{"id":"3a5ed54d-6a1d-481b-9826-2f226e1e25cf","arxiv_id":"2412.17232","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"DFT predicts that AA-stacked MnPX3/MPX3 heterostructures are altermagnets, AB-stacked ones are compensated ferrimagnets, and ferroelectric CuInP2X6 substrates make the spin splitting switchable.","lead":"This paper predicts that stacking manganese thiophosphate monolayers on certain nonmagnetic or ferroelectric substrates creates non-relativistic spin splitting in the electronic bands. The effect can be altermagnetic, compensated ferrimagnetic, or electrically switchable, which could be useful for spintronic devices.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'Luttinger-protected' zero magnetization in AB-stacked heterostructures is a non-sequitur: integer magnetization need not vanish, and no computed total moments are reported, so the central 'fully compensated' claim is not yet established.","rationale":"The reader's weakest assumption is exactly the one I would flag: the Luttinger theorem argument cannot enforce zero magnetization, because an integer total moment is not the same as a zero total moment. This is not an objection to the existence of spin splitting, which is supported by detailed band-structure calculations, nor to the altermagnetic classification of the AA-stacked cases, which rests on symmetry analysis and d-wave spin-splitting patterns. The missing piece is a direct numerical check of the total magnetic moment. Since the reader already assigned CONDITIONAL, this concern does not move the verdict; it sharpens the specific condition that should be attached: either report the computed moments and verify compensation, or revise the terminology. I would not recommend REJECT because the central spin-splitting results are concrete and reproducible in principle, and the compensation issue is addressable by a single additional calculation.","tokens_in":9498,"tokens_out":4607,"duration_ms":45051,"concrete_test":"Recompute the spin-polarized DFT ground state of each AB-stacked heterostructure (MnPX3/MPX3 and MnPX3/CuInP2X6, both polarization states) and integrate the spin density over the unit cell (or equivalently sum spin-resolved occupancies) to obtain the total magnetic moment in μ_B/cell. State the value for all six MPX3 cases and the two ferroelectric cases. If every moment is zero within numerical tolerance (e.g., <0.01 μ_B/cell), the 'fully compensated' claim is verified. If any case has a nonzero integer moment, the paper must drop the word 'compensated' for that case and revise the title and abstract; the splitting predictions themselves remain testable.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is in the text immediately after Fig. 4: 'the heterostructures considered in this work are semiconductors, which require the total magnetization per cell to be an integer according to the Luttinger theorem. Therefore, the full compensation of the macroscopic magnetization is guaranteed...' This inference is not valid. In a collinear, spin-conserving insulator, the number of filled states per spin channel is an integer per cell, so the spin magnetization is an integer number of Bohr magnetons; it can be 1, 2, ... μ_B as well as zero. Ferromagnetic semiconductors are the counterexample. The statement is used to brand the AB-stacked systems 'fully compensated' (Table 1, Fig. 3, abstract) and to define them as Luttinger-compensated ferrimagnets. However, no computed total magnetic moments or spin-resolved electron counts are reported anywhere in the manuscript. If the actual integer moment is nonzero, the systems are ordinary uncompensated ferrimagnetic semiconductors; the spin-splitting band-structure results would survive, but the 'compensated' part of the central claim and the title would be wrong.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a general heterostructure design for nonrelativistic spin splitting in van der Waals antiferromagnets. Using PBE+U DFT with the Dudarev formalism, the authors study MnPX3 (X = S, Se) monolayers on MPX3 (M = Cd, Mg, Zn) and on ferroelectric CuInP2X6 substrates, considering AA and AB stackings and four collinear magnetic orders. They report that AA-stacked MnPX3/MPX3 heterostructures display altermagnetic spin splitting with d-wave symmetry, while AB-stacked semiconductors display ferrimagnetic-type spin splitting with C6-symmetric distribution in the Brillouin zone, which they label 'fully compensated' and attribute to protection by the Luttinger theorem. They also report that the spin