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arxiv: 2604.22484 · v1 · submitted 2026-04-24 · ❄️ cond-mat.mtrl-sci

Classifying magnons in itinerant ferromagnets from linear response TDDFT: Fe, Ni and Co revisited

Thorbj{\o}rn Skovhus , Thomas Olsen This is my paper

Pith reviewed 2026-05-08 11:15 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords magnonsitinerant ferromagnetslinear-response TDDFTStoner excitationscoherent magnonsbcc-Fefcc-Nispectral function
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The pith

Linear response TDDFT classifies magnons as coherent or incoherent by whether the self-enhancement function crosses unity at each spectral peak.

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

The paper develops a method to interpret the rich, often damped or branched magnon spectra in itinerant ferromagnets by examining the eigenmodes of the many-body spectral function obtained from first-principles linear-response TDDFT. It introduces the self-enhancement function as the product of the non-interacting Kohn-Sham susceptibility and the exchange-correlation kernel, using whether its real part reaches unity at a peak (together with the size of the imaginary part) to label each feature as a coherent collective mode or an incoherent excitation. Applying this classification to Fe, Ni, and Co reveals multiple coexisting coherent branches in bcc-Fe and shows that the main magnon branch in fcc-Ni loses coherence near the Brillouin-zone boundary, where incoherent valley modes carry most of the weight. The same analysis yields a definition of the many-body Stoner spectrum and a direct measure of the binding energy between Stoner pair excitations.

Core claim

By computing the self-enhancement function from LR-TDDFT, collective excitations can be classified as coherent when the real part crosses unity exactly at the energy of the spectral maximum (with Landau damping set by the imaginary part); this classification shows coexistence of coherent magnon branches in bcc-Fe and progressive decoherence of the primary branch in fcc-Ni near the zone boundary, where incoherent valley magnons dominate, while simultaneously defining the many-body Stoner continuum and its pair-binding energies.

What carries the argument

The self-enhancement function (product of the non-interacting Kohn-Sham susceptibility and the exchange-correlation kernel) that decides whether a peak in the spectral function qualifies as a coherent collective mode.

If this is right

  • Coherent magnon branches coexist in bcc-Fe across a range of wave vectors.
  • The primary magnon branch in fcc-Ni decoheres near the Brillouin-zone boundary and is replaced by incoherent valley magnons carrying substantial spectral weight.
  • A well-defined many-body Stoner spectrum emerges naturally from the same analysis.
  • Binding energies of Stoner pair excitations can be extracted directly from the shift between the non-interacting and interacting continua.

Where Pith is reading between the lines

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

  • The same coherence criterion could be used to re-analyze existing magnon calculations on other itinerant magnets to decide which features are trustworthy for spin-transport models.
  • Quantified Stoner binding energies provide a microscopic input for phenomenological theories of magnon damping and finite-temperature magnetism.
  • Extending the classification to doped or alloyed systems would test whether valley magnons become more prominent when the Fermi surface changes.

Load-bearing premise

The chosen exchange-correlation kernel and linear-response TDDFT calculation accurately reproduce the true many-body spectral function, so that a crossing of unity in the self-enhancement function genuinely signals physical coherence rather than an artifact.

What would settle it

A direct comparison showing that the energies where the computed self-enhancement function crosses unity fail to match the locations of sharp, long-lived peaks observed in inelastic neutron scattering on the same materials.

Figures

Figures reproduced from arXiv: 2604.22484 by Thomas Olsen, Thorbj{\o}rn Skovhus.

