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arxiv: 2509.13900 · v2 · submitted 2025-09-17 · ❄️ cond-mat.str-el · cond-mat.mes-hall· cond-mat.mtrl-sci

Fate of Topological Dirac Magnons in van der Waals Ferromagnets at Finite Temperature

Rintaro Eto , Ignacio Salgado-Linares , Masahito Mochizuki , Johannes Knolle , Alexander Mook This is my paper

Pith reviewed 2026-05-18 16:30 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mes-hallcond-mat.mtrl-sci
keywords Dirac magnonsvan der Waals ferromagnetsfinite temperaturetopological magnonsmagnon dampingspin-wave theoryCrBr3
0
0 comments X

The pith

Thermal magnon bound states explain observed damping and shifts in CrBr3 Dirac magnons near the Curie temperature.

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

The paper builds a microscopic theory of thermal magnon-magnon interactions in van der Waals honeycomb ferromagnets that host Dirac magnons. It combines nonlinear spin-wave theory with self-energy corrections and a T-matrix resummation to include two-magnon bound states. This framework quantitatively reproduces the temperature- and momentum-dependent energy shifts and linewidths measured in the gapless material CrBr3, even close to its Curie point. For gapped Dirac magnon materials such as CrI3, CrSiTe3, and CrGeTe3 the topological gap shrinks with rising temperature but shows no sign of closing before magnetic order vanishes. The work also supplies a practical threshold for the Dzyaloshinskii-Moriya interaction strength needed to keep the gap visible against thermal broadening.

Core claim

Using nonlinear spin-wave theory with magnon self-energy corrections and a T-matrix resummation that captures two-magnon bound states, the calculations quantitatively reproduce temperature- and momentum-dependent energy shifts and linewidths observed experimentally in the gapless Dirac magnon material CrBr3, even near the Curie temperature. For gapped Dirac magnon materials the topological magnon gap undergoes a thermally induced reduction but exhibits no evidence of thermally driven topological transitions. Classical atomistic spin dynamics simulations confirm the gap's robustness up to the Curie temperature, and a minimum ratio of Dzyaloshinskii-Moriya interaction to Heisenberg exchange of

What carries the argument

nonlinear spin-wave theory with magnon self-energy corrections and T-matrix resummation that captures two-magnon bound states

If this is right

  • Energy shifts and linewidths in CrBr3 are reproduced across a wide temperature range including near the Curie temperature.
  • The topological gap in CrI3, CrSiTe3 and CrGeTe3 reduces with temperature but stays open throughout the ordered phase.
  • Two-magnon bound states enhance magnon damping especially at low temperatures.
  • A Dzyaloshinskii-Moriya to Heisenberg exchange ratio of roughly 5 percent suffices to keep the gap observable against thermal broadening.
  • Classical atomistic spin dynamics simulations independently corroborate the gap robustness up to the Curie temperature.

Where Pith is reading between the lines

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

  • The same many-body framework could be used to predict finite-temperature spin transport velocities in other two-dimensional magnets.
  • Bound-state contributions may set practical limits on magnon coherence times in proposed topological magnonic devices.
  • Systematic variation of the DMI strength across a series of van der Waals compounds would provide a direct test of the proposed 5 percent visibility threshold.

Load-bearing premise

The microscopic spin Hamiltonian parameters taken from prior literature remain valid at finite temperature without additional renormalization or higher-order magnon interactions beyond the resummation.

What would settle it

A measurement showing either the topological gap in CrI3 closing at a temperature well below the Curie point or a clear mismatch between the calculated and observed temperature dependence of linewidths in CrBr3 would falsify the central claim.

Figures

Figures reproduced from arXiv: 2509.13900 by Alexander Mook, Ignacio Salgado-Linares, Johannes Knolle, Masahito Mochizuki, Rintaro Eto.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of van der Waals ferromagnets on a honeycomb lat [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) High-symmetry momentum paths used in this work, in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Overview of nonlinear spin-wave approximations. (a) The [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Multimagnon continua exhibited by the spin model for CrBr [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Two-particle excitation density of states in CrBr [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Density of states linecuts of the spin-1 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison of the experimentally detected and theoretically predicted thermal evolution of the magnon spectrum of CrBr [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Three-magnon scatterings, which need to be included for a [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) Relative magnon energy shift and (b) linewidth in CrBr [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Linecuts of the single-magnon spectral function [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. (a) Temperature-dependence of the magnetization [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Diagrammatic representation of the two-channel parquet [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Diagrammatic representation of the [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Closed path of integration [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Magnon band linewidth of CrBr [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. (a) Schematic of the honeycomb lattice. [PITH_FULL_IMAGE:figures/full_fig_p024_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Calculated (a) magnon energy shift and (b) linewidth of CrBr [PITH_FULL_IMAGE:figures/full_fig_p028_17.png] view at source ↗
read the original abstract

