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arxiv: 2605.02683 · v1 · submitted 2026-05-04 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Recognition: 2 theorem links

· Lean Theorem

Exotic magnetism and persistent short-range spin correlations in a frustrated honeycomb lattice antiferromagnet

M. Barik , Q. Faure , F. Damay , J. P. Embs , S. Petit , P. Khuntia
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Pith reviewed 2026-05-08 18:24 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci
keywords frustrated magnetismhoneycomb latticeantiferromagnetshort-range spin correlationsinelastic neutron scatteringtricritical pointfield-induced transitionS=5/2 magnet
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The pith

Competing exchange interactions and weak Ising anisotropy in the S=5/2 honeycomb antiferromagnet CaZn2Fe(PO4)3 place the material near a mean-field tricritical point, producing exotic field-induced behavior and persistent short-range spin

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

The paper studies the magnetic ordering and excitations in CaZn2Fe(PO4)3, a distorted honeycomb lattice built from high-spin Fe3+ ions. Magnetization, specific heat, and inelastic neutron scattering show antiferromagnetic order below 1.67 K together with short-range spin correlations that survive to higher temperatures. Spin-wave modeling of the data identifies three competing exchange couplings plus weak Ising anisotropy. These parameters position the system close to the mean-field tricritical point in the plane of further-neighbor to nearest-neighbor exchange ratios. The resulting frustration and anisotropy account for the observed unconventional response to applied magnetic fields, including a field-induced canted state.

Core claim

Inelastic neutron scattering and thermodynamic measurements on CaZn2Fe(PO4)3 establish antiferromagnetic ordering at TN approximately 1.67 K with short-range spin correlations persisting above the transition. Classical spin-wave calculations fitted to the spectra reveal competing nearest-neighbor and further-neighbor exchanges together with weak Ising-like anisotropy. These parameters locate the compound near the mean-field tricritical point in the J2/J1 versus J3/J1 phase diagram, where the interplay of frustration and anisotropy produces an unconventional field-induced spin-canted state.

What carries the argument

The J2/J1–J3/J1 phase diagram for the honeycomb antiferromagnet, with the material positioned near the mean-field tricritical point; this diagram encodes how the ratios of further-neighbor exchanges relative to the nearest-neighbor coupling, combined with weak Ising anisotropy, control the ground state and field response.

Load-bearing premise

The low-energy physics is fully described by a classical spin-wave model with three fitted exchange parameters and weak Ising anisotropy, without significant quantum fluctuations, interlayer couplings, or higher-order terms that would shift the location relative to the tricritical point.

What would settle it

A clear observation of fractionalized excitations in zero or applied field, or a large discrepancy between measured critical fields and those predicted by the classical model after including quantum corrections, would show that the system lies farther from the tricritical point than claimed.

Figures

Figures reproduced from arXiv: 2605.02683 by F. Damay, J. P. Embs, M. Barik, P. Khuntia, Q. Faure, S. Petit.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Two-phase Rietveld refinement of the XRD pattern of polycrystalline CZFPO recorded at room temperature. The view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Temperature dependence of the magnetic susceptibility measured at various magnetic fields. The black arrows view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Temperature dependence of the zero-field specific heat. Top left inset: Temperature dependence of zero field view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Inelastic neutron scattering spectra. (a) Experimental INS spectrum collected at view at source ↗
read the original abstract

Two-dimensional high-spin bipartite honeycomb networks, where anisotropy, competing exchange interactions, and spin fluctuations interplay, provide an alternative platform to test theoretical models that distinguish between classical and quantum magnetism in the context of emergent many-body phenomena and exotic excitations. Here, we report the crystal structure, magnetization, specific heat, and inelastic neutron scattering measurements of the $S = 5/2$ distorted honeycomb magnet $\mathrm{CaZn_2Fe(PO_4)_3}$. Magnetization measurements reveal dominant antiferromagnetic interactions between the $\mathrm{Fe^{3+}}$ ($S = 5/2$) moments. The development and field evolution of a dip in the magnetic susceptibility under an external magnetic field indicate an unconventional field-induced transition, further supported by anomalies observed in magnetization isotherms. Zero-field specific heat measurements show an antiferromagnetic transition at $T_N \approx 1.67 \mathrm{K}$, which evolves under applied magnetic field, suggesting stabilization of a field-induced spin-canted state. Thermodynamic measurements reveal short-range spin correlations above the transition temperature. Inelastic neutron scattering results further corroborate antiferromagnetic ordering, consistent with specific heat data. Spin-wave calculations indicate competing exchange interactions that introduce magnetic frustration, along with weak Ising-like anisotropy. The interplay of competing interactions and anisotropy gives rise to exotic field-induced behavior and places the system in close proximity to a mean-field tricritical point in the $J_2/J_1$--$J_3/J_1$ phase diagram, opening a route to unconventional states in high-spin frustrated honeycomb 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 reports crystal structure determination, magnetization, specific heat, and inelastic neutron scattering measurements on the S=5/2 distorted honeycomb antiferromagnet CaZn2Fe(PO4)3. Thermodynamic data show antiferromagnetic order at TN ≈ 1.67 K with short-range correlations persisting above TN and field-induced anomalies interpreted as a spin-canted state. Inelastic neutron scattering spectra are modeled with linear spin-wave theory using three exchange constants (J1, J2, J3) plus weak Ising anisotropy; the resulting J2/J1 and J3/J1 ratios place the system near a mean-field tricritical point in the J2/J1–J3/J1 phase diagram, which the authors link to the observed exotic field-induced behavior.

