{"id":"4e1b2022-d33a-469c-aaba-d972a9b52cf9","arxiv_id":"2607.24599","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Hole-doped RuO2 shows a quasi-linear correlation between Ru magnetic moment and quantum-oscillation spin splitting, plus a distinct AM-state frequency spectrum usable as an experimental fingerprint.","lead":"DFT calculations show hole doping in RuO2 drives a nonmagnetic-to-altermagnetic transition and a quasi-linear link between Ru moment and a quantum-oscillation spin-splitting signature. That link, plus a simplified high-doping oscillation spectrum, is offered as an experimental fingerprint for altermagnetism in a still-debated material.","discovery_kind":"new_application","skeptic_critique":{"model":"moonshotai/kimi-k3","headline":"The entire Δ–m_Ru correlation and AM fingerprint inherit from a rigid electron-count doping model that is never checked against any realistic hole-doping realization (Ru vacancies, O excess, gating), even though the paper itself names these as the experimental routes.","rationale":"The reader's weakest assumption already identified this soft spot (small fixed U + rigid valence-electron-count doping in a compound whose magnetism is experimentally contested and methodologically fragile). My pass sharpens it: the most load-bearing element is not the U value per se — the U-collapse of the Δ–m_Ru data (Fig. 3c) is genuine internal evidence of robustness against U — but the doping representation, which is varied over zero alternatives. The paper names Ru vacancies and O excess as the physical doping routes yet tests only uniform electron removal; every quantitative element of the strongest claim (moment values, the 0.7/0.9 hole/cell transitions, Δ, the simplified AM spectrum) is conditional on that choice. I also note the quasi-linearity is analytically generic (Eq. 8 linearizes at small mJ_H regardless of d-wave character), which mildly deflates the correlation's diagnostic power but is not a correctness problem. Because the reader's verdict was already CONDITIONAL on precisely these theory caveats, and I find no internal inconsistency or circularity (the correlation is computed, not assumed; convergence checks on angular sampling are documented; the tight-binding model honestly labels itself qualitative and is extended in SM S3), the concern does not move the verdict — it specifies the single check that would resolve it. Verdict stays CONDITIONAL; the defect-supercell test would either solidify the fingerprint or confine it to gated devices.","tokens_in":19918,"tokens_out":3056,"duration_ms":112609,"concrete_test":"Recompute one high-doping case (1.3 hole/cell) and one transition case (0.7 hole/cell) with explicit doping realizations at matched hole concentration — e.g., a 2×2×1 supercell with one Ru vacancy (relaxed), and/or virtual-crystal approximation on the Ru site — using identical U=0.4 eV, SOC, and SKEAF pipeline. If m_Ru, the AM-vs-NM/FM energy ordering, or Δ for bands 5/6 shift by more than ~20% relative to the rigid-electron-count results (or the AM state destabilizes), the fingerprint is an artifact of the doping idealization and the experimental-identification claim must be restricted to electrostatic-gating scenarios.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The strongest claim — that Δ for the band-5/6 pockets correlates quasi-linearly with m_Ru and can fingerprint altermagnetism in hole-doped RuO2 — is computed entirely within DFT+U (U = 0.2–0.6 eV) where \"hole doping is modeled by adjusting the total number of valence electrons\" (Computational Details), i.e., a uniformly charged cell with compensating background, at an unrelaxed experimental structure. For the central claim to be experimentally meaningful, this idealized doping must reproduce what actual hole doping does to the magnetism and Fermi surface. Two specific fragilities: (1) The paper motivates the study by Ru vacancies and O excess (Sec. III A, citing Ref. 28), but never tests a single explicit defect. Ru vacancies introduce strong local potential perturbations and scattering; they can pin or destroy local moments, shift the Lifshitz transitions that define the 0.7 and 0.9 hole/cell jumps, and alter the band-5/6 pockets that Δ depends on. If the AM ground state at ≥0.9 hole/cell or the Δ values move substantially under realistic doping, the proposed fingerprint loses its