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REVIEW 3 major objections 5 minor 47 references

Phononic enhancement and detection of hidden spin-nematicity and dynamics in quantum magnets

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Pith's one-line read Spin-lattice coupling both stabilizes hidden quadrupolar order in a spin-1 triangular-lattice quantum magnet and imprints a field-tunable avoided-crossing signature on the phonon spectrum—a detection route for spin-nematic order accessible

desk verdict New bond-phonon detection signature for spin nematicity, but the enhancement claim rests on an unjustified independent-bond approximation and the spectra ignore the η-renormalized spins. read the letter →

arxiv 2602.22283 v1 pith:7UFHR4GZ submitted 2026-02-25 cond-mat.mes-hall cond-mat.mtrl-scicond-mat.str-el

Junyu Tang , Hong-hao Song , Gang v. Chen This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-scicond-mat.str-el
keywords spinnematicityquadrupolarordermagnetoelasticcouplingphonon-magnonavoidedcrossingtriangularlatticequantummagnetbiquadraticexchangetwo-magnonboundstateRamanandinelasticX-rayscattering
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 argues that the magnetoelastic (spin-lattice) coupling in a spin-1 triangular-lattice Mott insulator does two things at once: integrating out the bond phonons generates an effective biquadratic exchange that substantially enlarges the stability regions of the spin-nematic (SN) and spin-nematic-supersolid (SNS) phases, and retaining the phonons shows that the same coupling imprints a distinctive avoided-crossing signature on the phonon spectrum wherever quadrupolar order exists. The result is a practical detection route for the hidden, time-reversal-even quadrupolar order that neutron scattering cannot see directly: Raman and inelastic X-ray scattering can measure the phonon splitting and its strong, non-monotonic dependence on the external magnetic field. A sympathetic reader should care because it turns a longstanding obstacle in frustrated magnetism—the invisibility of spin nematics—into a lattice response that existing spectroscopic techniques can access.

What carries the argument

Central object: the bond-phonon magnetoelastic coupling H_me = -Jγ Σ_{⟨ij⟩} e_ij·u_ij (Sx_i Sx_j + Sy_i Sy_j + Δ Sz_i Sz_j). Integrating out the phonons (treating each bond displacement u_ij as an independent Gaussian variable) generates an effective biquadratic exchange -Jη(...)^2 with η = Jγ^2/k_E; this induced biquadratic term is the load-bearing object because (1) after the Schrieffer-Wolff projection it renormalizes Jxy and Jz asymmetrically, enlarging the SN and SNS phase regions, and (2) in the dynamical calculation it supplies the magnon-phonon vertex Π(k) that produces the phonon-magnon avoided crossings serving as the spectroscopic signature. The paper uses the model in two complem

What would settle it

Sweep the magnetic field through the predicted spin-nematic window (B_{c,2} < B < B_{c,3}) in a spin-1 triangular-lattice Mott insulator and measure the acoustic phonon dispersion by Raman or inelastic X-ray scattering; the central claim fails if no avoided crossing appears between the phonon and magnon branches whose gap vanishes when the crossing is tuned to the K point. A second check: repeat the Gaussian integration of the phonon fields with the constraint u_ij = u_i - u_j enforced; if the effective biquadratic coupling η vanishes, the enlarged SN/SNS phase regions do not follow from the m

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Extended reading notes

Core claim

Starting from a spin-1 XXZ model on the triangular lattice with an easy-axis anisotropy D>0, an applied field B, and a bond-phonon magnetoelastic coupling H_me = -Jγ Σ e_ij·u_ij (Sx_i Sx_j + Sy_i Sy_j + Δ Sz_i Sz_j), the author integrates out the bond-phonon displacements to obtain an effective spin Hamiltonian with an emergent biquadratic term -Jη(...)^2, η = Jγ^2/k_E. After projecting onto the low-energy |Sz=±1> manifold via a Schrieffer-Wolff transformation, this biquadratic term renormalizes the effective pseudospin exchange anisotropies Jxy = -J^2/D - 2Jη + (JηΔ)^2/D and Jz = J^2/D + 4JΔ - 2Jη + (JηΔ)^2/D. Because the bare Jxy is second order in J while Jz is first order, increasing η b

Load-bearing premise

The load-bearing premise is that each bond's lattice displacement behaves as an independent Gaussian variable when phonons are integrated out—even though every site displacement on the triangular lattice is shared by six bonds; if that shared-site constraint is enforced, the induced biquadratic coupling -Jη(...)^2 and the enlarged spin-nematic phases would not follow faithfully from the magnetoelastic Hamiltonian.

