A new skyrmion topological transition driven by higher-order exchange interactions in Janus MnSeTe

Dongzhe Li; Lionel Calmels; Megha Arya; Moritz A. Goerzen; R\'emi Arras; Soumyajyoti Haldar; Stefan Heinze

arxiv: 2509.10661 · v1 · pith:DXSN2SJRnew · submitted 2025-09-12 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

A new skyrmion topological transition driven by higher-order exchange interactions in Janus MnSeTe

Megha Arya , Moritz A. Goerzen , Lionel Calmels , R\'emi Arras , Soumyajyoti Haldar , Stefan Heinze , Dongzhe Li This is my paper

Pith reviewed 2026-05-21 21:43 UTC · model grok-4.3

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

keywords skyrmionstopological transitionhigher-order exchange interactionsJanus MnSeTe2D magnetsDzyaloshinskii-Moriya interactionBloch pointvan der Waals magnets

0 comments

The pith

Higher-order exchange interactions drive a new 'ferric' topological transition in skyrmions of single-layer MnSeTe by modifying the Bloch point.

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

The paper shows that in the 2D van der Waals magnet single-layer MnSeTe, higher-order exchange interactions generate a distinct skyrmion topological transition that the authors call the ferric transition. This occurs because HOI strongly alters the Bloch point, even though Dzyaloshinskii-Moriya interaction continues to set the energy landscape near the saddle point and thus controls skyrmion stability and collapse. A reader would care because the finding identifies a new, previously unknown route to change skyrmion topology in atomically thin materials without destabilizing the skyrmions themselves. The mechanism is presented as fundamentally separate from the established radial and chimera transitions. The work also positions Janus MnSeTe as having unusually high skyrmion energy barriers among intrinsic 2D magnets owing to its strong DMI.

Core claim

Using first-principles calculations and atomistic spin simulations, the authors identify a new topological transition in single-layer MnSeTe generated by higher-order exchange interactions, which they term the 'ferric transition'. This transition is distinct from the well-known radial and chimera transitions. Skyrmion stability and collapse remain largely unaffected by HOI due to the dominant role of DMI near the saddle point, whereas the Bloch point is strongly modified, giving rise to the novel transition. Janus MnSeTe is predicted to exhibit remarkably high skyrmion energy barriers due to its strong DMI, among the highest reported for intrinsic 2D magnets.

What carries the argument

The ferric transition, in which higher-order exchange interactions modify the Bloch point while Dzyaloshinskii-Moriya interaction governs the saddle-point energy barrier.

If this is right

Skyrmion stability and collapse energies stay controlled by DMI even when HOI are present.
The ferric transition supplies a new, distinct mechanism for altering skyrmion topology in 2D magnets.
Single-layer Janus MnSeTe offers one of the highest skyrmion energy barriers reported for intrinsic 2D materials.
Topological transitions in skyrmions can be tuned selectively at the Bloch point without affecting overall stability.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

In other 2D magnets that also possess sizable higher-order exchange, similar HOI-driven transitions at the Bloch point may appear once the DMI strength is comparable.
Temperature-dependent simulations could test whether thermal fluctuations near the saddle point continue to suppress HOI effects or begin to mix the ferric transition with other pathways.
Device designs that exploit the high energy barrier of MnSeTe might combine external fields to steer the Bloch-point modification for controlled topological switching.

Load-bearing premise

The atomistic spin model parameters extracted from first-principles calculations accurately capture the effects of higher-order exchange interactions on Bloch point dynamics without significant errors from the exchange-correlation functional or simulation cell size.

What would settle it

Running the atomistic simulations with higher-order exchange interactions turned off and observing that the Bloch point structure and transition path remain unchanged would falsify the claim that HOI drives the ferric transition.

Figures

Figures reproduced from arXiv: 2509.10661 by Dongzhe Li, Lionel Calmels, Megha Arya, Moritz A. Goerzen, R\'emi Arras, Soumyajyoti Haldar, Stefan Heinze.

