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REVIEW 3 major objections 4 minor 75 references

A Magnon Band Analysis of GdRu2Si2 in the Field-Polarized State

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The spin-wave spectrum of the skyrmion candidate GdRu2Si2 in its field-polarized phase is reproduced by eight bilinear Heisenberg exchange interactions, with no evidence for higher-order or anisotropic exchange.

desk verdict Valuable new magnon data and a useful fitting method, but the paper's central null result on higher-order exchange is not actually testable by the magnon band fit. read the letter →

arxiv 2501.01201 v1 pith:WHTFULYW submitted 2025-01-02 cond-mat.str-el

G. D. A. Wood , J. R. Stewart , D. A. Mayoh , J. A. M. Paddison , J. Bouaziz , S. M. Tobin , O. A. Petrenko , M. R. Lees
show 3 more authors
P. Manuel J. B. Staunton G. Balakrishnan
This is my paper · ORCID
classification cond-mat.str-el PACS 75.30.Ds75.40.Gb78.70.Nx
keywords GdRu2Si2magnondispersionlinearspinwavetheoryHeisenbergexchangeRKKYinteractionmulti-Qmagneticorderinelasticneutronscatteringskyrmioncandidate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper measures the magnon dispersion of the centrosymmetric skyrmion candidate GdRu2Si2 in the field-polarized phase using inelastic neutron scattering, and shows that the spectrum can be accounted for by a Hamiltonian containing eight bilinear Heisenberg exchange interactions, the Zeeman term, and negligible single-ion anisotropy. The authors find no evidence for anisotropic or higher-order (e.g., biquadratic) exchange, and argue that if such terms exist they are limited to roughly 1 micro-eV. This result matters because anisotropic and higher-order exchange are usually invoked to stabilize the multi-Q and skyrmion states that this material hosts in zero field; the paper's finding sharpens the puzzle of what actually stabilizes those states. The fitted exchange parameters are consistent with long-ranged RKKY interactions and with ab initio calculations, and the dispersion's incommensurate minima point toward the propagation direction of the lower-field multi-Q order.

What carries the argument

The central object is the linear spin-wave dispersion $\hbar\omega(\mathbf{q}) = S[J(\mathbf{q})-J(0)] - g\mu_B B - 2KS$, obtained from a Holstein-Primakoff transformation of a Hamiltonian with bilinear Heisenberg exchange, Zeeman, and single-ion anisotropy terms. The paper introduces 'interaction invariant path analysis': reciprocal-space cuts are chosen along which a particular interaction, such as $J_2$ with $\delta=[1/2,1/2,1/2]$, is non-dispersive (its cosine terms cancel), so that other weaker interactions can be refined independently. This method guides the selection of fits, and the final $J_1$-$J_8$ model is fitted to the extracted band by least-squares minimization of $\hbar\omega(\mathbf{q})$.

What would settle it

A measurement of the magnon dispersion below 0.8 meV—for example with a cold-neutron triple-axis spectrometer as the authors propose—would settle the claim: if the bottom of the band deviates from the $J_1$-$J_8$ bilinear prediction, or if a fit with a biquadratic exchange term significantly outperforms the bilinear model, the central null claim is refuted. A simpler check on existing data is to add an $(\mathbf{S}_i\cdot\mathbf{S}_j)^2$ term to the fit and test whether the residuals drop meaningfully.

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Extended reading notes

Core claim

Using time-of-flight inelastic neutron scattering on an isotopically enriched single crystal, the spin excitations of GdRu2Si2 in the field-polarized (forced ferromagnetic) phase were measured along a 90-degree arc of reciprocal space. After median-kernel filtering to extract the magnon band from strong absorption-limited noise, the dispersion was fitted with linear spin wave theory. A model with eight bilinear Heisenberg exchange interactions, $J_1$ through $J_8$ (with $J_2$ dominant at $-65.1$ $\mu$eV), plus a constant term consistent with the applied field, reproduces the measured dispersion. The key result is a null result: no anisotropic or higher-order exchange terms are required to fit the data, and the authors estimate that if present these terms are smaller than about $1$ $\mu$eV. The fitted model places the global dispersion minima at incommensurate wavevectors along the $[1,0,0]$ direction, consistent in direction with the magnetic propagation vector of the lower-field multi-Q state, although the exact minimum position is uncertain because the bottom of the band lies below the energy resolution.

Load-bearing premise

The null result for anisotropic and higher-order exchange relies on the measurement being sensitive enough to reveal such terms; the data are low signal-to-noise, median-filtered, and the dispersion is not resolved below about 0.8 meV, so terms below roughly 1 micro-eV would go undetected.

