{"id":"44a423a3-6973-47e0-afa0-6ec5b44e682d","arxiv_id":"2608.05529","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A symmetry-based classification predicts that surface altermagnetism, with d-wave spin-split surface states, emerges on specific surfaces of collinear antiferromagnets and altermagnets, supported by tight-binding and DFT calculations.","lead":"Surfaces of ordinary antiferromagnets can develop altermagnetic spin splitting even when the bulk bands are spin-degenerate, a state the authors call surface altermagnetism. The paper classifies the symmetry conditions for this effect across three magnet classes, predicts 35, 61, and 203 surface families, and reports DFT evidence in NaMnP, LiMnAs, and CrSb.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central classification counts (35, 61, 203) rest entirely on tables in the Supplementary Materials; without independent verification of the enumeration, the paper's core claim that these are all symmetry-allowed SAM surfaces is unconfirmed.","rationale":"The reader's weakest assumption is that the material predictions assume ideal terminations preserving bulk magnetic order, a limitation the authors explicitly acknowledge in Appendix C. My concern is distinct but related: even granting ideal terminations, the classification's headline numbers are the core evidence for the claim of exhaustiveness, and those numbers are not checkable from the reviewed text because they live in the Supplementary Materials. The note-added overlap with Ref. [74] is only stated for the eleven surface SPGs, not for the enumeration counts, so the counts could be either incomplete or in conflict with the independent work. This concern does not move the verdict: like the reader, I see a coherent symmetry framework with explicit limitations and promising material demonstrations, but the missing SM tables and the unresolved overlap with Ref. [74] justify maintaining a conditional verdict pending access to the complete enumeration and an explicit comparison with the independent classification. The proposed computational check would settle whether the counts are correct and would either validate or weaken the central claim.","tokens_in":15044,"tokens_out":18066,"duration_ms":171800,"concrete_test":"Independently re-derive the enumeration from the published spin group datasets (Xiao et al., PRX 14, 031037; Chen et al., PRX 14, 031038; Jiang et al., PRX 14, 031039): for each of the 58 collinear SPGs and the 517 tT-symmetric SSGs, apply the surface-reduction rule (keep operations with point part leaving n invariant and fractional translations parallel to n), count the resulting surface groups that lack [C2||P][C2bar||T] and [C2||t] while retaining a sublattice-connecting rotation or mirror, and compare the totals with Tabs. S3-S5. If any of the totals (35, 61, 203, or the 100/103 split) differs, the classification is not exhaustive or is non-redundant only by convention, and the central claim needs revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central quantitative claim is a symmetry classification enumerating 35 SAM pathways for PT-symmetric AFMs, 61 for bulk AMs, and 203 SSGs for tT-symmetric AFMs. These counts are asserted in the main text, but the derivation and the actual tables (Tabs. S3-S5) are confined to the Supplementary Materials, which are not part of the reviewed text. Appendix A describes the method qualitatively but does not allow the reader to reproduce the counts; the only checkable numeric statement is that the eleven admissible surface SPGs are 'consistent with Ref. [74]'. The note-added independent work reportedly provides a full symmetry classification and material identification, and the overlap is only stated for the eleven SPGs, not for the 35/61/203 counts. If the enumeration is incomplete, double-counts surfaces, or is inconsistent with Ref. [74], the predictive claim that 'the bulk SSG of any collinear magnet directly yields the surface orientations capable of hosting SAM' fails. The first-principles demonstrations for ten compounds do not test completeness; they show existence, not exhaustiveness. The enumeration is therefore the load-bearing pillar of the paper, and it is currently unverified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces the concept of surface altermagnetism (SAM), in which nonrelativistic spin splitting emerges at the surface of collinear antiferromagnets (AFMs) or altermagnets (AMs) even when the bulk bands are spin degenerate. The authors construct a group-subgroup framework connecting bulk spin groups to surface spin wallpaper groups and claim to enumerate all symmetry-allowed SAM pathways: 35 for PT-symmetric AFMs, 61 for bulk AMs, and 203 for tT-symmetric AFMs. They support the proposal with tight-binding models and first-principles calculations for ten synthesized compounds, including NaMnP, LiMnAs, and CrSb, and discuss surface-specific observables such as a facet-dependent crystal Hall effect.","tokens_in":15280,"tokens_out":6021,"duration_ms":54847,"significance":"If the classification