{"id":"75f49edb-e88c-4993-9675-b3dead1c7cb5","arxiv_id":"2507.11118","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Bilayer CrMoC2S6 is predicted to be a hidden fully-compensated ferrimagnet: PT symmetry hides each layer's ferrimagnetic spin splitting, and an out-of-plane electric field reveals it.","lead":"A new magnetic state called hidden fully-compensated ferrimagnetism is proposed, in which the total spin polarization is zero but each of two inversion-partner layers carries its own fully-compensated ferrimagnetic spin splitting. First-principles calculations identify a chromium molybdenum sulfide bilayer as the first candidate, where an electric field reveals the hidden layer-localized spin patterns.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The hidden fully-compensated ferrimagnetic state rests on the PT-symmetric AFM1 ordering being the ground state, but its 1.32 meV/cell advantage over AFM2 is within typical DFT error; an improved treatment could reverse the ordering and remove the PT symmetry.","rationale":"The reader's weakest-assumption analysis identifies the same load-bearing point: the entire hidden fully-compensated ferrimagnetic scenario depends on the AFM1 magnetic ordering being the ground state, and that ordering is favored by only 1.32 meV/cell. The paper's own three-point U-scan gives positive but small energy differences, and these are within the scatter expected from DFT functionals, Hubbard U choices, and vdW corrections in layered magnets. If AFM2 were stabilized by any of these or by strain, the PT symmetry would be lost, the global bands would no longer be forced degenerate, and the predicted hidden fully-compensated ferrimagnetic spin-splitting would not exist. The band-structure degeneracy under PT and the agreement of the CBM splitting with eEd are useful internal checks, but they presuppose the AFM1 ground state rather than proving it. No independent experimental realization is available, and no alternative functional or many-body benchmark is provided, so the concern is genuine rather than manufactured. Nevertheless, the concern is exactly the one the reader already flagged, and the CONDITIONAL verdict already reflects it; no adjustment is needed.","tokens_in":9310,"tokens_out":6092,"duration_ms":79259,"concrete_test":"Recompute the AFM1 versus AFM2 energy difference for the same optimized bilayer using HSE06 (or SCAN+rVV10) with U_eff=3 eV on Cr/Mo d orbitals, and also with an alternative vdW correction such as MBD or TS; if the PT-symmetric AFM1 is not lower by at least 5 meV per cell in both, the hidden fully-compensated ferrimagnetic ground state is not robustly established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In 'Material realization', the PT-symmetric AFM1 ordering is found to be only 1.32 meV per unit cell lower than AFM2 at U(Cr,Mo)=(3,3) eV; the U-scan gives 2.47, 1.32, and 1.71 meV for (3,2), (3,3), and (4,3). These energy differences are at or below the accuracy typically expected of GGA+U with DFT-D3 for magnetic and vdW-dominated layered systems. Since only AFM1 satisfies PT symmetry, the claimed global spin degeneracy, the hidden fully-compensated ferrimagnetic state, and the E-field-separated local spin splitting all disappear if a different functional, a different vdW correction, strain, or an experimental growth condition stabilizes AFM2. The authors note the smallness but do not test beyond three U points; no hybrid functional, SCAN, or many-body check is reported. The internal consistency of the band plots and the eEd estimate supports the calculation conditional on AFM1, but cannot validate the ground-state selection. This is the load-bearing point: the concept is sound, but the specific material realization is established by a 1.3 meV energy difference.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces the concept of hidden fully-compensated ferrimagnetism, in which a PT-symmetric system has zero total spin polarization while each of the two inversion-partner sectors is a fully-compensated ferrimagnet with nonzero local spin polarization. Using DFT+U calculations, the authors propose PT-symmetric bilayer CrMoC2S6 as a candidate realization, show that an out-of-plane electric field separates the local s-wave spin splitting, and report a CBM splitting of 248 meV at E=0.04 V/Å, consistent with the eEd estimate of 250 meV. The paper also discusses experimental detection via spin-ARPES and possible layer-locked transport effects.","tokens_in":9546,"tokens_out":8504,"duration_ms":107051,"significance":"If the material prediction holds, the