Editorial extensions

If this is right

  • If the Hamiltonian is correct, the spin dynamics of the field-polarized phase of GdRu2Si2 is governed by long-ranged bilinear RKKY exchange, and higher-order or anisotropic terms play no measurable role there.
  • The fitted exchange parameters support the Fermi-surface-based ab initio model cited in the paper, lending weight to the view that the exchange is RKKY-mediated.
  • The incommensurate minima of the dispersion along the [1,0,0] direction show that the tendency toward the lower-field multi-Q order is already present in the bilinear exchange; however, the exact minimum position differs from the observed propagation vector, suggesting that missing long-range exchange terms are important.
  • The absence of observable anisotropic or higher-order terms implies that the zero-field multi-Q state must be stabilized either by field- or temperature-dependent RKKY interactions tied to the Fermi surface, or by coupling to charge-density-wave modulations discussed in the paper.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct test of the null claim is to fit existing or future higher-resolution data with models that include a biquadratic term $(\mathbf{S}_i\cdot\mathbf{S}_j)^2$ or anisotropic exchange and compare the goodness of fit; a significant improvement would falsify the 'bilinear-only' conclusion.
  • The paper's own Curie-Weiss comparison shows the fitted model accounts for only about 72% of the net ferromagnetic molecular field, so the $J_1$-$J_8$ set is an effective truncation of a longer-range exchange tail; the 'no higher-order terms' conclusion should be read as applying to the resolvable portion of the spectrum, not as a complete Hamiltonian for the material.
  • The method of interaction invariant path analysis could be transferred to other strongly absorbing or low-signal magnets where full $\mathbf{S}(\mathbf{Q},\omega)$ fitting is impractical, and the authors note plans to extend it to non-linear invariant loops.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This paper reports inelastic neutron scattering measurements of the magnon dispersion in the field-polarized phase of GdRu2Si2 at T = 25 K and B = 8.8 T. The authors fit the dispersion using linear spin-wave theory with an effective bilinear Heisenberg exchange model including interactions J1 through J8 (with J7 set to zero) plus a constant term C. They introduce a 'method of interaction invariant path analysis' to select reciprocal-space cuts that decorrelate the exchange parameters. The fitted model reproduces the main features of the measured dispersion and is qualitatively consistent with earlier ab initio calculations. The paper concludes that no anisotropic or higher-order exchange terms are required, and estimates that such terms are likely limited to about 1 micro-eV. The implications for the zero-field multi-Q ground state are discussed.

Significance. If the central null result were established, the paper would be significant: it would show that bilinear RKKY exchange alone describes the spin dynamics in the field-polarized state, and that higher-order exchange is negligible, which bears directly on the mechanism stabilizing multi-Q order in this material. The experimental dataset is valuable, and the interaction invariant path analysis provides a systematic way to reduce parameter correlations in magnon fits. The paper is commendably transparent about its limitations, including low signal-to-noise, median kernel filtering, and the unresolved bottom of the magnon band. However, as detailed in the major comments, the central null result is not actually testable with the present linear spin-wave analysis, so the paper's headline conclusion overreaches the data.

major comments (3)
  1. [Discussion; Eq. (2)] The statement in the abstract and Discussion that 'No evidence for anisotropic or higher-order-exchange terms beyond bilinear Heisenberg exchange is found,' and the quantitative bound that such terms are 'likely small and limited to ≲ 1 µeV,' are not supported by the analysis. In linear spin-wave theory around a field-polarized state, a biquadratic term B_ij (S_i·S_j)^2 expands to quadratic order as -2 B S^3 (a_i†a_i + a_j†a_j - a_i†a_j - a_j†a_i), which is exactly the same operator form as the quadratic part of a bilinear Heisenberg coupling J_ij with the replacement J_eff = J_ij + 2S^2 B_ij. With S = 7/2, 2S^2 = 24.5, so the fitted exchange constants in Table I are effective transverse couplings that cannot distinguish biquadratic exchange from bilinear exchange. A similar degeneracy holds for the longitudinal component of anisotropic exchange and for single-ion anisotropy, which enter only through the fitted constant C in Eq. (2), as the paper itself notes. Consequently, the observation that the dispersion can be fitted without higher-order terms is trivially true, and the bound of ≲1 µeV does not follow from the data. To support such a bound, the authors would need to compare the fitted effective J values with independently known bare J values and quantitatively estimate how much of the difference could be attributed to biquadratic terms; the paper does not do this.
  2. [Analysis; Table I] The inclusion of J8 is explicitly motivated by the need to place the global minima of the dispersion at q = [0.15, 0, 0], i.e., in the experimentally observed propagation direction. Therefore the agreement between the model's minimum and the lower-field propagation vector is a fitting constraint, not an independent prediction. The paper also notes that the minimum is at 0.15 r.l.u. rather than the observed q_e = [0.22, 0, 0]. This limits the strength of the claim that the model 'captures the salient features of the magnon dispersion, including global minima at incommensurate positions which are characteristic of the lower-field magnetism.'
  3. [Analysis; Supplemental Material] The paper does not provide a sensitivity analysis or a model comparison that would justify the quantitative bound on higher-order terms. The data have low signal-to-noise, are processed with a nonlinear median kernel filter, and the bottom of the band below ~0.8 meV is not resolved. Without fitting models that explicitly include biquadratic or anisotropic terms and assessing their statistical significance (e.g., via a likelihood-ratio test or error propagation), the estimate that such terms are ≲1 µeV is an assertion rather than a derived result. The paper should either remove this bound or replace it with a statement that the data are consistent with zero within the sensitivity of the measurement, and provide an estimate of that sensitivity.
minor comments (4)
  1. [Supplemental Material] The name of the spin-wave code is written inconsistently: 'Sun(n)y' in the main text and 'Su(n)ny' in the Supplemental Material. It is likely 'Sunny'; please standardize.
  2. [Supplemental Material] There is a typo in Section II: 'consistent the the S(Q,ω ) calculations' should be 'consistent with the S(Q,ω ) calculations'.
  3. [Introduction] The phrase 'Gd 3+ and Eu 2+ intermetallics' has spacing issues; please correct the formatting.
  4. [Conclusion] The sentence 'A Hamiltonian accounting for the dispersion relation has been derived with linear spin wave theory' could be phrased more clearly: the Hamiltonian was fitted to the dispersion, not derived from it.

