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arxiv: 2606.10604 · v2 · pith:EXXUITJWnew · submitted 2026-06-09 · ❄️ cond-mat.str-el

Propagation and localization of spin excitations at altermagnetic domain walls

Oksana Peschanska , Jeroen van den Brink , Volodymyr P. Kravchuk This is my paper

Pith reviewed 2026-06-30 11:06 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords altermagnetsdomain wallsspin excitationsbound statesmagnon localizationd-wave symmetryNéel vector
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0 comments X

The pith

Altermagnetic domain walls support extra gapped bound spin states and frequency-dependent localization only when aligned along directions of strongest magnon splitting.

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

The paper studies how spin excitations propagate and localize along domain walls in easy-axial d-wave altermagnets. It shows that the altermagnetic spin splitting affects bound states in an orientation-dependent way. Walls along nodal directions [100] or [010] leave the number of bound states unchanged but produce nonlinear dispersion and wavefront tilt. Walls along [110] or [1-10] add gapped bound states, remove degeneracy between right- and left-handed polarizations, and make the localization length vary strongly with frequency. A static magnetic field along the easy axis further creates asymmetric localization on the two sides of the wall and imposes an upper bound on the wave vector of propagating states.

Core claim

In easy-axial d-wave altermagnets, domain walls oriented along the directions of strongest magnon splitting support additional gapped bound states, lift the degeneracy of eigenstates with respect to Néel-vector precession handedness, and exhibit eigenfrequency-dependent localization that can become very tight; walls along nodal directions produce only a nonlinear dispersion relation and tilted wavefronts without new states, while an applied static field along the easy axis breaks left-right symmetry in the localization profile and caps the allowable wave-vector magnitude.

What carries the argument

The directional spin splitting of the magnon spectrum produced by altermagnetic symmetry, which couples to the domain wall differently according to its angle relative to the crystal axes.

If this is right

  • Extra gapped bound states appear exclusively for domain walls along [110] or [1-10].
  • Polarization degeneracy is removed for those wall orientations.
  • Localization length of the bound states varies strongly with eigenfrequency, enabling tight confinement at certain frequencies.
  • A static field along the easy axis creates asymmetric localization regions on opposite sides of the wall and limits the wave vector.

Where Pith is reading between the lines

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

  • Frequency selection could be used to switch a given bound mode between weakly and strongly localized regimes along the wall.
  • The same orientation dependence may control whether spin excitations can propagate ballistically along the wall or remain confined to it.
  • The upper wave-vector cutoff induced by the field suggests a natural cutoff for magnon wavelengths that can be guided by such walls.

Load-bearing premise

The model assumes an easy-axial d-wave altermagnet whose symmetry produces spin splitting in the magnon spectrum and that linear spin-wave theory suffices to capture the bound states at the domain wall.

What would settle it

A calculation or measurement finding that bound states at [110]-oriented walls retain polarization degeneracy or show localization length independent of frequency would falsify the orientation-dependent effect.

Figures

Figures reproduced from arXiv: 2606.10604 by Jeroen van den Brink, Oksana Peschanska, Volodymyr P. Kravchuk.

Figure 1
Figure 1. Figure 1: FIG. 1. Profile of a static Bloch DW ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) – Dispersion relations ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Dispersion relations for the localized translational [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Properties of the bound eigenstates of an A [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Dependence of the size of the localization region of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Dependence of the critical value of the wave-vector [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Properties of the reflection [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

Altermagnets (A$\ell$Ms) are spin-compensated materials in which opposite-spin sublattices are connected by a symmetry that causes a spin splitting in their elementary excitations. As there is a strong effect of altermagnetism on domain wall properties, it is quite natural to also expect an enrichment of the physics of magnetic excitations at A$\ell$M domain walls. Here, we consider the propagation of spin eigen-excitations along domain walls in easy-axial $d$-wave A$\ell$Ms. Investigating the presence of bound states localized on a domain wall, we find that the effect of the A$\ell$M on the bound states strongly depends on the orientation of the domain wall relative to the crystallographic directions. If the domain wall is oriented along a nodal direction [100] or [010], A$\ell$M does not change the number of bound states; however, it leads to a nonlinear dispersion and a tilt of the wavefront. The effect of A$\ell$M is strongest when the domain wall is oriented along the directions [110] or [$\bar{1}$10], i.e., along the directions of the strongest A$\ell$M splitting in the magnon spectrum. In this case, (i) the additional gapped bound states appear, (ii) degeneracy of the eigenstates with respect to their polarization (right-handed or left-handed precession of the N{\'e}el vector) is removed, and (iii) the localization area of the bound states strongly depends on the eigenfrequency. The latter may lead to strong localization of the bound state at the domain wall. We further consider the influence of a static magnetic field that is applied along the easy axis, and find that the magnetic field induces an asymmetry between the localization regions on opposite sides of the domain wall and sets an upper limit on the absolute value of the propagating eigenstate's wave vector.