Editorial extensions

If this is right

  • In the spin-nematic phase, Raman or inelastic X-ray scattering should reveal a single avoided crossing between the acoustic phonon branch and the magnon branch, with a gap size that increases with the magnetoelastic coupling η and a crossing position that sweeps through the K point as the field is tuned; the gap should close exactly at the K point at one critical field.
  • In the spin-nematic-supersolid phase, the spectrum should show multiple avoided gaps, including splittings caused by Umklapp scattering between magnons and folded phonon branches; the high-energy flat magnon band should remain phonon-blind, so it will not confuse the signature.
  • If the effective biquadratic coupling picture is right, candidate materials with stronger spin-lattice coupling will show spin-nematic order over a substantially wider range of magnetic fields than the bare XXZ model predicts, with B_{c,2} decreasing with η while B_{c,3} stays fixed.
  • The scheme requires comparable phonon and magnon energy scales; when the phonon frequency is large, the crossings are pushed to the Γ point and the phononic probe becomes ineffective, setting a materials-selection criterion.

Reading between the lines

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

  • We infer that the paper's Gaussian integration treats each bond displacement as independent even though on the triangular lattice each site displacement is shared by six bonds; if a lattice-dynamics calculation enforcing u_ij = u_i - u_j gives a much smaller effective η, the enlarged SN/SNS phase regions would shrink, though the phonon-spectrum signature (which relies on the same η) would be weake
  • We infer that the same magnetoelastic mechanism should transfer to other quadrupolar and multipolar orders (e.g., in spin-orbit-entangled insulators or pyrochlore magnets), where bond phonons could serve both as a stabilizer and a detector; on-site (Einstein) phonon mechanisms that lift phonon degeneracies are complementary, whereas the bond-phonon route uses avoided crossings without lifting phon
  • We infer that a natural next step is to compute the dynamical quadrupolar structure factor in the coupled magnon-phonon system and compare it directly with Raman or IXS line shapes, which would test whether the avoided-crossing signature survives beyond the mean-field (linear spin-wave) level used in the paper.
  • We note that because the spectrum is computed with the η=0 ground-state angles (the paper states the magnon Hamiltonian is fixed at η=0), the spectral signatures are not fully self-consistent with the η>0 phase diagram; a self-consistent calculation could shift the precise field values at which the gap vanishes.
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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 / 5 minor

Summary. The paper proposes a phonon-based route to both stabilize and detect spin-nematic order in a spin-1 triangular-lattice magnet. Starting from a spin-1 XXZ model with single-ion anisotropy, a magnetic field, and a magnetoelastic coupling to lattice displacements, the authors integrate out the phonons to obtain an effective Hamiltonian with an induced biquadratic exchange. They argue that this biquadratic term substantially enlarges the spin-nematic (SN) and spin-nematic-supersolid (SNS) regions in the phase diagram. They then retain the phonons explicitly and compute coupled magnon-phonon spectra, identifying avoided crossings whose position and magnitude depend on the magnetic field and on the underlying quadrupolar order, and propose Raman or inelastic X-ray scattering as experimental probes. The paper contains two central claims: (i) magnetoelastic coupling enhances hidden spin nematicity, and (ii) the same coupling produces a distinctive, observable phonon signature of that order.

Significance. If both claims hold, the work would address a long-standing challenge in frustrated magnetism by providing a practical spectroscopic route to an order that is difficult to detect with neutron scattering, and it would supply a concrete microscopic mechanism for biquadratic exchange. The manuscript has notable strengths: the Schrieffer-Wolff reduction is presented in detail and matches the known η=0 limits of reference [5]; the phase diagram reproduces the expected sequence SNS–UUD–SN–FP at η=0; the spectral calculations are accompanied by explicit analytic expressions for the magnon-phonon couplings and projection operators; and the predicted avoided-crossing signatures are concrete and falsifiable. However, two load-bearing technical issues reduce confidence in the current form: the Gaussian phonon integration is performed over bond displacements as independent variables although the model Hamiltonian is expressed in terms of shared site displacements, and the spectral calculation fixes the spin ground state at η=0 while using an η>0 magnon-phonon coupling. Both issues need to be addressed before the central claims can be considered established.