Significance. If the classical spin-wave fit robustly locates the material near the tricritical point, the work supplies a concrete high-spin example of competing interactions and anisotropy on the honeycomb lattice, offering a platform to explore field-tuned states and the boundary between classical and quantum regimes in frustrated magnets. The multi-probe consistency (magnetization, specific heat, INS) for antiferromagnetic order and short-range correlations above TN provides a solid experimental base.

major comments (2)
  1. [spin-wave modeling] Spin-wave modeling section: The central claim that the system lies in close proximity to the mean-field tricritical point rests on the fitted J2/J1 and J3/J1 ratios extracted from linear spin-wave calculations of the INS data. The manuscript provides no quantitative propagation of parameter uncertainties, no goodness-of-fit metrics (e.g., χ² or R²), and no assessment of how modest quantum 1/S corrections or a small interlayer J⊥ (expected in the real 3D phosphate structure) would shift the location relative to the phase boundary.
  2. [abstract and field-induced transition discussion] Abstract and results on field-induced behavior: The interpretation of the susceptibility dip and magnetization anomalies as evidence for a field-induced spin-canted state near the tricritical point assumes the classical three-parameter model fully captures the low-energy physics. No explicit calculation or estimate is given for how frustration-induced quantum renormalization on the honeycomb lattice with competing J2 and J3 would alter the effective ratios or the canted/collinear/disordered boundaries for S = 5/2.
minor comments (2)
  1. [abstract] The abstract would benefit from stating the numerical values of the fitted J2/J1, J3/J1 ratios and anisotropy strength together with their uncertainties.
  2. [figures] Figure captions for the INS data and spin-wave fits should explicitly note the energy and momentum ranges used in the fitting procedure and any data exclusion criteria.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment below and will incorporate clarifications and additional analyses in the revised version to strengthen the presentation of the spin-wave results and the discussion of the field-induced behavior.

read point-by-point responses

  1. Referee: Spin-wave modeling section: The central claim that the system lies in close proximity to the mean-field tricritical point rests on the fitted J2/J1 and J3/J1 ratios extracted from linear spin-wave calculations of the INS data. The manuscript provides no quantitative propagation of parameter uncertainties, no goodness-of-fit metrics (e.g., χ² or R²), and no assessment of how modest quantum 1/S corrections or a small interlayer J⊥ (expected in the real 3D phosphate structure) would shift the location relative to the phase boundary.

    Authors: We agree that the original manuscript lacked these quantitative details. In the revised version we will report the χ² per degree of freedom for the linear spin-wave fits to the inelastic neutron scattering spectra and include uncertainties on the fitted exchange parameters obtained by propagating the covariance matrix from the fitting procedure. For the 1/S corrections, we will add a short estimate using the leading-order 1/S expansion for the honeycomb lattice; given S = 5/2 the renormalization shifts the effective ratios by at most ~10 % while still placing the system near the tricritical point. The interlayer coupling J⊥ is bounded by the crystal structure and the low TN; a simple 3D spin-wave estimate shows it does not move the point across the classical phase boundary. These additions will be included in the spin-wave modeling section. revision: partial

  2. Referee: Abstract and results on field-induced behavior: The interpretation of the susceptibility dip and magnetization anomalies as evidence for a field-induced spin-canted state near the tricritical point assumes the classical three-parameter model fully captures the low-energy physics. No explicit calculation or estimate is given for how frustration-induced quantum renormalization on the honeycomb lattice with competing J2 and J3 would alter the effective ratios or the canted/collinear/disordered boundaries for S = 5/2.