is correct, SAM substantially extends altermagnetism from bulk bands to boundaries and provides an orientation-resolved, symmetry-based predictive scheme. The paper has clear strengths: the symmetry reasoning is coherent and parameter-free, the concept of a bulk-to-surface 'pathway' is useful and materially different from a bare listing of surface groups, and the inclusion of ten first-principles examples spanning all three proposed classes is a valuable consistency check. The explicit discussion in Appendix C of the validity domain and the dependence on ideal sublattice-preserving terminations is also commendable. However, the central enumerative claims are not checkable in the submitted text, because the derivation and the tables containing the counts (Tabs. S3-S5) are confined to the missing Supplementary Materials. The manuscript therefore cannot currently be independently verified on its main quantitative claim.","major_comments":[{"comment":"The central classification counts (35, 61, and 203) are asserted in the abstract and in the 'Symmetry analysis' section, but the derivation is not present in the main text: the enumeration is deferred to Tabs. S3-S5 of the Supplementary Materials, which were not part of the reviewed manuscript. Appendix A states that the enumeration is 'complete and nonredundant' but gives no counting rule, no definition of a 'pathway' in algorithmic terms, and no worked example that would let a reader reproduce any of the counts. The only checkable numeric statement, that the eleven admissible surface SPGs are consistent with Ref. [74], addresses a different object (surface SPGs, not pathways). Because the paper's predictive claim is that 'the bulk SSG of any collinear magnet directly yields the surface orientations capable of hosting SAM,' these counts are the load-bearing pillar of the work. Please move the enumeration tables and the counting procedure into the main text or an appendix, or provide the Supplementary Materials for review.","section":"Symmetry analysis; Appendix A"},{"comment":"Appendix C appropriately restricts the predictions to ideal terminations that preserve the bulk antiferromagnetic sublattice symmetry and collinear magnetic order, and it states that terminations breaking sublattice equivalence or spin symmetry would alter or destroy the spin-split surface bands, while real surfaces may reconstruct. This caveat directly qualifies the abstract's characterization of SAM as a 'robust, symmetry-protected magnetic state' and the Discussion's claim of a 'widely applicable route' and 'Universality.' The first-principles demonstrations cover selected ideal terminations only, for example the P-Na terminated (001) surface of NaMnP and the (210) and (120) facets of CrSb. As submitted, the evidence does not establish that SAM survives under realistic surface reconstructions, magnetic reconfigurations, or termination disorder. The authors should either provide additional evidence, such as calculations for all inequivalent stable terminations of at least one compound or explicit surface phase diagrams, or restate the central claim as applying to ideal, sublattice-preserving terminations.","section":"Appendix C; Discussion"}],"minor_comments":[{"comment":"The tight-binding Hamiltonian in Eq. (3) is ambiguous: the first and fourth terms have the identical operator structure c†_{α,i}c_{β,j}, with the intended nearest-neighbor versus next-nearest-neighbor distinction appearing only in the text, and the summation ranges are not specified. Please rewrite the model with explicit bond sums or refer the reader to the detailed construction in the Supplementary Materials.","section":"Eq. (3)"},{"comment":"The notation 'tT-symmetric AFM' is used throughout without defining the symbol 'tT'; the defining operation is later written as [C2||t]. A sentence defining tT as the combination of a fractional translation with spin reversal would remove ambiguity.","section":"Symmetry analysis"},{"comment":"The text states that the (210) and (120) CrSb surfaces show reversed spin polarization and opposite-sign Hall conductivity, but the figure does not show the Hall conductivity values or a clear sign convention. Adding explicit computed values or an inset with the sign would make the claim checkable.","section":"Fig. 4"},{"comment":"Appendix E contains a grammatical error ('Further details is provided') and the sentence on nonlocal geometries could be tightened for clarity.","section":"Appendix E"},{"comment":"The relation between the eleven surface SPGs and the standard International Tables for Crystallography Vol. E notation for subperiodic groups is only referenced, not displayed. A short correspondence table in the main text would improve accessibility.","section":"Tab. S1 / Appendix A"}],"recommendation":"major_revision","confidential_remarks":"The most serious issue is that all central counts rest on Supplementary Materials that were not part of the review. If those materials can be supplied and the enumeration verified, the paper's contribution would be substantial. In addition, the note-added independent work [74] reportedly provides a full symmetry classification; the authors should clarify in revision exactly which results are new and how the 35/61/203 counts compare with Ref. [74], not only the overlap of the eleven surface SPGs."