+δSb: f-wave spin splitting with zero net moment","Triangular order, f-wave spin splitting: Fe1+δSb","Non-collinear Fe1+δSb splits spins without net moment","Fe1+δSb: 120° order yields f-wave spin splitting, no net moment","Zero net moment, f-wave spin splitting in triangular Fe1+δSb"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the calculated band structure of idealized stoichiometric FeSb represents the real $\\mathrm{Fe}_{1+\\delta}\\mathrm{Sb}$, even though the samples contain 17–30% interstitial Fe; if those interstitials significantly alter the low-energy bands or break the symmetry that forces the $S_z$-dominated splitting, the central claim would collapse.","fun_headline_variants_meta":{"raw":{"variants":["Fe1+δSb: f-wave spin splitting with zero net moment","Triangular order, f-wave spin splitting: Fe1+δSb","Non-collinear Fe1+δSb splits spins without net moment","Fe1+δSb: 120° order yields f-wave spin splitting, no net moment","Zero net moment, f-wave spin splitting in triangular Fe1+δSb"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001567,"raw_usage":{"total_tokens":6321,"prompt_tokens":1075,"completion_tokens":5246,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":691,"completion_tokens_details":{"reasoning_tokens":5145}},"tokens_in":691,"tokens_out":5246,"duration_ms":32992,"temperature":1.0,"reasoning_tokens":5145,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:15:36.518300+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the bands in a supercell that explicitly includes the experimentally refined interstitial Fe atoms and occupancies, and compare the low-energy $S_z$-projected bands with the predicted six-lobed pattern; if the interstitials erase the $S_z$-dominated splitting or change it qualitatively, the paper's central claim fails. A spin-resolved photoemission experiment on $\\mathrm{Fe}_{1.17}\\mathrm{Sb}$ looking for that same sign-changing pattern in the $k_z=0$ plane would provide the complementary experimental test.","supporting_citations":[],"review_version":2}