major comments (3)
  1. [SM Eq. (S5); main text Eqs. (3)–(5)] The derivation of the local biquadratic term integrates over each bond displacement u_ij as an independent Gaussian variable. This is inconsistent with Eq. (3), where u_ij ≡ u_i − u_j and H_p is a quadratic form in the 2N site displacements. On the triangular lattice, the 3N bond elongations are constrained by the 2N site displacements (rank 2N−2). The exact Gaussian integral over site displacements yields a nonlocal kernel of the form O^T B D^{-1} B^T O, not the local −Jη Σ_b O_b^2 used in Eq. (5). Since the enlarged SNS/SN regions in Fig. 1 and the critical η_c in Eq. (7) follow from the local coefficient, the enhancement half of the central claim is not established unless the off-diagonal and momentum-dependent parts of the exact induced interaction are shown to be negligible. No such demonstration appears in the paper or SM; reference [25] does not justify treating bond variables as
  2. [SM sections 'Spin-nematic phase' and 'Spin-nematic-supersolid phase'] The spectral calculation uses a magnon Hamiltonian H_s evaluated at η=0 (SM states that H_s retains the form of Eq. (S14) but with η=0), while the magnon-phonon coupling Π(k) in Eq. (S26) and the SNS couplings in Eq. (S31) are taken at finite η. Consequently, the spin configurations φ, θ_1, θ_2 are determined by the η=0 stability conditions (Eqs. (S24), (S30)), not by the effective Hamiltonian of Eq. (6) that governs the finite-η phase diagram. Since the figures use η=0.05–0.1, this is not an infinitesimal-η regime. The size and position of the avoided crossings, the non-monotonic Δ_a(B) curve in Fig. 3, and the sweeping of the crossing through K could all be quantitatively modified by the η-induced renormalization of the spin ground state. The authors should either compute the spectra self-consistently with the η>0 ground state or explicitly justify a perturbative η→0 treatment and esti
  3. [SM 'Estimation for η'; main text near Eq. (7)] The claim that η≈0.04–1 is physically accessible relies on choosing ω0=62.8 GHz, which is an extremely soft acoustic phonon frequency. Since η ∝ 1/ω0^2, a more typical zone-boundary phonon of about 1 THz suppresses η by roughly two orders of magnitude, placing the enlarged phase regions in Fig. 1 and the phonon-magnon crossings in Figs. 2–4 outside the range of the cited candidate materials. The paper should anchor the parameters to a specific material with a soft phonon branch, or clearly label the results as a proof-of-principle for such soft-phonon systems. Without this anchoring, the statement that the coupling is 'physically accessible' is not fully supported.
minor comments (5)
  1. [Main text, Eq. (3) and SM Eq. (S5)] The manuscript interchangeably calls the phonons 'bond phonons' and writes H_p in terms of site displacements u_i. This terminology is confusing and may obscure the constraint issue raised in the major comments. Please clarify whether the model is a site-displacement model or a genuine independent-bond-phonon model.
  2. [SM 'Projection operators'] The definitions of the phonon-like and magnon-like weights near the end of the SM denote both projection operators as 'P_b'; the second should be P_a. Please fix this typo.
  3. [Main text, after Eq. (5)] The phrase 'a biquadratic term emerges with the strength Jη ≡ Jη' is tautological. It should read 'with strength ηJ' or simply 'Jη'.
  4. [Main text, Fig. 2 and Fig. 4 captions] The color coding for phononic/magnonic weights is introduced only in the SM. A one-sentence explanation in the main-text caption would improve readability.
  5. [SM 'Estimation for η'] The statement that 'other choices of ω0, ωm, η do not qualitatively change the conclusions' is too strong given the strong 1/ω0^2 suppression of η. Please qualify this statement.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the phonon-induced biquadratic term and the spectral signatures are derived from the stated model; the independent-bond approximation is a technical validity concern, not a circular step.

