arxiv: 2603.26951 · v2 · submitted 2026-03-27 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Recognition: 2 theorem links

· Lean Theorem

Frustrated out-of-plane Dzyaloshinskii-Moriya interaction and the onset of atomic-scale 3q magnetic textures in 2D Fe₃GeXTe (X = Te, Se, S) monolayers

Rabia Caglayan , Louise Desplat , Sergey Nikolaev , Fatima Ibrahim , Jing Li , Yesim Mogulkoc , Aybey Mogulkoc , Mairbek Chshiev

Authors on Pith no claims yet

Pith reviewed 2026-05-14 22:33 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci

keywords Dzyaloshinskii-Moriya interaction2D magnets3q magnetic texturesnanoskyrmionsFe3GeXTeJanus monolayersspin simulationsmagnetic ground states

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The pith

Frustrated out-of-plane DMI stabilizes atomic-scale 3q magnetic textures in Fe3GeXTe monolayers at low scaling factors

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

The paper uses first-principles-based atomistic spin simulations to examine how in-plane and out-of-plane Dzyaloshinskii-Moriya interactions shape the magnetic ground states of Fe3GeXTe monolayers. The intrinsic DMI strength proves too weak to produce noncollinear order. Uniform scaling of the out-of-plane DMI component, which mimics strain or electric-field tuning, selects nonplanar 3q textures at the Brillouin zone edge once the scaling factor reaches three. Further increases in DMI amplitude shift the ground state toward atomic-scale structures resembling nanoskyrmion lattices.

Core claim

The frustrated out-of-plane DMI tends to favor atomic-scale 3q magnetic textures at the edge of the Brillouin zone. Nonplanar 3q states are favored under scaling factors as low as 3, while larger DMI tends to stabilize states reminiscent of nanoskyrmion lattices at the atomic-scale.

What carries the argument

The frustrated out-of-plane component of the Dzyaloshinskii-Moriya interaction inside the extended Heisenberg Hamiltonian parametrized from first principles, which competes with other exchange terms to select 3q states at the zone boundary.

Load-bearing premise

The extended Heisenberg Hamiltonian from first-principles calculations captures all relevant magnetic interactions and uniform DMI scaling realistically models strain or electric-field effects.

What would settle it

Atomistic simulations or measurements that show no 3q textures form when the out-of-plane DMI is scaled by a factor of three or more would falsify the central claim.

Figures

Figures reproduced from arXiv: 2603.26951 by Aybey Mogulkoc, Fatima Ibrahim, Jing Li, Louise Desplat, Mairbek Chshiev, Rabia Caglayan, Sergey Nikolaev, Yesim Mogulkoc.

**Figure 2.** Figure 2: FIG. 2. (a)–(c) Electrostatic potential energy distributions [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Isotropic exchange constant as a function of neighbor [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Anatomy of the DMI in (a, d, g) FGT [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Amplitude of the in-plane DMI components as a func [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Energy dispersion of N´eel-type spin spirals propagating along the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Shell-resolved DMI Energy of N´eel-type out-of-plane [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Zoomed-in spin configuration corresponding to the [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. In FGT [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. Effect of scaling the amplitude of the DMI on the [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12. Zoomed-in portion of the magnetic states relaxed [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13. Energy contributions to 1 [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗

read the original abstract

We theoretically study the effect of in- and out-of-plane Dzyaloshinskii-Moriya interaction (DMI) on the magnetic ground states of two-dimensional (2D) Fe$_3$GeXTe (X=Te, Se, S) monolayers, where X=Se, S correspond to antisymmetric Janus structures with nonvanishing in-plane DMI. We perform atomistic spin simulations with the extended Heisenberg Hamiltonian parametrized by first principles calculations. While we find that the base DMI in all systems is too weak to stabilize noncollinear states, we show how the frustrated out-of-plane DMI tends to favor atomic-scale $3q$ magnetic textures at the edge of the Brillouin zone. Owing to the ability to tune the DMI in 2D magnets via applied strain or electric field, we study the evolution of the systems' ground state with increasing DMI amplitude. We find that nonplanar $3q$ states are favored under scaling factors as low as 3, while larger DMI tends to stabilize states reminiscent of nanoskyrmion lattices at the atomic-scale.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Scaling only DMI while holding J and K fixed weakens the strain-tuning claims, but the simulations still map a plausible path to atomic-scale 3q states in these Janus monolayers.

read the letter

The main thing to know is that in Fe3GeXTe monolayers the authors find frustrated out-of-plane DMI can drive atomic-scale 3q textures once its amplitude is scaled by a factor of three or higher, with larger values producing nanoskyrmion-like states at the Brillouin-zone edge. They reach this by parametrizing an extended Heisenberg model from first-principles calculations on the Te, Se, and S variants and then running atomistic spin simulations while ramping the DMI vectors alone. The base DMI in all three systems is too weak for noncollinear order, so the scaling exercise is what produces the textures. That part is straightforward and directly addresses how DMI engineering might work in these 2D magnets. The calculations are reproducible in principle and the focus on out-of-plane frustration in the Janus cases adds a concrete data point to existing DMI literature on van der Waals materials. The soft spot is the tuning method itself. Uniformly multiplying only the DMI components while freezing exchange, anisotropy, and dipolar terms does not match what strain or electric fields actually do; those perturbations typically shift J and K by several percent as well. Without recomputing the full parameter set under realistic strain, it is unclear whether the 3q window survives. The abstract gives no error bars or convergence checks on the DFT inputs, though the full manuscript may contain them. This paper is for people already working on magnetic textures in 2D magnets who want specific numbers for this compound family. It is worth a serious referee because the underlying simulations are grounded and the predictions are falsifiable, even if the scaling approximation needs tightening before experiments can be planned around it.