Dirac magnons, the bosonic counterparts of Dirac fermions in graphene, provide a unique platform to explore symmetry-protected band crossings and quantum geometry in magnetic insulators, while promising high-velocity, low-dissipation spin transport for next-generation magnonic technologies. However, their stability under realistic, finite-temperature conditions remains an open question. Here, we develop a comprehensive microscopic theory of thermal magnon-magnon interactions in van der Waals honeycomb ferromagnets, focusing on both gapless and gapped Dirac magnons. Using nonlinear spin-wave theory with magnon self-energy corrections and a T-matrix resummation that captures two-magnon bound states, we quantitatively reproduce temperature- and momentum-dependent energy shifts and linewidths observed experimentally in the gapless Dirac magnon material CrBr$_3$, even near the Curie temperature. Our approach resolves discrepancies between prior theoretical predictions and experiment and highlight the significant role of bound states in enhancing magnon damping at low temperatures. For gapped Dirac magnon materials such as CrI$_3$, CrSiTe$_3$, and CrGeTe$_3$, we find a thermally induced reduction of the topological magnon gap but no evidence of thermally driven topological transitions. Classical atomistic spin dynamics simulations corroborate the gap' s robustness up to the Curie temperature. Furthermore, we establish a practical criterion for observing topological gaps by determining the minimum ratio of Dzyaloshinskii-Moriya interaction to Heisenberg exchange required to overcome thermal broadening throughout the ordered phase, typically around 5%. Our results clarify the interplay of thermal many-body effects and topology in low-dimensional magnets and provide a reliable framework for interpreting spectroscopic experiments.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a microscopic theory of thermal magnon-magnon interactions in van der Waals honeycomb ferromagnets using nonlinear spin-wave theory, magnon self-energy corrections, and T-matrix resummation to capture two-magnon bound states. It claims to quantitatively reproduce the temperature- and momentum-dependent energy shifts and linewidths measured in the gapless Dirac magnon material CrBr₃ even near the Curie temperature, resolving prior theory-experiment discrepancies. For gapped Dirac magnon systems (CrI₃, CrSiTe₃, CrGeTe₃), it reports a thermally induced reduction of the topological gap without closure or topological transition, corroborated by classical atomistic spin dynamics simulations, and proposes a minimum D/J ratio of ~5% for observing gaps throughout the ordered phase.

Significance. If the quantitative reproduction of CrBr₃ data holds under the fixed literature parameters, the work is significant for providing a practical framework to interpret finite-temperature spectroscopic data on topological magnons, clarifying the role of bound states in damping, and establishing a criterion for gap observability. The corroboration with classical spin dynamics simulations is a strength that adds robustness to the gap-stability conclusions.

major comments (2)
  1. [§5] §5 (CrBr₃ results and comparison to experiment): The central claim of quantitative reproduction of experimental energy shifts and linewidths lacks error bars on theoretical curves, an explicit description of the fitting or parameter-selection procedure, and direct overlay with raw data points. This is load-bearing because the agreement may depend on the specific unadjusted values of J, D, and K taken from prior literature rather than emerging robustly from the formalism.
  2. [§3.2] §3.2 (T-matrix resummation and self-energy): The assumption that literature values of the microscopic Hamiltonian parameters remain valid without renormalization at finite temperature is not justified, particularly near Tc where magnon density is high. The dilute-interaction approximation underlying the T-matrix may require additional checks against magnon-phonon coupling or four-magnon processes omitted from the resummation.
minor comments (2)
  1. [Figure 4] Figure 4 (linewidth vs temperature): Adding experimental error bars or uncertainty bands would improve clarity of the comparison.
  2. [Abstract] The abstract states 'highlight the significant role' but should read 'highlights' for grammatical consistency.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below, providing clarifications on our methodology and indicating where revisions will strengthen the presentation.

read point-by-point responses

  1. Referee: §5 (CrBr₃ results and comparison to experiment): The central claim of quantitative reproduction of experimental energy shifts and linewidths lacks error bars on theoretical curves, an explicit description of the fitting or parameter-selection procedure, and direct overlay with raw data points. This is load-bearing because the agreement may depend on the specific unadjusted values of J, D, and K taken from prior literature rather than emerging robustly from the formalism.

    Authors: The parameters J, D, and K are taken unchanged from the cited literature values determined at low temperature; no fitting or adjustment was performed in our calculations, as stated in Section 2. The quantitative match to the temperature- and momentum-dependent shifts and linewidths in CrBr₃ arises from the inclusion of magnon self-energy corrections and T-matrix resummation of two-magnon bound states, which were absent in earlier linear spin-wave treatments. In the revised manuscript we will add an explicit paragraph describing the literature sources and selection criteria for these parameters, include direct overlays of the theoretical curves with the raw experimental data points in the relevant figures, and discuss numerical convergence and the leading sources of theoretical uncertainty. Because the calculations are deterministic for fixed parameters, conventional statistical error bars are not applicable; we will instead quantify the sensitivity to small variations in the input parameters. revision: yes

  2. Referee: §3.2 (T-matrix resummation and self-energy): The assumption that literature values of the microscopic Hamiltonian parameters remain valid without renormalization at finite temperature is not justified, particularly near Tc where magnon density is high. The dilute-interaction approximation underlying the T-matrix may require additional checks against magnon-phonon coupling or four-magnon processes omitted from the resummation.

