pith. sign in

arxiv: 2303.16384 · v1 · submitted 2023-03-29 · ❄️ cond-mat.str-el

Continuous spin excitations in the three-dimensional frustrated magnet K2Ni2(SO4)3

Weiliang Yao , Qing Huang , Tao Xie , Andrey Podlesnyak , Alexander Brassington , Chengkun Xing , Ranuri S. Dissanayaka Mudiyanselage , Weiwei Xie
show 7 more authors
Shengzhi Zhang Minseong Lee Vivien S. Zapf Xiaojian Bai D. Alan Tennant Jian Liu Haidong Zhou
This is my paper

Pith reviewed 2026-05-24 09:39 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords quantum spin liquidinelastic neutron scatteringfrustrated magnethyper-trillium latticecontinuous spin excitationsK2Ni2(SO4)3corner-sharing tetrahedraspin-1 magnets
0
0 comments X

The pith

Inelastic neutron scattering on K2Ni2(SO4)3 reveals a dominant continuous spin excitation continuum rooted in quantum fluctuations on a hyper-trillium lattice.

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

The paper establishes that K2Ni2(SO4)3, built from two intersected spin-1 Ni2+ trillium lattices, shows a dominant excitation continuum in inelastic neutron scattering on single crystals. This continuum displays a temperature dependence distinct from spin waves and arises from strong quantum spin fluctuations, supplying evidence for quantum spin liquid features. Using the self-consistent Gaussian approximation, the authors identify the dominant fourth- and fifth-nearest neighbor exchanges, which together create a three-dimensional network of corner-sharing tetrahedra they name the hyper-trillium lattice. A sympathetic reader would care because the result points to a concrete three-dimensional structure that can sustain frustrated quantum magnetism.

Core claim

Our inelastic neutron scattering measurement on single crystals clearly shows a dominant excitation continuum, which exhibits a distinct temperature-dependent behavior from that of spin waves, and is rooted in strong quantum spin fluctuations. Further using the self-consistent-gaussian-approximation method, we determined the fourth- and fifth-nearest neighbor exchange interactions are dominant. These two bonds together form a unique three-dimensional network of corner-sharing tetrahedra, which we name as 'hyper-trillium' lattice. Our results provide direct evidence for the existence of QSL features in K2Ni2(SO4)3 and highlight the potential for the hyper-trillium lattice to host frustrated量子

What carries the argument

The hyper-trillium lattice, a three-dimensional network of corner-sharing tetrahedra formed by the dominant fourth- and fifth-nearest neighbor exchange interactions on the intersected trillium lattices of spin-1 Ni2+ ions.

If this is right

  • The material K2Ni2(SO4)3 exhibits quantum spin liquid features in three dimensions.
  • The hyper-trillium lattice supplies a new platform for realizing frustrated quantum magnetism.
  • Continuous excitations with distinct temperature dependence serve as a signature distinguishing quantum fluctuations from spin waves.
  • Longer-range exchanges can dominate the physics of trillium-based magnets and must be included in models.

Where Pith is reading between the lines

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

  • The same combination of neutron scattering and self-consistent Gaussian approximation could be applied to other three-dimensional frustrated magnets to identify similar lattices.
  • Theoretical studies of the hyper-trillium lattice may reveal additional dynamical signatures testable by future scattering experiments.
  • If the lattice geometry proves robust, related compounds could be synthesized to tune the relative strength of the fourth- and fifth-neighbor bonds.

Load-bearing premise

The self-consistent Gaussian approximation accurately identifies the fourth- and fifth-nearest neighbor exchanges as dominant and attributes the observed continuum specifically to quantum spin fluctuations rather than disorder or classical effects.

What would settle it

A direct measurement of the exchange constants by another technique such as high-field ESR or a calculation reproducing the continuum with a model lacking dominant fourth- and fifth-neighbor bonds would falsify the claim.