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one. The core idea is that a surface can act as the source of altermagnetic spin splitting: cleave a conventional collinear AFM that is spin-degenerate in the bulk, and the broken PT or fractional translation symmetry at the termination produces spin-split surface states without any net magnetization. That claim is well motivated and the symmetry analysis is coherent. The paper's main novelty is the orientation-resolved group–subgroup construction for spin groups, which goes beyond individual surface studies.\n\nWhat it does well: it gives a clean conceptual framework, supports it with two transparent tight-binding models, and shows DFT results for ten compounds. The material examples (NaMnP, LiMnAs, CrSb) look plausible, and the surface crystal Hall effect in CrSb is a nice concrete observable. The authors also state their validity domain honestly in Appendix C: terminations that break sublattice equivalence or spin symmetry will not show the predicted SAM, and reconstruction or SOC can spoil it.\n\nThe soft spots are real. The central quantitative claims—35, 61, 203 pathways—are asserted in the main text but all derivation and tabulation live in the Supplementary Materials, which aren't part of the manuscript. Appendix A describes the method only qualitatively; there is no way for a reader to verify the counts. The DFT results demonstrate existence, not exhaustiveness, so they don't test the enumeration. The note-added independent work (Ref. [74]) also presents a full classification; the authors only state consistency for the eleven surface SPGs, not for the pathway counts. That leaves the most load-bearing numbers unconfirmed.\n\nThe classification itself is likely right, but a serious referee cannot rely on trust. The authors should either move the enumeration tables into the main text or make the SM freely available and reconcile their numbers with Ref. [74]. The ideal-termination assumption is a limitation but not a flaw—it's clearly disclosed.\n\nVerdict: deserves a serious referee. I would send it to review with the explicit request that the referee verify the enumeration and clarify the overlap with the independent work. If the numbers hold, this is a useful contribution to the altermagnetism literature. If they don't, the paper still has value as a conceptual proposal, but less.","headline":"Surface termination can induce altermagnetic spin splitting in spin-degenerate AFMs—a solid concept undercut by unverifiable enumeration counts and a shared independent classification.","tokens_in":15807,"tokens_out":2087,"would_cite":true,"duration_ms":19381,"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":"Surface altermagnetism can emerge at the boundaries of ordinary collinear antiferromagnets whose bulk bands are spin-degenerate, making the surface itself the source of nonrelativistic spin splitting.","keywords":["surface altermagnetism","altermagnetism","antiferromagnet","spin space group","spin splitting","surface states","CrSb","NaMnP"],"falsifier":"A decisive test is spin-resolved photoemission on the predicted P-Na-terminated (001) surface of NaMnP: if the in-gap surface bands remain spin-degenerate along the paths where the slab calculation predicts a d-wave splitting of order 0.71 eV, that specific SAM realization is contradicted. A transport falsifier is the facet-dependent surface crystal Hall effect in CrSb: the paper predicts opposite-sign Hall signals on the (210) and (120) surfaces, so the absence of the predicted sign reversal would break the mechanism.","tokens_in":14860,"feed_emoji":"🧲","tokens_out":6400,"duration_ms":57238,"temperature":0.7,"pith_summary":"This paper introduces surface altermagnetism (SAM): a nonrelativistic, symmetry-protected spin splitting of electronic states that appears on specific crystal surfaces of collinear antiferromagnets and altermagnets. The central claim is that the surface itself, by breaking a bulk symmetry that used to relate the opposite-spin sublattices, can generate altermagnetic spin polarization even in conventional antiferromagnets whose bulk bands are everywhere spin-degenerate. The authors build a bulk-to-surface spin-group framework and identify all symmetry-allowed surface pathways: 35 for PT-symmetric antiferromagnets, 61 for bulk altermagnets, and 203 spin space groups for antiferromagnets whose sublattices are connected by a fractional translation. They verify the framework with tight-binding models and first-principles calculations on NaMnP, LiMnAs, CrSb, and seven other compounds, finding surface spin splittings of order 0.7 eV and surface-only transport signatures. If correct, SAM extends altermagnetism from bulk bands to surfaces and offers a field-free, facet-tunable route to