Circularity Check

1 steps flagged · score 6.0 of 10

The bound on biquadratic and anisotropic exchange (≲1 µeV) is not derivable from the fitted magnon dispersion, because in linear spin-wave theory those terms are degenerate with renormalized bilinear couplings and a q-independent constant.

  1. self definitional [Discussion, paragraph beginning 'More generally, the model Hamiltonian...' (after Eq. (2) and Table I).]
    "Crucially, to model the magnon band, higher-order exchange interactions, such as anisotropic and biquadratic exchange, are not required. Therefore, if these terms do exist, then it is likely they are small and limited to ≲ 1µeV."

    The fitted quantity is ℏω(q)=S[J(q)-J(0)]-gµBB-2KS. Around the fully polarized state, a biquadratic bond term B(S_i·S_j)^2 produces, to quadratic order in Holstein-Primakoff bosons, -2BS^3(n_i+n_j)+2BS^3(a_i†a_j+a_j†a_i), which has the same relative diagonal/off-diagonal structure as J S_i·S_j. Hence the data determine J_eff = J + 2S^2 B (S=7/2) plus a constant C; an arbitrary B can be absorbed by re-fitting J. Likewise K(S^z)^2 and longitudinal anisotropic exchange only shift C, which the paper concedes 'it is not possible to disentangle constant contributions'. Therefore the model's adequacy is guaranteed for any B, and the inference that B ≲ 1 µeV does not follow from the fit; it is an artifact of assuming the bilinear ansatz.

full rationale

The Hamiltonian parameters J1–J8 are fitted to the measured ω(q), so the statement that the model 'accounts for' the spectra is a fit statement rather than an independent prediction; this alone is normal practice and not circular. The paper's genuinely unsupported step is the bound on higher-order and anisotropic exchange. In linear spin-wave theory around the field-polarized state, biquadratic exchange and the q-independent terms (single-ion anisotropy, longitudinal anisotropic exchange) are degenerate with renormalized bilinear couplings and a constant C; the paper's own Eq. (2) and its admission that constant contributions cannot be disentangled establish this. Consequently, the fitted bilinear model cannot rule out such terms, and the '≲1 µeV' estimate does not follow from the data. The ab initio comparison and Curie-Weiss temperature provide external anchors and partially support the fitted J values, and the J8 propagation-direction adjustment is transparently a fit constraint, not a hidden circularity. Self-citations to Refs. [29] and [54] involve overlapping authorship, but the underlying DFT and powder-neutron results are independent evidence, so self-citation is not the load-bearing circularity. Overall, one central inferential step reduces by construction, giving partial circularity.

Assumptions & free parameters 10 free parameters · 7 assumptions · 1 invented entities

The model uses ten effective numerical parameters (J1 through J8, C, and the undetermined single-ion anisotropy K), several assumptions about linear spin wave theory and the restricted Hamiltonian, and one newly proposed mechanism (field-dependent RKKY exchange) that is not independently tested. These are the costs the reader pays for the derived Hamiltonian.