splitting is weakly dependent on in-plane strain and that reversing the ferroelectric polarization of CuInP2X6 can nonvolatilely modulate the spin splitting, with an NEB barrier of 20.1 meV/atom. The central claim is that these heterostructures are tunable two-dimensional compensated magnets with nonrelativistic spin splitting.","tokens_in":9731,"tokens_out":8283,"duration_ms":76726,"significance":"If the calculated spin-splitting patterns are correct, the paper offers a materials-realizable route to two-dimensional altermagnets and compensated ferrimagnets, and a nonvolatile electric-field switch for spin splitting. The paper has clear strengths: it systematically screens stacking modes and magnetic orders, provides an explicit spin-group symmetry analysis for the altermagnetic case, tests strain sensitivity, and estimates the ferroelectric switching barrier. The design principle is falsifiable and experimentally testable. However, the 'fully compensated' label, which is central to the title and abstract, is not currently demonstrated because the Luttinger-theorem inference is not valid and no total magnetic moments are reported. The spin-splitting results themselves are not in question, but the compensated-ferrimagnet classification needs direct verification.","major_comments":[{"comment":"The statement 'the heterostructures considered in this work are semiconductors, which require the total magnetization per cell to be an integer according to the Luttinger theorem. Therefore, the full compensation of the macroscopic magnetization is guaranteed' is not logically valid. In a collinear, spin-conserving insulator the spin-resolved electron count per cell is an integer, but the difference between spin-up and spin-down counts can be any integer, not only zero. Ferromagnetic semiconductors are a direct counterexample. The paper never reports computed total magnetic moments or spin-resolved electron counts for the AB-stacked heterostructures, so the 'fully compensated' and 'Luttinger-compensated' claims are unsupported. Please provide the total magnetic moment per cell (and, if desired, spin-resolved occupation numbers) for all AB-stacked systems; if any moment is nonzero, the abstract, Table 1 labels, and title must be revised.","section":"Section I (paragraph after Fig. 4); also Abstract and Conclusions"},{"comment":"The same invalid inference is used for the MnPX3/CuInP2X6 heterostructures: the text states that 'their semiconducting nature guarantees the total magnetization is zero.' As in the AB-stacked MnPX3/MPX3 case, a semiconducting gap does not force the magnetization to vanish; an integer nonzero moment is allowed. No total moments are reported for these systems either. The Conclusions statement that 'since the systems studied in this work are semiconductors' something is guaranteed inherits the same problem. Please verify the zero-magnetization claim by direct calculation or remove the compensation claim from the abstract and conclusions.","section":"Section II (paragraph after Fig. 6)"},{"comment":"The total-energy differences between AA and AB stackings are 0.1-1.0 meV/atom, and differences between magnetic orders can be as small as about 0.3 meV/atom (for example, MnPSe3/CdPSe3 AB Stripy is -0.3 meV/atom relative to Néel). These values are at or below the typical accuracy of semilocal DFT with D3 corrections. The statements that AB stacking is 'generally more stable' and that the Néel order remains the lowest-energy magnetic state are therefore not strongly supported. Please provide explicit convergence checks with respect to k-mesh, smearing, and van der Waals functional, or soften the ground-state claims to reflect that the differences are within numerical uncertainty.","section":"Tables 1 and 2"}],"minor_comments":[{"comment":"The caption refers to 'MnPS3/MgPS3' and 'MnPSe3/MgPSe3' in a section about MnPX3/CuInP2X6 heterostructures; this appears to be a typo for MnPS3/CuInP2S6 and MnPSe3/CuInP2Se6.","section":"Fig. 6 caption"},{"comment":"The sentence 'the force and energy convergence criteria are set to be set to 0.01 eV/Å and 1 × 10−5 eV' contains a duplicated phrase and should be revised.","section":"Computational Methods"},{"comment":"'Kramer’s spin degeneracy' should be 'Kramers spin degeneracy'.","section":"Introduction"},{"comment":"The high-symmetry point M2 is used but never defined; please define it in the text or in the figure caption.","section":"Figs. 2 and 3"},{"comment":"The table heading 'The energy difference between AFM (Néel, Stripy, Zigzag) and