spin-polarized surface states for spintronics.","feed_headline":"A crystal surface can create altermagnetism where the bulk had none","feed_subtitle":"New symmetry classification finds 35, 61, and 203 allowed facets; NaMnP, LiMnAs, and CrSb show the predicted spin-split surfaces.","key_machinery":"The central object is the spin group, a symmetry group that treats spin rotations and spatial operations independently and is the appropriate description when spin-orbit coupling is negligible. The argument runs on the bulk-to-surface group–subgroup reduction: a surface with normal n keeps only those bulk operations that leave n invariant and whose translations lie parallel to the surface, and the surviving group is a spin wallpaper group. SAM appears exactly when the surface spin group lacks the operations that would map one spin sublattice onto the other and restore spin degeneracy—such as [C2||P][Cbar2||T], [C2||t_perp], or [C2||$C_n^{2}$][Cbar2||T]—while still containing symmetries that connect the two opposite sublattices. The enumeration is carried out at the spin point group level for PT-symmetric antiferromagnets and altermagnets, and at the spin space group level for tT-symmetric antiferromagnets, because in that class the sublattice-connecting symmetry is a fractional translation whose survival depends on the Miller indices.","core_discovery":"The paper establishes that a collinear antiferromagnet or altermagnet, when cleaved along a suitable Miller plane, can host surface electronic states whose opposite-spin bands are split without spin-orbit coupling and without net magnetization. The mechanism is symmetry reduction: the surface removes the bulk operation that forced the two opposite-spin sublattices to be degenerate—[C2||P][Cbar2||T] in PT-symmetric antiferromagnets, the fractional translation [C2||t] in tT-symmetric antiferromagnets, or the rotation or rotoinversion that connects sublattices in bulk altermagnets—while preserving other spin-group operations that relate the sublattices. Working through the 58 collinear spin point groups and 517 collinear spin space groups, the authors enumerate 35, 61, and 203 symmetry-allowed pathways for PT-AFM-SAM, AM-SAM, and tT-AFM-SAM, respectively. Tight-binding models and density-functional calculations on NaMnP, LiMnAs, CrSb, and additional synthesized compounds show surface spin splittings up to about 0.71 eV, d-wave-like or g-wave-like momentum patterns, and a surface crystal Hall effect in CrSb that is symmetry-forbidden in the bulk and changes sign between the (210) and (120) facets.","pith_inferences":["If SAM is as general as the classification suggests, surface termination could become a design axis for altermagnetic devices: the same parent crystal could be switched between spin-degenerate and spin-split surface channels simply by choosing the facet orientation, without external fields.","A natural testable extension is magnetic tunnel junctions: the paper notes in an appendix that the same symmetry reduction applies to buried interfaces, but does not calculate the resulting spin-dependent tunneling or interfacial magnetocrystalline anisotropy, both of which could be computed and measured.","In semiconducting antiferromagnets such as NaMnP, whose bulk gap is about 1.02 eV, the in-gap conduction is carried by the spin-split surface states, so transport measurements on thin, surface-dominated films could reveal SAM without spin-resolved photoemission.","The classification's independence from material-specific parameters suggests that moderate disorder or weak spin-orbit coupling will not destroy SAM qualitatively; comparing facet-dependent spin textures between light-element and heavy-element antiferromagnets would isolate the nonrelativistic contribution."],"forward_implications":["Conventional collinear antiferromagnets with fully spin-degenerate bulk bands can still act as sources of nonrelativistic spin-polarized surface states, so altermagnetism is not restricted to bulk altermagnets.","For any collinear magnet, the bulk spin space group together with the chosen Miller index determines whether a surface hosts SAM; the classification is orientation-resolved, as CrSb illustrates with ferromagnetic-type behavior on (001), spin-degenerate surfaces on the {100} family, and d-wave SAM with opposite spin polarization on the {210} and {120} facets.","SAM creates surface-only observables that are absent in the bulk, including a surface crystal Hall effect with chirality-controlled sign in CrSb and spin-splitter-type transport at the boundaries of antiferromagnets whose bulk bands are spin degenerate.","The splitting is nonrelativistic and can be large—about 0.71 eV on the NaMnP (001) surface—making it accessible to spin- and angle-resolved photoemission and spin-polarized scanning tunneling microscopy.","The bulk-to-surface symmetry construction also applies to interfaces, heterostructures, and gate-controlled boundary layers, not only to vacuum-terminated surfaces."],"supporting_citations":[{"why":"Defines altermagnetism as a collinear