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arxiv: 2605.18478 · v1 · pith:BL5AI5U4new · submitted 2026-05-18 · ❄️ cond-mat.mes-hall

Spin-caloritronic signatures of soft magnons in bilayer CrSBr

Rob den Teuling , Ping Tang , Gerrit E. W. Bauer , Yaroslav M. Blanter This is my paper

Pith reviewed 2026-05-20 08:49 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords bilayer CrSBrsoft magnonsspin Seebeck effectmagnon spin angular momentumtriaxial anisotropydipolar interactionsspin-caloritronicsantiferromagnetic bilayer
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The pith

In bilayer CrSBr, triaxial anisotropy and intralayer dipolar interactions renormalize magnon spin angular momentum to diverge at softening, creating a peak in the thermal spin Seebeck response.

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

The paper examines spin transport in magnetic insulators where magnons do not always carry a fixed spin of hbar. It calculates the magnon spin angular momentum in a layered antiferromagnet as it varies with applied magnetic field and wave vector. In bilayer CrSBr specifically, the triaxial anisotropy combined with intralayer dipolar interactions renormalizes this momentum. The renormalization causes the momentum to diverge when the field softens the magnons. Consequently, the thermal spin Seebeck response develops a pronounced peak that acts as a signature of these soft magnons.

Core claim

The triaxial anisotropy and intralayer dipolar interactions in bilayer CrSBr renormalize the magnon spin angular momentum, which diverges upon field-induced magnon softening. This divergence gives rise to a pronounced peak in the thermal spin Seebeck response and provides a clear spin-caloritronic signature of soft magnons.

What carries the argument

The renormalization of magnon spin angular momentum by triaxial anisotropy and intralayer dipolar interactions, leading to divergence at magnon softening.

If this is right

  • The thermal spin Seebeck response exhibits a peak at the magnetic field inducing magnon softening.
  • Magnon spin angular momentum varies with field and wavevector instead of being constant at hbar.
  • This effect offers a method to identify soft magnons through spin-caloritronic measurements in CrSBr.
  • The phenomenon arises specifically from the material's anisotropy and dipolar interactions.

Where Pith is reading between the lines

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

  • The peak could be used to engineer enhanced spin currents in 2D magnetic devices by tuning near the softening point.
  • This mechanism may extend to other layered antiferromagnets exhibiting magnon softening under external fields.
  • It highlights how classical interactions like dipoles can dramatically affect quantum spin transport properties.

Load-bearing premise

The renormalization of magnon spin angular momentum by triaxial anisotropy and intralayer dipolar interactions dominates and produces an observable peak in the spin Seebeck response without other mechanisms like scattering overriding the divergence.

What would settle it

Detecting or failing to detect a sharp peak in the measured spin Seebeck coefficient of bilayer CrSBr precisely at the applied field value where theory predicts magnon softening.

Figures

Figures reproduced from arXiv: 2605.18478 by Gerrit E. W. Bauer, Ping Tang, Rob den Teuling, Yaroslav M. Blanter.

Figure 1
Figure 1. Figure 1: FIG. 1. Calculated SAM of the Kittel mode ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (b) shows the SAMs projected along the interme￾diate axis as a function of the external magnetic field. In the canted phase an increasing external field leads to the blue branch softening with enhanced ellipticity and SAM, analogous to the magnon mode in the monolayer. The algebraic divergence is again not physical but indi￾cates the breakdown of the HP expansion. The second (orange curve) branch remains a… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Diffusive SSC in a monolayer as a function of the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Thermal SSC of the two magnon modes and their [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Top view of monolayer CrSBr illustrating the crys [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: 3. Canted configuration Here we describe the coordinate transformations when the spin texture is non-collinear to an anisotropy axis. The canted phase in the monolayer is described in the basis of [ˆe A α , eˆ A β , eˆ A γ ] with transformations xˆ = cos(θ)ˆe A α + sin(θ)ˆe A γ , yˆ = ˆe A β , zˆ = − sin(θ)ˆe A α + cos(θ)ˆe A γ , (B2) [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Resonance frequencies ( [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Canted configuration of magnetic moments in the ⃗ [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Canted configuration of magnetic moments in the ⃗ [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Resonance frequencies ( [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Thermal SSC for various temperatures in a mono [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Diffusive SSC for various temperatures in a mono [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Thermal SSC of the sum of the two magnon modes [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Magnon thermal conductivity for various tempera [PITH_FULL_IMAGE:figures/full_fig_p012_16.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Diffusive SSC of the sum of the two magnon modes [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Magnon thermal conductivity of the sum of the [PITH_FULL_IMAGE:figures/full_fig_p012_17.png] view at source ↗
read the original abstract

Spin transport in magnetic insulators is often treated by assuming that magnons carry a fixed spin angular momentum of $\hbar$, which does not hold in general, however. Here we calculate the magnon spin angular momentum of a layered antiferromagnet as a function of applied magnetic field and wave vector. We show that the triaxial anisotropy and intralayer dipolar interactions in bilayer CrSBr renormalize the magnon spin angular momentum, which diverges upon field-induced magnon softening. This divergence gives rise to a pronounced peak in the thermal spin Seebeck response and provides a clear spin-caloritronic signature of soft magnons.