    Authors: The primary evidence for the field-induced spin-canted state is experimental: the susceptibility dip and magnetization anomalies observed in thermodynamic measurements. The classical spin-wave analysis supplies the exchange ratios that locate the system near the mean-field tricritical point. We acknowledge that a full quantum renormalization of the phase boundaries for S = 5/2 is not provided. In the revision we will add a brief estimate drawing on existing results for the J1–J2–J3 honeycomb model, showing that quantum corrections renormalize the effective ratios by 10–20 % without removing the proximity to the tricritical point. An explicit quantum phase diagram for this S value lies beyond the scope of the present experimental work. revision: partial

Circularity Check

0 steps flagged

No significant circularity: fitted exchanges locate system on independent phase diagram

full rationale

The paper measures magnetization, specific heat, and INS data directly, then performs standard linear spin-wave fits to extract J1, J2, J3 and weak anisotropy. These fitted ratios are plotted on a pre-existing mean-field J2/J1–J3/J1 phase diagram to note proximity to the tricritical point. No step reduces a claimed prediction to its own inputs by construction, no self-citation chain bears the central claim, and the phase-diagram location is a direct geometric consequence of the fitted values rather than a derived result. This is the normal, non-circular workflow for interpreting experimental data with a classical model.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on a classical Heisenberg spin model whose exchange constants are determined by fitting to data; no new particles or forces are postulated.

free parameters (2)
  • J1, J2, J3 exchange constants
    Three distinct nearest- and further-neighbor couplings whose values are adjusted to reproduce the observed spin-wave spectrum and susceptibility.
  • Ising anisotropy strength
    Weak directional preference added to the model to account for the field-induced canting behavior.
axioms (1)
  • domain assumption The low-energy magnetic excitations are adequately described by linear spin-wave theory on a classical Heisenberg Hamiltonian with up to third-neighbor interactions.
    Invoked when the abstract states that spin-wave calculations indicate competing exchanges and weak anisotropy.

pith-pipeline@v0.9.0 · 5606 in / 1397 out tokens · 43025 ms · 2026-05-08T18:24:47.638120+00:00 · methodology

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Reference graph

Works this paper leans on

63 extracted references · 1 canonical work pages

  1. [1]

    The field-induced behavior is further corroborated by isothermal magnetization data taken at 1.9 K (see SI ref

    associated with BEC of exotic excitations, in contrast to the conventional LRO. The field-induced behavior is further corroborated by isothermal magnetization data taken at 1.9 K (see SI ref. [31]). The field dependence of dM/d(µ0H), reveals a minimum around 0.4 T, which has also been observed in several frustrated magnets [17, 35], intensifies with decre...

  2. [2]

    and Li 2IrO3 [55]. In CZFPO, the nearly equivalent bond lengths, a common exchange pathway, and compa- rable bond angles along the superexchange route support modelling the spin Hamiltonian in the same framework [21, 56] with single-ion anisotropy as a first approxima- tion: H=J 1 ∑ ⟨i,j⟩ Si·Sj +J 2 ∑ ⟨⟨i,j⟩⟩ Si·Sj +J 3 ∑ ⟨⟨⟨i,j⟩⟩⟩ Si·Sj −D ∑ i (Sz i )2 (...

  3. [3]

    Although the buckled honeycomb mag- net CaMn2Sb2 also lies close to the tricritical point [22], CZFPO provides a better structural realization of a hon- eycomb lattice

    and MnPS 3 [30], all of which stabilize N´ eel ordered ground states. Although the buckled honeycomb mag- net CaMn2Sb2 also lies close to the tricritical point [22], CZFPO provides a better structural realization of a hon- eycomb lattice. Within this model, the Curie Weiss tem- perature expressed asθCW =−S(S+1)(J1+2J2+J3)/kB, yieldsθCW≃−24.01 K, slightly ...

  4. [4]

    Spin liquids in frustrated magnets,

    Leon Balents, “Spin liquids in frustrated magnets,” na- ture464, 199–208 (2010)

    2010

  5. [5]

    Experimental signatures of quantum and topological states in frustrated magnetism,

    J Khatua, B Sana, A Zorko, M Gomilˇ sek, K Sethupathi, MS Ramachandra Rao, M Baenitz, B Schmidt, and P Khuntia, “Experimental signatures of quantum and topological states in frustrated magnetism,” Physics Re- ports1041, 1–60 (2023)

    2023

  6. [6]

    Gapless ground state in the archetypal quantum kagome antifer- romagnet ZnCu3(OH)6Cl2,

    P Khuntia, Matias Velazquez, Quentin Barth´ elemy, Fab- rice Bert, Edwin Kermarrec, A Legros, Bernard Bernu, L Messio, Andrej Zorko, and P Mendels, “Gapless ground state in the archetypal quantum kagome antifer- romagnet ZnCu3(OH)6Cl2,” Nature Physics16, 469–474 7 (2020)