Figures

Figures reproduced from arXiv: 2303.16384 by Alexander Brassington, Andrey Podlesnyak, Chengkun Xing, D. Alan Tennant, Haidong Zhou, Jian Liu, Minseong Lee, Qing Huang, Ranuri S. Dissanayaka Mudiyanselage, Shengzhi Zhang, Tao Xie, Vivien S. Zapf, Weiliang Yao, Weiwei Xie, Xiaojian Bai.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of temperature-dependent behaviors for [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (d) and (e) show elastic magnetic scattering maps of the (H, H, L) and (H, 0, L) planes at 0.1 K. We can identify magnetic Bragg peaks at positions that are indexed by (1/3, 0, 0), (1/3, 1/3, 0), and (1/3, 1/3, 1/3), which is consistent with the previous report based on the powder sample [28]. Additionally, we also find intensity at Brillouin zone centers [e.g., at (1, 0, 0)], which might be caused by magn… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a)-(c) Constant energy slices of the ( [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Energy-integrated intensity map (from 0.15 meV [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
read the original abstract

Continuous spin excitations are widely recognized as one of the hallmarks of novel spin states in quantum magnets, such as quantum spin liquids (QSLs). Here, we report the observation of such kind of excitations in K2Ni2(SO4)3, which consists of two sets of intersected spin-1 Ni2+ trillium lattices. Our inelastic neutron scattering measurement on single crystals clearly shows a dominant excitation continuum, which exhibits a distinct temperature-dependent behavior from that of spin waves, and is rooted in strong quantum spin fluctuations. Further using the self-consistent-gaussian-approximation method, we determined the fourth- and fifth-nearest neighbor exchange interactions are dominant. These two bonds together form a unique three-dimensional network of corner-sharing tetrahedra, which we name as ''hyper-trillium'' lattice. Our results provide direct evidence for the existence of QSL features in K2Ni2(SO4)3 and highlight the potential for the hyper-trillium lattice to host frustrated quantum magnetism.

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

3 major / 2 minor

Summary. The manuscript reports inelastic neutron scattering measurements on single crystals of K2Ni2(SO4)3, which contains two interpenetrating trillium lattices of S=1 Ni2+ ions. The data reveal a dominant excitation continuum whose temperature dependence differs from conventional spin-wave behavior and is interpreted as arising from strong quantum spin fluctuations. Using the self-consistent Gaussian approximation (SCGA), the authors extract dominant fourth- and fifth-nearest-neighbor exchange couplings; these bonds define a new three-dimensional network of corner-sharing tetrahedra termed the 'hyper-trillium' lattice, which they propose hosts quantum spin liquid features.

Significance. If the SCGA-based identification of J4/J5 dominance and the quantum-fluctuation origin of the continuum are robust, the work would establish a new frustrated 3D lattice geometry for S=1 magnets and provide experimental support for QSL-like excitations in a material with accessible single crystals. The neutron data themselves add a concrete example of a continuum in a 3D frustrated system.

major comments (3)
  1. [SCGA modeling and exchange extraction] The central claim that J4 and J5 are the dominant exchanges (and therefore define the hyper-trillium lattice) rests on an SCGA fit performed directly to the measured continuum. The manuscript must supply the fitting protocol, chi-squared surface, parameter uncertainties, and explicit tests showing that other exchange combinations cannot reproduce the data at comparable quality; without these, the uniqueness of the J4/J5 solution and the resulting lattice identification remain unestablished.
  2. [Discussion of temperature dependence and fluctuation origin] SCGA is a classical/mean-field approximation whose accuracy for S=1 spins on the hyper-trillium geometry is not benchmarked in the paper against exact diagonalization, series expansion, or quantum Monte Carlo. A quantitative comparison of the SCGA-predicted continuum lineshape and temperature evolution against the data (and against alternative classical or disordered models) is required to support the assertion that the continuum originates specifically from quantum spin fluctuations.
  3. [Inelastic neutron scattering results] The temperature dependence is stated to be 'distinct from that of spin waves,' yet no direct overlay or statistical comparison is shown between the observed intensity versus temperature and either SCGA predictions or disorder-broadened classical spin-wave calculations. This comparison is load-bearing for ruling out non-QSL explanations.
minor comments (2)
  1. [Abstract] The abstract introduces the term 'hyper-trillium' lattice without a concise geometric definition or a figure reference; a short sentence or inset panel clarifying the connectivity relative to the conventional trillium lattice would improve readability.
  2. [Introduction or methods] Notation for the exchange parameters (J4, J5) should be defined explicitly at first use, together with a table or diagram of all considered neighbor shells.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address each major comment below and indicate the revisions that will be incorporated.