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

1 major / 1 minor

Summary. The manuscript examines propagation and localization of spin excitations along domain walls in easy-axial d-wave altermagnets. It reports that wall orientation relative to crystallographic axes controls the effect of altermagnetic spin splitting: [100]/[010] walls yield nonlinear magnon dispersion and wavefront tilt without changing bound-state count, while [110]/[1-10] walls produce additional gapped bound states, lift right/left polarization degeneracy, and make localization length strongly frequency-dependent. An applied static field along the easy axis further induces localization asymmetry across the wall and imposes an upper bound on the propagating wave vector.

Significance. If the central claims hold, the work demonstrates how altermagnetic symmetry enriches magnon bound-state physics at domain walls in an orientation-specific way, offering concrete, symmetry-derived predictions for dispersion, degeneracy lifting, and tunable localization that could be tested experimentally. The direct use of symmetry properties to obtain these results without additional free parameters is a clear strength.

major comments (1)
  1. [Model / linear spin-wave theory section] The derivation of additional gapped bound states, degeneracy removal, and frequency-dependent localization for [110]-oriented walls rests entirely on the linearized equations of motion (linear spin-wave theory) applied across the domain wall. The abstract and modeling section note the Néel-vector rotation but supply no explicit validity check (e.g., amplitude estimates or comparison to nonlinear dynamics) for the harmonic approximation in the presence of large spatial gradients; this assumption is load-bearing for all reported [110] effects.
minor comments (1)
  1. [Abstract] Direction notation in the abstract alternates between [1-10] and [ar{1}10]; adopting a single consistent format would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the importance of validating the linear spin-wave approximation. We address the single major comment below and will incorporate the requested discussion in a revised version.

read point-by-point responses

  1. Referee: [Model / linear spin-wave theory section] The derivation of additional gapped bound states, degeneracy removal, and frequency-dependent localization for [110]-oriented walls rests entirely on the linearized equations of motion (linear spin-wave theory) applied across the domain wall. The abstract and modeling section note the Néel-vector rotation but supply no explicit validity check (e.g., amplitude estimates or comparison to nonlinear dynamics) for the harmonic approximation in the presence of large spatial gradients; this assumption is load-bearing for all reported [110] effects.

    Authors: We agree that an explicit validity assessment of the linear spin-wave theory (LSWT) is warranted, especially for the [110] walls where spatial gradients are pronounced. While LSWT is the standard framework for magnon spectra in antiferromagnets and altermagnets (including prior domain-wall studies), the manuscript does not currently contain amplitude estimates or a direct comparison to nonlinear regimes. In the revised manuscript we will add a dedicated paragraph in the modeling section that (i) estimates the maximum spin-deviation amplitude consistent with the harmonic approximation using the derived bound-state profiles, (ii) recalls the conventional criterion |δS| ≪ S for LSWT validity, and (iii) notes that the reported frequencies lie well below the scale where nonlinear magnon-magnon interactions dominate in easy-axial antiferromagnets. This addition will make the applicability range of the [110] results explicit without altering the central claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation follows from model symmetries and linear equations

full rationale

The paper derives bound-state properties and localization from the symmetry-induced spin splitting in an easy-axial d-wave altermagnet by solving linearized equations of motion. No self-definitional relations, fitted inputs renamed as predictions, or load-bearing self-citations appear in the abstract or described chain. The central results (additional gapped states for [110] walls, lifted degeneracy, frequency-dependent localization) are direct consequences of the model assumptions rather than reductions to the inputs by construction. Linear spin-wave theory is an explicit modeling choice, not a circular step.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that d-wave altermagnets possess a symmetry-induced spin splitting in their magnon spectrum and that standard spin-wave methods apply to domain-wall bound states; no free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Altermagnets are spin-compensated materials in which opposite-spin sublattices are connected by a symmetry that causes spin splitting in elementary excitations
    Stated in the opening sentence of the abstract as the defining property used throughout the analysis
  • domain assumption The system is an easy-axial d-wave altermagnet whose domain walls support bound spin eigen-excitations whose properties can be obtained from the equations of motion
    Implicit in the choice of model and the calculation of bound states and dispersion

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Reference graph

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