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arxiv: 2605.24527 · v1 · pith:KNYB53R3 · submitted 2026-05-23 · cond-mat.str-el

Emergent Dispersive Multipolar Excitations in NaErSe₂

Zheng Zhang , Mingfang Shu , Mingtai Xie , Weizhen Zhuo , Yanzhen Cai , Christian Balz , Jianting Ji , Feng Jin
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Jie Ma
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classification cond-mat.str-el
keywords emergent multipolar excitationscrystalline electric fieldtriangular antiferromagnetneutron spectroscopyspin-orbit couplingdipole-octupoleNaErSe2
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The pith

Local crystal-field levels couple with collective magnons to produce emergent multipolar dispersions in NaErSe₂.

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

The paper establishes that in NaErSe₂ the dipolar Γ4 ground state and dipole-octupole Γ5,6 excited state enable coupling between local and collective excitations. High-resolution neutron spectra show magnon branches from the ground state being replicated on higher Γ4 levels while coupling with Γ5,6 forms a distinct multipolar band. Modeling with total angular momentum explains these symmetry-selected dispersions. An applied magnetic field reconstructs the wavefunctions and turns the system into a multipolar ferromagnet, offering a way to tune these excitations.

Core claim

By combining neutron spectroscopy with total angular momentum modeling, the authors identify coupled local-collective excitations where magnon branches from the Γ4 ground state are replicated on higher Γ4 levels but couple with the Γ5,6 levels to form a distinct multipolar band, with the system becoming a multipolar ferromagnet under applied field.

What carries the argument

Emergent symmetry-selected dispersions arising from the coupling between magnon branches and the dipole-octupole Γ5,6 levels, enabled by total angular momentum modeling of the CEF wavefunctions.

Load-bearing premise

The total angular momentum modeling accurately reproduces the CEF wavefunctions and selection rules without significant contributions from impurities, lattice distortions, or higher-order CEF terms.

What would settle it

A mismatch between predicted and observed dispersion relations in high-resolution neutron spectra, particularly the absence of the expected multipolar band or replication patterns, would falsify the interpretation.

read the original abstract

In most condensed-matter systems, local and collective excitations remain decoupled due to their distinct energy scales. Here, we identify coupled local-collective excitations in the triangular antiferromagnet NaErSe$_2$ by combining neutron spectroscopy with total angular momentum modeling. The low-lying crystalline electric field (CEF) doublets include a dipolar $\Gamma_4$ ground state forming stripe-$x$ order and a $\Gamma_{5,6}$ excited state with dipole-octupole character. High-resolution spectra reveal emergent symmetry-selected dispersions, where magnon branches from the ground state are replicated on higher $\Gamma_4$ levels but couple with the $\Gamma_{5,6}$ levels to form a distinct multipolar band. An applied magnetic field reconstructs the CEF wavefunctions and polarizes the system into a multipolar ferromagnet, further reshaping the spectra. This study demonstrates the emergent coupling of local and collective excitations driven by strong spin-orbit coupling and establishes NaErSe$_2$ as a platform for field-tunable multipolar excitations in frustrated magnets.

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 presents neutron spectroscopy data on the triangular antiferromagnet NaErSe₂ combined with total-angular-momentum (J=15/2) modeling of the crystalline electric field (CEF). It identifies a dipolar Γ₄ ground-state doublet that orders in a stripe-x pattern and a dipole-octupole Γ_{5,6} excited doublet. The central claim is that high-resolution spectra show emergent symmetry-selected dispersions in which magnon branches from the ground state are replicated on higher Γ₄ levels but couple specifically with the Γ_{5,6} levels to produce a distinct multipolar band; an applied field is reported to reconstruct the CEF wavefunctions and drive the system into a multipolar ferromagnet.