read point-by-point responses

  1. Referee: [SCGA modeling and exchange extraction] The central claim that J4 and J5 are the dominant exchanges (and therefore define the hyper-trillium lattice) rests on an SCGA fit performed directly to the measured continuum. The manuscript must supply the fitting protocol, chi-squared surface, parameter uncertainties, and explicit tests showing that other exchange combinations cannot reproduce the data at comparable quality; without these, the uniqueness of the J4/J5 solution and the resulting lattice identification remain unestablished.

    Authors: We agree that the details of the SCGA fitting procedure are required to substantiate the uniqueness of the J4/J5 solution. In the revised manuscript we will add the fitting protocol, the chi-squared surface over the relevant parameter space, the estimated uncertainties on the extracted exchanges, and explicit comparisons demonstrating that alternative exchange combinations yield substantially poorer agreement with the measured continuum. revision: yes

  2. Referee: [Discussion of temperature dependence and fluctuation origin] SCGA is a classical/mean-field approximation whose accuracy for S=1 spins on the hyper-trillium geometry is not benchmarked in the paper against exact diagonalization, series expansion, or quantum Monte Carlo. A quantitative comparison of the SCGA-predicted continuum lineshape and temperature evolution against the data (and against alternative classical or disordered models) is required to support the assertion that the continuum originates specifically from quantum spin fluctuations.

    Authors: We acknowledge that SCGA is an approximation whose accuracy has not been benchmarked against exact methods for this specific lattice. Full quantum Monte Carlo or exact diagonalization on the S=1 hyper-trillium lattice is currently intractable because of the large unit cell and strong frustration. In the revision we will expand the discussion of SCGA applicability with supporting references from the literature and will add quantitative overlays of the SCGA-predicted lineshape and temperature evolution directly compared to the experimental data and to classical spin-wave calculations. revision: partial

  3. Referee: [Inelastic neutron scattering results] The temperature dependence is stated to be 'distinct from that of spin waves,' yet no direct overlay or statistical comparison is shown between the observed intensity versus temperature and either SCGA predictions or disorder-broadened classical spin-wave calculations. This comparison is load-bearing for ruling out non-QSL explanations.

    Authors: We will revise the manuscript to include direct overlays of the measured temperature-dependent intensity with both the SCGA predictions and classical spin-wave calculations. Statistical measures of agreement (e.g., chi-squared values) will be added to quantify the distinction from conventional spin-wave behavior. revision: yes

standing simulated objections not resolved
  • Full benchmarking of the SCGA against exact diagonalization, series expansion, or quantum Monte Carlo specifically for the S=1 hyper-trillium lattice, as such calculations remain computationally prohibitive.

