Type III Valley Polarization and Anomalous Valley Hall Effect in Two-Dimensional Non-Janus and Janus Altermagnet Fe2WS2Se2

Chao Wu; Hanbo Sun; Ping Li; Weixi Zhang; Yanchao She; Yiding Wang

REVIEW 3 major objections 6 minor 55 references

Type III Valley Polarization and Anomalous Valley Hall Effect in Two-Dimensional Non-Janus and Janus Altermagnet Fe2WS2Se2

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Breaking a mirror symmetry alone separates the valleys of a 2D altermagnet, no spin-orbit coupling needed.

desk verdict Plausible symmetry-based mechanism for type III valley polarization, but the meV-scale linchpin splitting needs convergence proof. read the letter →

arxiv 2506.09675 v1 pith:XX44YMCT submitted 2025-06-11 cond-mat.mtrl-sci cond-mat.mes-hall

Yanchao She , Yiding Wang , Hanbo Sun , Chao Wu , Weixi Zhang , Ping Li This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.mes-hall

keywords valleypolarizationaltermagnetismtypeIIIHalleffectmagneticanisotropytwo-dimensionalmaterialsspin-orbitcouplingdensityfunctionaltheory

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 proposes and tests a third mechanism for spontaneous valley polarization, which it calls type III. Existing routes separate valleys by breaking time-reversal symmetry with magnetism or inversion symmetry with ferroelectricity; this one breaks a mirror symmetry, $M_{xy}$, that connects the two antiferromagnetic sublattices of an altermagnet. First-principles calculations on monolayer Non-Janus Fe$_2$WS$_2$Se$_2$ find that removing this symmetry alone lifts the degeneracy of the X and Y valleys, giving 2.27 meV valence and 8.40 meV conduction splittings even with spin-orbit coupling switched off. If the calculation is right, valley polarization becomes an intrinsic, nonrelativistic property of certain altermagnets, tunable by strain and magnetization direction, with an anomalous valley Hall effect for readout.

What carries the argument

The load-bearing object is the mirror symmetry $M_{xy}$ (and the combined spin-space symmetry $[C_2\parallel M_{xy}]$) that pairs the two Fe sublattices in the altermagnet. In the Janus Fe$_2$WS$_2$Se$_2$ monolayer this symmetry keeps the X and Y valleys degenerate; in the Non-Janus structure, with S and Se placed differently relative to the two Fe sites, it is absent, and the inequivalence of the two sublattices appears as a valley splitting. The mechanism is nonrelativistic, since it operates with SOC turned off, and the altermagnetic spin splitting supplies the spin-valley locking that leads to the anomalous valley Hall effect once carriers are doped.

What would settle it

Recompute the non-SOC band structure of Non-Janus Fe$_2$WS$_2$Se$_2$ with $U_\text{eff}$ varied from 0 to 6 eV and k-meshes from 12×12×1 to 24×24×1: if the X–Y valence splitting changes sign or drops below about 0.5 meV at any reasonable parameter set, the claimed intrinsic type III mechanism collapses.

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Extended reading notes

Core claim

In its own terms, the paper's central discovery is that valley polarization can be intrinsic to a crystal rather than imposed by magnetic or electric order. In monolayer Non-Janus Fe$_2$WS$_2$Se$_2$, the two Fe sublattices are not connected by the combined symmetry $[C_2\parallel M_{xy}]$ that exists in the Janus structure, so the X and Y valleys are no longer degenerate: the valence-band splitting is 2.27 meV and the conduction-band splitting 8.40 meV without SOC. With SOC the same material shows larger, direction-dependent splittings, and the Janus Fe$_2$WS$_2$Se$_2$, which preserves that symmetry, needs both magnetism and SOC to valley-split. The paper also reports a rare biaxial magnetic anisotropy with four equivalent in-plane easy directions, and shows that biaxial strain and magnetization orientation can tune the magnitude and sign of the valley polarization, enabling an anomalous valley Hall effect.

Load-bearing premise

The central claim stands on a first-principles calculation that uses a tuned electron-correlation parameter ($U_\text{eff}=3$ eV) to get meV-scale energy differences, with no test of how those differences vary when that parameter or the numerical grid is changed.

