Pith. sign in

REVIEW 4 major objections 5 minor 156 references

On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Two honeycomb cobalt oxides long treated as simple zigzag magnets are argued to order in triple-q and double-q spin textures.

desk verdict A useful, honest review of the multi-q case for the cobaltates, but the key Na3Co2SbO6 training result does not actually discriminate between single-q and multi-q. read the letter →

arxiv 2501.14229 v1 pith:JGSTRXCK submitted 2025-01-24 cond-mat.str-el

Yuchen Gu , Xianghong Jin , Yuan Li This is my paper · ORCID
classification cond-mat.str-el
keywords multi-qmagneticorderhoneycombcobaltoxideszigzagNa2Co2TeO6Na3Co2Sbfield-trainingneutrondiffractionringexchangespinvorticity
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

The paper argues that the magnetic ground states of two layered honeycomb cobalt oxides, Na2Co2TeO6 and Na3Co2SbO6, are multi-q variants of zigzag order—triple-q in the first, double-q in the second—rather than the single-q zigzag order assumed in earlier analyses. The main evidence is experimental: field-training neutron diffraction cannot repopulate the orientational domains a single-q state would have, spin-wave spectra show only one magnetic-domain branch, and the crystallographic symmetries make the multi-q reading the natural one. The authors review these observations together with the general mechanisms that stabilize multi-q order in solids. If the claim stands, earlier single-q-based refinements and spin models for these materials are incomplete, and higher-order spin interactions such as ring exchange must be included in the microscopic description.

What carries the argument

The argument is carried by three coupled pieces of machinery. First, the crystallographic symmetry analysis of the magnetic propagation vectors at the $M$-point of the (pseudo)hexagonal Brillouin zone: in these cobaltates the symmetry operations do not leave a single ordering vector invariant, so single-q order would break lattice rotational symmetry while a vector sum of all equivalent components, the multi-q order, preserves it. Second, the field-training experiment, which uses an in-plane magnetic field to try to repopulate single-q orientational domains: a genuine single-q order should respond to the training, while a coherent multi-q order should be insensitive. Third, the inelastic-neutron-scattering magnetic Brillouin zone argument, where a multi-q state's smaller zone predicts a single spin-wave dispersion branch. Higher-order spin interactions (six-spin ring exchange) are the theoretical mechanism proposed to select the multi-q ground state near a hidden SU(2)-symmetric point of the extended Heisenberg-Kitaev-Gamma model.

What would settle it

A controlled uniaxial-stress training experiment on Na2Co2TeO6 would settle the question: if single-q domains exist, changing the stress direction should rebalance the relative intensities of the three magnetic Bragg peaks related by the crystal's threefold rotation, while a triple-q state should stay insensitive; detecting the predicted higher-order harmonic peaks would likewise confirm a coherent superposition rather than random domains.

Watch

Extended reading notes

Core claim

The central claim is that the ordered states of Na2Co2TeO6 and Na3Co2SbO6 should be understood as coherent superpositions of symmetry-equivalent zigzag components, not as single-q zigzag domains: a triple-q state in hexagonal Na2Co2TeO6 and a double-q state in monoclinic Na3Co2SbO6. In these multi-q states the magnetic moment pattern is non-collinear, contains sites with reduced ordered moment, and in the triple-q case carries spin vorticity. The review assembles the supporting evidence: a 10 T in-plane field cannot detwin the presumed single-q domains in Na2Co2TeO6; in Na3Co2SbO6 the diffraction signal at an unfavored wave vector recovers after the field is removed, pointing to a component of a double-q order parameter; inelastic neutron scattering on Na2Co2TeO6 sees only one spin-wave branch, which is consistent with a triple-q magnetic Brillouin zone; and a model with six-spin ring exchange stabilizes the triple-q state near a hidden SU(2)-symmetric point.

Load-bearing premise

The inference to multi-q order assumes that the applied magnetic fields are strong enough to reorient and repopulate single-q orientational domains if they existed; if randomly distributed frozen-in strains pin those domains instead, the same training data would be produced without multi-q order.

Editorial extensions

If this is right

  • Magnetic structure refinements that imposed a single-q zigzag ansatz on Na2Co2TeO6 and Na3Co2SbO6 should be revisited, because the diffraction data are compatible with coherent multi-q order and the fitted moment sizes are not uniform.
  • Microscopic models need to go beyond bilinear Heisenberg-Kitaev interactions; higher-order terms such as six-spin ring exchange are needed to stabilize the observed triple-q ground state.
  • The existence of multi-q order in these insulating oxides extends a phenomenon long studied in itinerant magnets to Mott insulators, where electron hopping still matters.
  • A triple-q ground state with spin canting provides a natural account of the ferrimagnetic net moment observed in Na2Co2TeO6.
  • The intermediate vestigial phase observed in Na2Co2TeO6 before three-dimensional order sets in is naturally explained by ring-exchange models as a Z4 spin-current density wave, not by conventional single-q order.

Reading between the lines

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

  • A direct extension would be to apply the same field-training protocol to other high-symmetry honeycomb magnets, such as BaCo2(AsO4)2 or the monoclinic polymorph of Na2Co2TeO6, and predict training-resistant multi-q order wherever the ordering wave vectors come in symmetry-related sets.
  • If multi-q order is a general feature, then spin-wave fits and exchange-parameter extractions performed under single-q assumptions elsewhere may be systematically biased, not just in these two compounds.
  • The reduced-moment sites predicted by multi-q order give a testable local signature: spin-polarized neutron diffraction or nuclear hyperfine probes should resolve a bimodal distribution of ordered moment magnitudes, whereas a single-q zigzag state has uniform local moments.
  • The symmetry criterion used here—whether the magnetic propagation vector is invariant under lattice rotations—could serve as a screening rule for other candidate spin-liquid materials before detailed Hamiltonians are settled.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper is a mini-review arguing that the magnetic ground states of the honeycomb cobaltates Na2Co2TeO6 and Na3Co2SbO6 are multi-q variants of zigzag order rather than the single-q zigzag states assumed in many previous studies. The review lays out crystallographic symmetry conditions under which single-q M-point order can or cannot have multi-q variants, surveys examples of multi-q order in other materials (skyrmion lattices, SrFeO3, CeRh2Si2, iron pnictides), and then discusses field-training neutron diffraction experiments, inelastic neutron scattering symmetry arguments, and theoretical support from ring-exchange interactions. The central claim is that field-training results in these two cobaltates discriminate multi-q from single-q domain states, implying that microscopic models must include higher-order spin interactions.

Significance. The paper provides a useful and accessible synthesis of experimental strategies for identifying multi-q magnetic order, and it places the cobaltate problem in the broader context of itinerant and insulating magnets. The crystallographic comparison among Na2IrO3, alpha-RuCl3, and the cobaltates is clearly presented, and the authors are careful to note several caveats, including the J3-only degeneracy caveat for the INS argument and the generic possibility that disorder and lattice dynamics account for seemingly novel observations. If the multi-q claim is correct, the standard single-q zigzag interpretation for two prominent Kitaev-candidate materials would need revision, making this a significant claim for the field. However, the principal experimental evidence derives from the authors' own earlier publications, and one of the two key training experiments (Na3Co2SbO6) has a logical gap that weakens the central conclusion.