Circularity Check

0 steps flagged

Derivation chain is self-contained with no circular steps

full rationale

The paper reports INS data on a continuum with distinct temperature dependence, attributes it to quantum fluctuations, applies SCGA fitting to extract dominant J4/J5 exchanges, names the resulting bond network 'hyper-trillium', and interprets this as evidence for QSL features. No step reduces a claimed prediction or result to its own inputs by construction, self-definition, or load-bearing self-citation; parameter extraction via model fitting to data is standard analysis, the lattice naming is descriptive, and the central experimental observations stand independently of the modeling interpretation. No uniqueness theorems or ansatzes imported via self-citation are present.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on fitted exchange parameters extracted via an approximate method and on the standard assumption that the spin Hamiltonian is Heisenberg-like; the hyper-trillium lattice is a descriptive construct rather than an independently verified entity.

free parameters (1)
  • fourth- and fifth-nearest-neighbor exchange interactions
    Determined by fitting the self-consistent Gaussian approximation to the inelastic neutron scattering data.
axioms (1)
  • domain assumption Magnetic excitations are described by a Heisenberg spin Hamiltonian on the trillium lattice
    Invoked when mapping the observed continuum to specific exchange paths.
invented entities (1)
  • hyper-trillium lattice no independent evidence
    purpose: Descriptive name for the corner-sharing tetrahedra network formed by the dominant bonds
    Introduced to organize the geometry; no independent falsifiable prediction is supplied beyond the fit.

pith-pipeline@v0.9.0 · 5775 in / 1511 out tokens · 39888 ms · 2026-05-24T09:39:35.373600+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages

  1. [1]

    Bloch, Zeitschrift f¨ ur Physik61, 206 (1930)

    F. Bloch, Zeitschrift f¨ ur Physik61, 206 (1930)

    work page 1930

  2. [2]

    Balents, Nature 464, 199 (2010)

    L. Balents, Nature 464, 199 (2010)

    work page 2010

  3. [3]

    Wen, S.-L

    J. Wen, S.-L. Yu, S. Li, W. Yu, and J.-X. Li, npj Quan- tum Materials 4, 1 (2019)

    work page 2019

  4. [4]

    Wulferding, Y

    D. Wulferding, Y. Choi, W. Lee, and K.-Y. Choi, Journal of Physics: Condensed Matter 32, 043001 (2019)

    work page 2019

  5. [5]

    Knolle and R

    J. Knolle and R. Moessner, Annual Review of Condensed Matter Physics 10, 451 (2019)

    work page 2019

  6. [6]

    B. Gao, T. Chen, D. W. Tam, C.-L. Huang, K. Sasmal, D. T. Adroja, F. Ye, H. Cao, G. Sala, M. B. Stone, et al., Nature Physics 15, 1052 (2019)

    work page 2019

  7. [7]

    Gaudet, E

    J. Gaudet, E. M. Smith, J. Dudemaine, J. Beare, C. R. C. Buhariwalla, N. P. Butch, M. B. Stone, A. I. Kolesnikov, G. Xu, D. R. Yahne, K. A. Ross, C. A. Marjerrison, J. D. Garrett, G. M. Luke, A. D. Bianchi, and B. D. Gaulin, Phys. Rev. Lett. 122, 187201 (2019)

    work page 2019

  8. [8]

    E. M. Smith, O. Benton, D. R. Yahne, B. Placke, R. Sch¨ afer, J. Gaudet, J. Dudemaine, A. Fitterman, J. Beare, A. R. Wildes, S. Bhattacharya, T. DeLazzer, C. R. C. Buhariwalla, N. P. Butch, R. Movshovich, J. D. Garrett, C. A. Marjerrison, J. P. Clancy, E. Kermarrec, G. M. Luke, A. D. Bianchi, K. A. Ross, and B. D. Gaulin, Phys. Rev. X 12, 021015 (2022)

    work page 2022

  9. [9]

    B. Gao, T. Chen, H. Yan, C. Duan, C.-L. Huang, X. P. Yao, F. Ye, C. Balz, J. R. Stewart, K. Naka- jima, S. Ohira-Kawamura, G. Xu, X. Xu, S.-W. Cheong, E. Morosan, A. H. Nevidomskyy, G. Chen, and P. Dai, Phys. Rev. B 106, 094425 (2022)

    work page 2022

  10. [10]