concept extends hidden spin polarization from nonmagnetic and altermagnetic systems to fully-compensated ferrimagnets, providing a new class of zero-net-magnetization magnets with layer-resolved spin splitting. The DFT calculations are conventionally specified and include a U-scan, magnetic anisotropy energy, field-dependent band structures, and a quantitative consistency check against the simple eEd model, which strengthens confidence in the field-induced splitting. The conceptual framework is clearly presented and builds naturally on the author's prior hidden altermagnetism proposal, although the distinction from earlier symmetry classifications of hidden spin polarization in antiferromagnets could be sharpened.","major_comments":[{"comment":"The claim that the AFM1 configuration (intralayer AFM, interlayer FM) satisfies PT symmetry appears inconsistent with the standard transformation of axial magnetic moments. For a collinear configuration, time reversal T flips all spins, while spatial inversion P leaves axial vectors unchanged; hence PT maps a moment at r to the opposite moment at P(r). Since P relates the two layers, PT symmetry requires corresponding sublattice moments in the two layers to be antiparallel (interlayer AFM), not parallel (interlayer FM). As written, AFM1 would be P-symmetric but not PT-symmetric, and the globally degenerate bands shown in Figure 3(e) would not follow. Please provide the explicit spin arrangement for AFM1 and AFM2 (e.g., spin directions of Cr and Mo in each layer) and demonstrate that the PT operation maps AFM1 onto itself. If the labels are swapped, the text should be corrected; otherwise the central symmetry argument needs revision.","section":"Material realization"},{"comment":"The ground-state selection is load-bearing for the entire claim, but the AFM1 vs AFM2 energy difference is only 1.32 meV per cell at the chosen U=(3,3) eV, with values of 2.47, 1.32, and 1.71 meV from the three U sets. These differences are at or below the accuracy typically expected of GGA+U with DFT-D3 for magnetic and van der Waals layered materials. Because only AFM1 (as claimed) preserves PT symmetry, the hidden fully-compensated ferrimagnetic state, the global spin degeneracy, and the field-induced layer-separated spin splitting all depend on an ordering that could be reversed by a different treatment of correlations, a different vdW correction, strain, or growth conditions. The authors acknowledge the smallness but do not test beyond three U points. I recommend adding a cross-check with another functional (e.g., SCAN or HSE), a systematic vdW/strain dependence, or at least an explicit discussion of the robustness of the AFM1 ground state based on available experimental or computational evidence.","section":"Material realization"}],"minor_comments":[{"comment":"The phrase 'P T-bilayer' should be written as 'PT-bilayer' with no space; similar spacing issues appear in a few other places.","section":"Abstract"},{"comment":"Reference [33] is cited as 'Front. Phys. in press (2025)'; please update to the full published reference if available, as the paper relies on this prior concept for comparison.","section":"Introduction"},{"comment":"The sentence 'From a symmetry perspective, ferrimagnetism is often subsumed under ferromagnetism' is vague; it would be helpful to specify exactly how the fully-compensated ferrimagnetic sector differs from a ferromagnetic sector in the symmetry classification.","section":"Concept of hidden fully-compensated ferrimagnetism"},{"comment":"The label 'ss' in Figure 5 is not defined in the caption; it is defined in the text as the spin-splitting of the CBM, but the caption should state this explicitly.","section":"Figure 5"}],"recommendation":"major_revision","confidential_remarks":"The paper is an incremental extension of the author's own hidden altermagnetism concept, and the new contribution is the explicit fully-compensated ferrimagnetic sector. The distinction from Ref. [34] (which classifies HSP in antiferromagnets into six types) is argued but would be stronger with a formal symmetry comparison. The main technical risk is the ground-state ordering; the 1.32 meV energy difference is very small, and the symmetry labeling issue with AFM1/AFM2 needs careful resolution before the material prediction can be considered reliable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Good paper to know about if you track hidden spin polarization or 2D magnets. The new thing is the concept: hidden fully-compensated ferrimagnetism, where each inversion-partner sector of a PT-symmetric bilayer is a fully-compensated ferrimagnet with s-wave spin splitting, while the total spin polarization is zero. That is a clean extension of the author's earlier hidden altermagnetism, and the paper correctly emphasizes the difference in local splitting symmetry. The concrete candidate, PT-bilayer CrMoC2S6, is sensible, and the E-field response is internally consistent: 248 meV computed CBM splitting vs ~250 meV from eEd at 0.04 V/Å, with linear gap and splitting trends. The layer-locked current cartoon is a fair summary of the expected physics.