major comments (4)
  1. [Section 4, Na3Co2SbO6 field-training experiment] Section 4, Na2Co2TeO6 field-training experiment: The review correctly flags the alternative of frozen-in uniaxial strain pinning single-q domains, but the dismissal of this alternative rests on Ref. [121], a Faraday-rotation study from the same group. That study is not independent of the original neutron diffraction experiments, so the pinning scenario remains open. The review would need quantitative arguments, such as the expected strain-induced detwinning magnitude versus the observed insensitivity of the M2 intensity, or training results on multiple crystals, to substantiate the claim that the Na2Co2TeO6 data favor a triple-q ground state.
  2. [Section 4, Na3Co2SbO6 field-training experiment] The argument that recovery of the unfavored M-point peak after removing the training field supports a double-q ground state is not logically secure as written. The text states that the field was strong enough to fully suppress the magnetic order; if the order is destroyed, removing the field allows the system to renucleate from a state with no directional bias, and two degenerate single-q M-domains would naturally repopulate, producing a recovered peak at the unfavored position. This is exactly the expected single-q behavior, not evidence for a double-q order parameter. The review should either provide data or arguments that exclude this renucleation scenario (for example, in-field intensity ratios during controlled field sweeps, or domain statistics that differ from equal repopulation) or explicitly weaken the claim that the recovered signal is necessarily a component of a double-q order.
  3. [Section 4, Na2Co2TeO6 field-training experiment] The review correctly flags the alternative of frozen-in uniaxial strain pinning single-q domains, but the dismissal of this alternative rests on Ref. [121], a Faraday-rotation study from the same group. That study is not independent of the original neutron diffraction experiments, so the pinning scenario remains open. The review would need quantitative arguments, such as the expected strain-induced detwinning magnitude versus the observed insensitivity of the M2 intensity, or training results on multiple crystals, to substantiate the claim that the Na2Co2TeO6 data favor a triple-q ground state.
  4. [Section 6 and Table II] Given the two concerns above, the summary and Table II overstate the present evidence. Table II lists Na2Co2TeO6 and Na3Co2SbO6 in the same category as materials with established multi-q states, while the text itself documents the J3-only degeneracy caveat for the INS argument and the pinning/renucleation alternatives for the training experiments. The review should grade the evidence—e.g., by distinguishing 'proposed' from 'established'—and should state in the summary that the multi-q scenario is strongly suggested but not yet definitively established.
minor comments (5)
  1. [Abstract and Section 1] The phrase 'surveys on experimental strategies' is ungrammatical; 'surveys' should be used with a direct object or 'provides a survey of' would be clearer.
  2. [Section 5] The sentence 'The significance of hopping be indicated by the dimensionless quantity t/U' contains a typo; 'be' should be 'is'.
  3. [Table II] The entries 'N.A.' under the 'Stabilized by' column are not defined; consider replacing them with 'not discussed' or a fuller explanation.
  4. [Section 2 and Table I] The notation for the wave vector of alpha-RuCl3 is given in monoclinic notation, but the table does not make clear how the rhombohedral R3 phase would affect the M-point classification; a brief note would help readers.
  5. [Figure 1 caption] The caption mentions 'first 2D hexagonal Brillouin zone' but the figure itself is adapted from elsewhere; please ensure that the color coding of the three M points is legible in the printed version.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the multi-q claims rest on raw-data experiments and comparative fits, not on equations that reduce to their own inputs.

full rationale

This paper is a review, not a derivation paper. Its central claim that Na2Co2TeO6 and Na3Co2SbO6 host multi-q variants of zigzag order is supported by field-trained neutron diffraction (Refs. 39, 40), inelastic neutron scattering (Ref. 36), and Faraday rotation (Ref. 121) from the present group, together with independent theory (Refs. 136, 137). Under the review rules, cited raw-diffraction and excitation data are independent support because they are externally falsifiable and are not parameters fitted within this review. No equation in the paper is shown to be equivalent to an input by construction, and no fitted quantity is renamed as a prediction. The weakest step is the Na3Co2SbO6 field-training inference: the review argues that recovery of the unfavored peak after the field, which fully suppressed the order, was removed favors double-q, but in a single-q scenario renucleation after field removal would also repopulate both orientational domains. This is a logical or interpretive weakness, not a circularity of the self-definitional or fitted-input kind. The review explicitly flags the structural-pinning alternative for Na2Co2TeO6 ('The only remaining alternative possibility was that there existed unidentified structural pinning effects...') and closes it by citing a same-group Faraday study; that is self-citation, but it is an independent measurement rather than a restatement of the conclusion. The self-citation density is high, but it does not meet the evidentiary bar for load-bearing circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The review introduces no new free parameters or entities. Its arguments rest on standard assumptions about crystallographic symmetry, the semiclassical degeneracy of single-q and multi-q states in bilinear models, and the role of higher-order spin interactions from Hubbard-model expansions. The most fragile assumption is the effectiveness of field training in the absence of strong structural pinning, which the review itself flags.

assumptions (4)
  • domain assumption The crystallographic space groups and magnetic propagation wave vectors in Table I are accurate.
    The symmetry analysis of which materials can host multi-q variants depends on these structural assignments, especially the M-point location relative to the monoclinic C2 axis for Na3Co2SbO6 (Section 2).
  • domain assumption The multi-q variant of the magnetic structure preserves all crystallographic rotational symmetries.
    Used in Section 4 to construct the in-plane spin arrangements in Fig. 4(a) and (d) by summing single-q components related by 120-degree or C2 rotations. If this assumption fails, the illustrated spin textures would not be valid, though multi-q order itself could still exist.
  • domain assumption In models with only bilinear spin interactions, single-q and multi-q orders have degenerate semiclassical energy.
    Stated in Section 3 and used to argue that multi-q order requires higher-order interactions. Cited to Refs 38, 67.
  • domain assumption Higher-order spin interactions (e.g., ring exchange) emerge from the Hubbard model and can stabilize multi-q order.
    Used in Section 5 to connect the multi-q ground state to electron itinerancy. This is a theoretical framework cited from Refs 38, 106, 107, not derived in this review.

how reviews work

0 comments
Cite this review

Pith. "Pith review of On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides." pith.science (2026). https://pith.science/paper/JGSTRXCK

@misc{pith2026250114229,
  author       = {Pith},
  title        = {Pith review of: On the multi-$\mathbfq$ characteristics of magnetic ground states of honeycomb cobalt oxides},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JGSTRXCK}},
  note         = {Machine review of arXiv:2501.14229}
}
abstract

The Kitaev honeycomb model has received significant attention for its exactly solvable quantum spin liquid ground states and fractionalized excitations. For realizing the model, layered cobalt oxides have been considered a promising platform. Yet, in contrast to the conventional wisdom about single-$\mathbf{q}$ zigzag magnetic order inferred from previous studies of the Na$_2$IrO$_3$ and $\alpha$-RuCl$_3$ candidate materials, recent experiments on two of the representative honeycomb cobalt oxides, hexagonal Na$_2$Co$_2$TeO$_6$ and monoclinic Na$_3$Co$_2$SbO$_6$, have uncovered evidence for more complex multi-$\mathbf{q}$ variants of the zigzag order. This review surveys on experimental strategies to distinguish between single- and multi-$\mathbf{q}$ orders, along with the crystallographic symmetries of the cobalt oxides in comparison to the previously studied systems. General formation mechanism of multi-$\mathbf{q}$ order is also briefly discussed. The goal is to provide some rationales for examining the relevance of multi-$\mathbf{q}$ order in the honeycomb cobalt oxides, along with its implications on the microscopic model of these intriguing quantum magnets.

Figures

Figures reproduced from arXiv: 2501.14229 by the authors.

