{"id":"27a7196c-f644-4807-b5a5-1baed28211cf","arxiv_id":"2608.11089","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"DFT+U calculations predict altermagnetic (AFMo) order in Co-doped FeSb2 and a locally disordered spin-compensated (LDSC) state in Cr-doped FeSb2 at 15% doping.","lead":"Computer simulations of cobalt- and chromium-doped iron antimonide find different magnetic ground states for the two dopants: cobalt doping stabilizes an altermagnetic metal, while chromium doping stabilizes a locally disordered, spin-compensated arrangement. The study pairs a fast approximate search with detailed 120-atom supercell calculations and proposes a reusable protocol for exploring magnetic states in doped alloys.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The global ground-state claim rests on an unproven assumption that all low-energy non-AFMo states lie on swap paths between low-energy AFMo states; off-path configurations could overturn the 8.5 meV Cr ordering.","rationale":"The reader's weakest_assumption identifies exactly this bridge-sampling gap, and the conditional verdict is the right level of confidence. I would not move the verdict because the authors clearly disclose the search restriction and provide a physically motivated rationale: local swaps preserve low-energy local environments. However, the global 'ground state' language in the abstract goes beyond what the search establishes. The Hubbard-U sensitivity is a real but secondary concern: the VCA U-scan is nonmonotonic, and the explicit species-dependent U test (Table S1) does not include the LDSC competitor or Cr, so it does not settle the final ordering. A cluster-expansion exhaustive check of the 7,992 non-AFMo classes would directly test the bridge assumption; if it passes, the main qualitative conclusions are on much firmer ground. The paper deserves credit for its AMCheck verification, explicit enumeration of the AFMo manifold, and clear statement of limitations, all of which make the conditional verdict appropriate.","tokens_in":17145,"tokens_out":17104,"duration_ms":167924,"concrete_test":"Fit a cluster-expansion Hamiltonian to the DFT+U energies of all converged AFMo, LDSC, bridge, and SQS supercells at U = 5 eV, including single-site, pair, and triplet terms on the 40 transition-metal sites and the up/down spin-label degree of freedom. Use it to exhaustively score all 8,334 compensated spin-labeled classes, including the 7,992 non-AFMo classes, and re-run the full DFT+U relaxation at U = 5 eV for every class predicted to lie below the reported LDSC minimum by more than the cross-validation error. If any such class converges lower than LDSC for Cr, or lower than AFMo for Co, the bridge-sampling assumption is falsified; if none does, the ground-state claim is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing condition is not proven: the 7,992 non-AFMo compensated classes (Supplemental Sec. SIV.A) are not searched directly; only states on minimum-swap paths between converged low-energy AFMo endpoints are sampled. The claim that the Cr ground state is LDSC therefore assumes that no off-path non-AFMo decoration lies below the LDSC minimum, whose margin is only 8.5 meV per 120-atom cell. No argument is given that low-energy non-AFMo states must be geodesic intermediates between low-energy AFMo states, and the three SQS references are single macrostates that do not bound the remaining classes. Because the exchange moves are restricted to same-spin sublattices, clustered or chemically reorganized Cr/Co arrangements that are several swaps away from any low-energy AFMo endpoint are systematically excluded. The paper's transparent caveat that this is the lowest-energy state 'identified within our explicit-alloy search' does not remove the gap between that statement and the abstract's 'ground state' wording.