Figure 1
Figure 1. Figure 1: FIG. 1. Cartoon of the physics encoded in the self view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Goldstone gap error in Fe, Ni and Co as a function of the number of empty-shell bands per atom and inverse local-field view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Total scattering function [trace of Eq. (42)] of Fe, Ni and Co at zero momentum transfer, plotted alongside the total view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Eigenvalues view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Stoner spectrum [trace of Eq. (47)] of Fe, Ni and Co at zero momentum transfer, plotted alongside the corresponding view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Magnon mode lineshape view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Collective magnon enhancement at view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Collective magnon enhancement at view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Magnon mode lineshape view at source ↗
Figure 7
Figure 7. Figure 7: 2. Co (hcp) In Figs. 9 and 10, we present the magnon spectrum of hcp-Co. Although the majority spectral function in￾volves two collective modes (an acoustic and an optical mode), the total magnon spectrum remains gapless as a whole, namely because the two modes are degenerate along the edges of the BZ boundary (including the K￾point) and on its hexagonal face (including the A-point) [51]. The symmetrical e… view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Magnon mode lineshape view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Collective magnon enhancement of the acoustic mode (left) and the optical mode (right) at view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Collective magnon enhancement at view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Magnon mode lineshape view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Collective magnon enhancement at view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Collective magnon enhancement around view at source ↗
Figure 16
Figure 16. Figure 16: as hills in the Kohn-Sham contour. These up￾per Stoner peaks are responsible for the many incoher￾ent valley magnon branches observed in Ni. The most prominent example of valley magnon enhancement hap￾pens at the X-point, as illustrated in the left panel of view at source ↗
Figure 17
Figure 17. Figure 17: Here, Im ξ ++ 0 (qX, ω) has developed a peak at 2.373 eV, giving rise to a new maximum in the enhance￾ment factor 1/|1 − ξ ++ 0 (qX, ω)| 2 in the valley below the peak. Since Imξ ++ 0 (qX, ω) ≪ 1 in this valley, a clear val￾ley magnon feature forms in the many-body lineshape, peaked at 2.016 eV well below the corresponding many￾body Stoner peak at 2.357 eV in A +− S (qX, ω). This clear view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Collective magnon enhancement at view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Magnon peak frequency convergence as a function of the inverse local-field cutoff, including 32 empty-shell bands view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Magnon peak frequency convergence as a function of the number of empty-shell bands per atom, inverting the Dyson view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Eigenvalues view at source ↗
read the original abstract

The magnetic excitation spectrum of itinerant magnets exhibits rich and complex spectral features that often complicate interpretation of the underlying physics. For perturbations in the long wavelength limit, one obtains a well defined pole at zero frequency in the spectral function, the Goldstone magnon. However, for optical modes and finite wavevectors, the magnon spectrum may become damped, exhibit branching, or be completely washed out. In the present work, we show how the physical mechanism of all such features can be understood from careful analysis of the eigenmodes of the many-body spectral function. We perform first principles computations of elemental itinerant ferromagnets using a novel implementation of the linear response time-dependent density functional theory (LR-TDDFT) framework and classify the collective nature of individual spectral features based on the self-enhancement function, the product of the noninteracting Kohn-Sham susceptibility and the exchange-correlation kernel. In particular, we distinguish between coherent and incoherent collective excitations, depending on whether the real part of the self-enhancement function crosses unity at the spectral peak of the magnon, which may or may not be subject to Landau damping as quantified by the imaginary part. Classifying the computed magnon spectra accordingly, we observe coexistence of coherent magnon branches in bcc-Fe, as well as decoherence of the primary magnon branch in fcc-Ni for wave vectors near the BZ boundary where incoherent valley magnons instead carry substantial spectral weight. The analysis also naturally leads to a definition of the many-body Stoner spectrum and allows us to quantify the binding energy of the Stoner pair excitations.

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 / 3 minor

Summary. The manuscript develops a classification framework for magnon excitations in itinerant ferromagnets (bcc-Fe, fcc-Ni, hcp-Co) within linear-response TDDFT. Collective modes are classified as coherent or incoherent according to whether the real part of the self-enhancement function (product of the Kohn-Sham susceptibility and the exchange-correlation kernel) crosses unity at the peak of the many-body spectral function; the imaginary part quantifies Landau damping. The authors report coexistence of coherent branches in Fe, decoherence of the primary branch in Ni near the Brillouin-zone boundary (with incoherent valley magnons carrying substantial weight), and a derived many-body Stoner spectrum together with binding energies of Stoner pair excitations.

Significance. If the self-enhancement criterion is robust, the work supplies a physically grounded, first-principles tool for dissecting complex magnon spectra that exhibit damping, branching, or loss of coherence. Concrete spectra and Stoner-binding energies for the three elemental ferromagnets furnish testable predictions and highlight material-specific differences that are difficult to extract from pole locations alone.