Significance. If the wavefunction assignments and symmetry-selection rules are robust, the work would establish a concrete platform for field-tunable multipolar excitations arising from the interplay of strong spin-orbit coupling and frustrated magnetism. The experimental observation of replicated magnon branches and a distinct multipolar band would be a notable addition to the literature on rare-earth triangular lattices. The manuscript does not, however, supply independent verification that the reported dispersions are predictions rather than outputs of the CEF fit, which limits the strength of the significance assessment.

major comments (2)
  1. [CEF modeling section] CEF modeling section: the assignment of dipolar versus dipole-octupole character to the Γ₄ and Γ_{5,6} doublets is obtained by diagonalizing a fitted CEF Hamiltonian whose parameters are determined from the same neutron spectra used to extract the dispersions. No explicit test is shown that the observed intensity and dispersion patterns cannot be reproduced by alternative CEF parameter sets, inclusion of rank-6 terms, or impurity contributions, which directly undermines the claim that the dispersions are symmetry-selected multipolar excitations.
  2. [Dispersion analysis] Dispersion analysis: the manuscript states that magnon branches from the ground state are replicated on higher Γ₄ levels but couple with Γ_{5,6} to form a distinct band, yet provides no quantitative comparison (e.g., calculated versus measured dispersion relations or selection-rule intensities) demonstrating that this coupling is required by the data rather than being an interpretation imposed by the fitted wavefunctions.
minor comments (2)
  1. The abstract and modeling description do not state the number of fitted CEF parameters or the goodness-of-fit metrics for the spectra used to determine the wavefunctions.
  2. Figure captions should explicitly indicate which panels show raw data, fitted dispersions, and calculated intensities from the CEF model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to incorporate additional tests and quantitative comparisons.

read point-by-point responses

  1. Referee: [CEF modeling section] CEF modeling section: the assignment of dipolar versus dipole-octupole character to the Γ₄ and Γ_{5,6} doublets is obtained by diagonalizing a fitted CEF Hamiltonian whose parameters are determined from the same neutron spectra used to extract the dispersions. No explicit test is shown that the observed intensity and dispersion patterns cannot be reproduced by alternative CEF parameter sets, inclusion of rank-6 terms, or impurity contributions, which directly undermines the claim that the dispersions are symmetry-selected multipolar excitations.

    Authors: The D_{3d} point-group symmetry of the Er site fixes the irreducible representations and their multipolar characters within the J=15/2 manifold independently of the specific CEF parameter values; the Γ₄ doublet is dipolar while Γ_{5,6} is dipole-octupole by symmetry. The parameters are constrained by the measured transition energies. To address the referee's concern we have added a new supplementary section that (i) shows rank-6 Stevens operators produce only marginal changes to the wavefunctions within experimental resolution, (ii) demonstrates that alternative parameter sets consistent with the energies preserve the same multipolar characters, and (iii) rules out impurity contributions via the observed momentum dependence. These additions provide the requested independent verification. revision: yes

  2. Referee: [Dispersion analysis] Dispersion analysis: the manuscript states that magnon branches from the ground state are replicated on higher Γ₄ levels but couple with Γ_{5,6} to form a distinct band, yet provides no quantitative comparison (e.g., calculated versus measured dispersion relations or selection-rule intensities) demonstrating that this coupling is required by the data rather than being an interpretation imposed by the fitted wavefunctions.

    Authors: We agree that an explicit quantitative comparison strengthens the claim. The revised manuscript includes a new figure and text that overlay the measured dispersions with those obtained from linear spin-wave theory using the fitted CEF wavefunctions. The calculation reproduces the replicated branches on higher Γ₄ levels, the distinct multipolar band from Γ_{5,6} coupling, and the intensity modulations required by the multipolar selection rules, showing that this coupling is necessary to account for the data. revision: yes

Circularity Check

0 steps flagged

No circularity: modeling and spectroscopy combined without reduction to fitted inputs shown

full rationale

The provided abstract describes combining neutron spectroscopy with total angular momentum modeling to assign CEF doublet characters and interpret observed dispersions as emergent multipolar bands. No equations, self-citations, or explicit fitting procedures are quoted that would reduce the reported dispersions or symmetry selections to the input spectra by construction. The derivation therefore remains self-contained against external benchmarks in the given text, with the modeling serving as interpretive support rather than a tautological re-expression of the data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract; no explicit free parameters, axioms, or invented entities are stated. The modeling is described at a high level without listing fitted CEF parameters or additional assumptions.

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Reference graph

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