    2020

  7. [7]

    Spin liquid state in the 3d frustrated antiferromagnet PbCuTe2O6: Nmr and muon spin re- laxation studies,

    P. Khuntia, F. Bert, P. Mendels, B. Koteswararao, A. V. Mahajan, M. Baenitz, F. C. Chou, C. Baines, A. Amato, and Y. Furukawa, “Spin liquid state in the 3d frustrated antiferromagnet PbCuTe2O6: Nmr and muon spin re- laxation studies,” Physical Review Letters116, 107203 (2016)

    2016

  8. [8]

    Spin liquid state in the disordered trian- gular lattice Sc 2Ga2CuO7 revealed by NMR,

    P. Khuntia, R. Kumar, A. V. Mahajan, M. Baenitz, and Y. Furukawa, “Spin liquid state in the disordered trian- gular lattice Sc 2Ga2CuO7 revealed by NMR,” Physical Review B93, 140408 (2016)

    2016

  9. [9]

    Spin liquid state in a rare-earth hyper- kagome lattice,

    J. Khatua, S. Bhattacharya, Q. P. Ding, S. Vrtnik, A. M. Strydom, N. P. Butch, H. Luetkens, E. Kermar- rec, M. S. Ramachandra Rao, A. Zorko, Y. Furukawa, and P. Khuntia, “Spin liquid state in a rare-earth hyper- kagome lattice,” Phys. Rev. B106, 104404 (2022)

    2022

  10. [10]

    Frustration and quantum criticality,

    Matthias Vojta, “Frustration and quantum criticality,” Reports on Progress in Physics81, 064501 (2018)

    2018

  11. [11]

    Quantum criticality and the Tomonaga-Luttinger liquid in one-dimensional Bose gases,

    Bing Yang, Yang-Yang Chen, Yong-Guang Zheng, Hui Sun, Han-Ning Dai, Xi-Wen Guan, Zhen-Sheng Yuan, and Jian-Wei Pan, “Quantum criticality and the Tomonaga-Luttinger liquid in one-dimensional Bose gases,” Physical Review Letters.119, 165701 (2017)

    2017

  12. [12]

    Quantum criticality among entangled spin chains,

    N Blanc, J Trinh, L Dong, X Bai, Adam A Aczel, M Mourigal, L Balents, T Siegrist, and AP Ramirez, “Quantum criticality among entangled spin chains,” Na- ture Physics14, 273–276 (2018)

    2018

  13. [13]

    Field- induced condensation of magnons and long range order in BaCuSi 2O6,

    Han-Ting Wang, Bao Xu, and Yupeng Wang, “Field- induced condensation of magnons and long range order in BaCuSi 2O6,” Journal of Physics: Condensed Matter 18, 4719 (2006)

    2006

  14. [14]

    Pressure-induced quantum phase transition in the spin-liquid TlCuCl 3,

    Ch. R¨ uegg, A. Furrer, D. Sheptyakov, Th. Str¨ assle, K. W. Kr¨ amer, H.-U. G¨ udel, and L. M´ el´ esi, “Pressure-induced quantum phase transition in the spin-liquid TlCuCl 3,” Physical Review Letters93, 257201 (2004)

    2004

  15. [15]

    Effect of structural distortions on the mag- netism of doped spin-peierls CuGeO 3,

    Virginie Simonet, Beatrice Grenier, Fran¸ coise Villain, A- M Flank, Guy Dhalenne, Alexandre Revcolevschi, and J-P Renard, “Effect of structural distortions on the mag- netism of doped spin-peierls CuGeO 3,” The European Physical Journal B-Condensed Matter and Complex Sys- tems53, 155–167 (2006)

    2006

  16. [16]

    Bose- Einstein condensation in quantum magnets,

    Vivien Zapf, Marcelo Jaime, and C. D. Batista, “Bose- Einstein condensation in quantum magnets,” Rev. Mod. Phys.86, 563–614 (2014)

    2014

  17. [17]

    Universality of magnetic-field-induced bose- einstein condensation of magnons,

    Kazuki Shirasawa, Nobuyuki Kurita, and Hidekazu Tanaka, “Universality of magnetic-field-induced bose- einstein condensation of magnons,” Physical Review B 96, 144404 (2017)

    2017

  18. [18]

    Dzyaloshinskii-moriya anisotropy effect on field- induced magnon condensation in the kagome antifer- romagnetα−Cu3.26Mg0.74OH6Br2,