full rationale

The derivation chain is self-contained: Eqs. (2)-(4) define the spin, phonon, and magnetoelastic terms; integrating out phonons yields the biquadratic term in Eq. (5) with coefficient -Jη; the Schrieffer-Wolff projection gives Eqs. (6)-(7); the phase diagram and phonon/magnon spectra are then computed from these Hamiltonians. No experimental observable is used as an input, and no fitted parameter is relabeled as a prediction. The self-reference to SM [27] is for algebraic details of the Schrieffer-Wolff transformation and projection operators, not a load-bearing external result. The only substantive concern is the SM Eq. (S5) treatment of each bond displacement u_ij as an independent Gaussian variable, while Eq. (3) defines u_ij = u_i - u_j as site displacements; on the triangular lattice these bond variables are constrained, so the exact Gaussian integral would produce nonlocal/projector corrections. This is a correctness/approximation issue about whether the local biquadratic term is faithful to the stated model, not a circular step: the biquadratic term is derived from the assumed integration, not imposed by construction. Likewise, fixing the magnon Hamiltonian at η=0 in the spectral section is an internal inconsistency, not a circular prediction. The parameter choices (D=4J, Δ=1.2, ω0/J=0.41, γ range) are stated and used to produce the phase diagram and spectra, not fitted to the claimed signatures. There is no author-overlapping citation chain invoked to force the conclusion. Therefore the circularity score is 0.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

Central claim rests on standard spin-wave and perturbation machinery plus two hand-chosen model regimes (D=4J, Δ=1.2) and a tuned phonon frequency. No new physical entities are introduced. The free-parameter count is moderate and all parameters are within ranges used in the cited spin-nematic literature, but the spectral calculation's η=0 H_s is an ad hoc simplification.

free parameters (5)
  • D/J (single-ion easy-axis anisotropy) = 4
    Set to 4 in Fig. 1 and all spectra; controls the two-magnon bound-state scale and the width of the nematic phase.
  • Δ (XXZ anisotropy) = 1.2
    Set to 1.2 throughout; with D=4J it determines the η=0 critical fields and the Jxy/Jz ratio.
  • ħω0/J (intrinsic phonon frequency) = 0.41 (ω0≈62.8 GHz with J/ħ≈151.7 GHz)
    Chosen so the low-energy acoustic phonon bands cross the magnon band at an accessible field; the paper acknowledges this is a compromise to avoid parameter tuning.
  • γ (exchange-length sensitivity) = 0.1–0.5 Å^-1
    Used only for order-of-magnitude estimate of η; no material-specific value is pinned.
  • η (dimensionless magnetoelastic coupling) = 0–1 scanned; typical estimate 0.04–1
    Central control parameter; although derived as Jγ²/kE, it is treated as a free tuning parameter in the phase diagram and spectra.
assumptions (5)
  • domain assumption Independent bond-phonon Gaussian integration: each u_ij can be integrated independently despite shared site displacements.
    Used to derive Eq. (5) from Eq. (4); SM Eq. (S5) states u_ij couples only to a single bond and is independent. On a triangular lattice this ignores bond-constraint correlations.
  • domain assumption Large easy-axis anisotropy D≫J and moderate XXZ Δ>1 justify projecting to |±1> pseudospin manifold and second-order Schrieffer-Wolff.
    Used in Eq. (6) and SM; the effective pseudospin model and its Jxy, Jz are derived under this condition.
  • domain assumption Site-factorized SU(2) coherent-state variational states capture the ground-state phase diagram, with only small shifts of critical fields relative to DMRG/iPEPS.
    Used to compute Fig. 1; justified by citing [5,37].
  • standard math Holstein-Primakoff expansion truncated at leading order is valid for the effective S=1/2 model.
    Used to obtain linear magnon bands; the SM discusses the S=1/2 constraint and resummation [47].
  • ad hoc to paper Spectral calculation keeps H_s at η=0 while the magnon-phonon coupling carries η>0.
    SM states the free magnon Hamiltonian retains Eq. (S14) with η=0; this drops the static phonon renormalization that produces the enlarged phase diagram, so the spectra are not self-consistent with the η>0 ground state.

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Cite this review

Pith. "Pith review of Phononic enhancement and detection of hidden spin-nematicity and dynamics in quantum magnets." pith.science (2026). https://pith.science/paper/7UFHR4GZ

@misc{pith2026260222283,
  author       = {Pith},
  title        = {Pith review of: Phononic enhancement and detection of hidden spin-nematicity and dynamics in quantum magnets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7UFHR4GZ}},
  note         = {Machine review of arXiv:2602.22283}
}
read the original abstract

The spin nematic phase, characterized by long-range order of spin quadrupole moments in the absence of dipolar magnetism, presents a significant challenge for conventional experimental detection. We propose a novel method to detect this elusive order in quantum magnets with an illustration in the spin-1 triangular lattice Mott insulator. By integrating out the phonon degrees of freedom, we obtain a phase diagram with substantially enlarged regions for the spin-nematic and spin-nematic-supersolid phases. We then demonstrate that through the spin-lattice coupling, the emergence of spin nematic order imprints a distinctive signature onto the phonon spectra, providing a clear spectroscopic signature for the quadrupolar order accessible via Raman or inelastic X-ray scattering. Our formalism offers a direct and powerful method to uncover the hidden spin nematicity, opening a new pathway for diagnosing multipolar orders in quantum magnets.