Figure 1
Figure 1. FIG. 1. Magnetic diffraction pattern of different compounds [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Temperature dependence of magnetic intensi [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Temperature dependence of magnetic neutron diffrac [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: The experimental spectra [36] strongly contradict [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Schematic of triple- [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Upper half: Three orientational domains of the zigzag order, along with their corresponding propagating wave vectors [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Phase diagram of the quantum [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

156 extracted references · 70 canonical work pages

  1. [121]

    Burlet, E

    P. Burlet, E. Ressouche, B. Malaman, R. Welter, J. P. Sanchez, and P. Vulliet, Noncollinear magnetic struc- ture of MnTe2, Phys. Rev. B 56, 14013 (1997)

    work page 1997

  2. [1]

    Originating from the idea of the resonating valence bond concept [3], QSL has garnered widespread interest partly due to the suggestion of P

    INTRODUCTION Quantum spin liquid (QSL) is a novel phase of mat- ter in an interacting quantum many-body system [1, 2]. Originating from the idea of the resonating valence bond concept [3], QSL has garnered widespread interest partly due to the suggestion of P. W. Anderson that resonat- ing valence bonds may be the essence of superconduct- ing pairing in t...

  3. [2]

    On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides

    SINGLE-Q ORDER UNDER LA TTICE ROT A TIONAL SYMMETR Y The formation of magnetic order leads to spontaneous symmetry breaking from the paramagnetic phase. Accu- rate information about the crystallographic symmetry is thus crucial for understanding the symmetry of the mag- netic ground state. It is particularly important to ex- arXiv:2501.14229v1 [cond-mat.s...

    work page Pith review arXiv 2025

  4. [3]

    training

    MUL TI-Q ORDER: PREVIOUS EXAMPLES In crystals with sufficiently high rotational symme- try, conventional single-q magnetic order can break the original rotational symmetry when the symmetry oper- ations do not leave the ordering wave vector invariant. In these cases, a natural way to restore the symmetry is to conceptualize a multi-q variant of the magnet...

  5. [4]

    1, the crystallographic symmetries of Na 2Co2TeO6 and Na3Co2SbO6 are compatible with M -point magnetic or- der in either single- or multi- q form

    EVIDENCE FOR MUL TI-Q ORDER IN HONEYCOMB COBAL T OXIDES As discussed in Section 2 and illustrated in Fig. 1, the crystallographic symmetries of Na 2Co2TeO6 and Na3Co2SbO6 are compatible with M -point magnetic or- der in either single- or multi- q form. To tell which of these scenarios is more likely to be correct, single-crystal neutron diffraction experi...

  6. [5]

    blue” domain, but only twice (plus zone corner once) in the “green

    IMPLICA TIONS FOR THEORETICAL MODELS Information about the magnetic ground state imposes strong constraints on microscopic magnetic model con- struction, providing critical insights into the underlying interactions. As discussed in Section. 3, the multi-q order in centrosymmetric itinerant magnets highlights the sig- nificant role of long-range and higher...

  7. [6]

    This can be done either with reciprocal-space methods such as diffraction under ex- ternal fields, with real-space methods such as NMR and STM

    SUMMAR Y & OUTLOOK To summarize, we have reviewed how the possible ex- istence of multi-q order in magnetic materials can be ex- perimentally addressed. This can be done either with reciprocal-space methods such as diffraction under ex- ternal fields, with real-space methods such as NMR and STM. Current experimental evidence for such multi- q magnetic ord...

  8. [7]

    Kitaev, Anyons in an exactly solved model and be- yond, Ann

    A. Kitaev, Anyons in an exactly solved model and be- yond, Ann. Phys. 321, 2 (2006)

    2006

Show all 156 references
  1. [8]

    Broholm, R

    C. Broholm, R. Cava, S. Kivelson, D. Nocera, M. Nor- man, and T. Senthil, Quantum spin liquids, Science367, eaay0668 (2020)

    2020

  2. [9]

    Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    L. Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    2010

  3. [10]

    P. W. Anderson, Resonating valence bonds: A new kind of insulator?, Materials Research Bulletin 8, 153 (1973)

    1973

  4. [11]

    P. W. Anderson, The resonating valence bond state in La 2CuO4 and superconductivity, science 235, 1196 (1987)

    1987

  5. [12]

    Wen, S.-L

    J. Wen, S.-L. Yu, S. Li, W. Yu, and J.-X. Li, Experimen- tal identification of quantum spin liquids, npj Quantum Materials 4, 12 (2019)

    2019

  6. [13]

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

    2017

  7. [14]

    Liu and G

    H. Liu and G. Khaliullin, Pseudospin exchange inter- actions in d7 cobalt compounds: Possible realization of the Kitaev model, Phys. Rev. B 97, 014407 (2018)

    2018

  8. [15]

    Jackeli and G

    G. Jackeli and G. Khaliullin, Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models, Phys. Rev. Lett. 102, 017205 (2009)

    2009

  9. [16]

    Takagi, T

    H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, and S. E. Nagler, Concept and realization of Kitaev quantum spin liquids, Nat. Rev. Phys. 1, 264 (2019)

    2019

  10. [17]

    Motome, R

    Y. Motome, R. Sano, S. Jang, Y. Sugita, and Y. Kato, Materials design of Kitaev spin liquids beyond the Jack- eli–Khaliullin mechanism, Journal of Physics: Con- densed Matter 32, 404001 (2020)

    2020

  11. [18]

    Trebst and C

    S. Trebst and C. Hickey, Kitaev materials, Physics Re- ports 950, 1 (2022)

    2022

  12. [19]

    Chaloupka, G

    J. Chaloupka, G. Jackeli, and G. Khaliullin, Kitaev- Heisenberg Model on a Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides A2IrO3, Phys. Rev. Lett. 105, 027204 (2010)

    2010

  13. [20]

    K. W. Plumb, J. P. Clancy, L. J. Sandilands, V. V. Shankar, Y. F. Hu, K. S. Burch, H.-Y. Kee, and Y.-J. Kim, α−RuCl3: A spin-orbit assisted Mott insulator on a honeycomb lattice, Phys. Rev. B 90, 041112 (2014)

    2014

  14. [21]

    J.-Q. Yan, S. Okamoto, Y. Wu, Q. Zheng, H. D. Zhou, H. B. Cao, and M. A. McGuire, Magnetic order in single crystals of Na3Co2SbO6 with a honeycomb arrangement of 3d7 Co2+ ions, Phys. Rev. Mater. 3, 074405 (2019)

    2019

  15. [22]

    R. Sano, Y. Kato, and Y. Motome, Kitaev-Heisenberg Hamiltonian for high-spin d7 Mott insulators, Phys. Rev. B 97, 014408 (2018)

    2018

  16. [23]

    H. Liu, J. Chaloupka, and G. Khaliullin, Kitaev Spin Liquid in 3 d Transition Metal Compounds, Phys. Rev. Lett. 125, 047201 (2020)

    2020

  17. [24]

    Kim, H.-S

    C. Kim, H.-S. Kim, and J.-G. Park, Spin-orbital entan- gled state and realization of Kitaev physics in 3 d cobalt compounds: a progress report, Journal of Physics: Con- densed Matter 34, 023001 (2021)

    2021

  18. [25]

    Liu, Towards Kitaev spin liquid in 3 d transition metal compounds, Int

    H. Liu, Towards Kitaev spin liquid in 3 d transition metal compounds, Int. J. Mod. Phys. B 35, 2130006 (2021)

    2021

  19. [26]

    Lefran¸ cois, M

    E. Lefran¸ cois, M. Songvilay, J. Robert, G. Nataf, E. Jor- dan, L. Chaix, C. V. Colin, P. Lejay, A. Hadj-Azzem, R. Ballou, and V. Simonet, Magnetic properties of the honeycomb oxide Na 2Co2TeO6, Phys. Rev. B 94, 214416 (2016)

    2016

  20. [27]

    A. K. Bera, S. M. Yusuf, A. Kumar, and C. Ritter, Zigzag antiferromagnetic ground state with anisotropic correlation lengths in the quasi-two-dimensional honey- comb lattice compound Na2Co2TeO6, Phys. Rev. B 95, 094424 (2017)

    2017

  21. [28]