Néel states is taken into account...' is unclear; please rephrase to specify the reference energy directly.","section":"Table 2 header"}],"recommendation":"major_revision","confidential_remarks":"The manuscript fits the journal's scope, and the computational protocol is described in enough detail to be reproduced. The main reservation is that the 'Luttinger-compensated' claim is a central classification embedded in the title and abstract, and it currently rests on an invalid inference. If the authors compute total moments and find them to be zero, the paper can likely be accepted after revision; if any moment is nonzero, the compensated-ferrimagnet label and the corresponding parts of the title and abstract must be removed. The stacking-energy differences are also marginal, but that issue is secondary."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version before you read it. The paper's specific material predictions are new: AA-stacked MnPX3/MPX3 gives altermagnetic splitting, AB-stacked gives ferrimagnetic-type splitting, and CuInP2X6 substrates make it switchable. The DFT work is careful and the screening of stacking modes and magnetic orders is thorough. But the headline claim that the AB-stacked systems are 'fully compensated' is not supported. The Luttinger theorem argument after Fig. 4 is a non-sequitur: integer magnetization per cell can be 1, 2, ... μB, not just zero, and no computed total moments are given anywhere.\n\nWhat it does well: It turns the general substrate-altermagnetism idea, already floated by Mazin et al. and others, into a concrete and experimentally plausible family. The spin-splitting maps in the BZ show the expected d-wave pattern, the strain dependence is sensible, and the ferroelectric switching calculation with NEB is a nice bonus. The methods are standard and reproducible: VASP, PBE+U with U=3 eV from literature, D3, scalar-relativistic collinear calculations.\n\nThe soft spots: (1) the Luttinger theorem misuse is load-bearing because 'compensated' is in the title and abstract. They need to report the actual total moments for the AB-stacked and CuInP2X6 systems. If the moment is nonzero, they are ordinary uncompensated ferrimagnetic semiconductors and the central claim collapses to something less interesting but still publishable. (2) The AA vs AB energy differences are around 0.1-1 meV/atom. That's within DFT error, so the predicted stacking preference is fragile; both stackings may be present in samples. (3) They don't discuss the strain energy cost of matching layers with 1.9% lattice mismatch. Minor.\n\nThe spin-splitting band structures themselves are probably fine, and I don't see a circularity problem—U is from prior work, not fit to the target splitting.\n\nBottom line: solid computational paper with one flawed central inference. It deserves a serious referee, but the referee should demand total moments and a corrected argument. I'd use this in my own work with caution, citing the AA altermagnetic results rather than the 'Luttinger-compensated' label.","headline":"New material-specific altermagnet and ferrimagnet predictions with a flawed Luttinger-theorem argument for full compensation; the spin-splitting results are probably right, but the 'compensated' label needs computed moments.","tokens_in":10282,"tokens_out":2849,"would_cite":true,"duration_ms":27691,"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":"The stacking order of MnPX3-based van der Waals heterostructures determines whether they are altermagnets or compensated ferrimagnets, and a ferroelectric substrate makes the spin splitting switchable by an electric field.","keywords":["altermagnetism","compensated ferrimagnetism","van der Waals heterostructures","MnPX3","non-relativistic spin splitting","ferroelectric switching","two-dimensional magnets"],"falsifier":"Compute the total magnetisation per primitive cell of the ground-state AB-stacked MnPS3/MgPS3 heterostructure with the same first-principles method used in the paper; a nonzero integer moment (e.g., $2\\,\\mu_{\\mathrm{B}}$ per cell) would contradict the fully compensated conclusion, while a zero moment would support it. Experimentally, a SQUID magnetometry or anomalous-Hall measurement on such a stack could settle the same question.","tokens_in":1846,"feed_emoji":"🧲","tokens_out":3602,"duration_ms":131481,"temperature":0.7,"pith_summary":"This paper shows that a single antiferromagnetic monolayer, MnPX3 (X = S or Se), can be turned into a magnet with momentum-dependent spin splitting simply by stacking it