Editorial extensions

If this is right

Non-Janus Fe$_2$WS$_2$Se$_2$ is a dynamically stable, direct-gap N\'eel antiferromagnet whose X and Y valleys are spontaneously split by 2.27 meV (valence) and 8.40 meV (conduction) with SOC off.
Biaxial strain from -5% to +5% preserves the AFM1 ground state and the out-of-plane easy axis while tuning valley splitting by tens of meV, and reversing magnetization from x to y reverses the splitting signs.
Both Non-Janus and Janus Fe$_2$WS$_2$Se$_2$ display an anomalous valley Hall effect: under in-plane electric field, spin-up and spin-down carriers from inequivalent valleys accumulate on opposite sample edges.
The four-leaf-clover in-plane magnetic anisotropy gives four equivalent easy axes, which could encode four logic states in a biaxial magnetic tunnel junction.
The Janus structure, by contrast, exhibits type I valley polarization only when SOC and in-plane magnetization break the $[C_2\parallel M_{xy}]$ symmetry, so the two structures bracket the type III/type I distinction in one material family.

Reading between the lines

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

A testable extension is to scan other Non-Janus altermagnets with two different chalcogen heights: if the mechanism is generic, the without-SOC valley splitting should scale with the structural asymmetry between the two sublattices rather than with atomic spin-orbit strength.
Because the splitting appears without SOC, it should also survive in light-element isostructural compounds where spin-orbit coupling is weak, which would separate this mechanism cleanly from type I in experiment.
Computing the Berry curvature and intrinsic anomalous Hall conductivity would put the schematic anomalous valley Hall effect on quantitative footing; the paper stops at a schematic diagram.
If the 2.27 meV without-SOC splitting is confirmed at higher $U$ values and denser k-meshes, the mechanism implies that valley degeneracy in altermagnets is not protected by time reversal alone, revising the usual symmetry classification of valleytronic materials.

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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

The interesting thing here is conceptual: they propose a third route to spontaneous valley polarization in altermagnets by breaking the Mxy mirror symmetry with a non-Janus atomic arrangement, and support it with a symmetry analysis that is independent of the DFT numbers. That part holds up. The problem is the central quantitative evidence: the zero-field, no-SOC valley splitting that defines 'type III' is 2.27 meV at the VBM and 8.40 meV at the CBM, from a single PBE+U calculation with Ueff = 3 eV and a 20x20x1 mesh. No U-dependence or k-mesh convergence is shown. At that energy scale, Kohn-Sham eigenvalue differences are within typical numerical uncertainty, so the linchpin may be noise. This is not a fatal flaw—the symmetry argument says the splitting must exist—but the magnitude and even the sign need to be established more robustly before the 'type III' label carries weight.

What the paper does well: the non-Janus design is genuinely new, and the contrast with the Janus structure gives a clean symmetry-controlled comparison. The phonon spectra show dynamical stability, the magnetic ground state analysis is standard and seems solid, and the four-leaf clover biaxial MAE is a nice find. The strain and magnetization-direction maps of valley splitting are thorough, though they inherit the same numerical robustness question.

Soft spots, in order: (1) the missing U/k-mesh tests on the no-SOC splitting; (2) the anomalous valley Hall effect is only a schematic—no Berry curvature, no anomalous Hall conductivity; (3) no deposited structures or code, so the numbers are not independently checkable. The self-citation pattern is noticeable but not abusive; the central claim does not depend on it.

Who is this for: the altermagnet/valleytronics DFT community. A serious referee should look at it, but with a clear request for convergence data and a computed Berry curvature.

Recommendation: send to peer review, and in the review ask for the robustness tests. The concept deserves the referee time; the current evidence does not yet justify the strength of the abstract's claim.

Referee Report

3 major / 6 minor

Summary. This paper proposes a third mechanism for spontaneous valley polarization, named ‘type III’, based on breaking the mirror symmetry Mxy in a collinear antiferromagnet, and claims its realization in monolayer Non-Janus Fe2WS2Se2. Using PBE+U calculations, the authors find a Néel-type AFM ground state, direct band gaps, a biaxial magnetic anisotropy in the xy plane, a no-SOC valley splitting of 2.27 meV (VBM) and 8.40 meV (CBM) in the Non-Janus structure, and a variety of SOC-induced valley splittings for both Non-Janus and Janus phases. The paper also reports strain and magnetization-direction tuning of the splittings and presents schematic anomalous valley Hall effects.