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the magnetic ground states of Co- and Cr-doped FeSb2 at x=0.15 using DFT+U with a first-principles DFPT Hubbard parameter, combined with the Romeo occupation-matrix search in the virtual-crystal approximation and explicit 120-atom supercell calculations. In the VCA, the lowest-energy solution is ferrimagnetic for Co doping and altermagnetic for Cr doping at U=5 eV, but this ordering is nonmonotonic in U. In explicit supercells, the authors enumerate 342 symmetry-inequivalent AFMo-compatible decorations and 7,992 compensated non-AFMo classes, and they sample the latter along shortest atomic-swap paths between low-energy AFMo states. For Co doping, the lowest-energy sampled state is AFMo, about 3 meV per 120-atom cell below the lowest LDSC state; for Cr doping, the lowest sampled state is an LDSC configuration, about 8.5 meV per cell below the lowest sampled AFMo state. The paper argues that the Cr LDSC state is compatible with Néel's L-type fully compensated ferrimagnetism and consistent with the experimental short-range disordered magnetism, whereas Co doping stabilizes altermagnetism.","tokens_in":17349,"tokens_out":3738,"duration_ms":39220,"significance":"If the central claim holds, the paper resolves an apparent contradiction between altermagnetic predictions and experimentally observed disordered magnetism in Cr-doped FeSb2, and it provides a practical protocol for combining VCA-based magnetic-state searches with explicit alloy supercells. The work has notable strengths: the Hubbard U is obtained from DFPT rather than fitted, the explicit supercell enumeration is symmetry-based and independently verified with AMCheck, the numerical energy convergence is carefully controlled with a stated 0.01 meV error bar, and the limitations are discussed transparently, including the periodic-supercell caveat and the restricted sampling of non-AFMo configurations. The main risk to the central claim is the incompleteness of the non-AFMo search and the single value of the common Hubbard U used for the explicit comparisons.","major_comments":[{"comment":"The Cr ground-state claim rests on the unproven assumption that every low-energy non-AFMo compensated configuration lies on a shortest atomic-swap path between low-energy AFMo decorations. The paper itself states that the bridge search 'does not enumerate or relax that full set' of 7,992 non-AFMo classes, and the main text carefully says 'lowest-energy state identified within our explicit-alloy search.' However, the abstract and conclusions state without qualification that the ground state is LDSC for Cr doping. Since the Cr LDSC-vs-AFMo separation is only 8.5 meV per 120-atom cell (Fig. 3), an off-path non-AFMo decoration could overturn the ordering. The three SQS references are single macrostates that do not bound the remaining 7,989 classes. No argument is given that low-energy non-AFMo states must be geodesic intermediates between low-energy AFMo states, and the restriction to same-spin-sublattice swaps excludes clustered or chemically reorganized dopant arrangements. Please either provide a physical or statistical argument bounding the off-path states, or consistently phrase the central claim as 'lowest-energy state identified within our explicit-alloy search' and state the resulting uncertainty for the Cr interpretation.","section":"Supplemental Sec. SIV.A; main text Figs. 2-3"},{"comment":"The explicit-supercell comparisons use a common Hubbard U = 5 eV for Fe and the dopant, justified by DFPT values of about 5.1 eV (Co) and 5.3 eV (Cr) for the AFMo VCA states. The VCA landscape is itself nonmonotonic in U (Figs. S7-S8), and the Cr explicit ordering depends on an energy difference of only 8.5 meV per cell. The only species-dependent Hubbard test in explicit supercells is for Co doping (Table S1, with U_Fe,U_Co = 3.5,3.5 and 3.5,5.0 eV); no analogous test is provided for Cr. At minimum, the paper should report the Cr AFMo and LDSC energies for at least two additional U values or provide a clear argument for why the Cr LDSC-vs-AFMo ordering is robust to U. As written, the sensitivity of the central Cr conclusion to the common-U choice is untested.","section":"Supplemental Sec. SI and SIII.C; Table S1"},{"comment":"The statement that Cr doping 'makes long-range altermagnetism unlikely' extrapolates from a single low-energy LDSC motif in a 120-atom periodic cell. The paper correctly notes that the supercell is an ordered computational snapshot and does not determine a magnetic correlation length, but the conclusion goes beyond the evidence: a periodic LDSC motif does not exclude the possibility that other low-energy disordered or partially ordered configurations could support long-range AFMo coherence, nor does it exclude a state with multiple nearby defects. I recommend softening the conclusion to say that the sampled low-energy LDSC motif is the lowest-energy configuration found in this search and is consistent with, but