    Rousochatzakis, J

    I. Rousochatzakis, J. Reuther, R. Thomale, S. Rachel, and N. B. Perkins, Phase diagram and quantum order by disorder in the kitaev K1 − K2 honeycomb magnet, Phys. Rev. X 5, 041035 (2015)

    2015

  22. [29]

    Chaloupka, G

    J. Chaloupka, G. Jackeli, and G. Khaliullin, Zigzag Magnetic Order in the Iridium Oxide Na 2IrO3, Phys. Rev. Lett. 110, 097204 (2013)

    2013

  23. [30]

    Kimchi and Y.-Z

    I. Kimchi and Y.-Z. You, Kitaev-Heisenberg- J2-J3 model for the iridates A2IrO3, Phys. Rev. B 84, 180407 (2011)

    2011

  24. [31]

    Sizyuk, C

    Y. Sizyuk, C. Price, P. W¨ olfle, and N. B. Perkins, Impor- tance of anisotropic exchange interactions in honeycomb iridates: Minimal model for zigzag antiferromagnetic or- der in Na 2IrO3, Phys. Rev. B 90, 155126 (2014)

    2014

  25. [32]

    J. G. Rau, E. K.-H. Lee, and H.-Y. Kee, Generic spin model for the honeycomb iridates beyond the kitaev limit, Phys. Rev. Lett. 112, 077204 (2014)

    2014

  26. [33]

    Chaloupka and G

    J. Chaloupka and G. Khaliullin, Magnetic anisotropy in the Kitaev model systems Na 2IrO3 and RuCl 3, Phys. Rev. B 94, 064435 (2016)

    2016

  27. [34]

    S. M. Winter, Y. Li, H. O. Jeschke, and R. Valent ´ ı, Challenges in design of kitaev materials: Magnetic in- teractions from competing energy scales, Phys. Rev. B 93, 214431 (2016)

    2016

  28. [35]

    A. M. Samarakoon, Q. Chen, H. Zhou, and V. O. Gar- lea, Static and dynamic magnetic properties of honey- comb lattice antiferromagnets Na 2M2TeO6, M = Co and Ni, Phys. Rev. B 104, 184415 (2021)

    2021

  29. [36]

    Yadav, N

    R. Yadav, N. A. Bogdanov, V. M. Katukuri, S. Nishi- moto, J. Van Den Brink, and L. Hozoi, Kitaev exchange and field-induced quantum spin-liquid states in honey- comb α-RuCl3, Scientific reports 6, 37925 (2016)

    2016

  30. [37]

    Hickey and S

    C. Hickey and S. Trebst, Emergence of a field-driven U (1) spin liquid in the Kitaev honeycomb model, Nat. Commun. 10, 530 (2019)

    2019

  31. [38]

    H. B. Cao, A. Banerjee, J.-Q. Yan, C. A. Bridges, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, B. C. Chak- oumakos, and S. E. Nagler, Low-temperature crystal and magnetic structure of α − RuCl3, Phys. Rev. B 93, 134423 (2016)

    2016

  32. [39]

    vortices

    and Na 3Co2SbO6 [40]. Here we only focus on the training effects of the fields on the magnetic domains, as have been discussed in the previous Section. In Na 2Co2TeO6, the single- q magnetic structure (or single-q component in a multi-q structure) has been con- strained [19, 2...

  33. [40]

    X. Liu, T. Berlijn, W.-G. Yin, W. Ku, A. Tsvelik, Y.-J. Kim, H. Gretarsson, Y. Singh, P. Gegenwart, and J. P. Hill, Long-range magnetic ordering in Na 2IrO3, Phys. Rev. B 83, 220403 (2011)

    2011

  34. [41]

    F. Ye, S. Chi, H. Cao, B. C. Chakoumakos, J. A. Fernandez-Baca, R. Custelcean, T. F. Qi, O. B. Kor- neta, and G. Cao, Direct evidence of a zigzag spin-chain structure in the honeycomb lattice: A neutron and x- ray diffraction investigation of single-crystal Na 2IrO3, Phys. Rev...

    2012

  35. [42]

    Songvilay, J

    M. Songvilay, J. Robert, S. Petit, J. A. Rodriguez- Rivera, W. D. Ratcliff, F. Damay, V. Bal´ edent, M. Jim´ enez-Ruiz, P. Lejay, E. Pachoud, A. Hadj- Azzem, V. Simonet, and C. Stock, Kitaev interactions in 11 the Co honeycomb antiferromagnets Na 3Co2SbO6 and Na2Co2TeO6, Phys....

    2020

  36. [43]

    W. Chen, X. Li, Z. Hu, Z. Hu, L. Yue, R. Sutarto, F. He, K. Iida, K. Kamazawa, W. Yu, X. Lin, and Y. Li, Spin- orbit phase behavior of Na 2Co2TeO6 at low tempera- tures, Phys. Rev. B 103, L180404 (2021)

    2021

  37. [44]

    C. H. Lee, S. Lee, Y. S. Choi, Z. H. Jang, R. Kalaivanan, R. Sankar, and K.-Y. Choi, Multistage development of anisotropic magnetic correlations in the Co-based hon- eycomb lattice Na2Co2TeO6, Phys. Rev. B 103, 214447 (2021)

    2021

  38. [45]

    W. G. F. Kr¨ uger, W. Chen, X. Jin, Y. Li, and L. Janssen, Triple-q Order in Na 2Co2TeO6 from Prox- imity to Hidden-SU(2)-Symmetric Point, Phys. Rev. Lett. 131, 146702 (2023)

    2023

  39. [46]

    W. Yao, Y. Zhao, Y. Qiu, C. Balz, J. R. Stewart, J. W. Lynn, and Y. Li, Magnetic ground state of the Kitaev Na2Co2TeO6 spin liquid candidate, Phys. Rev. Res. 5, L022045 (2023)

    2023

  40. [47]

    Y. Gu, X. Li, Y. Chen, K. Iida, A. Nakao, K. Mu- nakata, V. O. Garlea, Y. Li, G. Deng, I. A. Zaliznyak, J. M. Tranquada, and Y. Li, In-plane multi-q mag- netic ground state of Na 3Co2SbO6, Phys. Rev. B 109, L060410 (2024)

    2024

  41. [48]

    Z. Hu, Y. Chen, Y. Cui, S. Li, C. Li, X. Xu, Y. Chen, X. Li, Y. Gu, R. Yu, R. Zhou, Y. Li, and W. Yu, Field- induced phase transitions and quantum criticality in the honeycomb antiferromagnet Na3Co2SbO6, Phys. Rev. B 109, 054411 (2024)

    2024

  42. [49]

    V. O. Garlea and C. L. Sarkis, Review of honeycomb- based kitaev materials with zigzag magnetic ordering (2024), arXiv:2410.11083 [cond-mat.str-el]

    2024 arXiv

  43. [50]

    Singh and P

    Y. Singh and P. Gegenwart, Antiferromagnetic Mott in- sulating state in single crystals of the honeycomb lattice material Na2IrO3, Phys. Rev. B 82, 064412 (2010)

    2010

  44. [51]

    S. K. Choi, R. Coldea, A. N. Kolmogorov, T. Lancaster, I. I. Mazin, S. J. Blundell, P. G. Radaelli, Y. Singh, P. Gegenwart, K. R. Choi, S.-W. Cheong, P. J. Baker, C. Stock, and J. Taylor, Spin Waves and Revised Crystal Structure of Honeycomb Iridate Na 2IrO3, Phys. Rev. Lett. ...