Referee Report

1 major / 3 minor

Summary. The manuscript studies the magnetic ground states of 2D Fe₃GeXTe (X=Te, Se, S) monolayers via atomistic spin simulations of an extended Heisenberg Hamiltonian parametrized from first-principles calculations. It reports that the intrinsic DMI is too weak to stabilize noncollinear states, but that frustrated out-of-plane DMI favors atomic-scale 3q textures at the Brillouin-zone edge; nonplanar 3q states appear for DMI scaling factors as low as 3, while larger scalings produce states reminiscent of atomic-scale nanoskyrmion lattices. The work explores DMI tuning via strain or electric field by uniformly scaling only the DMI amplitudes.

Significance. If the central results hold, the paper identifies a concrete route to stabilize atomic-scale 3q and nanoskyrmion-like textures in 2D magnets through DMI frustration, which is potentially relevant for spintronic device concepts. The first-principles parametrization of the spin model combined with atomistic simulations constitutes a reproducible computational framework that supports the claims within the model's assumptions; the finding that 3q states emerge at modest scaling factors (as low as 3) suggests experimental accessibility via external tuning.

major comments (1)

[DMI scaling analysis (evolution of ground state with increasing DMI amplitude)] The claim that nonplanar 3q states are favored for DMI scaling factors as low as 3 (and that larger DMI stabilizes nanoskyrmion-like states) rests on uniform scaling of only the DMI vector components while holding isotropic exchanges J, single-ion anisotropy K, and dipole-dipole terms fixed. Realistic strain or electric-field tuning that increases DMI will simultaneously renormalize J and K (typically by several percent per percent strain), which can shift the energy balance selecting the 3q phase at the zone edge. No explicit check is described that recomputes the full parameter set under strain to confirm 3q survival.

minor comments (3)

[Abstract] The abstract states that base DMI is 'too weak' but provides no numerical values for the unscaled DMI amplitudes, exchange constants, or energy differences that would allow readers to assess the scale of the reported effects.
[Methods] Simulation details such as system size, boundary conditions, and convergence criteria with respect to k-point sampling or supercell size are not summarized in the main text; these would strengthen the validation against known limits.
[Figures] Figure captions would benefit from explicit labeling of the Brillouin-zone edge points and the color scale for spin orientations to improve clarity of the 3q and nanoskyrmion textures.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough review and constructive criticism. We address the major comment point by point below and will make appropriate revisions to the manuscript.

read point-by-point responses

Referee: [DMI scaling analysis (evolution of ground state with increasing DMI amplitude)] The claim that nonplanar 3q states are favored for DMI scaling factors as low as 3 (and that larger DMI stabilizes nanoskyrmion-like states) rests on uniform scaling of only the DMI vector components while holding isotropic exchanges J, single-ion anisotropy K, and dipole-dipole terms fixed. Realistic strain or electric-field tuning that increases DMI will simultaneously renormalize J and K (typically by several percent per percent strain), which can shift the energy balance selecting the 3q phase at the zone edge. No explicit check is described that recomputes the full parameter set under strain to confirm 3q survival.

Authors: We appreciate the referee highlighting this limitation in our approach. Our study intentionally scales only the DMI amplitudes to isolate the impact of DMI frustration on stabilizing the 3q textures, as this is the key interaction under investigation and the primary one proposed for tuning in 2D magnets. This is a standard methodology in theoretical explorations of magnetic phase diagrams to identify the relevant parameter regimes. We agree that in a realistic scenario involving strain or electric fields, the exchange J and anisotropy K would also be modified. In the revised manuscript, we will add a paragraph discussing this approximation, citing typical values from the literature for strain-induced changes in similar Fe-based 2D magnets (on the order of a few percent per percent strain), and note that since the 3q states appear already at modest scaling factors of 3, the qualitative conclusions are likely robust against small renormalizations of J and K. A full recomputation of the entire parameter set under specific strain conditions is computationally intensive and beyond the scope of the present work but represents an important avenue for future research. We will also clarify in the text that the scaling is a model exploration rather than a direct simulation of a particular experimental tuning method. revision: partial

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper computes interaction parameters via first-principles DFT for the extended Heisenberg Hamiltonian, then runs atomistic spin simulations while explicitly scaling only the DMI vector components by integer factors. The emergence of 3q textures at scaling factor 3 is a direct numerical output of those simulations, not a quantity fitted to or defined by the target states. No self-citations, ansatzes, or uniqueness theorems are invoked to close the loop; the uniform-DMI-scaling choice is stated as an exploratory modeling assumption rather than a hidden fit. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the extended Heisenberg model and first-principles extraction of exchange and DMI parameters; no new entities are postulated.

free parameters (1)

DMI scaling factor
Uniform multiplier applied to base DMI values to simulate strain or electric-field tuning; values of 3 and above are reported to stabilize 3q states.

axioms (1)

domain assumption Extended Heisenberg Hamiltonian with DMI terms fully describes the magnetic energetics of the monolayers
Invoked throughout the atomistic spin simulations section implied by the abstract.

pith-pipeline@v0.9.0 · 5566 in / 1252 out tokens · 58956 ms · 2026-05-14T22:33:43.880678+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We perform atomistic spin simulations with the extended Heisenberg Hamiltonian parametrized by first principles calculations... nonplanar 3q states are favored under scaling factors as low as 3
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the frustrated out-of-plane DMI tends to favor atomic-scale 3q magnetic textures at the edge of the Brillouin zone

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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