target. (2) The method's calibration is weak for this compound: the same DFT+U framework at small U fails to produce an AM ground state in stoichiometric RuO2 (paper admits \"unphysically large Hubbard interaction\" is required, Sec. III A), and experiments match NM quantum-oscillation frequencies (Refs. 32–33). So the doping-induced moments that drive the whole correlation are predictions from a method whose magnetic ground state is known to be delicately balanced in exactly this material. A secondary, lesser point: linearity of Δ in m at small m is generic — Eq. (8) shows splitting is linear in mJ_H for any two-sublattice exchange splitting by Taylor expansion — so the quasi-linearity itself carries little AM specificity; the discriminative content lives in the angle dependence and the simplified high-doping spectrum, which inherit the same doping-model risk.","agreement_with_reader":"agree"},"referee_report":{"model":"moonshotai/kimi-k3","summary":"The manuscript presents DFT+U (PBE, U=0.2–0.6 eV, SOC) calculations of hole-doped RuO2, with doping implemented by varying the total valence electron count, and computes angle-dependent quantum-oscillation (QO) frequencies via SKEAF. The authors track a pair of closed Fermi-surface pockets (bands 5 and 6), define a normalized angularly averaged frequency-splitting measure Δ, and report a quasi-linear correlation between Δ and the Ru local moment m_Ru (linear fit below 0.5 μB, R²=0.992, with data for different U collapsing onto one line). A minimal 2D d-wave altermagnet tight-binding model reproduces the small-moment linearity analytically, and an extended model with next-nearest-neighbor hopping and a doping-dependent Fermi level removes the saturation plateau. Two jumps in m_Ru and Δ near 0.7 and 0.9 hole/cell are interpreted as an NM→intermediate→AM sequence, and the simplified QO spectrum above 0.9 hole/cell is proposed as an experimental fingerprint of the stable AM state.","tokens_in":20394,"tokens_out":4315,"duration_ms":156061,"significance":"If the rigid-doping idealization is a reasonable guide to real hole-doped RuO2, this work provides the first systematic map of how QO spectra evolve through the NM–AM transition and gives concrete, falsifiable predictions: (i) a low-frequency (3–9 kT) pair of branches degenerate at θ=0 and splitting at finite θ as a d-wave spin-splitting diagnostic, and (ii) a sharply simplified spectrum above ~0.9 hole/cell as a fingerprint of the stable AM state. The angular-sampling convergence tests (Fig. S3), robustness checks across U = 0.2–0.6 eV and ±1% strain (Figs. S4–S5), and an analytic small-moment expansion (Eq. 8) that explains rather than merely fits the linearity are genuine strengths, as is the extended model in §S3 that removes the artificial saturation. The significance is tempered by the contested experimental status of RuO2 magnetism and by the fact that all moments and frequencies derive from a single uncalibrated doping model; the predictions are useful to experimentalists only to the extent that idealized electron removal mimics vacancies, O excess, or gating.","major_comments":[{"comment":"The entire doping evolution is computed by changing the total valence electron count in a uniformly compensated cell at an unrelaxed experimental structure. Yet §III A motivates the study with Ru vacancies and O excess (citing Ref. 28) and electrostatic gating (Ref. 42) as the experimental realizations. No explicit-defect or gated supercell calculation is presented. Vacancy potentials can pin or destroy local moments and shift the Lifshitz features that define the 0.7 and 0.9 hole/cell jumps, on which the proposed fingerprint depends. The concern is amplified by the paper's own admission (§III A) that stoichiometric RuO2 needs an unphysically large U for an AM ground state in this framework, while experiments match NM QO frequencies (Refs. 32–33): the doping-induced moments driving the correlation are uncalibrated predictions of this method. At minimum, one explicit Ru-vacancy or O-exces","section":"§II (Computational Details); §III A"},{"comment":"The 'intermediate state' is inferred solely from two jumps in m_Ru, Δ, and the DOS, plus a spectrum simplification. No total-energy comparison across the transitions is shown (the only energy given is AM vs FM at 1.3 hole/cell, ~16 meV/cell), and no symmetry or order-parameter analysis