free parameters (10)
  • J1 = -33.9 +/- 1.0 micro-eV
    First-nearest-neighbor Heisenberg exchange fitted to the magnon dispersion (Table I).
  • J2 = -65.1 +/- 0.7 micro-eV
    Dominant exchange interaction, inferred from the parabolic (1,-1,eta) cut and included in all models.
  • J3 = 13.6 +/- 0.7 micro-eV
    Fitted in-plane Heisenberg exchange (Table I).
  • J4 = -1.1 +/- 0.4 micro-eV
    Fitted exchange interaction with delta = [3/2, 1/2, 1/2].
  • J5 = 10.8 +/- 0.8 micro-eV
    Fitted exchange; its antiferromagnetic sign is required for the global minimum to sit at incommensurate positions.
  • J6 = 6.0 +/- 0.5 micro-eV
    Fitted exchange interaction with delta = [1, 2, 0].
  • J7 = 0 (fixed)
    Set to zero because the (1,-0.5,eta) J2-invariant cut is flat; not refined as a free parameter.
  • J8 = 3.0 +/- 0.4 micro-eV
    Included specifically so the dispersion minima lie at q = [0.15, 0, 0], the direction of lower-field magnetic propagation.
  • C = 0.94 +/- 0.01 meV
    Global constant in the dispersion fit; absorbs -g mu_B B, -2KS, and any unaccounted exchange terms.
  • K (single-ion anisotropy) = not determined (absorbed into C)
    Single-ion anisotropy appears in Eq. (1) but cannot be disentangled from C in Eq. (2), so it is effectively assumed negligible.
assumptions (7)
  • domain assumption Linear spin wave theory and the Holstein-Primakoff expansion are valid for the S=7/2 Gd3+ ferromagnet at 25 K.
    Invoked in Analysis, Eq. (2); assumes small spin fluctuations and ignores magnon-magnon interactions.
  • domain assumption The magnetic Hamiltonian is restricted to bilinear Heisenberg exchange, Zeeman coupling, and single-ion anisotropy.
    Equation (1) excludes Dzyaloshinskii-Moriya, biquadratic, and four-spin interactions from the outset, which underlies the central null conclusion.
  • domain assumption Median kernel filtering identifies pixels belonging to the magnon band.
    Supplemental Section I; assumes noise is sparse and the magnon band dominates non-zero median pixels.
  • ad hoc to paper J7 is negligible because the (1,-0.5,eta) cut is flat.
    Analysis and Fig. 2(d); the model omits J7 based on one invariant path, with no quantitative upper bound.
  • ad hoc to paper The unresolved bottom of the magnon band does not bias the fitted J1 through J8 beyond quoted errors.
    Discussion states the global minimum is inferred from higher-energy parts because elastic scattering obscures energies below 0.8 meV.
  • ad hoc to paper The refined constant C is consistent with -g mu_B B, with negligible single-ion anisotropy K and small unaccounted exchange.
    Discussion; C varies with the number of exchange terms and absorbs -2KS and missing interactions, so K is not independently determined.
  • domain assumption Dipolar interactions are negligible for the fitted dispersion.
    Supplemental Figure S6 shows changes of about 20 micro-eV, smaller than the resolution of the data.
invented entities (1)
  • Field- and temperature-dependent RKKY exchange J_ij(B,T)
    purpose: Explains why the field-polarized Hamiltonian does not reproduce the lower-field multi-Q order despite the absence of higher-order exchange.
    Proposed in the Discussion as a possibility, supported only by qualitative references to Fermi surface nesting and quantum oscillations; no direct measurement of field-dependent exchange is presented in this paper.

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Cite this review

Pith. "Pith review of A Magnon Band Analysis of GdRu2Si2 in the Field-Polarized State." pith.science (2026). https://pith.science/paper/WHTFULYW

@misc{pith2026250101201,
  author       = {Pith},
  title        = {Pith review of: A Magnon Band Analysis of GdRu2Si2 in the Field-Polarized State},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WHTFULYW}},
  note         = {Machine review of arXiv:2501.01201}
}
read the original abstract

Understanding the formation of skyrmions in centrosymmetric materials is a problem of fundamental and technological interest. GdRu2Si2 is one such candidate material which has been shown to host a variety of multi-Q magnetic structures, including in zero-field. Here, inelastic neutron scattering is used to measure the spin excitations in the field-polarized phase of GdRu2Si2. Linear spin wave theory and a method of interaction invariant path analysis are used to derive a Hamiltonian accounting for the observed spectra, and comparisons to \textit{ab initio} calculations are made. No evidence for anisotropic or higher order-exchange terms beyond bilinear Heisenberg exchange is found. This is discussed in the context of the multi-Q states existing at lower fields, for which these types of terms have previously been conceived to be significant in the formation of multi-Q ground states.

Figures

Figures reproduced from arXiv: 2501.01201 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Conventional unit cell of GdRu [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Various momentum-resolved inelastic neutron scattering spectra of GdRu [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Comparison of dispersions between the model [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Works this paper leans on

75 extracted references · 72 canonical work pages

  1. [1]

    Q. L. He, T. L. Hughes, N. P. Armitage, Y. Tokura, and K. L. Wang, Topological spintronics and magnetoelec- tronics, Nature Materials 21, 15 (2022)

    work page 2022

  2. [2]

    A. Fert, N. Reyren, and V. Cros, Magnetic skyrmions: advances in physics and potential applications, Nature Reviews Materials 2, 17031 (2017)

    work page 2017

  3. [3]

    Lancaster, Skyrmions in magnetic materials, Contem- porary Physics 60, 246 (2019)

    T. Lancaster, Skyrmions in magnetic materials, Contem- porary Physics 60, 246 (2019)

    work page 2019

  4. [4]

    Tokura and N

    Y. Tokura and N. Kanazawa, Magnetic skyrmion mate- rials, Chemical Reviews 121, 2857 (2020)

    work page 2020

  5. [5]

    Z. Wang, Y. Su, S.-Z. Lin, and C. D. Batista, Meron, skyrmion, and vortex crystals in centrosymmetric tetrag- onal magnets, Physical Review B 103, 104408 (2021)

    work page 2021

  6. [6]