    2012

  45. [52]

    R. D. Johnson, S. C. Williams, A. A. Haghighirad, J. Singleton, V. Zapf, P. Manuel, I. I. Mazin, Y. Li, H. O. Jeschke, R. Valent ´ ı, and R. Coldea, Monoclinic crystal structure of α-RuCl3 and the zigzag antiferromagnetic ground state, Phys. Rev. B 92, 235119 (2015)

    2015

  46. [53]

    S. Mu, K. D. Dixit, X. Wang, D. L. Abernathy, H. Cao, S. E. Nagler, J. Yan, P. Lampen-Kelley, D. Mandrus, C. A. Polanco, L. Liang, G. B. Hal´ asz, Y. Cheng, A. Banerjee, and T. Berlijn, Role of the third dimen- sion in searching for Majorana fermions in α−RuCl3 via phonons, Ph...

    2022

  47. [54]

    Zhang, M

    H. Zhang, M. A. McGuire, A. F. May, H.-Y. Chao, Q. Zheng, M. Chi, B. C. Sales, D. G. Mandrus, S. E. Na- gler, H. Miao, F. Ye, and J. Yan, Stacking disorder and thermal transport properties of α−RuCl3, Phys. Rev. Mater. 8, 014402 (2024)

    2024

  48. [55]

    S. Park, S. Do, K.-Y. Choi, D. Jang, T. Jang, J. Schefer, C.-M. Wu, J. S. Gardner, S. Park, J.-H. Park, and S. Ji, Emergence of the Isotropic Kitaev Honeycomb Lattice α−RuCl3 and its magnetic properties, Journal of Physics: Condensed Matter (2024)

    2024

  49. [56]

    S. Kim, E. Horsley, C. Nelson, J. Ruff, and Y.-J. Kim, Re-investigation of Moment Direction in a Kitaev Mate- rial α-RuCl3, (2024), arXiv:2403.04176 [cond-mat.str- el]

    2024 arXiv

  50. [57]

    Regnault, P

    L. Regnault, P. Burlet, and J. Rossat-Mignod, Magnetic ordering in a planar X-Y model: BaCo 2(AsO4)2, Phys- ica B+ C 86, 660 (1977)

    1977

  51. [58]

    Halloran, F

    T. Halloran, F. Desrochers, E. Z. Zhang, T. Chen, L. E. Chern, Z. Xu, B. Winn, M. Graves-Brook, M. B. Stone, A. I. Kolesnikov, Y. Qiu, R. Zhong, R. Cava, Y. B. Kim, and C. Broholm, Geometrical frustration versus Kitaev interactions in BaCo 2(AsO4)2, Proceedings of the Na- tion...

    2023

  52. [59]

    Dufault, F

    E. Dufault, F. Bahrami, A. Streeter, X. Yao, E. Gonza- lez, Q. Zhang, and F. Tafti, Introducing the monoclinic polymorph of the honeycomb magnet Na 2Co2TeO6, Phys. Rev. B 108, 064405 (2023)

    2023

  53. [60]

    Zhong, T

    R. Zhong, T. Gao, N. P. Ong, and R. J. Cava, Weak-field induced nonmagnetic state in a Co-based honeycomb, Science Advances 6, eaay6953 (2020)

    2020

  54. [61]

    Viciu, Q

    L. Viciu, Q. Huang, E. Morosan, H. Zandbergen, N. Greenbaum, T. McQueen, and R. Cava, Structure and basic magnetic properties of the honeycomb lat- tice compounds Na2Co2TeO6 and Na3Co2SbO6, J. Solid State Chem. 180, 1060 (2007)

    2007

  55. [62]

    Regnault, C

    L.-P. Regnault, C. Boullier, and J. Lorenzo, Polarized- neutron investigation of magnetic ordering and spin dy- namics in BaCo 2(AsO4)2 frustrated honeycomb-lattice magnet, Heliyon 4, e00507 (2018)

    2018

  56. [63]

    X. Li, Y. Gu, Y. Chen, V. O. Garlea, K. Iida, K. Ka- mazawa, Y. Li, G. Deng, Q. Xiao, X. Zheng, Z. Ye, Y. Peng, I. A. Zaliznyak, J. M. Tranquada, and Y. Li, Giant Magnetic In-Plane Anisotropy and Competing In- stabilities in Na 3Co2SbO6, Phys. Rev. X 12, 041024 (2022)

    2022

  57. [64]

    I. I. Mazin, H. O. Jeschke, K. Foyevtsova, R. Valent ´ ı, and D. I. Khomskii, Na 2IrO3 as a Molecular Orbital Crystal, Phys. Rev. Lett. 109, 197201 (2012)

    2012

  58. [65]

    Foyevtsova, H

    K. Foyevtsova, H. O. Jeschke, I. I. Mazin, D. I. Khomskii, and R. Valent ´ ı, Ab initio analysis of the tight-binding parameters and magnetic interactions in Na2IrO3, Phys. Rev. B 88, 035107 (2013)

    2013

  59. [66]

    Streltsov, I

    S. Streltsov, I. I. Mazin, and K. Foyevtsova, Localized itinerant electrons and unique magnetic properties of SrRu2O6, Phys. Rev. B 92, 134408 (2015)

    2015

  60. [67]

    Gretarsson, J

    H. Gretarsson, J. P. Clancy, X. Liu, J. P. Hill, E. Bozin, Y. Singh, S. Manni, P. Gegenwart, J. Kim, A. H. Said, D. Casa, T. Gog, M. H. Upton, H.-S. Kim, J. Yu, V. M. Katukuri, L. Hozoi, J. van den Brink, and Y.-J. Kim, Crystal-Field Splitting and Correlation Effect on the Ele...

    2013

  61. [68]

    I. I. Mazin, S. Manni, K. Foyevtsova, H. O. Jeschke, P. Gegenwart, and R. Valent ´ ı, Origin of the insulating state in honeycomb iridates and rhodates, Phys. Rev. B 88, 035115 (2013)

    2013

  62. [69]

    B. H. Kim, T. Shirakawa, and S. Yunoki, From a quasi- molecular band insulator to a relativistic mott insulator in t5 2g systems with a honeycomb lattice structure, Phys. Rev. Lett. 117, 187201 (2016)

    2016

  63. [70]

    B. H. Kim, G. Khaliullin, and B. I. Min, Electronic ex- citations in the edge-shared relativistic Mott insulator: 12 Na2IrO3, Phys. Rev. B 89, 081109 (2014)

    2014

  64. [71]

    Igarashi and T

    J.-I. Igarashi and T. Nagao, Collective excitations in Na2IrO3, Journal of Physics: Condensed Matter 28, 026006 (2015)

    2015

  65. [72]

    Suzuki, H

    H. Suzuki, H. Gretarsson, H. Ishikawa, K. Ueda, Z. Yang, H. Liu, H. Kim, D. Kukusta, A. Yaresko, M. Minola, et al., Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet, Na- ture materials 18, 563 (2019)

    2019

  66. [73]

    B. W. Lebert, S. Kim, B. H. Kim, S. H. Chun, D. Casa, J. Choi, S. Agrestini, K. Zhou, M. Garcia-Fernandez, and Y.-J. Kim, Nonlocal features of the spin-orbit ex- citon in Kitaev materials, Phys. Rev. B 108, 155122 (2023)

    2023

  67. [74]

    S.-S. Diop, G. Jackeli, and L. Savary, Anisotropic ex- change and noncollinear antiferromagnets on a noncen- trosymmetric fcc half-heusler structure, Phys. Rev. B 105, 144431 (2022)

    2022

  68. [75]

    C. L. Henley, Ordering due to disorder in a frus- trated vector antiferromagnet, Phys. Rev. Lett.62, 2056 (1989)

    1989

  69. [76]

    Sheng and C

    Q. Sheng and C. L. Henley, Ordering due to disorder in a triangular heisenberg antiferromagnet with exchange anisotropy, Journal of Physics: Condensed Matter 4, 2937 (1992)

    1992

  70. [77]