    Ying Fu, Jian Chen, Jieming Sheng, Han Ge, Lian- glong Huang, Cai Liu, Zhenxing Wang, Zhongwen Ouyang, Xiaobin Chen, Dapeng Yu, Shanmin Wang, Liusuo Wu, Hai-Feng Li, Le Wang, and Jia-Wei Mei, “Dzyaloshinskii-moriya anisotropy effect on field- induced magnon condensation in the kagome antifer- romagnetα−Cu3.26Mg0.74OH6Br2,” Physical Review B 104, 245107 (2021)

    2021

  19. [19]

    Bose–einstein condensation in magnetic in- sulators,

    Thierry Giamarchi, Christian R¨ uegg, and Oleg Tch- ernyshyov, “Bose–einstein condensation in magnetic in- sulators,” Nature Physics4, 198–204 (2008)

    2008

  20. [20]

    Double dome structure of the bose–einstein condensation in diluted s= 3/2 quantum magnets,

    Yoshito Watanabe, Atsushi Miyake, Masaki Gen, Yuta Mizukami, Kenichiro Hashimoto, Takasada Shibauchi, Akihiko Ikeda, Masashi Tokunaga, Takashi Kurumaji, Yusuke Tokunaga,et al., “Double dome structure of the bose–einstein condensation in diluted s= 3/2 quantum magnets,” Nature Communications14, 1260 (2023)

    2023

  21. [21]

    Field-induced supersolid phase in spin-one Heisenberg models,

    P. Sengupta and C. D. Batista, “Field-induced supersolid phase in spin-one Heisenberg models,” Physical Review Letters98, 227201 (2007)

    2007

  22. [22]

    N´ eel-type antifer- romagnetic order and magnetic field–temperature phase diagram in the spin- 1 2 rare-earth honeycomb compound YbCl3,

    Jie Xing, Erxi Feng, Yaohua Liu, Eve Emmanouilidou, Chaowei Hu, Jinyu Liu, David Graf, Arthur P. Ramirez, Gang Chen, Huibo Cao, and Ni Ni, “N´ eel-type antifer- romagnetic order and magnetic field–temperature phase diagram in the spin- 1 2 rare-earth honeycomb compound YbCl3,” Phys. Rev. B102, 014427 (2020)

    2020

  23. [23]

    A quantum critical bose gas of magnons in the quasi-two-dimensional antiferromagnet YbCl3 under magnetic fields,

    Yosuke Matsumoto, Simon Schnierer, Jan AN Bruin, J¨ urgen Nuss, Pascal Reiss, George Jackeli, Kentaro Kita- gawa, and Hidenori Takagi, “A quantum critical bose gas of magnons in the quasi-two-dimensional antiferromagnet YbCl3 under magnetic fields,” Nature Physics20, 1131– 1138 (2024)

    2024

  24. [24]

    An investiga- tion of the quantumJ 1 −J 2 −J 3 model on the honeycomb lattice,

    JB Fouet, P Sindzingre, and C Lhuillier, “An investiga- tion of the quantumJ 1 −J 2 −J 3 model on the honeycomb lattice,” The European Physical Journal B-Condensed Matter and Complex Systems20, 241–254 (2001)

    2001

  25. [25]

    CaMn2Sb2: Spin waves on a frustrated antiferromag- netic honeycomb lattice,

    D. E. McNally, J. W. Simonson, J. J. Kistner-Morris, G. J. Smith, J. E. Hassinger, L. DeBeer-Schmitt, A. I. Kolesnikov, I. A. Zaliznyak, and M. C. Aronson, “CaMn2Sb2: Spin waves on a frustrated antiferromag- netic honeycomb lattice,” Phys. Rev. B91, 180407 (2015)

    2015

  26. [26]

    Frustrated magnetism in theJ 1 −J 2 honeycomb lattice compounds MgMnO3 and ZnMnO3 synthesized via a metathesis re- action,

    Yuya Haraguchi, Kazuhiro Nawa, Chishiro Michioka, Hi- roaki Ueda, Akira Matsuo, Koichi Kindo, Maxim Avdeev, Taku J. Sato, and Kazuyoshi Yoshimura, “Frustrated magnetism in theJ 1 −J 2 honeycomb lattice compounds MgMnO3 and ZnMnO3 synthesized via a metathesis re- action,” Phys. Rev. Mater.3, 124406 (2019)

    2019

  27. [27]

    CaMn 2Sb2: a fully frustrated classical mag- netic system,

    II Mazin, “CaMn 2Sb2: a fully frustrated classical mag- netic system,” arXiv:1309.3744 (2013)

    work page arXiv 2013

  28. [28]

    Spin dynamics in the stripe-ordered buckled honeycomb lattice antiferromagnet Ba2NiTeO6,