distinguishes this regime. Notably, the 0.7–0.9 hole/cell range already has finite m_Ru (0.138–0.17 μB) and finite Δ — by the paper's own definition it is an AM state with a smaller moment, not a distinct phase. The jumps appear to be Lifshitz/magnetic-moment discontinuities (band 4's new Fermi crossing at 0.9, Fig. S8), not evidence for a new state. The term 'intermediate state' and the NM→intermediate→AM narrative in the abstract and §IV need either substantiation (energetics, magnetic-space-group characterization) or replacement by a description in terms of two successive transitions.","section":"§III C; Fig. 3(b), Fig. 5"},{"comment":"The central quantitative result — quasi-linearity of Δ vs m_Ru below 0.5 μB — is, as the authors' own Eq. (8) shows, the generic small-moment limit: ΔE ≈ 2Δε·mJH/√(Δε²+t₃²T²) is linear in m by perturbation theory. The DFT fit (R²=0.992) therefore largely confirms the expected small-moment expansion rather than revealing a new correlation. What is genuinely non-trivial is the collapse of the slope across U = 0.2–0.6 eV and the persistence of linearity up to ~0.5 μB without saturation. The text should be restructured to state precisely which aspects are non-obvious, and the abstract phrase 'meaningful correlation ... quasi-linear trend over a broad doping range' should be qualified accordingly.","section":"§III B, Fig. 3(c); Eq. (8)"},{"comment":"Bands 5–6 are tracked across the full 0–1.5 hole/cell range, but the Fermi surface undergoes reconstructions in this interval (band 4 develops a new Fermi-level crossing at 0.9 hole/cell, Fig. S8; band 2 becomes multi-lobed). Since band indices are assigned by energy ordering at each k, Lifshitz events can permute or hybridize band identity. The SM (Fig. S2) states the branches are identified by degeneracy at θ=0 and continuity, but the procedure for maintaining a consistent band-5/6 assignment through the 0.7 and 0.9 jumps should be made explicit, with a statement on whether Δ is continuous in the band-resolved sense across the jumps or is a post-hoc pairing of branches.","section":"§III B; Figs. 2–3; Fig. S8"}],"minor_comments":[{"comment":"Eq. (2) defines Δ with the absolute value inside the angular average, ⟨|F5−F6|⟩, while Eq. (3) writes |⟨A5⟩−⟨A6⟩|. These coincide only if F5−F6 has a fixed sign over the averaging range. Given the d-wave symmetry (branches degenerate at θ=0, splitting at finite θ), please state explicitly whether the sign is preserved over the integration window and, if not, which expression is actually evaluated.","section":"Eqs. (2)–(3)"},{"comment":"The linear fit gives intercept 0.025±0.008 (in units of 10⁻¹), which is ~3σ from zero; calling it 'negligible' is loose. Also, the notation 'Δ(10⁻¹)' for the fit variable is unclear — define the rescaled quantity explicitly.","section":"§III B, Fig. 3(c)"},{"comment":"For the unstrained calculations the structure from Ref. 28 is used 'without further structural relaxation', while strained cases are relaxed internally. Please justify that residual forces on the unrelaxed structure are negligible, or report them, since Fermi-surface areas (and hence Δ) are sensitive to small structural changes.","section":"§II"},{"comment":"Fig. 1(c)–(d): the caption refers to red arrows marking DOS peaks, but the arrow colors/labels are hard to discern; please check figure legibility. Similarly, in Fig. 3(a) the hollow vs solid dot convention for bands 5/6 should be restated in the caption of each panel where used.","section":"Figs. 1, 3"},{"comment":"Data availability is 'upon reasonable request'. Given that the paper's predictive value lies in the angle-resolved frequency tables, depositing the SKEAF inputs and the computed F(θ) branch data (or a repository link) would substantially aid experimental comparison.","section":"Data Availability"},{"comment":"Several key citations (Refs. 9, 12, 25–27, 29) carry 2025–2026 dates and some appear to be in press; please verify volume/page details at proof stage.