    Schick, T

    R. Schick, T. Ziman, and M. E. Zhitomirsky, Quantum versus thermal fluctuations in the fcc antiferromagnet: Alternative routes to order by disorder, Phys. Rev. B 102, 220405 (2020)

    2020

  71. [78]

    C. Liu, R. Yu, and X. Wang, Semiclassical ground-state phase diagram and multi-q phase of a spin-orbit-coupled model on triangular lattice, Phys. Rev. B 94, 174424 (2016)

    2016

  72. [79]

    Seabra, P

    L. Seabra, P. Sindzingre, T. Momoi, and N. Shannon, Novel phases in a square-lattice frustrated ferromagnet : 1 3 -magnetization plateau, helicoidal spin liquid, and vortex crystal, Phys. Rev. B 93, 085132 (2016)

    2016

  73. [80]

    M¨ uhlbauer, B

    S. M¨ uhlbauer, B. Binz, F. Jonietz, C. Pflei- derer, A. Rosch, A. Neubauer, R. Georgii, and P. B¨ oni, Skyrmion lattice in a chi- ral magnet, Science 323, 915 (2009), https://www.science.org/doi/pdf/10.1126/science.1166767

    2009 doi

  74. [81]

    Bogdanov and A

    A. Bogdanov and A. Hubert, Thermodynamically stable magnetic vortex states in magnetic crystals, Journal of Magnetism and Magnetic Materials 138, 255 (1994)

    1994

  75. [82]

    Kanazawa, Y

    N. Kanazawa, Y. Onose, T. Arima, D. Okuyama, K. Ohoyama, S. Wakimoto, K. Kakurai, S. Ishiwata, and Y. Tokura, Large topological hall effect in a short- period helimagnet mnge, Phys. Rev. Lett. 106, 156603 (2011)

    2011

  76. [83]

    Nakatsuji, N

    S. Nakatsuji, N. Kiyohara, and T. Higo, Large anoma- lous hall effect in a non-collinear antiferromagnet at room temperature, Nature 527, 212 (2015)

    2015

  77. [84]

    Takagi, J

    R. Takagi, J. S. White, S. Hayami, R. Arita, D. Ho- necker, H. M. Rønnow, Y. Tokura, and S. Seki, Multiple- q noncollinear magnetism in an itinerant hexagonal magnet, Science Advances 4, eaau3402 (2018)

    2018

  78. [85]

    U. K. Roessler, A. Bogdanov, and C. Pfleiderer, Sponta- neous skyrmion ground states in magnetic metals, Na- ture 442, 797 (2006)

    2006

  79. [86]

    Ishiwata, T

    S. Ishiwata, T. Nakajima, J.-H. Kim, D. S. Inosov, N. Kanazawa, J. S. White, J. L. Gavilano, R. Georgii, K. M. Seemann, G. Brandl, P. Manuel, D. D. Khalyavin, S. Seki, Y. Tokunaga, M. Kinoshita, Y. W. Long, Y. Kaneko, Y. Taguchi, T. Arima, B. Keimer, and Y. Tokura, Emergent to...

    2020

  80. [87]

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

    2024

  81. [88]

    J. M. Allred, K. M. Taddei, D. E. Bugaris, M. J. Krogstad, S. H. Lapidus, D. Y. Chung, H. Claus, M. G. Kanatzidis, D. E. Brown, J. Kang, R. M. Fernandes, I. Eremin, S. Rosenkranz, O. Chmaissem, and R. Os- born, Double-q spin-density wave in iron arsenide su- perconductors, Nat...

  82. [89]

    J. M. Allred, S. Avci, D. Y. Chung, H. Claus, D. D. Khalyavin, P. Manuel, K. M. Taddei, M. G. Kanatzidis, S. Rosenkranz, R. Osborn, and O. Chmaissem, Tetrag- onal magnetic phase in Ba 1−xKxFe2As2 from x-ray and neutron diffraction, Phys. Rev. B 92, 094515 (2015)

    2015

  83. [90]

    K. M. Taddei, J. M. Allred, D. E. Bugaris, S. Lapidus, M. J. Krogstad, R. Stadel, H. Claus, D. Y. Chung, M. G. Kanatzidis, S. Rosenkranz, R. Osborn, and O. Chmais- sem, Detailed magnetic and structural analysis mapping a robust magnetic C4 dome in Sr 1−xNaxFe2As2, Phys. Rev. B...

    2016

  84. [91]

    Kawarazaki, M

    S. Kawarazaki, M. Sato, Y. Miyako, N. Chigusa, K. Watanabe, N. Metoki, Y. Koike, and M. Nishi, Ground-state magnetic structure of CeRh 2Si2 and the response to hydrostatic pressure as studied by neutron diffraction, Phys. Rev. B 61, 4167 (2000)

    2000

  85. [92]

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

    2022

  86. [93]

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

    2023

  87. [94]

    Saito, F

    H. Saito, F. Kon, H. Hidaka, H. Amitsuka, C. Kwanghee, M. Hagihala, T. Kamiyama, S. Itoh, and T. Nakajima, In-plane anisotropy of single- q and multiple-q ordered phases in the antiferromagnetic metal CeRh2Si2, Phys. Rev. B 108, 094440 (2023)

    2023

  88. [95]

    Okubo, T

    T. Okubo, T. H. Nguyen, and H. Kawamura, Cubic and noncubic multiple- q states in the heisenberg anti- ferromagnet on the pyrochlore lattice, Phys. Rev. B 84, 144432 (2011)

    2011

  89. [96]

    Okubo, S

    T. Okubo, S. Chung, and H. Kawamura, Multiple- q states and the skyrmion lattice of the triangular-lattice heisenberg antiferromagnet under magnetic fields, Phys. Rev. Lett. 108, 017206 (2012)

    2012

  90. [97]

    Kamiya and C

    Y. Kamiya and C. D. Batista, Magnetic vortex crystals in frustrated mott insulator, Phys. Rev. X 4, 011023 (2014)

    2014

  91. [98]

    Hayami, S.-Z

    S. Hayami, S.-Z. Lin, and C. D. Batista, Bubble and skyrmion crystals in frustrated magnets with easy-axis anisotropy, Phys. Rev. B 93, 184413 (2016)

    2016

  92. [99]

    Hayami and Y

    S. Hayami and Y. Motome, Effect of magnetic anisotropy on skyrmions with a high topological number 13 in itinerant magnets, Phys. Rev. B 99, 094420 (2019)

    2019

  93. [100]

    Hayami and Y

    S. Hayami and Y. Motome, Noncoplanar multiple- Q spin textures by itinerant frustration: Effects of single- ion anisotropy and bond-dependent anisotropy, Phys. Rev. B 103, 054422 (2021)

    2021

  94. [101]

    Yambe and S

    R. Yambe and S. Hayami, Anisotropic spin model and multiple-q states in cubic systems, Phys. Rev. B 107, 174408 (2023)

    2023

  95. [102]

    R. Yu, M. Yi, B. A. Frandsen, R. J. Birgeneau, and Q. Si, Emergent phases in iron pnictides: Double-Q an- tiferromagnetism, charge order and enhanced nematic correlations 10.48550/arXiv.1706.07087 (2017)

    2017 doi arXiv

  96. [103]

    Hayami, R

    S. Hayami, R. Ozawa, and Y. Motome, Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets, Phys. Rev. B 95, 224424 (2017)

    2017

  97. [104]

    Y.-W. Fang, R. Yang, and H. Chen, The complex non-collinear magnetic orderings in Ba 2YOsO6: a new approach to tuning spin-lattice interactions and con- trolling magnetic orderings in frustrated complex ox- ides, Journal of Physics: Condensed Matter 31, 445803 (2019)

    2019

  98. [105]

    S. Paul, S. Haldar, S. von Malottki, and S. Heinze, Role of higher-order exchange interactions for skyrmion sta- bility, Nature Communications 11, 4756 (2020)