does not prove, the absence of long-range altermagnetic order.","section":"Conclusions; main text around Figs. 4-5"}],"minor_comments":[{"comment":"The caption states 'Nswaps w.r.t. min-E AFMo config.' and 'Nswaps w.r.t. min-E LDSC config.' without defining 'w.r.t.'; please spell out 'with respect to' or use a notation that is immediately clear to the reader.","section":"Main text, Fig. 2 caption"},{"comment":"The caption of Fig. S11 refers to curves for AFMo, LDSC, and SQS macrostates, but the plot axes and the meaning of the crossing near 25 K would benefit from an explicit statement that the crossing does not imply an equilibrium transition because atomic exchange is frozen; the main text already explains this, but the caption alone is ambiguous.","section":"Supplemental Sec. SVI, Fig. S11"},{"comment":"The sentence 'We therefore discard this FM state' is slightly abrupt; since the discard is based on a known DFT+U high-spin bias and experimental consistency, please add a sentence explaining that this branch is not used in the explicit-supercell initializations and why it cannot be the physical ground state.","section":"Main text, Sec. on VCA-Romeo"}],"recommendation":"major_revision","confidential_remarks":"The paper is potentially important and the computational protocol is carefully presented, but the central claim for Cr doping is stronger than the evidence from the restricted sampling and the single common-U comparison. The authors may be able to address these by additional explicit calculations at a few U values and by consistently qualifying the Cr conclusion as applying to the sampled configuration space. The paper fits well within the scope of the journal, provided the claims are adjusted to match the demonstrated search. I do not see grounds for rejection, because the methods and transparency are sound and the gap is clearly acknowledged in the supplement."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First: the paper's real contribution is the workflow, not just the two ground-state assignments. Combining VCA-Romeo occupation-matrix search with a symmetry-first enumeration of 342 explicit AFMo supercells and then constructing LDSC states along shortest-swap paths is genuinely new, and it's a sensible way to attack a configurational space that can't be enumerated exhaustively. The authors are also honest about what they did not do: they state plainly that LDSC is the lowest-energy state identified within their explicit-alloy search, and they flag the DFT+U high-spin bias when discarding the FM VCA branch.\n\nThe central qualitative result—Co doping stabilizes altermagnetic order, Cr doping stabilizes a locally disordered compensated state—is consistent with the cited experiments and is supported by the calculations at U=5 eV, with energy separations of ~3 and ~8.5 meV per cell, numerically well resolved. The explicit test at U=3.5 eV for Co, and the full U scan for VCA, show the robustness is at least partially checked.\n\nThe load-bearing soft spot is the one the stress-test identifies: the non-AFMo space is not searched; only states on minimum-swap paths between low-energy AFMo endpoints are sampled. The claim that no off-path non-AFMo class lies below the LDSC minimum is unproven, and with only 8.5 meV separating Cr LDSC from the lowest AFMo state, a single off-path configuration could change the ordering. The paper's own caveat—'identified within our explicit-alloy search'—is accurate, but the abstract's 'ground state' phrasing glides past that caveat. I'd like to see either a denser sampling of the 7,992 classes (perhaps cluster expansion or Monte Carlo on the energies of a subset) or at least an explicit statement that the global claim is conditional on the bridge assumption.\n\nThe common U=5 eV is a minor concern; the U scan for VCA shows nonmonotonic switching, and the authors do not test Cr at a second U in explicit cells. That's a gap, but not a fatal one given the first-principles DFPT U and the explicit Co test.