    J. W. Krizan and R. J. Cava, Phys. Rev. B 92, 014406 (2015)

    work page 2015

  11. [11]

    Plumb, H

    K. Plumb, H. J. Changlani, A. Scheie, S. Zhang, J. Krizan, J. Rodriguez-Rivera, Y. Qiu, B. Winn, R. Cava, and C. L. Broholm, Nature Physics 15, 54 (2019)

    work page 2019

  12. [12]

    Savary and L

    L. Savary and L. Balents, Reports on Progress in Physics 80, 016502 (2016)

    work page 2016

  13. [13]

    Zunger and O

    A. Zunger and O. I. Malyi, Chemical Reviews 121, 3031 (2021)

    work page 2021

  14. [14]

    Z. Ma, K. Ran, J. Wang, S. Bao, Z. Cai, S. Li, and J. Wen, Chinese Physics B 27, 106101 (2018)

    work page 2018

  15. [15]

    Biesner and E

    T. Biesner and E. Uykur, Crystals 10 (2020)

    work page 2020

  16. [16]

    Banerjee, C

    A. Banerjee, C. Bridges, J.-Q. Yan, A. Aczel, L. Li, M. Stone, G. Granroth, M. Lumsden, Y. Yiu, J. Knolle, et al. , Nature materials 15, 733 (2016)

    work page 2016

  17. [17]

    Banerjee, J

    A. Banerjee, J. Yan, J. Knolle, C. A. Bridges, M. B. Stone, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, R. Moessner, and S. E. Nagler, Science 356, 1055 (2017)

    work page 2017

  18. [18]

    Do, S.-Y

    S.-H. Do, S.-Y. Park, J. Yoshitake, J. Nasu, Y. Motome, Y. S. Kwon, D. Adroja, D. Voneshen, K. Kim, T.-H. Jang, J.-H. Park, K.-Y. Choi, and S. Ji, Nature Physics 13, 1079 (2017)

    work page 2017

  19. [19]

    Banerjee, P

    A. Banerjee, P. Lampen-Kelley, J. Knolle, C. Balz, A. A. Aczel, B. Winn, Y. Liu, D. Pajerowski, J. Yan, C. A. Bridges, A. T. Savici, B. C. Chakoumakos, M. D. Lums- den, D. A. Tennant, R. Moessner, D. G. Mandrus, and S. E. Nagler, npj Quantum Materials 3, 8 (2018)

    work page 2018

  20. [20]

    Han, S.-H

    J.-H. Han, S.-H. Do, K.-Y. Choi, S.-Y. Park, J.-Y. Kim, S. Ji, K.-S. Kim, and J.-H. Park, arXiv preprint arXiv:2203.13407 (2022)

    work page arXiv 2022

  21. [21]

    L. J. Sandilands, Y. Tian, K. W. Plumb, Y.-J. Kim, and K. S. Burch, Phys. Rev. Lett. 114, 147201 (2015)

    work page 2015

  22. [22]

    Wulferding, Y

    D. Wulferding, Y. Choi, S.-H. Do, C. H. Lee, P. Lem- mens, C. Faugeras, Y. Gallais, and K.-Y. Choi, Nature Communications 11, 1 (2020)

    work page 2020

  23. [23]

    Little, L

    A. Little, L. Wu, P. Lampen-Kelley, A. Banerjee, S. Patankar, D. Rees, C. A. Bridges, J.-Q. Yan, D. Man- drus, S. E. Nagler, and J. Orenstein, Phys. Rev. Lett. 119, 227201 (2017)

    work page 2017

  24. [24]

    J. A. Sears, Y. Zhao, Z. Xu, J. W. Lynn, and Y.-J. Kim, Phys. Rev. B 95, 180411 (2017)

    work page 2017

  25. [25]

    Baek, S.-H

    S.-H. Baek, S.-H. Do, K.-Y. Choi, Y. S. Kwon, A. U. B. Wolter, S. Nishimoto, J. van den Brink, and B. B¨ uchner, Phys. Rev. Lett. 119, 037201 (2017)

    work page 2017

  26. [26]