    Shinichiro Asai, Minoru Soda, Kazuhiro Kasatani, Toshio Ono, V. Ovidiu Garlea, Barry Winn, and Takatsugu Masuda, “Spin dynamics in the stripe-ordered buckled honeycomb lattice antiferromagnet Ba2NiTeO6,” Phys. Rev. B96, 104414 (2017)

    2017

  29. [29]

    Spin dynamics and magnetic phase transitions in the quasi-two-dimensional antiferromagnet Mn[C10H6(OH)(COO−)]2 ×2H 2O,

    KG Dergachev, MI Kobets, EN Khatsko, VM Khrustalev, and VA Pashchenko, “Spin dynamics and magnetic phase transitions in the quasi-two-dimensional antiferromagnet Mn[C10H6(OH)(COO−)]2 ×2H 2O,” Low Tempera- ture Physics33, 427–432 (2007)

    2007

  30. [30]

    Magnetic prop- erties of a metal-organic antiferromagnet on a dis- torted honeycomb lattice,

    Ivan Spremo, Florian Sch¨ utz, Peter Kopietz, Volodymyr Pashchenko, Bernd Wolf, Michael Lang, Jan W. Bats, Chunhua Hu, and Martin U. Schmidt, “Magnetic prop- erties of a metal-organic antiferromagnet on a dis- torted honeycomb lattice,” Physical Review B72, 174429 (2005)

    2005

  31. [31]

    Static and dynamic critical properties of the quasi-two-dimensional antiferromagnet MnPS 3,

    AR Wildes, Henrik M Rønnow, B Roessli, MJ Harris, and KW Godfrey, “Static and dynamic critical properties of the quasi-two-dimensional antiferromagnet MnPS 3,” Physical Review B74, 094422 (2006)

    2006

  32. [32]

    Contrasting magnetism in VPS 3 and CrI3 monolayers with the common honeycombs= 3/2 spin lattice,

    Ke Yang, Yueyue Ning, Yaozhenghang Ma, Yuxuan Zhou, and Hua Wu, “Contrasting magnetism in VPS 3 and CrI3 monolayers with the common honeycombs= 3/2 spin lattice,” Phys. Rev. B111, 134421 (2025)

    2025

  33. [33]

    Spin waves and the critical behaviour of the magnetiza- tion in MnPS 3,

    AR Wildes, B Roessli, B Lebech, and KW Godfrey, “Spin waves and the critical behaviour of the magnetiza- tion in MnPS 3,” Journal of Physics: Condensed Matter 10, 6417–6428 (1998)

    1998

  34. [34]

    See Supplementary Materials for experimental details 8 supporting analysis and figures, submitted as part of this manuscript

  35. [35]

    The ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid can- didate,

    T Arh, B Sana, M Pregelj, P Khuntia, Z Jagliˇ ci´ c, MD Le, PK Biswas, P Manuel, L Mangin-Thro, A Ozarowski, et al., “The ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid can- didate,” Nature Materials21, 416–422 (2022)

    2022

  36. [36]

    Magnetic properties of a spin-orbit entangledJ eff = 1 2 honeycomb lattice,

    J. Khatua, Q. P. Ding, M. S. Ramachandra Rao, K. Y. Choi, A. Zorko, Y. Furukawa, and P. Khuntia, “Magnetic properties of a spin-orbit entangledJ eff = 1 2 honeycomb lattice,” Phys. Rev. B108, 054442 (2023)

    2023

  37. [37]

    Field-induced two-step phase transi- tions in the singlet ground state triangular antiferromag- net CsFeBr3,

    Yosuke Tanaka, Hidekazu Tanaka, Toshio Ono, Akira Oosawa, Kiyoko Morishita, Katsunori Iio, Tetsuya Kato, Hiroko Aruga Katori, Mikhail I Bartashevich, and Tsuneaki Goto, “Field-induced two-step phase transi- tions in the singlet ground state triangular antiferromag- net CsFeBr3,” Journal of the Physical Society of Japan 70, 3068–3075 (2001)

    2001

  38. [38]

    Bose-Einstein condensation of triplons in thes= 1 tetramer antiferromagnet K 2Ni2(MoO4)3: A compound close to a quantum critical point,

    B. Koteswararao, P. Khuntia, R. Kumar, A. V. Mahajan, Arvind Yogi, M. Baenitz, Y. Skourski, and F. C. Chou, “Bose-Einstein condensation of triplons in thes= 1 tetramer antiferromagnet K 2Ni2(MoO4)3: A compound close to a quantum critical point,” Physical Review B95, 180407 (2017)

    2017

  39. [39]

    Magnetism and field-induced effects in the s= 5 2 honeycomb lattice antiferromagnet FeP 3SiO11,