    Hayami, Zero-field skyrmion, meron, and vortex crys- tals in centrosymmetric hexagonal magnets, Journal of Magnetism and Magnetic Materials 564, 170036 (2022)

    S. Hayami, Zero-field skyrmion, meron, and vortex crys- tals in centrosymmetric hexagonal magnets, Journal of Magnetism and Magnetic Materials 564, 170036 (2022)

    work page 2022

  7. [7]

    X. Yu, M. Mostovoy, Y. Tokunaga, W. Zhang, K. Ki- moto, Y. Matsui, Y. Kaneko, N. Nagaosa, and Y. Tokura, Magnetic stripes and skyrmions with helicity reversals, Proceedings of the National Academy of Sciences 109, 8856 (2012)

    work page 2012

  8. [8]

    X. Yao, J. Chen, and S. Dong, Controlling the helicity of magnetic skyrmions by electrical field in frustrated mag- nets, New Journal of Physics 22, 083032 (2020)

    work page 2020

Show all 75 references
  1. [9]

    Yao and S

    X. Yao and S. Dong, Vector vorticity of skyrmionic tex- ture: An internal degree of freedom tunable by magnetic field, Physical Review B 105, 014444 (2022)

    2022

  2. [10]

    Kurumaji, T

    T. Kurumaji, T. Nakajima, M. Hirschberger, A. Kikkawa, Y. Yamasaki, H. Sagayama, H. Nakao, Y. Taguchi, T.-H. Arima, and Y. Tokura, Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet, Science 365, 914 (2019)

    2019

  3. [11]

    J. A. M. Paddison, B. K. Rai, A. F. May, S. Calder, M. B. Stone, M. D. Frontzek, and A. D. Christianson, Magnetic interactions of the centrosymmetric skyrmion material Gd2PdSi3, Physical Review Letters 129, 137202 (2022)

    2022

  4. [12]

    J. Ju, H. Saito, T. Kurumaji, M. Hirschberger, A. Kikkawa, Y. Taguchi, T.-h. Arima, Y. Tokura, and T. Nakajima, Polarized neutron scattering study of the centrosymmetric skyrmion host material Gd 2PdSi3, Physical Review B 107, 024405 (2023)

    2023

  5. [13]

    Hirschberger, T

    M. Hirschberger, T. Nakajima, S. Gao, L. Peng, A. Kikkawa, T. Kurumaji, M. Kriener, Y. Yamasaki, H. Sagayama, H. Nakao, et al., Skyrmion phase and com- peting magnetic orders on a breathing kagom´ e lattice, Nature Communications 10, 5831 (2019)

    2019

  6. [14]

    N. D. Khanh, T. Nakajima, X. Yu, S. Gao, K. Shibata, M. Hirschberger, Y. Yamasaki, H. Sagayama, H. Nakao, L. Peng, et al. , Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet, Nature Nanotech- nology 15, 444 (2020)

    2020

  7. [15]

    Yasui, C

    Y. Yasui, C. J. Butler, N. D. Khanh, S. Hayami, T. Nomoto, T. Hanaguri, Y. Motome, R. Arita, T.-H. Arima, Y. Tokura, et al. , Imaging the coupling between itinerant electrons and localised moments in the cen- trosymmetric skyrmion magnet GdRu 2Si2, Nature Com- munications 11, ...

    2020

  8. [16]

    O. I. Utesov, Thermodynamically stable skyrmion lattice in a tetragonal frustrated antiferromagnet with dipolar interaction, Physical Review B 103, 064414 (2021)

    2021

  9. [17]

    N. D. Khanh, T. Nakajima, S. Hayami, S. Gao, Y. Ya- masaki, H. Sagayama, H. Nakao, R. Takagi, Y. Motome, Y. Tokura, T.-H. Arima, and S. Seki, Zoology of multiple- Q spin textures in a centrosymmetric tetragonal magnet with itinerant electrons, Advanced Science 9, 2105452 (2022)

    2022

  10. [18]

    G. D. A. Wood, D. D. Khalyavin, D. A. Mayoh, J. Bouaziz, A. E. Hall, S. J. R. Holt, F. Orlandi, P. Manuel, S. Bl¨ ugel, J. B. Staunton, O. A. Petrenko, M. R. Lees, and G. Balakrishnan, Double-Q ground state with topological charge stripes in the centrosymmetric skyrmion candid...

    2023

  11. [19]

    Spethmann, N

    J. Spethmann, N. D. Khanh, H. Yoshimochi, R. Tak- agi, S. Hayami, Y. Motome, R. Wiesendanger, S. Seki, and K. von Bergmann, SP-STM study of the multi-Q phases in GdRu2Si2, Physical Review Materials8, 064404 (2024)

    2024

  12. [20]

    B. M. Huddart, A. Hern´ andez-Meli´ an, G. D. A. Wood, D. A. Mayoh, M. Gomilˇ sek, Z. Guguchia, C. Wang, S. J. Blundell, G. Balakrishnan, and T. Lancaster, Field- orientation-dependent magnetic phases in GdRu 2Si2 probed with muon-spin spectroscopy, arXiv preprint arXiv:2403.0...