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is technically competent and internally consistent, but the referee should note for the editor that all quantitative predictions inherit the unresolved experimental status of RuO2 magnetism: the authors' own framework requires unphysically large U for an AM ground state at zero doping, and measured QO frequencies favor the NM phase. The doping-induced moments driving the headline correlation are thus predictions of an uncalibrated method in a contested material. This does not invalidate the calculations, but it bears on how strongly the 'fingerprint' language should be allowed to stand. The citation pattern is appropriate to the altermagnetism literature; I see no novelty-disclosure issues. Fit for the journal is good if the doping-model and 'intermediate state' issues are addressed."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The useful core here is a full doping trajectory of angle-dependent quantum oscillations in RuO2, not another generic altermagnet manifesto. They track closed pockets (bands 5/6), define a normalized frequency split Δ, and show it tracks m_Ru quasi-linearly below ~0.5 μB across U=0.2–0.6 eV and modest strain, with a clean R² fit. The high-doping AM spectrum also simplifies in a way that is visually distinct from the NM/intermediate mess. That is new relative to the Li and Huang QO papers they cite, and the intermediate regime near 0.7–0.9 hole/cell is documented with DOS, bands, and spectra rather than hand-waved.\n\nMethods are standard and transparent: VASP PBE+U, dense k-mesh, SKEAF, SOC on. The 2D d-wave model is not oversold; it explains small-m linearity (which is partly generic from the exchange-split two-band expansion) and they improve the match with next-nearest hoppings in the SM. Circularity is low—Δ and m_Ru come from the same DFT but the correlation is an observation, not an assumption.\n\nThe real soft spot is the doping model. Hole doping is a uniform valence-electron shift on the unrelaxed experimental cell. They motivate Ru vacancies, O excess, and gating, then never compute a single defect or gated slab. If vacancies scramble the band-5/6 pockets or move the Lifshitz jumps, the experimental fingerprint moves with them. Related: small-U DFT is known not to stabilize AM in stoichiometric RuO2, and existing QO experiments favor NM frequencies—so the moments that drive the whole story are predictions from a delicately balanced method. That does not kill the paper; it bounds how hard they can sell “signatures for identifying the AM state.”\n\nThis is for people already in the RuO2/altermagnet fight and for anyone planning QO on doped samples. Worth a serious referee. I would engage, cite the Δ construction and the doping maps, and push authors to either defect-check or state the rigid-doping caveat up front.","headline":"Solid DFT map of QO vs hole doping in RuO2 with a usable Δ–moment correlation; the fingerprint claim is only as strong as rigid electron-count doping.","tokens_in":20484,"tokens_out":555,"would_cite":true,"duration_ms":18059,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Hole doping turns RuO2 altermagnetic, and quantum oscillations track the spin splitting as a near-linear function of the Ru moment.","keywords":["altermagnetism","RuO2","quantum oscillations","hole doping","Fermi surface","spin splitting","d-wave altermagnet","density functional theory"],"falsifier":"Measure angle-dependent quantum-oscillation frequencies on hole-doped RuO2 samples across roughly 0.5–1.5 holes per cell; check whether the low-frequency pair that is degenerate at θ=0 and splits at finite angle yields a Δ that rises quasi-linearly with an independently measured Ru moment, and whether the spectrum abruptly simplifies above about 0.9 hole per cell.","tokens_in":20107,"feed_emoji":"🧲","tokens_out":986,"duration_ms":22747,"temperature":0.7,"pith_summary":"RuO2 is a debated candidate for altermagnetism: compensated magnetic order with ferromagnet-like spin-split bands. This work uses first-principles calculations to show what happens when holes are added. Hole doping rebuilds the Fermi surface, grows the Ru magnetic moment, and strengthens spin splitting. For one pair of simple closed pockets, a normalized difference of quantum-oscillation frequencies rises almost linearly with that moment over a wide doping window, matching a minimal two-dimensional d-wave altermagnet model at small moment. The system also passes through an intermediate regime before locking into a stable altermagnetic state whose angle-dependent oscillation spectrum is distinctly simpler. Those two signatures—the quasi-linear correlation and the simplified spectrum—are offered as practical fingerprints for experiments that want to confirm