Significance. The proposed mechanism is conceptually interesting and, if the meV-scale splittings are numerically robust, would expand the known routes to valley polarization beyond time-reversal-breaking and inversion-breaking systems. The symmetry arguments are clean, and the predicted strain and magnetization dependencies are falsifiable. The phonon stability and magnetic ground-state calculations are useful supporting results. The main reservation is that the central quantitative result rests on a single DFT+U parameter set and the anomalous valley Hall effect is not backed by Berry curvature calculations; the significance is therefore conditional on the missing numerical robustness tests.

major comments (3)

[§C, Fig. 3(a), Methods] The central claim of spontaneous type III valley polarization rests on the 2.27 meV no-SOC VBM splitting and the 8.40 meV CBM splitting. These are Kohn-Sham eigenvalue differences from a single PBE+U calculation with Ueff = 3 eV and a 20×20×1 k-mesh. At this energy scale, eigenvalue differences are sensitive to the Hubbard U and to k-mesh convergence, and the paper reports no U-dependence study, no k-mesh convergence test, and no comparison with an alternative functional. The symmetry analysis proves only that the X/Y degeneracy may be lifted; it does not establish that the mean-field eigenvalue difference is converged or physical. Without such tests, the type III classification is not yet established.
[§F, Fig. 7] The anomalous valley Hall effect is presented only as a schematic, with no Berry curvature, Chern number, or anomalous Hall conductivity calculation. Since the sign of the valley Hall response is determined by the Berry curvature around the X and Y valleys, the assignment of spin-up electrons to the left boundary and spin-down holes to the right boundary is not demonstrated by the band-structure data alone. A Berry curvature calculation, or at least a symmetry-constrained argument for the Berry curvature, is needed to support the AVHE claims.
[§A, §B, title/abstract] The title and abstract describe both Non-Janus and Janus Fe2WS2Se2 as altermagnets, but §B states that the Janus structure has the [C2||Mxy] spin symmetry and possesses d-wave altermagnet characteristics, while the Non-Janus structure has no such spin symmetry. If the Non-Janus structure lacks a spin-space symmetry connecting the two Fe sublattices, its classification as an altermagnet needs to be justified explicitly, or the central claim should be reframed as a broken-mirror-symmetry mechanism in a Néel antiferromagnet rather than an altermagnetic mechanism.

minor comments (6)

[Introduction] The opening sentence beginning ‘Due to its unparalleled advantages’ is a sentence fragment; please revise for clarity.
[Fig. 1 caption] The caption contains a corrupted symbol ‘[C /g3671||Mxy]’; this should be printed as [C2||Mxy].
[§D] The strain definition sentence contains a missing symbol: ‘where a0 and represent the lattice constant’ should be ‘where a0 and a represent the lattice constant’.
[Methods, Data and Code availability] The code availability statement is ungrammatical (‘The codes are available from the findings of this study are available from the corresponding author on reasonable request’); in addition, depositing the input structures, pseudopotential settings, and analysis scripts would substantially aid reproducibility.
[Supplementary material] The main text repeatedly refers to Tables SI–SVII and SX–SXI, but these supplementary tables are not included in the provided manuscript; the authors should ensure that all cited tables are present and consistent.
[§B, Fig. 2] The MAE values are of order 1 meV, and the angular plots in Fig. 2 are presented without any numerical uncertainty estimate; a brief statement of k-mesh and Ueff convergence for the MAE would strengthen the biaxial anisotropy claim.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the valley splitting is a DFT output, not a fitted input; symmetry analysis is independent.