    2024 doi arXiv

  13. [21]

    Yoshimochi, R

    H. Yoshimochi, R. Takagi, J. Ju, N. Khanh, H. Saito, H. Sagayama, H. Nakao, S. Itoh, Y. Tokura, T. Arima, et al., Multistep topological transitions among meron and skyrmion crystals in a centrosymmetric magnet, Nature Physics 20, 1001 (2024)

    2024

  14. [22]

    Takagi, N

    R. Takagi, N. Matsuyama, V. Ukleev, L. Yu, J. S. White, S. Francoual, J. R. Mardegan, S. Hayami, H. Saito, K. Kaneko, et al. , Square and rhombic lattices of mag- netic skyrmions in a centrosymmetric binary compound, Nature Communications 13, 1472 (2022)

    2022

  15. [23]

    Hayami, Orthorhombic distortion and rectangular skyrmion crystal in a centrosymmetric tetragonal host, Journal of Physics: Materials 6, 014006 (2022)

    S. Hayami, Orthorhombic distortion and rectangular skyrmion crystal in a centrosymmetric tetragonal host, Journal of Physics: Materials 6, 014006 (2022)

    2022

  16. [24]

    M. Gen, R. Takagi, Y. Watanabe, S. Kitou, H. Sagayama, N. Matsuyama, Y. Kohama, A. Ikeda, Y. ¯Onuki, T. Ku- rumaji, et al., Rhombic skyrmion lattice coupled with or- thorhombic structural distortion in EuAl 4, Physical Re- view B 107, L020410 (2023)

    2023

  17. [25]

    J. M. Moya, S. Lei, E. M. Clements, C. S. Kengle, S. Sun, K. Allen, Q. Li, Y. Peng, A. A. Husain, M. Mitrano, et al. , Incommensurate magnetic orders and topological Hall effect in the square-net centrosymmetric EuGa 2Al2 system, Physical Review Materials 6, 074201 (2022). 7

    2022

  18. [26]

    A. M. Vibhakar, D. D. Khalyavin, J. M. Moya, P. Manuel, F. Orlandi, S. Lei, E. Morosan, and A. Bom- bardi, Competing charge and magnetic order in the can- didate centrosymmetric skyrmion host EuGa 2Al2, Phys- ical Review B 108, L100404 (2023)

    2023

  19. [27]

    perovskite

    M. Shatruk, ThCr 2Si2 structure type: The “perovskite” of intermetallics, Journal of Solid State Chemistry 272, 198 (2019)

    2019

  20. [28]

    Nomoto and R

    T. Nomoto and R. Arita, Ab initio exploration of short- pitch skyrmion materials: Role of orbital frustration, Journal of Applied Physics 133, 150901 (2023)

    2023

  21. [29]

    Bouaziz, E

    J. Bouaziz, E. Mendive-Tapia, S. Bl¨ ugel, and J. B. Staunton, Fermi-surface origin of skyrmion lattices in centrosymmetric rare-earth intermetallics, Physical Re- view Letters 128, 157206 (2022)

    2022

  22. [30]

    spin-cholesteric

    N. Andriushin, J. Muller, N. Pavlovskii, J. Grum- bach, S. Granovsky, Y. Tymoshenko, O. Zaharko, A. Ivanov, J. Ollivier, M. Doerr, et al. , Reentrant multiple-q magnetic order and a “spin-cholesteric” phase in Sr 3Fe2O7, arXiv preprint arXiv:2405.12889 10.48550/arXiv.2405.12889 (2024)

    2024 doi arXiv

  23. [31]

    Puphal, V

    P. Puphal, V. Pomjakushin, N. Kanazawa, V. Ukleev, D. J. Gawryluk, J. Ma, M. Naamneh, N. C. Plumb, L. Keller, R. Cubitt, et al. , Topological magnetic phase in the candidate weyl semimetal cealge, Physical review letters 124, 017202 (2020)

    2020

  24. [32]

    Luttinger and L

    J. Luttinger and L. Tisza, Theory of dipole interaction in crystals, Physical Review 70, 954 (1946)

    1946

  25. [33]

    Lyons and T

    D. Lyons and T. Kaplan, Method for determining ground-state spin configurations, Physical Review 120, 1580 (1960)

    1960

  26. [34]

    P. Kurz, G. Bihlmayer, K. Hirai, and S. Bl¨ ugel, Three- dimensional spin structure on a two-dimensional lattice: Mn/Cu (111), Physical Review Letters 86, 1106 (2001)

    2001

  27. [35]

    Garnier, D

    A. Garnier, D. Gignoux, D. Schmitt, and T. Shigeoka, Giant magnetic anisotropy in tetragonal GdRu 2Ge2 and GdRu2Si2, Physica B: Condensed Matter 222, 80 (1996)

    1996

  28. [36]

    Janoschek, F

    M. Janoschek, F. Bernlochner, S. Dunsiger, C. Pfleiderer, P. B¨ oni, B. Roessli, P. Link, and A. Rosch, Helimagnon bands as universal excitations of chiral magnets, Physical Review B 81, 214436 (2010)

