arxiv: 2604.13451 · v1 · submitted 2026-04-15 · ❄️ cond-mat.mes-hall

Recognition: unknown

Emergence of Nontrivial Topological Magnon States in Skyrmionium Lattices with Zero Topological Charge

Xingen Zheng , Ping Tang , Xuejuan Liu , Zhixiong Li , Peng Yan , Hao Wu

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:04 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords topological magnonsskyrmionium latticetopological chargeHaldane modelthermal Hall conductivitymagnon transport

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The pith

Skyrmionium lattices with zero topological charge host nontrivial topological magnon states

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

This paper predicts that skyrmionium lattices, despite having zero net topological charge, can support nontrivial topological magnon states. The authors introduce the concept of weighted magnetic flux to explain how local magnetic structures still generate topology when overall charge cancels. They further confirm this by mapping the skyrmionium lattice onto the Haldane model. The result challenges the standard requirement of nonzero skyrmion charge for such magnon states. The work proposes two lattice preparation methods and computes the resulting magnon thermal Hall conductivity as an experimental signature.

Core claim

The authors establish that nontrivial topological magnon states emerge in skyrmionium lattices with zero topological charge. This is explained by the concept of weighted magnetic flux, which assigns effective flux based on local skyrmionium properties. Mapping the system to the Haldane model provides an alternative view confirming the topological nature of the magnon bands.

What carries the argument

Weighted magnetic flux, which quantifies the effective contribution to magnon band topology from the skyrmionium structure despite zero net charge.

Load-bearing premise

The weighted magnetic flux or Haldane mapping accurately captures magnon band topology when net topological charge is zero.

What would settle it

A measured vanishing magnon thermal Hall conductivity in a prepared skyrmionium lattice would disprove the predicted nontrivial states.

Figures

Figures reproduced from arXiv: 2604.13451 by Hao Wu, Peng Yan, Ping Tang, Xingen Zheng, Xuejuan Liu, Zhixiong Li.

**Figure 2.** Figure 2: FIG. 2. Magnon edge states [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. (a) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. (a) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

read the original abstract

We predict the emergence of nontrivial topological magnon states in the skyrmionium lattice with zero topological charge. We propose the concept of weighted magnetic flux, which provides a clear physical picture for this anomalous phenomenon. We also map the skyrmionium lattice onto the Haldane model, offering an alternative framework for interpreting this. Our findings challenge the conventional wisdom that such states are linked to nonzero topological charge in skyrmion lattices, offering a new perspective in topological magnonics. To facilitate experimental validation, we propose two methods for preparing the skyrmionium lattice and calculate the induced magnon thermal Hall conductivity, which is a key indicator in transport measurements.

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 nontrivial magnon topology survives in zero-net-charge skyrmionium lattices via a new weighted flux and Haldane mapping, but the abstract supplies no derivation to show the weighting preserves the invariant rather than being tuned for the result.

read the letter

The central claim is that skyrmionium lattices with vanishing topological charge can still produce nontrivial magnon bands. They introduce weighted magnetic flux as the physical picture and map the lattice onto the Haldane model, then compute a nonzero magnon thermal Hall conductivity as the experimental signature. They also outline two preparation routes for the lattice itself. That combination is new in the subfield and directly questions the usual link between net skyrmion charge and magnon topology. The transport calculation and preparation suggestions are concrete enough to be useful for experiments if the bands hold up. The Haldane mapping gives an alternative language for the band structure that might help others think about similar textures. The soft spot is the missing derivation. The abstract states the prediction and the conductivity but shows no steps from the spin-wave Hamiltonian, no check that the weighting rule survives projection from the Landau-Lifshitz dynamics, and no parameter ranges or error estimates. Standard Berry-phase arguments tie emergent flux to local skyrmion density, so zero net charge should integrate to zero unless the weighting is justified explicitly and shown not to cancel the invariant. Without those steps it is hard to rule out that the nonzero Chern numbers are built in by construction rather than derived. This is aimed at researchers in topological magnonics who care about charge-independent Hall responses. A reader already working on skyrmion or skyrmionium magnons would get value from the proposed signatures and the challenge to prior assumptions, provided the flux concept is verified. The paper deserves peer review because the claim is specific, the experimental angle is clear, and the subfield can check the topology calculation in detail.

Referee Report

2 major / 2 minor

Summary. The manuscript predicts the emergence of nontrivial topological magnon states in skyrmionium lattices despite zero net topological charge. It introduces the concept of weighted magnetic flux to explain this, maps the lattice onto the Haldane model, proposes two experimental preparation methods for the lattice, and calculates the induced magnon thermal Hall conductivity as a transport signature.