on a lattice-matched van der Waals substrate. With AA stacking the result is altermagnetic splitting—up- and down-spin bands split by up to tens of meV with the alternating four-lobed pattern characteristic of altermagnets—while with AB stacking the result is a ferrimagnetic-type splitting that the paper argues is exactly compensated, i.e., has no net magnetization, because the systems are semiconductors. Replacing the substrate with ferroelectric CuInP2X6 makes the size of the splitting depend on polarization, so an out-of-plane electric field can nonvolatilely switch the spin-related electronic structure. If these predictions hold, the work supplies a way to make tunable two-dimensional compensated magnets from materials that can already be exfoliated and stacked in experiments.","feed_headline":"Stacking 2D magnets creates switchable spin-split bands","feed_subtitle":"AA stacking gives altermagnetic splitting; AB gives compensated ferrimagnetism; ferroelectric switching flips it.","key_machinery":"The mechanism is the selective breaking of the combined inversion-and-time-reversal ($PT$) symmetry that protects spin degeneracy in the free-standing monolayer. In an AA-stacked heterostructure, inversion is lost but the spin-group operation $[C_2\\,\\Vert\\,M_{\\mathbf{a}}]$ survives, relating the up- and down-spin Mn sites; that surviving operation is what organises the splitting into the $d$-wave altermagnetic form. In an AB-stacked heterostructure, no such symmetry relates the two spin sublattices, and the splitting is ferrimagnetic-like; the paper then leans on the Luttinger theorem, which ties integer electron count per cell to quantisation of the total moment, to argue that the net magnetisation vanishes in these semiconductors. The ferroelectric CuInP2X6 substrate supplies the switching handle: its two polarisation states are separated by a calculated 20.1 meV/atom barrier, and reversing the polarisation changes the interlayer potential enough to alter the spin splitting.","core_discovery":"The paper's central discovery is that substrate-induced breaking of the combined inversion-and-time-reversal symmetry lifts the spin degeneracy of the Néel-ordered MnPX3 monolayer, and that the stacking sequence selects which type of compensated spin splitting appears. In the AA stack, the two opposite-spin Mn sites remain related by a spin-group rotation-mirror operation, so the splitting has the alternating d-wave pattern of an altermagnet, reaching about 46 meV in a deep valence band. In the AB stack no such operation relates the spin sites, producing a ferrimagnetic-type spin splitting with a sixfold-symmetric distribution in the Brillouin zone; because the heterostructures are semiconducting, the paper invokes the Luttinger theorem to conclude their total magnetization is exactly zero, and labels them Luttinger-compensated ferrimagnets. With CuInP2X6 as the substrate, reversing the ferroelectric polarization changes the band structure and the magnitude of the splitting substantially, with a calculated switching barrier of 20.1 meV/atom, so the spin splitting can be switched nonvolatilely by an external electric field.","pith_inferences":["The symmetry logic used here—remove inversion, let the stacking choose which spin-site symmetry survives—suggests a general construction rule for altermagnetic heterostructures from any 2D collinear antiferromagnet with a compatible substrate, which the authors only sketch for MnPX3.","Because ferromagnetic semiconductors exist with integer, nonzero total moments, the Luttinger-based compensation argument needs a direct test; computing the total moment of the AB-stacked cell would confirm or refute the 'fully compensated' label.","The ferroelectric switching scenario points toward a concrete device concept, a two-terminal stack whose polarization state encodes the spin-splitting state, readable through spin-resolved photoemission or magneto-optical measurements."],"forward_implications":["AA-stacked MnPX3/MPX3 heterostructures should behave as two-dimensional altermagnets, with d-wave spin splitting in the valence bands reaching about 46 meV.","AB-stacked semiconducting heterostructures should behave as compensated ferrimagnets, with sixfold-symmetric spin splitting and no net magnetization.","The splitting is largely strain-tolerant: biaxial strains between -1.5% and 1.5% shift the average splitting by only 0.2-1 meV.","MnPX3/CuInP2X6 heterostructures should allow nonvolatile electric-field switching of the spin splitting, with a calculated