    2020

  99. [106]

    Kato and Y

    Y. Kato and Y. Motome, Magnetic field–temperature phase diagrams for multiple- Q magnetic ordering: Ex- act steepest descent approach to long-range interacting spin systems, Phys. Rev. B 105, 174413 (2022)

    2022

  100. [107]

    Hayami, Checkerboard bubble lattice formed by octuple-period quadruple- Q spin density waves, Phys

    S. Hayami, Checkerboard bubble lattice formed by octuple-period quadruple- Q spin density waves, Phys. Rev. B 108, 094415 (2023)

    2023

  101. [108]

    Hayami and R

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

    2024

  102. [109]

    Pohle, N

    R. Pohle, N. Shannon, and Y. Motome, Spin nematics meet spin liquids: Exotic quantum phases in the spin- 1 bilinear-biquadratic model with Kitaev interactions, Phys. Rev. B 107, L140403 (2023)

    2023

  103. [110]

    Martin and C

    I. Martin and C. D. Batista, Itinerant electron-driven chiral magnetic ordering and spontaneous quantum hall effect in triangular lattice models, Phys. Rev. Lett. 101, 156402 (2008)

    2008

  104. [111]

    Y. Kato, I. Martin, and C. D. Batista, Stability of the spontaneous quantum hall state in the triangular kondo- lattice model, Phys. Rev. Lett. 105, 266405 (2010)

    2010

  105. [112]

    Ozawa, S

    R. Ozawa, S. Hayami, and Y. Motome, Zero-field skyrmions with a high topological number in itinerant magnets, Phys. Rev. Lett. 118, 147205 (2017)

    2017

  106. [113]

    H.-Y. Yang, A. F. Albuquerque, S. Capponi, A. M. L¨ auchli, and K. P. Schmidt, Effective spin couplings in the Mott insulator of the honeycomb lattice Hubbard model, New Journal of Physics 14, 115027 (2012)

    2012

  107. [114]

    Swain, R

    N. Swain, R. Tiwari, and P. Majumdar, Mott-hubbard transition and spin-liquid state on the pyrochlore lat- tice, Phys. Rev. B 94, 155119 (2016)

    2016

  108. [115]

    Kawarazaki, K

    S. Kawarazaki, K. Fujita, K. Yasuda, Y. Sasaki, T. Mizusaki, and A. Hirai, Direct Evidence for Triple- Q Spin-Density Wave in fcc Antiferromagnetic Mn-Ni Alloy, Phys. Rev. Lett. 61, 471 (1988)

    1988

  109. [116]

    E. M. Forgan, B. D. Rainford, S. L. Lee, J. S. Abell, and Y. Bi, The magnetic structure of CeAl 2 is a non-chiral spiral, Journal of Physics: Condensed Matter 2, 10211 (1990)

    1990

  110. [117]

    P. S. Normile, W. G. Stirling, D. Mannix, G. H. Lan- der, F. Wastin, J. Rebizant, F. Boudarot, P. Burlet, B. Lebech, and S. Coburn, (U1−xPux)Sb solid solutions. I. Magnetic configurations, Phys. Rev. B 66, 014405 (2002)

    2002

  111. [118]

    E. M. Forgan, E. P. Gibbons, K. A. McEwen, and D. Fort, Observation of a Quadruple-q Magnetic Struc- ture in Neodymium, Phys. Rev. Lett. 62, 470 (1989)

    1989

  112. [119]

    L. Yue, X. Ren, T. Han, J. Guo, Z. Wu, Y. Zhang, and Y. Li, Raman scattering study of the tetragonal mag- netic phase in Sr 1−xNaxFe2As2: Structural symmetry and electronic gap, Phys. Rev. B 96, 180505 (2017)

    2017

  113. [120]

    Jensen and P

    J. Jensen and P. Bak, Spin waves in triple- → q structures. Application to USb, Phys. Rev. B 23, 6180 (1981)

    1981

  114. [122]

    P. Park, W. Cho, C. Kim, Y. An, Y.-G. Kang, M. Avdeev, R. Sibille, K. Iida, R. Kajimoto, K. H. Lee, et al., Tetrahedral triple-q magnetic ordering and large spontaneous hall conductivity in the metallic tri- angular antiferromagnet Co 1/3TaS2, Nature Communi- cations 14, 8346 (2023)

    2023

  115. [123]

    P. Park, W. Cho, C. Kim, Y. An, K. Iida, R. Kajimoto, S. Matin, S.-S. Zhang, C. D. Batista, and J.-G. Park, Contrasting dynamical properties of single-q and triple- q magnetic orderings in a triangular lattice antiferro- magnet, (2024), arXiv:2410.02180 [cond-mat.str-el]

    2024 arXiv

  116. [124]

    Y. Dong, B. Zhang, Y. Cao, H. Guo, W. Ren, A. Zhang, Z. Li, Z. Wei, H. Liu, L. Tang, H. Pang, F. Li, and Z. Li, Simple yet clear local evidence for the tetrahe- dral triple- Q magnetic ground state in the triangular antiferromagnet Co1/3NbS2, Phys. Rev. B 109, 094401 (2024)

    2024

  117. [125]

    M. N. Gastiasoro, I. Eremin, R. M. Fernandes, and B. M. Andersen, Scanning tunnelling spectroscopy as a probe of multi-Q magnetic states of itinerant magnets, Nature communications 8, 14317 (2017)

    2017

  118. [126]

    Spethmann, S

    J. Spethmann, S. Meyer, K. von Bergmann, R. Wiesen- danger, S. Heinze, and A. Kubetzka, Discovery of Mag- netic Single- and Triple-q States in Mn/Re(0001), Phys. Rev. Lett. 124, 227203 (2020)

    2020

  119. [127]

    Tokunaga, Y

    Y. Tokunaga, Y. Homma, S. Kambe, D. Aoki, H. Sakai, E. Yamamoto, A. Nakamura, Y. Shiokawa, R. E. Walst- edt, and H. Yasuoka, NMR Evidence for Triple- → q Mul- tipole Structure in NpO 2, Phys. Rev. Lett. 94, 137209 (2005)

    2005

  120. [128]

    X. Jin, M. Geng, F. Orlandi, D. Khalyavin, P. Manuel, Y. Liu, and Y. Li, Robust triple-q magnetic order with trainable spin vorticity in Na 2Co2TeO6 (2025), arXiv:2501.07843 [cond-mat.str-el]

    2025

  121. [129]

    Wang and Z.-X

    J. Wang and Z.-X. Liu, Effect of ring-exchange interac- tions in the extended kitaev honeycomb model, Phys. Rev. B 108, 014437 (2023)

    2023

  122. [130]

    Shimokawa, T

    T. Shimokawa, T. Okubo, and H. Kawamura, Multiple-q states of the J1 − J2 classical honeycomb-lattice heisen- berg antiferromagnet under a magnetic field, Phys. Rev. B 100, 224404 (2019)

    2019

  123. [131]

    Yao and Y

    W. Yao and Y. Li, Ferrimagnetism and Anisotropic Phase Tunability by Magnetic Fields in Na 2Co2TeO6, Phys. Rev. B 101, 085120 (2020)

    2020

  124. [132]

    P. Miao, X. Jin, W. Yao, Y. Chen, A. Koda, Z. Tan, W. Xie, W. Ji, T. Kamiyama, and Y. Li, Persistent spin 14 dynamics in magnetically ordered honeycomb-lattice cobalt oxides, Phys. Rev. B 109, 134431 (2024)

    2024

  125. [133]

    W. Yao, K. Iida, K. Kamazawa, and Y. Li, Excitations in the Ordered and Paramagnetic States of Honeycomb Magnet Na 2Co2TeO6, Phys. Rev. Lett. 129, 147202 (2022)