    J. Khatua, M. Gomilˇ sek, Kwang-Yong Choi, and P. Khuntia, “Magnetism and field-induced effects in the s= 5 2 honeycomb lattice antiferromagnet FeP 3SiO11,” Physical Review B110, 184402 (2024)

    2024

  40. [40]

    Spin ordering in a triangular xy antifer- romagnet: CsFeCl 3 and RbFeCl3,

    Taiichiro Haseda, Nobuo Wada, Masanari Hata, and Ki- ichi Amaya, “Spin ordering in a triangular xy antifer- romagnet: CsFeCl 3 and RbFeCl3,” Physica B+ C108, 841–842 (1981)

    1981

  41. [41]

    Field-induced mag- netic states in geometrically frustrated SrEr2O4,

    Navid Qureshi, Oscar Fabelo, P Manuel, Dmitry Khalyavin, Elsa Lhotel, SXM Riberolles, Geetha Bal- akrishnan, and Oleg Petrenko, “Field-induced mag- netic states in geometrically frustrated SrEr2O4,” SciPost Physics11, 007 (2021)

    2021

  42. [42]

    Critical exponents and intrinsic broadening of the field-induced transition in NiCl2·4SC(NH2)2,

    E. Wulf, D. H¨ uvonen, R. Sch¨ onemann, H. K¨ uhne, T. Her- rmannsd¨ orfer, I. Glavatskyy, S. Gerischer, K. Kiefer, S. Gvasaliya, and A. Zheludev, “Critical exponents and intrinsic broadening of the field-induced transition in NiCl2·4SC(NH2)2,” Phys. Rev. B91, 014406 (2015)

    2015

  43. [43]

    Direct measurement of the bose-einstein condensation universality class in NiCl 2- 4SC(NH2)2 at ultralow temperatures,

    L. Yin, J. S. Xia, V. S. Zapf, N. S. Sullivan, and A. Paduan-Filho, “Direct measurement of the bose-einstein condensation universality class in NiCl 2- 4SC(NH2)2 at ultralow temperatures,” Phys. Rev. Lett. 101, 187205 (2008)

    2008

  44. [44]

    Fingerprinting triangular-lattice antiferromagnet by excitation gaps,

    K. E. Avers, P. A. Maksimov, P. F. S. Rosa, S. M. Thomas, J. D. Thompson, W. P. Halperin, R. Movshovich, and A. L. Chernyshev, “Fingerprinting triangular-lattice antiferromagnet by excitation gaps,” Phys. Rev. B103, L180406 (2021)

    2021

  45. [45]

    Field-induced quantum criticality in the kitaev system α−RuCl3,

    A. U. B. Wolter, L. T. Corredor, L. Janssen, K. Nenkov, S. Sch¨ onecker, S.-H. Do, K.-Y. Choi, R. Albrecht, J. Hunger, T. Doert, M. Vojta, and B. B¨ uchner, “Field-induced quantum criticality in the kitaev system α−RuCl3,” Phys. Rev. B96, 041405 (2017)

    2017

  46. [46]

    Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7 pyrochlore antiferromagnet from low-temperature spe- cific heat measurements,

    J. A. Quilliam, K. A. Ross, A. G. Del Maestro, M. J. P. Gingras, L. R. Corruccini, and J. B. Kycia, “Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7 pyrochlore antiferromagnet from low-temperature spe- cific heat measurements,” Phys. Rev. Lett.99, 097201 (2007)

    2007

  47. [47]

    Exotic magnetic field-induced spin-superstructures in a mixed honeycomb-triangular lattice system,

    V. Ovidiu Garlea, Liurukara D. Sanjeewa, Michael A. McGuire, Cristian D. Batista, Anjana M. Samarakoon, David Graf, Barry Winn, Feng Ye, Christina Hoffmann, and Joseph W. Kolis, “Exotic magnetic field-induced spin-superstructures in a mixed honeycomb-triangular lattice system,” Physical Review X9, 011038 (2019)

    2019

  48. [48]

    Gapped ground state in a spin-1 2 frus- trated square lattice,

    H. Yamaguchi, N. Uemoto, T. Okubo, Y. Kono, S. Kit- taka, T. Sakakibara, T. Yajima, S. Shimono, Y. Iwasaki, and Y. Hosokoshi, “Gapped ground state in a spin-1 2 frus- trated square lattice,” Physical Review B104, L060411 (2021)

    2021

  49. [49]

    Frustrated magnetism in octahedra-based Ce6Ni6p17,

    D. G. Franco, R. Avalos, D. Hafner, K. A. Modic, Yu. Prots, O. Stockert, A. Hoser, P. J. W. Moll, M. Brando, A. A. Aligia, and C. Geibel, “Frustrated magnetism in octahedra-based Ce6Ni6p17,” Phys. Rev. B109, 054405 (2024)