\n\nWho should read this: anyone working on doped FeSb2 or on altermagnet candidate screening. It's a useful protocol paper. It deserves a serious referee—the workflow is important enough and the calculations are careful enough. My recommendation: send it to review, with a request that the authors either strengthen the configurational sampling or soften the abstract's ground-state language.","headline":"A genuinely useful workflow for magnetic alloy searches, with a global ground-state claim that slightly overreaches its sampled configurational space.","tokens_in":17892,"tokens_out":2019,"would_cite":true,"duration_ms":18268,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"First-principles calculations say Co-doped FeSb2 is an altermagnetic metal, while Cr-doped FeSb2 is a locally disordered, spin-compensated magnet.","keywords":["altermagnetism","FeSb2","DFT+U","magnetic disorder","virtual-crystal approximation","supercell","Hubbard U","doped magnetic semiconductor"],"falsifier":"A calculation that relaxes all 7,992 compensated non-AFMo configurations for Cr0.15Fe0.85Sb2 at the same Hubbard U and finds one lower than the LDSC minimum would falsify the central claim; so would an experiment that fails to find the predicted AFMo splitting pattern in Co-doped crystals.","tokens_in":16898,"feed_emoji":"🧲","tokens_out":5882,"duration_ms":70919,"temperature":0.7,"pith_summary":"This paper uses first-principles calculations to determine what happens magnetically when the narrow-gap semiconductor FeSb2 is doped with cobalt or chromium. It argues that Co0.15Fe0.85Sb2 is an altermagnetic metal, with opposite-spin sublattices related by symmetry and no net moment, while Cr0.15Fe0.85Sb2 is instead a locally disordered, spin-compensated state that breaks the altermagnetic symmetry but keeps local antiparallel correlations. If correct, this explains why the Co-doped crystal shows altermagnetic-like optical signatures while the Cr-doped crystal behaves as a short-range or disordered magnet. The paper also introduces a way to search magnetic states without preselecting a magnetic class, using an approximate averaged-potential calculation to seed explicit supercell calculations.","feed_headline":"Co turns FeSb2 altermagnetic; Cr makes it disordered","feed_subtitle":"First-principles search says the same host becomes either a compensated altermagnet or a locally disordered magnet.","key_machinery":"The load-bearing construction is a 120-atom $4\\times1\\times5$ supercell (Fe$_{34}M_6$Sb$_{80}$) that is the smallest cell at $x=0.15$ supporting an exact altermagnetic operation. Because exhaustive relaxation of all 7,992 compensated non-altermagnetic configurations is out of reach, the authors sample only the subset lying on shortest atomic-swap paths between converged low-energy AFMo endpoints; the lowest-energy such non-AFMo interior state is the LDSC motif. A single same-spin Fe–dopant occupation swap converts the AFMo minimum into the LDSC minimum.","core_discovery":"The central result is that the two dopants push the same host into different magnetic ground states. For Co0.15Fe0.85Sb2, the lowest-energy explicit supercell configuration found is AFMo, an altermagnetic state in which a symmetry operation exchanges the fully spin-polarized sublattices and the total moment vanishes. For Cr0.15Fe0.85Sb2, the lowest-energy state is the LDSC configuration, obtained from the AFMo minimum by one same-spin Fe-dopant swap; this removes every global spin-sublattice-exchanging operation while preserving most local antiparallel Fe–Fe and Fe–Cr environments, so it is formally compatible with Néel's fully compensated L-type ferrimagnetism. The authors conclude that long-range altermagnetic order is unlikely in the Cr-doped compound at low temperature.","pith_inferences":["The bridge assumption is the main unproven step: non-altermagnetic states that are not on shortest swap paths between low-energy AFMo endpoints are never relaxed. A full enumeration or a genetic search over the 7,992 classes could either confirm the LDSC minimum or reveal a deeper state.","The same local-disorder mechanism may explain why other predicted altermagnets fail to show spin-split bands in experiment: quenched dopant disorder could realize LDSC-like motifs even when the ordered altermagnetic state is lower in energy.","The approximate configurational free energy for Co doping crosses near 25 K because LDSC has many more realizations; if such configurations can be frozen during growth, samples might display finite-temperature disorder signatures even though the zero-temperature ground state is altermagnetic."],"forward_implications":["If the Co result is right, Co$_{0.15}$Fe$_{0.85}$Sb$_2$ is a zero-temperature altermagnetic metal, in line with its nearly compensated magnetization and optical-conductivity