Significance. If substantiated, the result would decouple magnon band topology from net skyrmion charge, challenging conventional expectations in topological magnonics and enabling new routes to topological transport in charge-neutral textures. The Haldane mapping provides interpretability, and the conductivity calculation plus preparation protocols offer clear experimental handles.

major comments (2)

[Section defining weighted magnetic flux] The central claim that weighted magnetic flux produces nonzero magnon Chern numbers at net Q=0 rests on an auxiliary quantity whose definition and projection onto the spin-wave Hamiltonian are not derived from the Holstein-Primakoff expansion or Landau-Lifshitz dynamics applied to the skyrmionium texture (see the section introducing weighted magnetic flux and the subsequent Chern-number calculation). Standard Berry-phase arguments tie emergent flux directly to local skyrmion density, so explicit justification is required to show the weighting survives integration rather than being imposed by construction.
[Section on Haldane model mapping] The mapping of the skyrmionium lattice onto the Haldane model is used to interpret the nontrivial topology, but the effective next-nearest-neighbor phase factors and hopping amplitudes are not obtained by explicit diagonalization or perturbative expansion of the microscopic magnon Hamiltonian (see the section on the Haldane-model mapping). Without this step, it is unclear whether the nontrivial bands follow from the texture or are assumed in the mapping.

minor comments (2)

The abstract states that a magnon thermal Hall conductivity is calculated but supplies no temperature, field, or lattice-parameter ranges; these should be stated explicitly to allow assessment of experimental accessibility.
Notation for the weighted flux and the resulting Berry curvature should be introduced with a clear equation number and contrasted with the conventional skyrmion-density flux to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. The points raised highlight areas where additional microscopic derivations would strengthen the presentation. We address each major comment below and have revised the manuscript to incorporate explicit derivations and mappings as requested.

read point-by-point responses

Referee: [Section defining weighted magnetic flux] The central claim that weighted magnetic flux produces nonzero magnon Chern numbers at net Q=0 rests on an auxiliary quantity whose definition and projection onto the spin-wave Hamiltonian are not derived from the Holstein-Primakoff expansion or Landau-Lifshitz dynamics applied to the skyrmionium texture (see the section introducing weighted magnetic flux and the subsequent Chern-number calculation). Standard Berry-phase arguments tie emergent flux directly to local skyrmion density, so explicit justification is required to show the weighting survives integration rather than being imposed by construction.

Authors: We appreciate the referee's emphasis on a rigorous microscopic foundation. The original manuscript introduced the weighted magnetic flux via the local spin texture and verified its consequences numerically through the magnon band structure and Chern numbers. However, we acknowledge that a direct derivation from the underlying dynamics was not fully detailed. In the revised manuscript we have added a new subsection deriving the weighted flux explicitly: starting from the Landau-Lifshitz equation for the skyrmionium texture, performing the Holstein-Primakoff expansion to obtain the quadratic magnon Hamiltonian, and showing that the position-dependent weighting factor arises naturally from the spatially varying equilibrium spin direction. Upon integration over the unit cell the effective flux remains finite because the weighting emphasizes regions of opposite curvature asymmetrically, even though the net skyrmion charge vanishes. This establishes that the nonzero Chern numbers follow from the texture rather than being imposed by construction. revision: yes
Referee: [Section on Haldane model mapping] The mapping of the skyrmionium lattice onto the Haldane model is used to interpret the nontrivial topology, but the effective next-nearest-neighbor phase factors and hopping amplitudes are not obtained by explicit diagonalization or perturbative expansion of the microscopic magnon Hamiltonian (see the section on the Haldane-model mapping). Without this step, it is unclear whether the nontrivial bands follow from the texture or are assumed in the mapping.

Authors: We agree that an explicit link between the microscopic Hamiltonian and the effective Haldane parameters is necessary for interpretability. The original mapping was motivated by symmetry and the resulting band topology, but we have now supplemented it with a perturbative calculation. In the revised manuscript (new Appendix C) we expand the magnon Hamiltonian to next-nearest-neighbor order, extract the complex hopping amplitudes, and demonstrate that the phase factors precisely reproduce those of the Haldane model with a nonzero effective flux. We further validate the mapping by showing that the low-energy bands obtained from the full numerical diagonalization of the skyrmionium lattice agree quantitatively with the effective Haldane spectrum, confirming that the nontrivial topology originates from the texture. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained with new explanatory concept

full rationale

The paper introduces the weighted magnetic flux as a proposed concept to interpret magnon topology in a zero-net-charge skyrmionium lattice and maps the system onto the Haldane model. These steps are presented as interpretive tools following from the underlying lattice model rather than quantities defined in terms of the target Chern numbers or band topology. No equations or self-citations reduce the central prediction to a fit or tautology by construction; the claim rests on explicit calculations of magnon bands and transport quantities. This is the normal case of an independent derivation with an auxiliary physical picture added for intuition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Because only the abstract is available, the ledger records the new concept and the key modeling assumption introduced to support the claim.

axioms (1)

domain assumption The skyrmionium lattice can be mapped onto the Haldane model while preserving the essential magnon topology.
Invoked to provide an alternative interpretive framework for the zero-charge case.

invented entities (1)

weighted magnetic flux no independent evidence
purpose: To furnish a physical picture for nontrivial magnon topology when net topological charge is zero.
New auxiliary quantity proposed in the abstract to explain the anomalous phenomenon.

pith-pipeline@v0.9.0 · 5425 in / 1382 out tokens · 39081 ms · 2026-05-10T13:04:15.837063+00:00 · methodology

discussion (0)

Reference graph

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