    2010

  29. [37]

    Kugler, G

    M. Kugler, G. Brandl, J. Waizner, M. Janoschek, R. Georgii, A. Bauer, K. Seemann, A. Rosch, C. Pflei- derer, P. B¨ oni,et al. , Band structure of helimagnons in MnSi resolved by inelastic neutron scattering, Physical Review Letters 115, 097203 (2015)

    2015

  30. [38]

    Portnichenko, J

    P. Portnichenko, J. Romh´ anyi, Y. Onykiienko, A. Hen- schel, M. Schmidt, A. Cameron, M. Surmach, J. Lim, J. Park, A. Schneidewind, et al. , Magnon spectrum of the helimagnetic insulator Cu 2OSeO3, Nature Commu- nications 7, 10725 (2016)

    2016

  31. [39]

    C. Balz, B. Lake, A. N. Islam, Y. Singh, J. A. Rodriguez- Rivera, T. Guidi, E. M. Wheeler, G. G. Simeoni, and H. Ryll, Magnetic Hamiltonian and phase diagram of the quantum spin liquid Ca10Cr7O28, Physical Review B 95, 174414 (2017)

    2017

  32. [40]

    J. A. M. Paddison, M. Daum, Z. Dun, G. Ehlers, Y. Liu, M. B. Stone, H. Zhou, and M. Mourigal, Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4, Nature Physics 13, 117 (2017)

    2017

  33. [41]

    Matsuyama, T

    N. Matsuyama, T. Nomura, S. Imajo, T. Nomoto, R. Arita, K. Sudo, M. Kimata, N. Khanh, R. Takagi, Y. Tokura, et al., Quantum oscillations in the centrosym- metric skyrmion-hosting magnet GdRu2Si2, Physical Re- view B 107, 104421 (2023)

    2023

  34. [42]

    The 160Gd isotope was procured from the National Iso- tope Development Center, Oak Ridge National Labora- tory, USA

  35. [43]

    Bewley, J

    R. Bewley, J. Taylor, and S. Bennington, LET, a cold neutron multi-disk chopper spectrometer at isis, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 637, 128 (2011)

    2011

  36. [44]

    The two lower incident energies would have been useful for resolving the dispersion at the lowest en- ergies

    With the multiplexing capability of LET, three other incident energies were available ( Ei = 2 .2, 3 .7 and 22.80 meV). The two lower incident energies would have been useful for resolving the dispersion at the lowest en- ergies. However, the absorption of the sample at these ...

  37. [45]

    Arnold, J.-C

    O. Arnold, J.-C. Bilheux, J. Borreguero, A. Buts, S. I. Campbell, L. Chapon, M. Doucet, N. Draper, R. F. Leal, M. Gigg, et al., mantid—Data analysis and visualization package for neutron scattering andµSR experiments, Nu- clear instruments and methods in physics research secti...

    2014

  38. [46]

    Ewings, A

    R. Ewings, A. Buts, M. Le, J. Van Duijn, I. Bustin- duy, and T. Perring, horace: Software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments, Nuclear Instruments and Methods in Physics Research Section A: Acceler- ators,...

    2016

  39. [47]

    Zhang and C

    H. Zhang and C. D. Batista, Classical spin dynamics based on SU(N ) coherent states, Physical Review B 104, 104409 (2021)

    2021

  40. [48]

    Dahlbom, H

    D. Dahlbom, H. Zhang, C. Miles, X. Bai, C. D. Batista, and K. Barros, Geometric integration of classical spin dynamics via a mean-field Schr¨ odinger equation, Physical Review B 106, 054423 (2022)

    2022

  41. [49]

    See Supplemental Material at [link to Supplemental]

  42. [50]

    Note that throughout the manuscript we retain the con- ventional body-centered setting of GdRu2Si2 (I4/mmm)

  43. [52]

    Newville, T

    M. Newville, T. Stensitzki, D. B. Allen, M. Rawlik, A. In- gargiola, and A. Nelson, LMFIT: Non-linear least-square minimization and curve-fitting for Python (2015)

    2015

  44. [53]

    We define B = −8.8 T so that it is directed along the z direction in this model

  45. [54]

    J. A. M. Paddison, J. Bouaziz, A. F. May, Q. Zhang, S. Calder, D. Abernathy, J. B. Staunton, S. Bl¨ ugel, and A. D. Christianson, Spin dynamics of the centrosymmet- ric skyrmion material GdRu 2Si2, Cell Reports Physical Science 5, 102280 (2024)

    2024

  46. [55]

    Future experimental plans exist to measure the base of the magnon band with ℏω < 0.8 meV this with cold- neutron triple-axis spectroscopy for a more focused and directed flux experiment to overcome the absorption and flux issues currently preventing this

  47. [56]

    Hayami, Three-sublattice antiferro-type and ferri-type skyrmion crystals in magnets without the Dzyaloshinskii- Moriya interaction, Physical Review B 109, 014415 (2024)