    C. Balz, P. Lampen-Kelley, A. Banerjee, J. Yan, Z. Lu, 6 X. Hu, S. M. Yadav, Y. Takano, Y. Liu, D. A. Tennant, M. D. Lumsden, D. Mandrus, and S. E. Nagler, Phys. Rev. B 100, 060405 (2019)

    work page 2019

  27. [27]

    Momma and F

    K. Momma and F. Izumi, Journal of Applied Crystallog- raphy 44, 1272 (2011)

    work page 2011

  28. [28]

    ˇZivkovi´ c, V

    I. ˇZivkovi´ c, V. Favre, C. Salazar Mejia, H. O. Jeschke, A. Magrez, B. Dabholkar, V. Noculak, R. S. Freitas, M. Jeong, N. G. Hegde, L. Testa, P. Babkevich, Y. Su, P. Manuel, H. Luetkens, C. Baines, P. J. Baker, J. Wos- nitza, O. Zaharko, Y. Iqbal, J. Reuther, and H. M. Rønnow, Phys. Rev. Lett. 127, 157204 (2021)

    work page 2021

  29. [29]

    Speer and E

    D. Speer and E. Salje, Physics and Chemistry of Minerals 13, 17 (1986)

    work page 1986

  30. [30]

    See Supplemental Material for additional data and anal- yses

    work page

  31. [31]

    Ehlers, A

    G. Ehlers, A. A. Podlesnyak, J. L. Niedziela, E. B. Iver- son, and P. E. Sokol, Review of Scientific Instruments82, 085108 (2011)

    work page 2011

  32. [32]

    Ewings, A

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

    work page 2016

  33. [33]

    G. J. MacDougall, D. Gout, J. L. Zarestky, G. Ehlers, A. Podlesnyak, M. A. McGuire, D. Mandrus, and S. E. Nagler, Proceedings of the National Academy of Sciences 108, 15693 (2011)

    work page 2011

  34. [34]

    Young, A

    O. Young, A. R. Wildes, P. Manuel, B. Ouladdiaf, D. D. Khalyavin, G. Balakrishnan, and O. A. Petrenko, Phys. Rev. B 88, 024411 (2013)

    work page 2013

  35. [35]

    J. W. Lynn, Phys. Rev. B 11, 2624 (1975)

    work page 1975

  36. [36]

    J. W. Lynn and H. A. Mook, Phys. Rev. B23, 198 (1981)

    work page 1981

  37. [37]

    G. Xu, C. Broholm, Y.-A. Soh, G. Aeppli, J. F. DiTusa, Y. Chen, M. Kenzelmann, C. D. Frost, T. Ito, K. Oka, and H. Takagi, Science 317, 1049 (2007)

    work page 2007

  38. [38]

    Clark, G

    L. Clark, G. Sala, D. D. Maharaj, M. B. Stone, K. S. Knight, M. T. Telling, X. Wang, X. Xu, J. Kim, Y. Li, S.-W. Cheong, and B. D. Gaulin, Nature Physics 15, 262 (2019)

    work page 2019

  39. [39]

    P. H. Conlon and J. T. Chalker, Phys. Rev. B 81, 224413 (2010)

    work page 2010

  40. [40]

    Benton and N

    O. Benton and N. Shannon, Journal of the Physical So- ciety of Japan 84, 104710 (2015)

    work page 2015

  41. [41]

    X. Bai, J. A. M. Paddison, E. Kapit, S. M. Koohpayeh, J.-J. Wen, S. E. Dutton, A. T. Savici, A. I. Kolesnikov, G. E. Granroth, C. L. Broholm, J. T. Chalker, and M. Mourigal, Phys. Rev. Lett. 122, 097201 (2019)

    work page 2019

  42. [42]