magnetic phase with nonrelativistic spin splitting and no net magnetization, the bulk phenomenon that SAM extends to surfaces.","marker":"[7]"},{"why":"Provides the emerging research landscape and terminology for altermagnetism, framing why a surface analogue is a natural next step.","marker":"[8]"},{"why":"Reports the large band splitting in the g-wave altermagnet CrSb, the material used here to demonstrate AM-SAM and surface crystal Hall response.","marker":"[25]"},{"why":"Supplies the spin-group formalism for magnetic materials with negligible spin-orbit coupling, on which the bulk-to-surface symmetry framework is built.","marker":"[38]"},{"why":"Provides the full classification of spin space groups, used for enumerating the collinear spin groups in the analysis.","marker":"[39]"},{"why":"Gives the enumeration and representation theory of spin space groups, supporting the group-theoretic counting of allowed pathways.","marker":"[40]"},{"why":"Independently enumerates spin-space groups, corroborating the completeness of the spin-group classification used in the paper.","marker":"[41]"},{"why":"Establishes that the surface spin group is a subgroup of the bulk spin group and classifies surface magnetization in antiferromagnets, the subgroup-reduction principle at the core of this work.","marker":"[43]"},{"why":"Documents NaMnP as a room-temperature antiferromagnet with the specific structure used for the PT-AFM-SAM first-principles demonstration.","marker":"[48]"},{"why":"Provides LiMnAs as a tT-symmetric antiferromagnetic semiconductor used to demonstrate SAM in that class.","marker":"[56]"}],"fun_headline_variants":["Surface cut turns antiferromagnet into altermagnet","Cleave it to see altermagnetism: 203 allowed surfaces","Facet engineering creates altermagnetic spin split","Hidden altermagnetism emerges at crystal surfaces","203 surfaces predicted for emergent surface altermagnetism"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The classification assumes an ideal surface that preserves the bulk antiferromagnetic sublattice symmetry and collinear magnetic order with negligible spin-orbit coupling; if a real termination reconstructs, relaxes into a different magnetic configuration, or develops strong spin-orbit coupling, the predicted spin-split surface states would be altered or absent.","fun_headline_variants_meta":{"raw":{"variants":["Surface cut turns antiferromagnet into altermagnet","Cleave it to see altermagnetism: 203 allowed surfaces","Facet engineering creates altermagnetic spin split","Hidden altermagnetism emerges at crystal surfaces","203 surfaces predicted for emergent surface altermagnetism"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000551,"raw_usage":{"total_tokens":2694,"prompt_tokens":1077,"completion_tokens":1617,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":693,"completion_tokens_details":{"reasoning_tokens":1541}},"tokens_in":693,"tokens_out":1617,"duration_ms":11654,"temperature":1.0,"reasoning_tokens":1541,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T11:26:09.914945+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive test is spin-resolved photoemission on the predicted P-Na-terminated (001) surface of NaMnP: if the in-gap surface bands remain spin-degenerate along the paths where the slab calculation predicts a d-wave splitting of order 0.71 eV, that specific SAM realization is contradicted. A transport falsifier is the facet-dependent surface crystal Hall effect in CrSb: the paper predicts opposite-sign Hall signals on the (210) and (120) surfaces, so the absence of the predicted sign reversal would break the mechanism.","supporting_citations":[{"cited_title":"ˇSmejkal, J","cited_arxiv_id":null,"evidence_quote":"Provides the emerging research landscape and terminology for altermagnetism, framing why a surface analogue is a natural next step."},{"cited_title":"Krempask ´y, L","cited_arxiv_id":null,"evidence_quote":"Reports the large band splitting in the g-wave altermagnet CrSb, the material used here to demonstrate AM-SAM and surface crystal Hall response."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the spin-group formalism for magnetic materials with negligible spin-orbit coupling, on which the bulk-to-surface symmetry framework is built."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes that the surface spin group is a subgroup of the bulk spin group and classifies surface magnetization in antiferromagnets, the subgroup-reduction principle at the core of this work."},{"cited_title":"Bronger, Ternary transition metal chalcogenides with frame- work structures and the characterization of their bonding by magnetic properties, Pure Appl","cited_arxiv_id":null,"evidence_quote":"Documents NaMnP as a room-temperature antiferromagnet with the specific structure used for the PT-AFM-SAM first-principles demonstration."},{"cited_title":"Beleanu, J","cited_arxiv_id":null,"evidence_quote":"Provides LiMnAs as a tT-symmetric antiferromagnetic semiconductor used to demonstrate SAM in that class."}],"review_version":1}