comparison.","If the Cr result is right, Cr$_{0.15}$Fe$_{0.85}$Sb$_2$ has no long-range altermagnetic order at low temperature; its nearly compensated, disordered magnetism is captured by the LDSC motif rather than by a conventional antiferromagnet.","The virtual-crystal approximation by itself is misleading for these alloys: at the computed Hubbard U it predicts a weak ferrimagnetic ground state for Co doping that does not survive in explicit supercells, so approximate and explicit simulations need to be used together.","The swap-based bridge sampling provides a tractable way to explore compensated magnetic disorder in doped magnets, reducing 7,992 classes to a handful of physically motivated configurations.","The LDSC motif's low energy means that local chemical disorder can disrupt altermagnetic coherence even at zero temperature, a consideration for any candidate altermagnet where dopant placement is quenched."],"supporting_citations":[{"why":"Predicts that doped FeSb2 becomes an altermagnetic metal in VCA; supplies the starting prediction this work tests with explicit supercells.","marker":"[23]"},{"why":"Experimental optical-conductivity evidence that Co0.15Fe0.85Sb2 is nearly compensated and consistent with AFMo; the Co half of the claim is compared against this.","marker":"[24]"},{"why":"Experimental evidence of short-range/disordered, nearly compensated magnetism in Cr0.15Fe0.85Sb2; the LDSC interpretation is built to match these observations.","marker":"[25]"},{"why":"Romeo algorithm searches the magnetic energy landscape without preselecting a magnetic state, producing the VCA minima used to seed supercells.","marker":"[31]"},{"why":"Self-consistent DFPT method from which the common U ≈ 5 eV Hubbard parameter is computed.","marker":"[34]"},{"why":"AMCheck independently verifies that the 342 enumerated supercell classes are genuinely altermagnetic.","marker":"[41]"}],"fun_headline_variants":["Co dopes FeSb2 into altermagnet; Cr into spin disorder","Doping splits FeSb2: Co altermagnet, Cr local spin disorder","Dopant decides: FeSb2 becomes altermagnet or disordered magnet","Same host, two dopants: Co gives altermagnet, Cr local spin disorder","Co doping altermagnetizes FeSb2; Cr doping disorders spins"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The search assumes that the true low-energy non-altermagnetic states all appear on shortest atomic-swap paths between low-energy altermagnetic states, so the 7,992 unsearched non-altermagnetic configurations cannot hide a state lower than the sampled LDSC minimum.","fun_headline_variants_meta":{"raw":{"variants":["Co dopes FeSb2 into altermagnet; Cr into spin disorder","Doping splits FeSb2: Co altermagnet, Cr local spin disorder","Dopant decides: FeSb2 becomes altermagnet or disordered magnet","Same host, two dopants: Co gives altermagnet, Cr local spin disorder","Co doping altermagnetizes FeSb2; Cr doping disorders spins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001047,"raw_usage":{"total_tokens":4419,"prompt_tokens":984,"completion_tokens":3435,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":600,"completion_tokens_details":{"reasoning_tokens":3332}},"tokens_in":600,"tokens_out":3435,"duration_ms":21702,"temperature":1.0,"reasoning_tokens":3332,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T10:32:19.291530+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A calculation that relaxes all 7,992 compensated non-AFMo configurations for Cr0.15Fe0.85Sb2 at the same Hubbard U and finds one lower than the LDSC minimum would falsify the central claim; so would an experiment that fails to find the predicted AFMo splitting pattern in Co-doped crystals.","supporting_citations":[{"cited_title":"Experimental investigation of altermagnetic order in Cr-doped FeSb2","cited_arxiv_id":"2605.01088","evidence_quote":"Experimental evidence of short-range/disordered, nearly compensated magnetism in Cr0.15Fe0.85Sb2; the LDSC interpretation is built to match these observations."},{"cited_title":"Ponet , author E","cited_arxiv_id":null,"evidence_quote":"Romeo algorithm searches the magnetic energy landscape without preselecting a magnetic state, producing the VCA minima used to seed supercells."},{"cited_title":"Timrov , author N","cited_arxiv_id":null,"evidence_quote":"Self-consistent DFPT method from which the common U ≈ 5 eV Hubbard parameter is computed."}],"review_version":1}