    J. A. M. Paddison, Phys. Rev. Lett. 125, 247202 (2020)

    work page 2020

  43. [43]

    Y. Gu, Q. Wang, H. Wo, Z. He, H. C. Walker, J. T. Park, M. Enderle, A. D. Christianson, W. Wang, and J. Zhao, Phys. Rev. B 106, L060504 (2022)

    work page 2022

  44. [44]

    S. Gao, M. A. McGuire, Y. Liu, D. L. Abernathy, C. d. Cruz, M. Frontzek, M. B. Stone, and A. D. Christianson, Phys. Rev. Lett. 128, 227201 (2022)

    work page 2022

  45. [45]

    J. N. Reimers, A. J. Berlinsky, and A.-C. Shi, Phys. Rev. B 43, 865 (1991)

    work page 1991

  46. [46]

    J. S. Gardner, M. J. P. Gingras, and J. E. Greedan, Rev. Mod. Phys. 82, 53 (2010)

    work page 2010

  47. [47]

    J. M. Hopkinson and H.-Y. Kee, Phys. Rev. B 74, 224441 (2006)

    work page 2006

  48. [48]

    J. M. Hopkinson and H.-Y. Kee, Phys. Rev. B 75, 064430 (2007)

    work page 2007

  49. [49]

    S. V. Isakov, J. M. Hopkinson, and H.-Y. Kee, Phys. Rev. B 78, 014404 (2008)

    work page 2008

  50. [50]

    J. M. Bulled, J. A. M. Paddison, A. Wildes, E. Lhotel, S. J. Cassidy, B. Pato-Dold´ an, L. C. G´ omez-Aguirre, P. J. Saines, and A. L. Goodwin, Phys. Rev. Lett.128, 177201 (2022)

    work page 2022

  51. [51]

    Gattow and J

    G. Gattow and J. Zemann, Zeitschrift f¨ ur anorganische und allgemeine Chemie 293, 233 (1958)

    work page 1958

  52. [52]

    McMurdie, M

    H. McMurdie, M. Morris, J. DeGroot, and H. Swanson, Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry 75, 435 (1971)

    work page 1971

  53. [53]

    L. S. Wu, W. J. Gannon, I. A. Zaliznyak, A. M. Tsvelik, M. Brockmann, J.-S. Caux, M. S. Kim, Y. Qiu, J. R. D. Copley, G. Ehlers, A. Podlesnyak, and M. C. Aronson, Science 352, 1206 (2016)

    work page 2016

  54. [54]

    G. G. Marcus, D.-J. Kim, J. A. Tutmaher, J. A. Rodriguez-Rivera, J. O. Birk, C. Niedermeyer, H. Lee, Z. Fisk, and C. L. Broholm, Phys. Rev. Lett.120, 097201 (2018)

    work page 2018

  55. [55]

    Y. Luo, G. G. Marcus, B. A. Trump, J. Kindervater, M. B. Stone, J. A. Rodriguez-Rivera, Y. Qiu, T. M. Mc- Queen, O. Tchernyshyov, and C. Broholm, Phys. Rev. B 101, 144411 (2020)

    work page 2020

  56. [56]

    Shirane, S

    G. Shirane, S. M. Shapiro, and J. M. Tranquada, Neu- tron scattering with a triple-axis spectrometer: basic tech- niques (Cambridge University Press, 2002)

    work page 2002

  57. [57]

    Continuous spin excitations in the three-dimensional frustrated magnet K 2Ni2(SO4)3

    S. Toth and B. Lake, Journal of Physics: Condensed Mat- ter 27, 166002 (2015). 1 Supplemental Material for “Continuous spin excitations in the three-dimensional frustrated magnet K 2Ni2(SO4)3” I. K 2NI2(SO4)3 SINGLE CRYSTALS AND CHARACTERIZATIONS A. Single crystal growth method K2Ni2(SO4)3 single crystals were prepared with a self-flux method. We first prep...

    work page 2015