    2022

  126. [134]

    G. Lin, J. Jeong, C. Kim, Y. Wang, Q. Huang, T. Ma- suda, S. Asai, S. Itoh, G. G¨ unther, M. Russina, et al., Field-induced quantum spin disordered state in spin-1/2 honeycomb magnet Na 2Co2TeO6, Nature communica- tions 12, 5559 (2021)

    2021

  127. [135]

    C. Kim, J. Jeong, G. Lin, P. Park, T. Masuda, S. Asai, S. Itoh, H.-S. Kim, H. Zhou, J. Ma, and J.-G. Park, An- tiferromagnetic Kitaev interaction in Jeff = 1/2 cobalt honeycomb materials Na 3Co2SbO6 and Na 2Co2TeO6, Journal of Physics: Condensed Matter 34, 045802 (2021)

    2021

  128. [136]

    Singh, S

    Y. Singh, S. Manni, J. Reuther, T. Berlijn, R. Thomale, W. Ku, S. Trebst, and P. Gegenwart, Relevance of the Heisenberg-Kitaev Model for the Honeycomb Lattice Iridates A2IrO3, Phys. Rev. Lett. 108, 127203 (2012)

    2012

  129. [137]

    Janssen, E

    L. Janssen, E. C. Andrade, and M. Vojta, Honeycomb- Lattice Heisenberg-Kitaev Model in a Magnetic Field: Spin Canting, Metamagnetism, and Vortex Crystals, Phys. Rev. Lett. 117, 277202 (2016)

    2016

  130. [138]

    Chern, Y

    G.-W. Chern, Y. Sizyuk, C. Price, and N. B. Perkins, Kitaev-heisenberg model in a magnetic field: Order- by-disorder and commensurate-incommensurate transi- tions, Phys. Rev. B 95, 144427 (2017)

    2017

  131. [139]

    S. M. Winter, Magnetic couplings in edge-sharing high- spin d7 compounds, Journal of Physics: Materials 5, 045003 (2022)

    2022

  132. [140]

    Wellm, W

    C. Wellm, W. Roscher, J. Zeisner, A. Alfonsov, R. Zhong, R. J. Cava, A. Savoyant, R. Hayn, J. van den Brink, B. B¨ uchner, O. Janson, and V. Kataev, Frustra- tion enhanced by Kitaev exchange in a ˜ jeff = 1 2 triangu- lar antiferromagnet, Phys. Rev. B 104, L100420 (2021)

    2021

  133. [141]

    H. S. Nair, J. M. Brown, E. Coldren, G. Hester, M. P. Gelfand, A. Podlesnyak, Q. Huang, and K. A. Ross, Short-range order in the quantum XXZ honeycomb lat- tice material BaCo 2(PO4)2, Phys. Rev. B 97, 134409 (2018)

    2018

  134. [142]

    P. A. Maksimov, A. V. Ushakov, Z. V. Pchelkina, Y. Li, S. M. Winter, and S. V. Streltsov, Ab initio guided min- imal model for the “Kitaev” material BaCo 2(AsO4)2: Importance of direct hopping, third-neighbor exchange, and quantum fluctuations, Phys. Rev. B 106, 165131 (2022)

    2022

  135. [143]

    Francini and L

    N. Francini and L. Janssen, Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to Na 2Co2TeO6, Phys. Rev. B 109, 075104 (2024)

    2024

  136. [144]

    Francini and L

    N. Francini and L. Janssen, Ferrimagnetism from triple- q order in Na 2Co2TeO6, Phys. Rev. B 110, 235118 (2024)

    2024

  137. [145]

    Merino and A

    J. Merino and A. Ralko, Role of quantum fluctuations on spin liquids and ordered phases in the heisenberg model on the honeycomb lattice, Phys. Rev. B 97, 205112 (2018)

    2018

  138. [146]

    Zhu and S

    Z. Zhu and S. R. White, Quantum phases of the frus- trated xy models on the honeycomb lattice, Modern Physics Letters B 28, 1430016 (2014)

    2014

  139. [147]

    R. F. Bishop, P. H. Y. Li, D. J. J. Farnell, and C. E. Campbell, The frustrated Heisenberg antiferromagnet on the honeycomb lattice: J1 − J2 model, Journal of Physics: Condensed Matter 24, 236002 (2012)

    2012

  140. [148]

    A. Bose, M. Routh, S. Voleti, S. K. Saha, M. Ku- mar, T. Saha-Dasgupta, and A. Paramekanti, Proxi- mate Dirac spin liquid in the honeycomb lattice J1−J3 XXZ model: Numerical study and application to cobal- tates, Phys. Rev. B 108, 174422 (2023)

    2023

  141. [149]

    L. Y. Shi, X. M. Wang, R. D. Zhong, Z. X. Wang, T. C. Hu, S. J. Zhang, Q. M. Liu, T. Dong, F. Wang, and N. L. Wang, Magnetic excitations of the field-induced states in BaCo 2(AsO4)2 probed by time-domain tera- hertz spectroscopy, Phys. Rev. B 104, 144408 (2021)

    2021

  142. [150]

    Zhang, Y

    X. Zhang, Y. Xu, T. Halloran, R. Zhong, C. Bro- holm, R. Cava, N. Drichko, and N. Armitage, A mag- netic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2, Nature Materials 22, 58 (2023)

    2023

  143. [151]

    J. Jiao, X. Li, G. Lin, M. Shu, W. Xu, O. Zaharko, T. Shiroka, T. Hong, A. I. Kolesnikov, G. Deng, et al., Static magnetic order with strong quantum fluctuations in spin-1/2 honeycomb magnet Na 2Co2TeO6, Commu- nications Materials 5, 159 (2024)

    2024

  144. [152]

    Lefran¸ cois, G

    E. Lefran¸ cois, G. Grissonnanche, J. Baglo, P. Lampen- Kelley, J.-Q. Yan, C. Balz, D. Mandrus, S. E. Nagler, S. Kim, Y.-J. Kim, N. Doiron-Leyraud, and L. Taillefer, Evidence of a Phonon Hall Effect in the Kitaev Spin Liquid Candidate α−RuCl3, Phys. Rev. X 12, 021025 (2022)

    2022

  145. [153]

    Lefran¸ cois, J

    E. Lefran¸ cois, J. Baglo, Q. Barth´ elemy, S. Kim, Y.-J. Kim, and L. Taillefer, Oscillations in the magnetother- mal conductivity of α − RuCl3: Evidence of transition anomalies, Phys. Rev. B 107, 064408 (2023)

    2023

  146. [154]

    Sears, Y

    J. Sears, Y. Shen, M. J. Krogstad, H. Miao, J. Yan, S. Kim, W. He, E. S. Bozin, I. K. Robinson, R. Os- born, S. Rosenkranz, Y.-J. Kim, and M. P. M. Dean, Stacking disorder in α−RuCl3 investigated via x-ray three-dimensional difference pair distribution function analysis, Phys....

    2023

  147. [155]

    X. Hong, M. Gillig, W. Yao, L. Janssen, V. Kocsis, S. Gass, Y. Li, A. U. Wolter, B. B¨ uchner, and C. Hess, Phonon thermal transport shaped by strong spin- phonon scattering in a Kitaev material Na 2Co2TeO6, npj Quantum Materials 9, 18 (2024)

    2024

  148. [156]

    Takeda, J

    H. Takeda, J. Mai, M. Akazawa, K. Tamura, J. Yan, K. Moovendaran, K. Raju, R. Sankar, K.-Y. Choi, and M. Yamashita, Planar thermal Hall effects in the Kitaev spin liquid candidate Na 2Co2TeO6, Phys. Rev. Res. 4, L042035 (2022)

    2022

Pith tools

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