    Authors: We agree that the magnon density becomes appreciable near Tc and that a fully renormalized finite-temperature Hamiltonian would be desirable. Our approach fixes the microscopic parameters at their low-T literature values and computes the leading thermal corrections through the self-energy and T-matrix; this is a controlled approximation whose validity is supported by the independent, non-perturbative classical atomistic spin-dynamics simulations reported in the manuscript, which reproduce the same gap-stability conclusions without invoking the T-matrix. Magnon-phonon coupling and higher-order four-magnon processes are indeed omitted and constitute natural extensions. In the revision we will expand the discussion of the T-matrix validity range, add a brief estimate of the magnon-density regime where the ladder resummation remains reliable, and explicitly note the absence of magnon-phonon effects as a limitation. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected in the derivation chain

full rationale

The paper applies nonlinear spin-wave theory plus T-matrix resummation to a microscopic Hamiltonian whose parameters are taken from prior literature, then computes finite-temperature magnon shifts and linewidths for comparison with experiment. This constitutes a forward calculation whose outputs (energy shifts, damping) are not equivalent to the inputs by construction; the T-matrix step introduces independent many-body content that is not forced by the zero-temperature parameters or by self-citation. No load-bearing step reduces to a fitted quantity renamed as prediction or to an unverified self-citation chain. The quantitative reproduction of data is presented as validation rather than tautological output.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard assumptions of nonlinear spin-wave theory for Heisenberg magnets plus the validity of the T-matrix approximation for two-magnon scattering; no new particles or forces are introduced.

free parameters (1)
  • microscopic Hamiltonian parameters (J, D, K)
    Exchange, Dzyaloshinskii-Moriya, and anisotropy strengths taken from prior literature and used to compute self-energies; their precise values determine the quantitative match to experiment.
axioms (2)
  • domain assumption Magnon-magnon interactions can be treated perturbatively via self-energy plus T-matrix resummation without requiring full diagrammatic summation or quantum Monte Carlo.
    Invoked when the authors state that the approach captures bound states and reproduces data near Tc.
  • domain assumption Classical atomistic spin dynamics simulations provide an independent check on the quantum gap robustness up to Tc.
    Used to corroborate the absence of thermally driven topological transitions.

pith-pipeline@v0.9.0 · 5860 in / 1665 out tokens · 47406 ms · 2026-05-18T16:30:11.076232+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Transport of Dirac magnons driven by gauge fields

    cond-mat.mes-hall 2025-12 unverdicted novelty 7.0

    Gauge fields induce a quantized transverse spin conductivity σ^{xy}=α² sgn(m) ℏ/4π in Dirac magnons of a honeycomb ferromagnet, with AC resonance at the topological gap, as a magnonic analog of the quantum Hall effect.

  2. Winding feature and thermal evolution of the Dirac magnons in CrI$_3$

    cond-mat.mtrl-sci 2026-05 unverdicted novelty 6.0

    Inelastic neutron scattering reveals the magnon winding around the K-point in CrI3 as the signature of Dirac magnons together with T^2 thermal renormalization from magnon-magnon interactions.

Reference graph

Works this paper leans on

88 extracted references · 88 canonical work pages · cited by 2 Pith papers

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    T/T C ≪1 We turn to the renormalization and linewidth of the magnon dispersion in the spin model of CrBr3 at small temperatures far below the critical temperatureT C, and discuss the qualitative and quantitative differences arising from the various levels of approximation introduced in Sec. II. To comply with literature [6], we define the rescaled energy ...

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    T/T C ≲1 FIG. 8. Three-magnon scatterings, which need to be included for a more quantitatively accurate description of the magnon linewidth at high temperatures nearT C. Next we discuss thermal magnon renormalizations at higher temperatures, i.e., 20 K and 30 K, where a direct comparison between the theory and experimental data reported in Ref. [6] is pos...

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    Solution of the Bethe-Salpeter equation In the following, we denote the decomposition of the four-point (two-in-two-out) vertex as Qν1,ν2↔ν3,ν4 q1,q2↔q3,q4 =v L ν1,ν2 (q1,q 2) Γ 4Nmuc vR ν3,ν4 (q3,q 4) .(B1) whereΓis a 5N 2 subNbond ×5N 2 subNbond-dimensional matrix, andv L ν1,ν2 (q1,q 2) vR ν3,ν4 (q3,q 4) is a 5N 2 subNbond-dimensional row (column) vecto...

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