altermagnetism in doped RuO2.","feed_headline":"Hole doping leaves a quantum-oscillation fingerprint of altermagnetism","feed_subtitle":"In RuO2, spin-splitting frequency gaps track the Ru moment nearly linearly and the stable magnetic state has a simpler spectrum","key_machinery":"The normalized relative frequency difference Δ = ⟨|F5−F6|⟩ / ⟨(F5+F6)/2⟩ for the closed pockets of bands 5 and 6. It converts the d-wave spin splitting of those pockets into a single angle-averaged number that can be plotted against the Ru moment and compared with a minimal tight-binding altermagnet model.","core_discovery":"In hole-doped RuO2, first-principles quantum-oscillation spectra show that a normalized frequency splitting Δ between a pair of closed Fermi-surface pockets (bands 5 and 6) correlates quasi-linearly with the local Ru magnetic moment over a broad doping range, a trend captured by a minimal 2D d-wave altermagnet model at small moment. The material evolves from nonmagnetic through an intermediate regime into a stable altermagnetic state whose angle-dependent frequencies are distinctly simplified, giving concrete oscillation-based signatures of altermagnetism.","pith_inferences":["If the linear Δ–moment slope is material-generic for d-wave altermagnets, a single calibrated quantum-oscillation run could estimate local moments when neutron or XMCD data are unavailable.","Electrostatic gating or controlled Ru-vacancy engineering that reaches the high-doping simplified-spectrum window would be the cleanest experimental path to settle the RuO2 magnetism debate.","Failure of Δ to track moment under strain that preserves the closed pockets would falsify the claim that the correlation is symmetry-driven rather than DFT-specific."],"forward_implications":["Quantum-oscillation frequency maps can fingerprint the stable altermagnetic regime in hole-doped RuO2 via a simplified, compact spectrum.","The quasi-linear Δ–m_Ru relation gives an experimental proxy for altermagnetic spin splitting without needing full spin-resolved ARPES.","An intermediate doping window (roughly 0.7–0.9 hole/cell) should show mixed or partially reconstructed Fermi-surface topology between nonmagnetic and fully altermagnetic limits.","Similar closed-pocket frequency differences may serve as spin-splitting diagnostics in other d-wave altermagnet candidates under doping or strain."],"fun_headline_variants":["Hole doping fingerprints altermagnetism in RuO2 quantum oscillations","Spin-splitting gaps track Ru moment quasi-linearly in doped RuO2","Quantum oscillations reveal altermagnetic transition in hole-doped RuO2","RuO2 Fermi-surface pockets show altermagnetic spin splitting under doping","Angle-dependent oscillations mark stable altermagnetism in doped RuO2"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"That ordinary density-functional calculations with a small fixed Hubbard U on ruthenium and a simple change in total electron count correctly describe the real magnetic ground state and Fermi surface of hole-doped RuO2.","fun_headline_variants_meta":{"raw":{"variants":["Hole doping fingerprints altermagnetism in RuO2 quantum oscillations","Spin-splitting gaps track Ru moment quasi-linearly in doped RuO2","Quantum oscillations reveal altermagnetic transition in hole-doped RuO2","RuO2 Fermi-surface pockets show altermagnetic spin splitting under doping","Angle-dependent oscillations mark stable altermagnetism in doped RuO2"]},"model":"grok-4.5","effort":"low","cost_usd":0.004498,"raw_usage":{"total_tokens":1354,"prompt_tokens":852,"num_sources_used":0,"completion_tokens":83,"cost_in_usd_ticks":44984000,"prompt_tokens_details":{"text_tokens":852,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":419,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":852,"tokens_out":83,"duration_ms":8212,"temperature":1.0,"reasoning_tokens":419,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T10:54:10.589545+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Measure angle-dependent quantum-oscillation frequencies on hole-doped RuO2 samples across roughly 0.5–1.5 holes per cell; check whether the low-frequency pair that is degenerate at θ=0 and splits at finite angle yields a Δ that rises quasi-linearly with an independently measured Ru moment, and whether the spectrum abruptly simplifies above about 0.9 hole per cell.","supporting_citations":[],"review_version":1}