Figures

Figures reproduced from arXiv: 2602.22283 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Triangular lattice structure with ordering wavevector at [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Magnitude of the avoided crossing gap [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Phonon–magnon band spectra in SN phase under different [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Phonon–magnon band spectra in SNS phase with magnetic field [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Works this paper leans on

47 extracted references · 1 linked inside Pith

  1. [25]

    D. L. Bergman, R. Shindou, G. A. Fiete, and L. Balents, Models of degeneracy breaking in pyrochlore antiferromagnets, Phys. Rev. B74, 134409 (2006)

    2006

  2. [5]

    Sheng, J

    J. Sheng, J. Hu, L. Xu, L. Wang, X. Shi, R. Chi, D. Yu, A. Podlesnyak, P. Piyawongwatthana, N. Murai, S. Ohira- Kawamura, H. Yuan, L. Wang, J.-W. Mei, H.-J. Liao, T. Xi- ang, L. Wu, and Z. Wang, Possible Observation of Quadrupole Waves in Spin Nematics, Phys. Rev. Lett.135, 156704 (2025)

    2025

  3. [1]

    Penc and A

    K. Penc and A. M. Läuchli, Spin nematic phases in quantum spin systems, inIntroduction to Frustrated Magnetism: Mate- rials, Experiments, Theory, edited by C. Lacroix, P. Mendels, and F. Mila (Springer Berlin Heidelberg, Berlin, Heidelberg,

  4. [2]

    L. V . Pourovskii, D. Fiore Mosca, L. Celiberti, S. Khmelevskyi, A. Paramekanti, and C. Franchini, Hidden orders in spin–orbit- entangled correlated insulators, Nature Reviews Materials10, 674 (2025)

    2025

  5. [3]

    Tsunetsugu and M

    H. Tsunetsugu and M. Arikawa, Spin Nematic Phase in S=1 Triangular Antiferromagnets, Journal of the Physical Society of Japan75, 083701 (2006)

    2006

  6. [4]

    Papanicolaou, Unusual phases in quantum spin-1 systems, Nuclear Physics B305, 367 (1988)

    N. Papanicolaou, Unusual phases in quantum spin-1 systems, Nuclear Physics B305, 367 (1988)

    1988

  7. [6]

    Bhattacharjee, V

    S. Bhattacharjee, V . B. Shenoy, and T. Senthil, Possible ferro- spin nematic order in NiGa 2S4, Phys. Rev. B74, 092406 (2006)

    2006

  8. [7]

    O. A. Starykh, Unusual ordered phases of highly frustrated magnets: a review, Reports on Progress in Physics78, 052502 (2015)

    2015

Show all 47 references
  1. [8]

    Chandra and P

    P. Chandra and P. Coleman, Quantum spin nematics: Moment- free magnetism, Phys. Rev. Lett.66, 100 (1991)

    1991

  2. [9]

    Smerald and N

    A. Smerald and N. Shannon, Theory of spin excitations in a quantum spin-nematic state, Phys. Rev. B88, 184430 (2013)

    2013

  3. [10]

    Huang, S

    Y . Huang, S. Yunoki, and S. Maekawa, Emergent spin super- solids in frustrated quantum materials (2026)

    2026

  4. [11]

    Podolsky and E

    D. Podolsky and E. Demler, Properties and detection of spin ne- matic order in strongly correlated electron systems, New Jour- nal of Physics7, 59 (2005). 6

    2005

  5. [12]

    Kohama, H

    Y . Kohama, H. Ishikawa, A. Matsuo, K. Kindo, N. Shannon, and Z. Hiroi, Possible observation of quantum spin-nematic phase in a frustrated magnet, Proceedings of the National Academy of Sciences116, 10686 (2019)

    2019

  6. [13]

    Kim, J.-K

    H. Kim, J.-K. Kim, J. Kwon, J. Kim, H.-W. J. Kim, S. Ha, K. Kim, W. Lee, J. Kim, G. Y . Cho, H. Heo, J. Jang, C. J. Sahle, A. Longo, J. Strempfer, G. Fabbris, Y . Choi, D. Haskel, J. Kim, J.-W. Kim, and B. J. Kim, Quantum spin nematic phase in a square-lattice iridate, Nature6...