    2024

  50. [50]

    Physical properties of the quasi-two-dimensional square lattice antiferromag- net Ba2FeSi2O7,

    Tae-Hwan Jang, Seung-Hwan Do, Minseong Lee, Hui Wu, Craig M. Brown, Andrew D. Christianson, Sang- Wook Cheong, and Jae-Hoon Park, “Physical properties of the quasi-two-dimensional square lattice antiferromag- net Ba2FeSi2O7,” Physical Review B104, 214434 (2021)

    2021

  51. [51]

    Ordered magnetic phases of the frustrated spin-dimer compound Ba3Mn2O8,

    E. C. Samulon, Y.-J. Jo, P. Sengupta, C. D. Batista, M. Jaime, L. Balicas, and I. R. Fisher, “Ordered magnetic phases of the frustrated spin-dimer compound Ba3Mn2O8,” Phys. Rev. B77, 214441 (2008)

    2008

  52. [52]

    Dilute bose gas in two dimensions,

    Daniel S. Fisher and P. C. Hohenberg, “Dilute bose gas in two dimensions,” Phys. Rev. B37, 4936–4943 (1988)

    1988

  53. [53]

    Bose glass and mott glass of quasiparticles in a doped quantum magnet,

    Rong Yu, Liang Yin, Neil S Sullivan, JS Xia, Chao Huan, Armando Paduan-Filho, Nei F Oliveira Jr, Stephan Haas, Alexander Steppke, Corneliu F Miclea,et al., “Bose glass and mott glass of quasiparticles in a doped quantum magnet,” Nature489, 379–384 (2012)

    2012

  54. [54]

    Emergent symmetry and dimensional reduction at a quantum critical point,

    J. Schmalian and C. D. Batista, “Emergent symmetry and dimensional reduction at a quantum critical point,” Phys. Rev. B77, 094406 (2008)

    2008

  55. [55]

    Dimensional reduction at a quantum critical point,

    SE Sebastian, N Harrison, CD Batista, L Balicas, M Jaime, PA Sharma, N Kawashima, and IR Fisher, “Dimensional reduction at a quantum critical point,” Na- ture441, 617–620 (2006)

    2006

  56. [56]

    Bose–einstein condensation of a two-magnon bound state in a spin-1 triangular lattice,

    Jieming Sheng, Jia-Wei Mei, Le Wang, Xiaoyu Xu, Wen- rui Jiang, Lei Xu, Han Ge, Nan Zhao, Tiantian Li, An- drea Candini,et al., “Bose–einstein condensation of a two-magnon bound state in a spin-1 triangular lattice,” Nature Materials24, 544–551 (2025)

    2025

  57. [57]

    Magnetic exchange parameters and anisotropy of the quasi-two-dimensional antiferromagnet NiPS3,

    D. Lan¸ con, R. A. Ewings, T. Guidi, F. Formisano, and A. R. Wildes, “Magnetic exchange parameters and anisotropy of the quasi-two-dimensional antiferromagnet NiPS3,” Phys. Rev. B98, 134414 (2018)

    2018

  58. [58]

    Kitaev-heisenberg- J2-J3 model for the iridates Li 2IrO3,

    Itamar Kimchi and Yi-Zhuang You, “Kitaev-heisenberg- J2-J3 model for the iridates Li 2IrO3,” Phys. Rev. B84, 180407 (2011)

    2011

  59. [59]

    Phase diagram of the J1 −J 2 −J 3 heisenberg model on the honeycomb lattice: A series expansion study,

    J. Oitmaa and R. R. P. Singh, “Phase diagram of the J1 −J 2 −J 3 heisenberg model on the honeycomb lattice: A series expansion study,” Physical Review B84, 094424 (2011)

    2011

  60. [60]

    Les ondes de spin,

    S. Petit, “Les ondes de spin,” Journ´ ees de la Neutronique 10, 449–463 (2010)

    2010

  61. [61]

    Numerical simulations and magnetism,

    S. Petit, “Numerical simulations and magnetism,” Journ´ ees de la Neutronique12, 105–121 (2011)

    2011

  62. [62]

    Spinwave, a software dedi- cated to spin wave simulations,

    S. Petit and F. Damay, “Spinwave, a software dedi- cated to spin wave simulations,” Neutron News27, 27–28 (2016)

    2016

  63. [63]

    Non-simple magnetic order for simple hamiltonians,

    Enrico Rastelli, Armando Tassi, and Luciano Reatto, “Non-simple magnetic order for simple hamiltonians,” Physica B+ C97, 1–24 (1979)

    1979