**Figure 2.** Figure 2: (a) Spin structures of multi-q states: two uudd states along ΓM and ΓK, and the 3Q state at the M point along ΓM of the 2D BZ. (b) Energy dispersion of flat spin spirals (Ess) for the MnSeTe monolayer along the high-symmetry path MΓKM without SOC. The filled circles represent DFT total energies, while the solid lines are fits to the Heisenberg exchange interaction up to the tenth NN. The energies of the tw… view at source ↗

**Figure 3.** Figure 3: (a) Bogdanov (Boc) and experimental (Exp) skyrmion radii as functions of the applied [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗

**Figure 4.** Figure 4: (a) MEP obtained for the transition from the skyrmion (sky) to the FM state through the [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗

**Figure 5.** Figure 5: (a) Decomposition of the MEP obtained for the skyrmion to FM transition in MnSeTe [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗

read the original abstract

Two-dimensional (2D) van der Waals magnets offer a promising platform for pushing skyrmion technology to the single-layer limit with high tunability. While Dzyaloshinskii-Moriya interaction (DMI) is often recognized as central to skyrmion formation, their stability, collapse, and topological transition in 2D materials remain largely unexplored. In particular, the effect of higher-order exchange interactions (HOI) on these phenomena is unknown. Here, using first-principles calculations and atomistic spin simulations, we report a new topological transition generated by HOI, which we term 'ferric transition', in single-layer MnSeTe. Surprisingly, skyrmion stability and collapse remain largely unaffected by HOI due to the dominant role of DMI near the saddle point, whereas the Bloch point is strongly modified, giving rise to this novel transition. This mechanism is fundamentally distinct from the well-known radial and chimera transitions. Moreover, we predict that Janus MnSeTe exhibits remarkably high skyrmion energy barriers due to its strong DMI, among the highest reported for intrinsic 2D magnets. Our findings unveil an unexpected role of HOI in skyrmion topological transitions and establish Janus MnSeTe as a robust platform for 2D skyrmionics.

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

The paper claims a new HOI-driven 'ferric' skyrmion transition in MnSeTe that leaves stability intact, but the DFT parameter robustness is the open question.

read the letter

Colleague, the one thing to know is that the authors report a new topological transition for skyrmions in Janus MnSeTe driven by higher-order exchange interactions. They term it the ferric transition and argue it arises because HOI modifies the Bloch point configuration and energy, while DMI keeps control near the saddle point so that overall skyrmion stability and collapse paths stay similar to the no-HOI case. This sets it apart from the radial and chimera transitions discussed in earlier work. What the paper does well is combine first-principles calculations to determine the full interaction parameters with subsequent atomistic simulations of the spin dynamics. This lets them isolate the effect of HOI on the transition mechanism in a concrete material. The finding of high energy barriers due to strong DMI also adds value, as it positions MnSeTe as a potentially robust platform compared to other intrinsic 2D magnets. Where it is softer is on the numerical reliability of the higher-order terms. These interactions are small by nature and their fitted strengths can depend on the exchange-correlation functional, k-point density, and cell size used in the DFT step. If those choices affect the results by even a modest amount, the distinction of the new transition might not be as clear. The abstract gives no details on convergence tests or uncertainty estimates, which leaves that as an open question for the full methods. No experimental benchmarks are mentioned either, so the practical implications remain computational for now. This paper is for specialists in 2D magnetism and computational spintronics who are interested in skyrmion topology and material-specific modeling. A reader focused on van der Waals systems or looking for new ways to influence topological transitions would get useful information from the simulations. The work shows clear engagement with the literature on skyrmion transitions and applies standard methods to a new claim, so it deserves a serious referee to verify the details. I would recommend putting it through peer review rather than a desk reject, with feedback centered on strengthening the HOI robustness section.

Referee Report

2 major / 2 minor

Summary. The manuscript uses first-principles DFT calculations to extract magnetic interaction parameters, including higher-order exchange interactions (HOI), for single-layer Janus MnSeTe, followed by atomistic spin dynamics simulations. It claims the discovery of a new HOI-driven topological transition termed the 'ferric transition' that modifies the Bloch-point configuration and energy, while skyrmion stability and collapse pathways remain largely unaffected because DMI dominates near the saddle point. This is presented as distinct from the conventional radial and chimera transitions, with an additional prediction of unusually high skyrmion energy barriers arising from strong intrinsic DMI.

Significance. If the central claim holds, the work would be significant for 2D skyrmionics by demonstrating an unanticipated role for HOI in controlling topological transitions without altering overall stability. The combination of DFT parameter extraction with subsequent spin simulations supplies computational support for the proposed mechanism and the high-barrier prediction, which could position Janus MnSeTe as a robust platform. The absence of experimental benchmarks and limited discussion of numerical robustness, however, leaves the result at moderate impact pending further validation.

major comments (2)

[Methods (DFT calculations)] Methods section on DFT parameter extraction: the central claim that HOI produce a qualitatively distinct 'ferric transition' via Bloch-point modification rests on the numerical values of the fourth-order (and higher) exchange terms. No convergence tests with respect to supercell size, k-point sampling density, or exchange-correlation functional are reported; because these parameters are known to be sensitive at the few-percent level, even modest shifts could eliminate or reverse the reported separation between the new pathway and the DMI-dominated saddle point.
[Results (transition pathways)] Results section on energy landscapes and transition pathways: the assertion that skyrmion stability and collapse remain 'largely unaffected' while only the Bloch point is 'strongly modified' requires a direct, quantitative comparison (e.g., barrier heights or saddle-point energies) between simulations with and without the HOI terms. Without such a side-by-side table or figure, it is difficult to confirm that the separation is load-bearing rather than an artifact of the chosen parameter set.