    2024

  7. [14]

    Halpern and M

    O. Halpern and M. H. Johnson, On the magnetic scattering of neutrons, Phys. Rev.55, 898 (1939)

    1939

  8. [15]

    B. N. Brockhouse, Scattering of neutrons by spin waves in mag- netite, Phys. Rev.106, 859 (1957)

    1957

  9. [16]

    J. Cui, E. V . Boström, M. Ozerov, F. Wu, Q. Jiang, J.-H. Chu, C. Li, F. Liu, X. Xu, A. Rubio, and Q. Zhang, Chirality selec- tive magnon-phonon hybridization and magnon-induced chiral phonons in a layered zigzag antiferromagnet, Nature Commu- nications14, 3396 (2023)

    2023

  10. [17]

    Loudon, The raman effect in crystals, Advances in Physics 13, 423 (1964)

    R. Loudon, The raman effect in crystals, Advances in Physics 13, 423 (1964)

    1964

  11. [18]

    Burkel, J

    E. Burkel, J. Peisl, and B. Dorner, Observation of inelastic x-ray scattering from phonons, Europhysics Letters3, 957 (1987)

    1987

  12. [19]

    Krisch and F

    M. Krisch and F. Sette, Inelastic x-ray scattering from phonons, inLight Scattering in Solid IX, edited by M. Cardona and R. Merlin (Springer Berlin Heidelberg, Berlin, Heidelberg,

  13. [20]

    Silberglitt and J

    R. Silberglitt and J. B. Torrance, Effect of Single-Ion Anisotropy on Two-Spin-Wave Bound State in a Heisenberg Ferromagnet, Phys. Rev. B2, 772 (1970)

    1970

  14. [21]

    Oguchi, Theory of two-magnon bound states in the heisen- berg ferro- and antiferromagnet, Journal of the Physical Society of Japan31, 394 (1971)

    T. Oguchi, Theory of two-magnon bound states in the heisen- berg ferro- and antiferromagnet, Journal of the Physical Society of Japan31, 394 (1971)

    1971

  15. [22]

    Bai, S.-S

    X. Bai, S.-S. Zhang, Z. Dun, H. Zhang, Q. Huang, H. Zhou, M. B. Stone, A. I. Kolesnikov, F. Ye, C. D. Batista, and M. Mourigal, Hybridized quadrupolar excitations in the spin- anisotropic frustrated magnet FeI 2, Nature Physics17, 467 (2021)

    2021

  16. [23]

    Sheng, J.-W

    J. Sheng, J.-W. Mei, L. Wang, X. Xu, W. Jiang, L. Xu, H. Ge, N. Zhao, T. Li, A. Candini, B. Xi, J. Zhao, Y . Fu, J. Yang, Y . Zhang, G. Biasiol, S. Wang, J. Zhu, P. Miao, X. Tong, D. Yu, R. Mole, Y . Cui, L. Ma, Z. Zhang, Z. Ouyang, W. Tong, A. Podlesnyak, L. Wang, F. Ye, D. Y...

    2025

  17. [24]

    In the spin-only treatment, the phonons are integrated out, which captures their static backaction on the spin sector and is used to determine the static spin phase diagram

    These two methods are complementary limits of the same mag- netoelastic model. In the spin-only treatment, the phonons are integrated out, which captures their static backaction on the spin sector and is used to determine the static spin phase diagram. In the spectral calculat...

  18. [26]

    Streib, N

    S. Streib, N. Vidal-Silva, K. Shen, and G. E. W. Bauer, Magnon- phonon interactions in magnetic insulators, Phys. Rev. B99, 184442 (2019)

    2019

  19. [27]

    See supplemental material at [URL will be inserted by pub- lisher] for the details of the effective Hamiltonian and projec- tion operators

  20. [28]

    Blume and Y

    M. Blume and Y . Y . Hsieh, Biquadratic exchange and quadrupo- lar ordering, Journal of Applied Physics40, 1249 (1969)

    1969

  21. [29]

    Läuchli, F

    A. Läuchli, F. Mila, and K. Penc, Quadrupolar phases of the s=1 bilinear-biquadratic heisenberg model on the triangular lattice, Phys. Rev. Lett.97, 087205 (2006)