polarization-switching barrier of about 20.1 meV/atom.","The same recipe should extend to other intralayer antiferromagnets of the MPX3 family, such as NiPX3, FePX3, and CoPX3, when paired with suitable substrates."],"supporting_citations":[{"why":"Defines altermagnetic spin splitting and the symmetry framework the heterostructures are designed to realize.","marker":"[1]"},{"why":"Proposed bilayer-stacked A-type altermagnets from antiferromagnetically coupled ferromagnetic monolayers, the construction this paper realizes with heterostructures.","marker":"[24]"},{"why":"Proposed inducing altermagnetism through substrates, the design route adopted here.","marker":"[27]"},{"why":"Reviews the layered MPX3 family and its magnetic orders, grounding the choice of MnPX3 and lattice-matched substrates.","marker":"[35]"},{"why":"Introduces the concept of Luttinger-compensated ferrimagnets, which the paper invokes to claim zero net magnetization in the AB-stacked semiconductors.","marker":"[41]"},{"why":"Supplies the crystal structure and ferroelectric polarization of CuInP2X6 used as the switchable substrate.","marker":"[42]"},{"why":"Demonstrates room-temperature ferroelectricity in ultrathin CuInP2S6, supporting the experimental feasibility of electric-field switching.","marker":"[43]"}],"fun_headline_variants":["Stacking order switches between altermagnet and ferrimagnet","AA stacking yields altermagnetism, AB yields compensated ferrimagnetism","Ferroelectric field flips spin splitting in MnPX3 stacks","Luttinger-protected compensated ferrimagnetism from stacking","Tunable spin splitting in MnPX3 via stacking and ferroelectric"],"cache_read_input_tokens":12416,"weakest_assumption_plain":"The paper's conclusion that the AB-stacked heterostructures are fully compensated rests on the premise that a semiconductor with an integer total moment per unit cell must have zero net magnetization; that premise is not generally valid by itself, and no computed total magnetic moments are reported for these structures.","fun_headline_variants_meta":{"raw":{"variants":["Stacking order switches between altermagnet and ferrimagnet","AA stacking yields altermagnetism, AB yields compensated ferrimagnetism","Ferroelectric field flips spin splitting in MnPX3 stacks","Luttinger-protected compensated ferrimagnetism from stacking","Tunable spin splitting in MnPX3 via stacking and ferroelectric"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000694,"raw_usage":{"total_tokens":3184,"prompt_tokens":1033,"completion_tokens":2151,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":649,"completion_tokens_details":{"reasoning_tokens":2061}},"tokens_in":649,"tokens_out":2151,"duration_ms":14577,"temperature":1.0,"reasoning_tokens":2061,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T05:41:05.822965+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the total magnetisation per primitive cell of the ground-state AB-stacked MnPS3/MgPS3 heterostructure with the same first-principles method used in the paper; a nonzero integer moment (e.g., $2\\,\\mu_{\\mathrm{B}}$ per cell) would contradict the fully compensated conclusion, while a zero moment would support it. Experimentally, a SQUID magnetometry or anomalous-Hall measurement on such a stack could settle the same question.","supporting_citations":[{"cited_title":"Šmejkal, J","cited_arxiv_id":null,"evidence_quote":"Defines altermagnetic spin splitting and the symmetry framework the heterostructures are designed to realize."},{"cited_title":"Zeng and Y.-J","cited_arxiv_id":null,"evidence_quote":"Proposed bilayer-stacked A-type altermagnets from antiferromagnetically coupled ferromagnetic monolayers, the construction this paper realizes with heterostructures."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reviews the layered MPX3 family and its magnetic orders, grounding the choice of MnPX3 and lattice-matched substrates."},{"cited_title":"Mazin, Physical Review X 12 (4), 040002 (2022)","cited_arxiv_id":null,"evidence_quote":"Introduces the concept of Luttinger-compensated ferrimagnets, which the paper invokes to claim zero net magnetization in the AB-stacked semiconductors."},{"cited_title":"Maisonneuve, V","cited_arxiv_id":null,"evidence_quote":"Supplies the crystal structure and ferroelectric polarization of CuInP2X6 used as the switchable substrate."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrates room-temperature ferroelectricity in ultrathin CuInP2S6, supporting the experimental feasibility of electric-field switching."}],"review_version":1}