full rationale

The central claim—that Non-Janus Fe2WS2Se2 shows a spontaneous X/Y valley splitting without SOC—rests on a direct DFT calculation (Section C, Fig. 3a) rather than on any parameter fitted to that splitting. The 2.27 meV and 8.40 meV values are outputs of a standard PBE+U calculation and are not fed back into the model as constraints. The symmetry analysis (Sections A and B) independently establishes that Non-Janus lacks the [C2||Mxy] operation that protects X/Y degeneracy in the Janus case; that group-theoretic statement is not derived from the band structure. The MAE description via Eq. (2) is a fitting of angular energy surfaces, but it is not used to predict the valley splitting and is not load-bearing for the type III claim. Self-citations appear in introductory framing (e.g., refs 7, 16–18, 41, 43–45) but none is invoked as a uniqueness theorem or as the proof of the central mechanism. The absence of U-dependence and k-mesh convergence tests is a numerical robustness concern about the meV-scale splitting, not a circularity: it concerns whether the DFT output is converged, not whether the output was assumed. The anomalous valley Hall discussion is schematic but again uses computed band order rather than a fitted prediction.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The calculations rest on standard DFT approximations and one empirical Hubbard U parameter. No new particles, forces, or conserved quantities are introduced. The only invented item is the classification label 'type III valley polarization', which is a naming choice, not a physical entity.

free parameters (1)

Ueff (Hubbard U for Fe 3d) = 3 eV
GGA+U parameter taken from prior literature; the magnitude of the valley splitting and even the magnetic ground state can depend on U, and no U-dependence test is reported.

assumptions (3)

domain assumption PBE+U with Ueff=3 eV accurately describes the electronic structure and magnetic ordering of Fe2WS2Se2.
The entire band structure and valley splitting are computed with this functional; no hybrid or GW cross-check is provided.
domain assumption The three magnetic configurations considered (FM, AFM1, AFM2) in a 1x2x1 supercell span the relevant magnetic orderings.
The ground state AFM1 is selected from these three; more complex noncollinear orders are not examined.
standard math Phonon spectra without imaginary frequencies establish dynamical stability.
PHONOPY calculations are used to confirm stability; thermodynamic or lattice stability is not assessed.

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Cite this review

Pith. "Pith review of Type III Valley Polarization and Anomalous Valley Hall Effect in Two-Dimensional Non-Janus and Janus Altermagnet Fe2WS2Se2." pith.science (2026). https://pith.science/paper/XX44YMCT

@misc{pith2026250609675,
  author       = {Pith},
  title        = {Pith review of: Type III Valley Polarization and Anomalous Valley Hall Effect in Two-Dimensional Non-Janus and Janus Altermagnet Fe2WS2Se2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XX44YMCT}},
  note         = {Machine review of arXiv:2506.09675}
}

read the original abstract

Exploiting the valley degree of freedom introduces a novel paradigm for advancing quantum information technology. Currently, the investigation on spontaneous valley polarization mainly focuses on two major types of systems. One type magnetic systems by breaking the time-reversal symmetry, the other is ferroelectric materials through breaking the inversion symmetry. Might there be additional scenarios? Here, we propose to realize spontaneous valley polarization by breaking the mirror symmetry in the altermagnets, named type III valley polarization. Through symmetry analysis and first-principles calculations, we confirm that this mechanism is feasible in Non-Janus Fe2WS2Se2. Monolayer Non-Janus and Janus Fe2WS2Se2 are stable Neel-type antiferromagnetic state with the direct band gap semiconductor. More interestingly, their magnetic anisotropy energy exhibits the rare biaxial anisotropy and a four-leaf clover shape in the xy plane, while the xz and yz planes show the common uniaxial anisotropy. This originated from the fourth-order single ion interactions. More importantly, the valley splitting is spontaneously generated in the Non-Janus Fe2WS2Se2 due to the Mxy symmetry breaking, without requiring the SOC effect. Both the Non-Janus and Janus Fe2WS2Se2 exhibit diverse valley polarization and anomalous valley Hall effect properties. In addition, the magnitude and direction of valley polarization can be effectively tuned by the biaxial strain and magnetic field. Our findings not only expand the realization system of spontaneous valley polarization, but also provide a theoretical basis for the high-density storage of valley degrees of freedom.

Figures

Figures reproduced from arXiv: 2506.09675 by the authors.

**Figure 2.** FIG. 2. (a-c) and (g-i) represent three magnetic configurati [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Band structures of monolayer (a-d) Non-Janus and (e- [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. (a, e) Calculated the total energies of different magn [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. The valley splitting of monolayer (a-d) Non-Janus an [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: FIG. 6. Magnetization direction dependence of the valley sp [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: FIG. 7. Schematic diagram of anomalous valley Hall effect [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

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