\n\nThe soft spot is the one the author flags himself: the AFM1 ground state (intralayer AFM, interlayer FM) beats AFM2 by only 1.32 meV per cell at U=3,3, and 2.47 and 1.71 meV at the other two U values. That is inside typical error for GGA+U+DFT-D3. Since only AFM1 has PT symmetry, the entire hidden state is contingent on that ordering. The paper does not test beyond three U points, no hybrid/SCAN or vdW-scheme sensitivity, and no strain dependence. That is a genuine weakness, but it is not a fatal one: the symmetry argument is sound and the U-scan at least shows no accidental flips. A referee should ask for more rigorous ground-state verification or at least a clear caveat that the material prediction is provisional.\n\nThe novelty relative to ref [34] is asserted more than it is mapped. The paper says [34] does not explicitly single out the fully-compensated ferrimagnet sector, and from a symmetry standpoint ferrimagnetism is often subsumed under ferromagnetism. That may be true, but it would be better to show directly where the six-type classification does or does not cover this case. Also, no input structures or energies are provided, which slows independent checking, though the calculations are conventional.\n\nWho this is for: people working on altermagnetism, hidden spin polarization, and 2D spintronics. It deserves a serious referee; the concept is clear, the candidate is concrete, and the main risk is the ground-state energetics, which is exactly what a referee should test. I would cite it if I worked on 2D magnets.","headline":"Useful symmetry-based concept with a concrete 2D candidate, but the PT-symmetric ground state rests on a sub-meV energy difference that needs stronger support.","tokens_in":10102,"tokens_out":2211,"would_cite":true,"duration_ms":26502,"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":"A $\\mathcal{PT}$-symmetric bilayer of CrMoC$_2$S$_6$ is predicted to be a hidden fully-compensated ferrimagnet, with zero total spin polarization but layer-localized fully-compensated ferrimagnetic order and field-separable spin splitting.","keywords":["hidden fully-compensated ferrimagnetism","hidden spin polarization","PT symmetry","bilayer CrMoC2S6","density functional theory","electric-field-controlled spin splitting","zero net magnetization"],"falsifier":"If a density-functional, hybrid-functional, or experimental measurement finds the AFM2 ordering (intralayer antiferromagnetic with interlayer antiferromagnetic) to be lower in energy under any reasonable Hubbard U, exchange-correlation functional, van der Waals scheme, or strain within the considered range, the central claim fails because AFM1 is required for $\\mathcal{PT}$ symmetry. Likewise, spin-resolved photoemission or spin-polarized transport on bilayer CrMoC$_2$S$_6$ under an out-of-plane field that shows no layer-locked s-wave spin splitting, or a splitting very different from the predicted 248 meV at $E=0.04$ V/\\AA{}, would contradict the prediction.","tokens_in":9074,"feed_emoji":"⚡","tokens_out":7274,"duration_ms":80218,"temperature":0.7,"pith_summary":"The paper introduces hidden fully-compensated ferrimagnetism as a magnetic state in which a $\\mathcal{PT}$-symmetric system has zero total spin polarization while each of the two inversion-partner layers is itself a fully-compensated ferrimagnet with nonzero local spin polarization. It argues that this is the fully-compensated-ferrimagnet counterpart of hidden altermagnetism, producing local momentum-independent (s-wave) spin splitting instead of momentum-dependent d-wave splitting. Using density-functional calculations with a Hubbard U, the paper predicts that $\\mathcal{PT}$-symmetric bilayer CrMoC$_2$S$_6$ in the intralayer-antiferromagnetic, interlayer-ferromagnetic ordering realizes this state. An out-of-plane electric field is shown to break the effective $\\mathcal{PT}$ symmetry and separate the layer-localized spin-split bands, with a calculated 248 meV conduction-band splitting at $E=0.04$ V/\\AA{} that matches the simple $eEd$ estimate