Hidden fully-compensated ferrimagnetism

San-Dong Guo

REVIEW 2 major objections 4 minor 47 references

Hidden fully-compensated ferrimagnetism

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2507.11118 v1 pith:7BR7UC46 submitted 2025-07-15 cond-mat.mtrl-sci

San-Dong Guo This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords hiddenfully-compensatedferrimagnetismspinpolarizationPTsymmetrybilayerCrMoC2S6densityfunctionaltheoryelectric-field-controlledsplittingzeronetmagnetization

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

The 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.

The 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.

Who 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.

Referee Report

2 major / 4 minor

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.

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 (2)

[Material realization] 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.
[Material realization] 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.

minor comments (4)

[Abstract] The phrase 'P T-bilayer' should be written as 'PT-bilayer' with no space; similar spacing issues appear in a few other places.
[Introduction] 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.
[Concept of hidden fully-compensated ferrimagnetism] 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.
[Figure 5] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the material-specific DFT prediction is self-contained; the eEd comparison is a consistency check, and self-citations are contextual.

full rationale

The paper's derivation chain for the central claim is: define hidden fully-compensated ferrimagnetism by PT symmetry plus fully-compensated ferrimagnetic inversion sectors; compute monolayer and bilayer CrMoC2S6 with DFT+U+D3; find AFM1 PT-symmetric ground state; apply E field and read off local spin splitting; compare the 248 meV CBM splitting with the eEd estimate of 250 meV. None of these steps fits a parameter to the target or imports the target through a self-citation: the eEd estimate uses the geometric interlayer distance d=6.24 Å and is not fitted to the DFT splitting; the PT-required global degeneracy is shown by the computed band structure; and the local fully-compensated ferrimagnetic character is read from layer-resolved DFT, not from the author's previous papers. Self-citations ([31], [33]) are used to define the taxonomy (fully-compensated ferrimagnetism, hidden altermagnetism) and to motivate construction, but they are not the basis for the CrMoC2S6 result, which is an independent first-principles calculation. The one caveat—AFM1 is only 1.32 meV/cell below AFM2 at U=(3,3) eV—is a robustness/correctness concern about the magnetic ground state, not a circularity: the prediction is conditional on that ordering, and the paper does not assert PT symmetry as a self-fulfilling input. Therefore no equation in the paper reduces to another by construction.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on DFT-based energetics and band structures, on the prior identification of monolayer CrMoC2S6 as a fully-compensated ferrimagnet, and on a symmetry argument; no experimental data are used, and no new physical entities are postulated.

free parameters (1)

Hubbard U for Cr and Mo d orbitals = 3.00 eV
Fixed from prior literature (ref [36]); the paper tests (3,2) and (4,3) eV variants for the AFM ordering, but all band-structure results use U=3.00 eV.

assumptions (4)

domain assumption Density functional theory with PBE+U and DFT-D3 accurately describes the magnetic ground state and band structure of CrMoC2S6 bilayer.
All central claims rest on the DFT results; no experimental validation or comparison to higher-level theory (e.g., HSE06, GW) is provided.
domain assumption The monolayer CrMoC2S6 is a fully-compensated ferrimagnet as defined in refs [31,35,36].
The bilayer construction relies on the monolayer building block having the claimed fully-compensated ferrimagnetism, established in prior self-cited work.
standard math PT symmetry enforces exact global band degeneracy E_up(k)=E_down(k).
Symmetry argument in the Concept section; valid for collinear PT-symmetric magnets.
domain assumption The out-of-plane electric field is modeled as a uniform potential drop across the slab; layer projection cleanly separates the two sectors.
DFT with an applied field in slab geometry; details of the field implementation are not given, and the layer-projected spin splitting is taken as the local observable.

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Cite this review

Pith. "Pith review of Hidden fully-compensated ferrimagnetism." pith.science (2026). https://pith.science/paper/7BR7UC46

@misc{pith2026250711118,
  author       = {Pith},
  title        = {Pith review of: Hidden fully-compensated ferrimagnetism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7BR7UC46}},
  note         = {Machine review of arXiv:2507.11118}
}

abstract

Incorporating zero-net-magnetization magnets that exhibit spin-splitting into spintronics delivers key advantages: faster switching dynamics, greater immunity to destabilizing fields, lower power consumption, and markedly improved overall efficiency. The collinear magnets with net-zero magnetization and spin-splitting mainly include altermagnet and fully-compensated ferrimagnet, which provide possibility to achieve hidden spin polarization (HSP) with net-zero spin polarization in total but non-zero local spin polarization. In addition to proposal of hidden altermagnetism, we hereby introduce this concept of hidden fully-compensated ferrimagnetism, where the total spin polarization is zero, but either of the two inversion-partner sectors possesses fully-compensated ferrimagnetism with non-zero local spin polarization in the real space. By the first-principle calculations, we predict that $PT$-bilayer $\mathrm{CrMoC_2S_6}$ is a possible hidden fully-compensated ferrimagnet, showing fully-compensated ferrimagnetic HSP, which can be separated and observed by an out-of-plane external electric field. Our works provide a class of hidden spin-polarized materials that facilitates the advancement of spintronics.

Figures

Figures reproduced from arXiv: 2507.11118 by the authors.

**Figure 4.** FIG. 4. (Color online) For bilayer CrMoC [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗

**Figure 6.** FIG. 6. (Color online) The energy band structures [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗

Figures from the paper (1 more)

**Figure 7.** Figure 7: FIG. 7. (Color online) For hidden fully-compensated ferri [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

Discussion (0). Continue with ORCID to comment.

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See Supplemental Material at [] for the magnetic configu- rations; the energy difference between AFM2 and AFM1 ordering vs E; the MAE vs E; the related energy band structures

Pith tools

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