    2006

  22. [30]

    Moreno-Cardoner, H

    M. Moreno-Cardoner, H. Perrin, S. Paganelli, G. De Chiara, and A. Sanpera, Case study of the uniaxial anisotropic spin- 1 bilinear-biquadratic heisenberg model on a triangular lattice, Phys. Rev. B90, 144409 (2014)

    2014

  23. [31]

    Tanaka, Y

    K. Tanaka, Y . Yokoyama, and C. Hotta, Origin of biquadratic exchange interactions in a mott insulator as a driving force of spin nematic order, Journal of the Physical Society of Japan87, 023702 (2018)

    2018

  24. [32]

    Hayami, R

    S. Hayami, R. Ozawa, and Y . Motome, Effective bilinear- biquadratic model for noncoplanar ordering in itinerant mag- nets, Phys. Rev. B95, 224424 (2017)

    2017

  25. [33]

    Akagi, M

    Y . Akagi, M. Udagawa, and Y . Motome, Hidden multiple-spin interactions as an origin of spin scalar chiral order in frustrated kondo lattice models, Phys. Rev. Lett.108, 096401 (2012)

    2012

  26. [34]

    J. G. Rau, S. Petit, and M. J. P. Gingras, Order by virtual crystal field fluctuations in pyrochloreXYantiferromagnets, Phys. Rev. B93, 184408 (2016)

    2016

  27. [35]

    Santini, S

    P. Santini, S. Carretta, G. Amoretti, R. Caciuffo, N. Magnani, and G. H. Lander, Multipolar interactions inf-electron sys- tems: The paradigm of actinide dioxides, Rev. Mod. Phys.81, 807 (2009)

    2009

  28. [36]

    Tchernyshyov, R

    O. Tchernyshyov, R. Moessner, and S. L. Sondhi, Order by dis- tortion and string modes in pyrochlore antiferromagnets, Phys. Rev. Lett.88, 067203 (2002)

    2002

  29. [37]

    Yamamoto, G

    D. Yamamoto, G. Marmorini, and I. Danshita, Quantum Phase Diagram of the Triangular-LatticeXXZModel in a Magnetic Field, Phys. Rev. Lett.112, 127203 (2014)

    2014

  30. [38]

    Heidarian and K

    D. Heidarian and K. Damle, Persistent supersolid phase of hard-core bosons on the triangular lattice, Phys. Rev. Lett.95, 127206 (2005)

    2005

  31. [39]

    G. H. Wannier, Antiferromagnetism. The Triangular Ising Net, Phys. Rev.79, 357 (1950)

    1950

  32. [40]

    Wen, Quantum orders and symmetric spin liquids, Phys

    X.-G. Wen, Quantum orders and symmetric spin liquids, Phys. Rev. B65, 165113 (2002)

    2002

  33. [41]

    Y . Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys.89, 025003 (2017)

    2017

  34. [42]

    A. S. Patri, A. Sakai, S. Lee, A. Paramekanti, S. Nakatsuji, and Y . B. Kim, Unveiling hidden multipolar orders with mag- netostriction, Nature Communications10, 4092 (2019)

    2019

  35. [43]

    B.-Q. Liu, P. ˇCermák, C. Franz, C. Pfleiderer, and A. Schnei- dewind, Lattice dynamics and coupled quadrupole-phonon ex- citations in CeAuAl3, Phys. Rev. B98, 174306 (2018)

    2018

  36. [44]

    K. Hart, R. Sutcliffe, G. Refael, and A. Paramekanti, Phonon- driven multipolar dynamics in a spin-orbit coupled mott insula- tor (2025)

    2025

  37. [45]

    Sutcliffe, K

    R. Sutcliffe, K. Hart, S. Chaudhary, and A. Paramekanti, Pseudo-chiral phonon splitting from octupolar magnetic order (2025), arXiv:2506.18978 [cond-mat.str-el]

    2025 arXiv

  38. [46]

    Holstein and H

    T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev.58, 1098 (1940)

    1940

  39. [47]

    Phononic enhancement and detection of hidden spin-nematicity and dynamics in quantum magnets

    M. V ogl, P. Laurell, H. Zhang, S. Okamoto, and G. A. Fiete, Re- summation of the holstein-primakoff expansion and differential equation approach to operator square roots, Phys. Rev. Res.2, 043243 (2020). 7 Supplementary material for “Phononic enhancement and detection of hidd...

    2020

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