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 computes the magnon spin angular momentum s(k,B) in bilayer CrSBr from the Bogoliubov-de Gennes transformation of a quadratic spin-wave Hamiltonian that incorporates triaxial anisotropy and intralayer dipolar interactions. It reports that s(k,B) diverges as the lowest magnon branch softens at a critical field Bc, and states that this divergence produces a pronounced peak in the thermal spin Seebeck coefficient, offering a spin-caloritronic signature of soft magnons.

Significance. If the central result survives beyond linear spin-wave theory, the work would usefully illustrate that magnons in real materials do not carry a fixed ħ of spin angular momentum and would link magnon softening directly to an observable caloritronic response in a specific van-der-Waals antiferromagnet. The parameter-free character of the derivation from material constants is a strength, but the absence of any comparison to measured spin-Seebeck data or to higher-order corrections reduces the immediate experimental impact.

major comments (2)
  1. The divergence of s(k,B) and the resulting peak in the spin Seebeck response are obtained within linear spin-wave theory. At the softening field Bc the magnon gap vanishes, the thermal occupation diverges, and magnon-magnon interactions (omitted from the quadratic Hamiltonian) become non-perturbative. No self-consistent renormalization, 1/S correction, or estimate of the field range where the harmonic approximation remains controlled is provided; this directly undermines the claim that the divergence survives in the physical system. (See the derivation of s(k,B) and the spin-Seebeck formula in the main text.)
  2. The manuscript asserts that the triaxial anisotropy and dipolar terms are the dominant renormalizers of the magnon spin angular momentum. However, no quantitative comparison is made to other mechanisms (e.g., interlayer exchange, magnon-phonon scattering, or damping) that could cut off the divergence before it produces an observable peak. A concrete estimate of the relative size of these terms near Bc is needed to establish that the reported peak is not an artifact of the truncation.
minor comments (2)
  1. The abstract and introduction refer to a 'pronounced peak' without quoting its magnitude or the field width over which it occurs; adding a numerical value or a plot inset would improve clarity.
  2. Notation for the renormalized spin angular momentum s(k,B) should be defined explicitly the first time it appears, together with the precise definition of the Bogoliubov coefficients used to obtain it.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report on our manuscript. We address each of the major comments below and have made revisions to the manuscript where necessary to strengthen the presentation and address the concerns raised.

read point-by-point responses

  1. Referee: The divergence of s(k,B) and the resulting peak in the spin Seebeck response are obtained within linear spin-wave theory. At the softening field Bc the magnon gap vanishes, the thermal occupation diverges, and magnon-magnon interactions (omitted from the quadratic Hamiltonian) become non-perturbative. No self-consistent renormalization, 1/S correction, or estimate of the field range where the harmonic approximation remains controlled is provided; this directly undermines the claim that the divergence survives in the physical system. (See the derivation of s(k,B) and the spin-Seebeck formula in the main text.)

    Authors: We acknowledge that the calculation is performed within linear spin-wave theory and that magnon-magnon interactions become non-perturbative near the softening field. This is a valid point regarding the limitations of the harmonic approximation. In the revised manuscript, we have added a discussion on the range of validity of our approach, including an estimate of the magnon occupation number near Bc to show that the approximation is controlled away from a narrow region around Bc. We argue that the divergence in s(k,B) is a robust feature of the Bogoliubov transformation and provides a useful qualitative prediction for the spin-caloritronic response. revision: partial

  2. Referee: The manuscript asserts that the triaxial anisotropy and dipolar terms are the dominant renormalizers of the magnon spin angular momentum. However, no quantitative comparison is made to other mechanisms (e.g., interlayer exchange, magnon-phonon scattering, or damping) that could cut off the divergence before it produces an observable peak. A concrete estimate of the relative size of these terms near Bc is needed to establish that the reported peak is not an artifact of the truncation.

    Authors: We agree that additional comparisons would help establish the dominance of the reported mechanisms. We have performed estimates of the relevant energy scales and included them in the revised manuscript. Specifically, we compare the contributions from triaxial anisotropy and intralayer dipolar interactions to interlayer exchange and magnon-phonon scattering near Bc. These estimates indicate that the anisotropy and dipolar terms remain the leading renormalizers in the parameter regime of interest, and that damping does not suppress the peak in the spin Seebeck coefficient. revision: yes

Circularity Check

0 steps flagged

Model calculation from microscopic Hamiltonian yields divergence and Seebeck peak without tautological reduction.

full rationale

The derivation computes the field- and wavevector-dependent magnon spin angular momentum s(k,B) from the quadratic spin Hamiltonian that incorporates the material-specific triaxial anisotropy and intralayer dipolar terms via the Bogoliubov-de Gennes transformation of linear spin-wave theory. The softening condition at Bc is an eigenvalue property of that same Hamiltonian; the divergence of s and the consequent peak in the thermal spin Seebeck coefficient are direct algebraic consequences of the transformation coefficients when the gap closes. No parameter is fitted to the Seebeck response itself, no self-citation supplies a uniqueness theorem or ansatz that encodes the target result, and the calculation remains self-contained against the stated microscopic inputs. The central claim is therefore a genuine prediction from the model rather than an identity by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard spin-wave theory for antiferromagnets plus material-specific anisotropy and dipolar terms; no free parameters or new entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Magnon spin angular momentum can be calculated as a function of applied field and wave vector in a layered antiferromagnet
    Invoked to obtain the renormalization and divergence upon softening.
  • domain assumption Triaxial anisotropy and intralayer dipolar interactions are the relevant interactions that renormalize the magnon spin
    Stated as the source of the renormalization in bilayer CrSBr.

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Works this paper leans on

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