    S. Hayami, Three-sublattice antiferro-type and ferri-type skyrmion crystals in magnets without the Dzyaloshinskii- Moriya interaction, Physical Review B 109, 014415 (2024)

    2024

  48. [57]

    Hayami, Double-Q and quadruple-Q instabilities at low-symmetry ordering wave vectors under tetragonal symmetry, Physical Review B 110, 014404 (2024)

    S. Hayami, Double-Q and quadruple-Q instabilities at low-symmetry ordering wave vectors under tetragonal symmetry, Physical Review B 110, 014404 (2024). 8

    2024

  49. [58]

    J. A. M. Paddison, H. Zhang, J. Yan, M. J. Cliffe, M. A. McGuire, S.-H. Do, S. Gao, M. B. Stone, D. Dahlbom, K. Barros, et al., Cubic double perovskites host noncopla- nar spin textures, npj Quantum Materials 9, 48 (2024)

    2024

  50. [59]

    Hayami and R

    S. Hayami and R. Yambe, Stabilization mechanisms of magnetic skyrmion crystal and multiple-q states based on momentum-resolved spin interactions, Materials Today Quantum 3, 100010 (2024)

    2024

  51. [60]

    Eremeev, D

    S. Eremeev, D. Glazkova, G. Poelchen, A. Kraiker, K. Ali, A. V. Tarasov, S. Schulz, K. Kliemt, E. V. Chulkov, V. Stolyarov, et al. , Insight into the elec- tronic structure of the centrosymmetric skyrmion magnet GdRu2Si2, Nanoscale Advances 5, 6678 (2023)

    2023

  52. [61]

    Y. Dong, Y. Kinoshita, M. Ochi, R. Nakachi, R. Higashinaka, S. Hayami, Y. Wan, Y. Arai, S. Huh, M. Hashimoto, et al. , Magnetic-domain- dependent pseudogap induced by fermi surface nesting in a centrosymmetric skyrmion magnet, arXiv preprint arXiv:2307.08000 10.48550/arXiv.230...

    2023 doi arXiv

  53. [62]

    I. A. Zaliznyak, Heisenberg magnet with modulated ex- change, Physical Review B 68, 134451 (2003)

    2003

  54. [63]

    I. A. Zaliznyak, Spiral order induced by distortion in a frustrated square-lattice antiferromagnet, Physical Re- view B 69, 092404 (2004)

    2004

  55. [64]

    Balakrishnan, G

    G. Balakrishnan, G. D. A. Wood, J. R. Stewart, S. M. Tobin, D. A. Mayoh, and J. Bouaziz, Magnon dispersions in the centrosymmetric skyrmion host GdRu 2Si2 (2023). Supplementary Information: A Magnon Band Analysis of GdRu2Si2 in the Field-Polarized State G. D. A. Wood, 1, 2,∗ J...

    2023 arXiv

  56. [65]

    The cuts should be finely binned, so that if there is random noise, the surrounding pixels likely have a zero value

    On a given cut, mask the tail of the elastic scattering at low energies and spurious background signals in the measurement. The cuts should be finely binned, so that if there is random noise, the surrounding pixels likely have a zero value. This is essential for the median fil...

  57. [66]

    After this process, extract any pixels which have non-zero median values, assuming that these pertain to the magnon band

    Apply a 3 × 3 median-kernel grid to each pixel in a given cut. After this process, extract any pixels which have non-zero median values, assuming that these pertain to the magnon band. We have used the NDimage code from SciPy to perform this image processing procedure [3]

  58. [67]

    We use the intensity of the pixels to weight the ℏω(q) fitting

    So that the fitting procedure operates on real data, we map back to the original inten- sity values of the pixels which identified as non-zero in the median kernel filter process. We use the intensity of the pixels to weight the ℏω(q) fitting. This is motivated by assuming tha...

  59. [68]

    Tobyfit as part of the Horace package was attempted for this [4]

  60. [69]

    G. R. Arce, Nonlinear signal processing: a statistical approach (John Wiley & Sons, 2004)

    2004

  61. [70]

    Virtanen, R

    P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wil- son, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, ˙I. Polat, Y. Fe...

    2020

  62. [71]

    Ewings, A

    R. Ewings, A. Buts, M. Le, J. Van Duijn, I. Bustinduy, and T. Perring, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 834, 132 (2016)

    2016

  63. [72]

    Zhang and C

    H. Zhang and C. D. Batista, Physical Review B 104, 104409 (2021)

    2021

  64. [73]

    Dahlbom, H

    D. Dahlbom, H. Zhang, C. Miles, X. Bai, C. D. Batista, and K. Barros, Physical Review B 106, 054423 (2022)

    2022

  65. [74]

    A. T. Boothroyd, Principles of Neutron Scattering from Condensed Matter (Oxford University Press, 2020)

    2020

  66. [75]

    Note that the inclusion of the symmetry equivalent δ’s are implicit here when referring to the δ vector a given interaction

  67. [76]

    The J7 interaction is trivially invariant against any reciprocal path which is not active along c∗. 15

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.