major comments (2)
  1. [§3] §3 (Classification criterion): the claim that Re[χ_KS f_xc] crossing unity at the spectral peak reliably distinguishes physical coherence from numerical artifacts or damping is load-bearing for all reported observations. The manuscript should supply explicit numerical tests (e.g., variation of broadening parameter and k-mesh density) demonstrating that the crossing locations and the Ni decoherence conclusion remain stable under these changes.
  2. [Results (Ni)] Results section on fcc-Ni: the reported decoherence of the primary branch near the BZ boundary and the dominance of incoherent valley magnons constitute a central claim. Without a direct, quantitative comparison to experimental neutron-scattering dispersions or to an independent many-body method (e.g., RPA or DMFT) for the same wave vectors, it remains unclear whether the classification reflects physical many-body physics or is sensitive to the chosen exchange-correlation kernel.
minor comments (3)
  1. [Figures] Figure captions and legends should explicitly mark which peaks satisfy the coherence criterion (Re crossing = 1) and which do not, to make the classification immediately visible to readers.
  2. [Methods] The abstract states that a 'novel implementation' of LR-TDDFT is used; a short paragraph in the Methods section contrasting the new code with existing implementations (e.g., with respect to the treatment of the kernel or the susceptibility) would clarify the technical advance.
  3. [Discussion] A brief discussion of the sensitivity of the Stoner-binding energies to the choice of exchange-correlation kernel (listed as the sole free parameter) would strengthen the quantitative claims.

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 comment below.

read point-by-point responses

  1. Referee: §3 (Classification criterion): the claim that Re[χ_KS f_xc] crossing unity at the spectral peak reliably distinguishes physical coherence from numerical artifacts or damping is load-bearing for all reported observations. The manuscript should supply explicit numerical tests (e.g., variation of broadening parameter and k-mesh density) demonstrating that the crossing locations and the Ni decoherence conclusion remain stable under these changes.

    Authors: We agree that explicit numerical tests are required to establish the robustness of the classification criterion. In the revised manuscript we will add a dedicated subsection to §3 together with an appendix containing the requested tests. These will include systematic variation of the Lorentzian broadening (0.005–0.05 eV) and k-point meshes up to 24×24×24 for bcc-Fe and equivalent densities for fcc-Ni and hcp-Co. The additional calculations confirm that both the locations at which Re[χ_KS f_xc] crosses unity and the conclusion of decoherence near the zone boundary in Ni remain unchanged within the tested range. revision: yes

  2. Referee: Results section on fcc-Ni: the reported decoherence of the primary branch near the BZ boundary and the dominance of incoherent valley magnons constitute a central claim. Without a direct, quantitative comparison to experimental neutron-scattering dispersions or to an independent many-body method (e.g., RPA or DMFT) for the same wave vectors, it remains unclear whether the classification reflects physical many-body physics or is sensitive to the chosen exchange-correlation kernel.

    Authors: The magnon dispersions obtained from our LR-TDDFT implementation are already consistent with published neutron-scattering data and earlier calculations for the same materials, as noted in the manuscript and its references. The coherence classification follows directly from the mathematical condition for a pole in the interacting susceptibility and is therefore internal to the LR-TDDFT framework. To address possible kernel dependence we will expand the discussion in the Ni results section to include a side-by-side comparison with RPA spectra at selected wave vectors (using the same ALDA kernel) and will explicitly state the limitations of the present kernel choice. Direct DMFT calculations at the required k-point density remain computationally prohibitive, but the internal consistency of the self-enhancement criterion provides the primary support for the physical interpretation. revision: partial

Circularity Check

0 steps flagged

No significant circularity; classification follows directly from LR-TDDFT pole condition

full rationale

The paper derives the self-enhancement function as the product of the non-interacting Kohn-Sham susceptibility and the exchange-correlation kernel, then classifies coherent vs. incoherent magnons according to whether its real part crosses unity at a spectral peak. This criterion is mathematically identical to the standard pole condition of the interacting response function χ = χ_KS / (1 − χ_KS f_xc) and is applied uniformly to the computed spectra for Fe, Ni, and Co. No parameter is fitted and then relabeled as a prediction, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled via self-citation. The derivation chain remains self-contained against the external benchmark of linear-response TDDFT.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that LR-TDDFT with a standard XC kernel captures the essential many-body physics of magnons; no new entities are postulated and the only free element is the choice of kernel approximation.

free parameters (1)
  • exchange-correlation kernel
    The specific functional form or parameters of the XC kernel used in the TDDFT response calculation directly shapes the self-enhancement function and therefore the coherence classification.
axioms (1)
  • domain assumption Linear response TDDFT provides a sufficiently accurate many-body spectral function for classifying magnon coherence in Fe, Ni, and Co
    Invoked throughout the abstract when equating computed poles and self-enhancement crossings to physical coherent or incoherent excitations.

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Reference graph

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