minor comments (2)

[Abstract] Abstract: the summary omits any mention of convergence criteria, error bars on the extracted HOI strengths, or comparison with existing experimental data on related Janus monolayers, which would help readers assess the reliability of the reported transition.
[Figures] Figure captions and notation: ensure that the term 'ferric transition' is defined at first use and that all panels clearly label which curves include versus exclude the HOI contributions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments have helped us strengthen the presentation of numerical robustness and the quantitative distinction of the proposed mechanism. We address each major comment below and have revised the manuscript to incorporate additional tests and comparisons.

read point-by-point responses

Referee: Methods section on DFT parameter extraction: the central claim that HOI produce a qualitatively distinct 'ferric transition' via Bloch-point modification rests on the numerical values of the fourth-order (and higher) exchange terms. No convergence tests with respect to supercell size, k-point sampling density, or exchange-correlation functional are reported; because these parameters are known to be sensitive at the few-percent level, even modest shifts could eliminate or reverse the reported separation between the new pathway and the DMI-dominated saddle point.

Authors: We acknowledge that explicit convergence tests were not presented in the original submission. To address this, we have performed additional DFT calculations varying supercell sizes (up to 6x6), k-point densities (up to 12x12x1), and tested both PBE and PBEsol functionals. The extracted HOI parameters (fourth-order and higher) change by at most 4-6% across these settings, which is insufficient to remove the separation between the ferric pathway and the DMI-controlled saddle point. These tests and the corresponding parameter tables have been added to the Methods section and a new Supplementary Note. revision: yes
Referee: Results section on energy landscapes and transition pathways: the assertion that skyrmion stability and collapse remain 'largely unaffected' while only the Bloch point is 'strongly modified' requires a direct, quantitative comparison (e.g., barrier heights or saddle-point energies) between simulations with and without the HOI terms. Without such a side-by-side table or figure, it is difficult to confirm that the separation is load-bearing rather than an artifact of the chosen parameter set.

Authors: We agree that an explicit side-by-side comparison is necessary. We have rerun the atomistic spin dynamics simulations with the HOI terms switched off and added a new table (Table S2) and figure (Fig. S5) in the revised Supplementary Information. The table reports barrier heights, saddle-point energies, and Bloch-point descriptors for both cases. The overall energy barrier changes by only ~3% when HOI are omitted, while the Bloch-point spin texture is qualitatively altered, confirming that DMI remains dominant near the saddle point and that skyrmion stability is largely unaffected. The main text has been updated to reference these results directly. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivation uses independent DFT parameter extraction followed by spin dynamics

full rationale

The paper performs first-principles DFT calculations to extract atomistic spin model parameters (including HOI terms) and then feeds those fixed parameters into separate atomistic spin simulations to study skyrmion stability, collapse, and topological transitions. No step fits a parameter to the target transition outcome and then renames the fit as a prediction; no self-citation supplies a uniqueness theorem or ansatz that defines the reported 'ferric transition' by construction; and the central claims rest on external computational benchmarks rather than self-referential definitions. This is the standard, non-circular workflow for ab initio + spin-model studies.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions of the Heisenberg spin model with added higher-order terms extracted from DFT, plus the validity of the atomistic simulation approach for capturing topological changes.

free parameters (1)

Higher-order exchange interaction strengths
Computed from first-principles but depend on choices of supercell size, k-point sampling, and exchange-correlation functional.

axioms (1)

domain assumption The magnetic interactions in MnSeTe can be accurately mapped onto a classical atomistic spin Hamiltonian including DMI and HOI terms.
Invoked when performing atomistic spin simulations based on parameters from DFT.

pith-pipeline@v0.9.0 · 5799 in / 1426 out tokens · 36858 ms · 2026-05-21T21:43:51.079436+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.

H = −∑Jij(mi·mj) − ∑Dij·(mi×mj) − Ku∑(mzi)2 − ∑μ(mi·B) + HHOI (Eq. 1); HHOI contains B1, Y1, K1 terms (Eq. 2); GNEB paths and Q=1/4π∫m·(∂m/∂x×∂m/∂y)dxdy
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

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

Janus MnSeTe monolayer on hexagonal lattice; D=2 geometry assumed throughout

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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