of 250 meV. The material is therefore presented as an observable, electrically switchable member of a new class of zero-magnetization spintronic magnets.","feed_headline":"Electric field lifts hidden spin degeneracy in zero-magnet ferrimagnet","feed_subtitle":"A vertical electric field separates the layer-localized spin splitting hidden in a zero-magnetization bilayer.","key_machinery":"The carrying construction is $\\mathcal{PT}$ symmetry in a bilayer, enforced by stacking two fully-compensated ferrimagnetic monolayers so that spatial inversion $P$ and time reversal $T$ swap the two layers. This forces $E_\\uparrow(\\mathbf{k})=E_\\downarrow(\\mathbf{k})$ for every band, guaranteeing zero net spin polarization, while each layer separately retains fully-compensated ferrimagnetism whose opposite-spin sublattices are related by null symmetry, giving nonzero local spin polarization and s-wave (momentum-independent) spin splitting. The tunable mechanism is the out-of-plane electric field, which breaks the effective $\\mathcal{PT}$ symmetry and lifts the degeneracy with a splitting approximately equal to $eEd$, where $d$ is the interlayer distance of the two magnetic layers.","core_discovery":"The central claim is that a $\\mathcal{PT}$-symmetric bilayer built from a fully-compensated ferrimagnetic monolayer is a hidden fully-compensated ferrimagnet: every band of the whole system is doubly degenerate because the joint $\\mathcal{PT}$ operation maps each state to its spin-reversed partner, yet each inversion-partner sector independently hosts fully-compensated ferrimagnetic order in which spin-up and spin-down magnetic atoms occupy different environments and are connected by null symmetry rather than by rotation or mirror symmetry. The paper predicts that bilayer CrMoC$_2$S$_6$ in the AFM1 ordering (intralayer antiferromagnetic, interlayer ferromagnetic) realizes this state, with a strictly zero total magnetic moment and global spin degeneracy. When an out-of-plane electric field is applied, it breaks the effective $\\mathcal{PT}$ symmetry and produces s-wave spin splitting localized on each layer; the predicted 248 meV splitting of the conduction-band minimum at $E=0.04$ V/\\AA{} agrees with the $eEd$ estimate of 250 meV, and reversing the field reverses the layer/spin order. The paper thus claims to establish a concrete, electrically controllable example of hidden fully-compensated ferrimagnetism.","pith_inferences":["Editorial inference: the 1.32 meV per cell energy difference between AFM1 and AFM2 orderings at $U=3$ eV lies within typical density-functional error, so tests with alternative Hubbard parameters, hybrid functionals, or van der Waals corrections could determine whether this hidden state survives in practice.","Editorial inference: the same bilayer stacking recipe could be applied to other reported fully-compensated ferrimagnetic monolayers, and one would expect similar field-tunable layer-localized s-wave splitting in those systems.","Editorial inference: spin- and angle-resolved photoemission on bilayer CrMoC$_2$S$_6$ under an applied vertical field could directly test the predicted layer-separated spin splitting, with the splitting appearing only under the field as a clean fingerprint of hidden fully-compensated ferrimagnetism.","Editorial inference: the approximately linear $eEd$ scaling suggests that increasing the interlayer separation through spacer layers could amplify or tune the spin splitting, potentially making the effect stronger at practical electric fields."],"forward_implications":["Bilayer CrMoC$_2$S$_6$ in the AFM1 ordering behaves as a net-zero-magnetization magnet with globally spin-degenerate bands yet carries local fully-compensated ferrimagnetic order, enabling spintronic functions with high immunity to magnetic-field disturbance.","An out-of-plane electric field separates the hidden spin splitting layer by layer, and reversing the field reverses the layer and spin order, providing an electrical switch for layer-locked spin transport.","The near-quantitative match between the calculated 248 meV splitting and the $eEd$ estimate of 250 meV at $E=0.04$ V/\\AA{} indicates that the field-induced splitting is predictable and approximately linear in the applied field.","Because each sector is a fully-compensated ferrimagnet, the paper implies that field-enabled layer-locked anomalous Hall/Nernst effects and magneto-optical Kerr effects should appear while total magnetization remains zero.","The stacking recipe of taking any fully-compensated ferrimagnetic monolayer as a building block for a $\\mathcal{PT}$-symmetric bilayer makes hidden fully-compensated ferrimagnetism a general material class rather than a single-compound accident."],"supporting_citations":[{"why":"Defines hidden spin polarization in inversion-symmetric nonmagnetic crystals, the effect the paper extends to fully-compensated ferrimagnets.","marker":"[1]"},{"why":"Supplies the $eEd$ estimate for gate-field-controlled spin splitting that the paper compares with its 248 meV DFT result.","marker":"[25]"},{"why":"Establishes two-dimensional fully-compensated ferrimagnetism and the net-zero-magnetization condition used to define each sector.","marker":"[31]"},{"why":"Proposes hidden altermagnetism, the sibling construction whose $\\mathcal{PT}$-bilayer symmetry logic the paper adapts to fully-compensated ferrimagnets.","marker":"[33]"},{"why":"Classifies antiferromagnets hosting hidden spin polarization and provides the symmetry context for why an individual sector can be a fully-compensated ferrimagnet.","marker":"[34]"},{"why":"Provides the CrMoC$_2$S$_6$ material platform whose stability, magnetic ordering, and electronic structure the paper builds on.","marker":"[36]"}],"fun_headline_variants":["Electric field unveils hidden ferrimagnetism in zero-magnet bilayer","Zero-magnet bilayer exposes layer-localized spin splitting under field","Hidden ferrimagnet CrMoC2S6 responds to field with 248 meV split","Field splits hidden spin states in fully-compensated ferrimagnet bilayer","Voltage-controlled hidden ferrimagnetism in a PT-symmetric bilayer"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The construction depends on the AFM1 magnetic ordering (intralayer antiferromagnetic, interlayer ferromagnetic) being the true ground state of bilayer CrMoC$_2$S$_6$; the calculations place it only 1.32 meV per cell below the competing AFM2 ordering at $U=3$ eV, so any correlation treatment, van der Waals correction, strain, or field that reverses this ordering would destroy the $\\mathcal{PT}$ symmetry and the hidden fully-compensated ferrimagnetic state.","fun_headline_variants_meta":{"raw":{"variants":["Electric field unveils hidden ferrimagnetism in zero-magnet bilayer","Zero-magnet bilayer exposes layer-localized spin splitting under field","Hidden ferrimagnet CrMoC2S6 responds to field with 248 meV split","Field splits hidden spin states in fully-compensated ferrimagnet bilayer","Voltage-controlled hidden ferrimagnetism in a PT-symmetric bilayer"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000432,"raw_usage":{"total_tokens":2234,"prompt_tokens":1008,"completion_tokens":1226,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":624,"completion_tokens_details":{"reasoning_tokens":1129}},"tokens_in":624,"tokens_out":1226,"duration_ms":13284,"temperature":1.0,"reasoning_tokens":1129,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:16:25.459662+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"If a density-functional, hybrid-functional, or experimental measurement finds the AFM2 ordering (intralayer antiferromagnetic with interlayer antiferromagnetic) to be lower in energy under any reasonable Hubbard U, exchange-correlation functional, van der Waals scheme, or strain within the considered range, the central claim fails because AFM1 is required for $\\mathcal{PT}$ symmetry. Likewise, spin-resolved photoemission or spin-polarized transport on bilayer CrMoC$_2$S$_6$ under an out-of-plane field that shows no layer-locked s-wave spin splitting, or a splitting very different from the predicted 248 meV at $E=0.04$ V/\\AA{}, would contradict the prediction.","supporting_citations":[{"cited_title":"Zhang, Q","cited_arxiv_id":null,"evidence_quote":"Defines hidden spin polarization in inversion-symmetric nonmagnetic crystals, the effect the paper extends to fully-compensated ferrimagnets."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the $eEd$ estimate for gate-field-controlled spin splitting that the paper compares with its 248 meV DFT result."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proposes hidden altermagnetism, the sibling construction whose $\\mathcal{PT}$-bilayer symmetry logic the paper adapts to fully-compensated ferrimagnets."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Classifies antiferromagnets hosting hidden spin polarization and provides the symmetry context for why an individual sector can be a fully-compensated ferrimagnet."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the CrMoC$_2$S$_6$ material platform whose stability, magnetic ordering, and electronic structure the paper builds on."}],"review_version":1}