Pith. sign in

REVIEW 3 major objections 5 minor 3 cited by

The Saga of $\alpha$-RuCl$_3$: Parameters, Models, and Phase Diagrams

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Three measured quantities pin down the exchange model of $\alpha$-RuCl$_3$.

desk verdict A strong, valuable paper with a genuinely useful staged strategy and beautiful DMRG work on the IC phases, but the quoted parameter bounds are softer than claimed because the DMRG checks show quantum corrections varying across the region. read the letter →

arxiv 2502.08698 v4 pith:5EZMVM3W submitted 2025-02-12 cond-mat.str-el

Marius Möller , P. A. Maksimov , Shengtao Jiang , Steven R. White , Roser Valenti , A. L. Chernyshev This is my paper · ORCID
classification cond-mat.str-el
keywords $\alpha$-RuCl$_3$Kitaevspinliquidanisotropic-exchangemagnethoneycomblatticegeneralizedKitaev-Heisenbergmodelzigzagorderincommensuratespiraldensity-matrixrenormalizationgroup
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the long-disputed low-energy spin model of $\alpha$-RuCl$_3$ can be pinned down by combining three measured observables that exist only because of spin-orbit-induced anisotropic exchange: the out-of-plane tilt of the ordered moments in the zigzag state, the high-field shift of the lowest spin-flip excitation, and the small difference between the two in-plane critical fields. Together these nearly orthogonal constraints put the Kitaev coupling $K$ between $-10$ and $-4.4$ meV, the off-diagonal exchange $\Gamma$ between $3.2$ and $5.0$ meV, and $\Gamma'$ between $1.8$ and $2.85$ meV, with $\Gamma+2\Gamma'$ between $7.5$ and $10$ meV. Read in a crystallographic parametrization, the resulting model is a strongly easy-plane ferromagnet with dominant $J_1$ and a sizable bond-dependent $J_{z\pm}$ term, placing $\alpha$-RuCl$_3$ far from the pure Kitaev limit. A representative complete parameter set reproduces the measured critical fields and magnetization curve in density-matrix renormalization group calculations. The paper's broader claim is that the same staged strategy can settle effective models of other anisotropic-exchange magnets.

What carries the argument

The load-bearing device is a chain of three nearly orthogonal phenomenological constraints, each tied to a quasiclassical formula for an observable that vanishes if the anisotropic exchanges vanish: the zigzag tilt angle $\tan 2\alpha = 4\sqrt{2}(\Gamma-K-\Gamma')/(7\Gamma+2K+2\Gamma')$; the ESR gap $\Delta E_g=3S(\Gamma+2\Gamma')=-3S J_1(1-\Delta)$; and the critical-field difference $\Delta H_c$ from the quasiclassical expressions for the two in-plane transition fields, which depend only on $\{K,\Gamma,\Gamma'\}$. These formulas convert experimental ranges ($\alpha\in[30^\circ,37^\circ]$, $\Gamma+2\Gamma'\in[7.5,10]$ meV, $\Delta H_c\in[0,1.5]$ T) into a compact region in parameter space. The other half of the machinery is the transformation from the cubic-axis $K$-$J$-$\Gamma$-$\Gamma'$ language to the crystallographic $XXZ$-$J_{\pm\pm}$-$J_{z\pm}$ language, which exposes the easy-plane ferromagnetic hierarchy and makes the constraints intuitive. Numerical phase diagrams from Luttinger-Tisza, exact diagonalization, and DMRG then check that the quasiclassical constraints survive quantum fluctuations and characterize the proximate phases.

What would settle it

Measure the lowest spin-flip gap $E_0(H)$ in fields from 35 to 60 T in crystals with known $g$-factor and subtract the two-magnon repulsion: if the extracted $\Gamma+2\Gamma'$ falls outside $7.5$-$10$ meV, the bounds are wrong. Alternatively, resolve the zero-field zigzag tilt angle in a clean single crystal to better than $1^\circ$: if it lies outside $30^\circ$-$37^\circ$ while the same sample shows the quoted critical fields, at least one of the three constraints is inconsistent with the model.

Watch

Extended reading notes

Core claim

The central discovery is that the effective spin model of $\alpha$-RuCl$_3$ is not underdetermined: three decades of seemingly conflicting parameter estimates collapse onto a single narrow region once three observables are required to match experiment. The physically allowed ranges are $K\in[-10.0,-4.4]$ meV, $\Gamma\in[3.2,5.0]$ meV, and $\Gamma'\in[1.8,2.85]$ meV, with $\Gamma+2\Gamma'\in[7.5,10]$ meV; in the crystallographic frame this corresponds to a dominant ferromagnetic $J_1(1-\Delta)\approx-9$ meV, a sizable $J_{z\pm}\approx-4.5$ meV, a small $J_{\pm\pm}\approx0.6$ meV, and $\Delta\approx0.1$. The representative Point-$\star$ set $\{K,\Gamma,\Gamma',J,J_3\}=\{-7.567,4.276,2.362,-4.75,3.4\}$ meV reproduces the in-plane critical fields and the full magnetization curve in DMRG, and the proximate incommensurate phases are identified as two counter-rotating deformed helices with ordering vectors along $\Gamma M$ and $\Gamma K$.

Load-bearing premise

The weakest point is that three measured quantities are turned into parameter bounds with semiclassical formulas even though $\alpha$-RuCl$_3$ is a strongly fluctuating spin-$1/2$ magnet, and the upper edge of the $\Gamma+2\Gamma'$ range is a plausibility argument about quantum corrections, while the numerical checks sample only a few representative parameter sets rather than the whole accepted region.

Editorial extensions

If this is right

  • Future fits for $\alpha$-RuCl$_3$ can restrict themselves to the narrow ranges $K\in[-10.0,-4.4]$, $\Gamma\in[3.2,5.0]$, and $\Gamma'\in[1.8,2.85]$ meV, making full model searches tractable.
  • The material is effectively a strongly easy-plane ferromagnet with dominant $J_1$ and sizable $J_{z\pm}$, not a near-Kitaev spin liquid; the Kitaev-only and pure $K$-$J$ points lie on the $\Delta=1$ plane that the physical parameter space avoids.
  • The zigzag phase is separated from the ferromagnetic phase by two incommensurate phases, IC1 and IC2, which are counter-rotating helices; the ZZ-IC1 boundary is first order while the FM-IC2 boundary is soft, so small perturbations can move the system between them.
  • The Point-$\star$ parameter set reproduces the measured critical fields and magnetization curve in DMRG, providing a concrete starting point for computing spectra, thermodynamics, and field-driven behavior.
  • The staged constraint strategy transfers to other anisotropic-exchange magnets: pick observables that vanish without anisotropy, convert them to parameter bounds, then verify with unbiased numerics.

Reading between the lines

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

  • The authors leave implicit that the older parameter sets with near-zero $\Gamma'$ or $\Gamma+2\Gamma'\approx3$ meV, including machine-learning fits restricted to an abbreviated model, are effectively excluded by the ESR-gap constraint; if these ranges are right, those derived predictions need revisiting.
  • The near-degeneracy of the IC1 and IC2 helices suggests that strain, stacking faults, or interlayer coupling could select one helix over the other, so field- or pressure-driven transitions between them are a testable consequence for real crystals with small three-dimensional couplings.
  • The same three-observable protocol could be applied to other Kitaev candidates such as cobaltates or iridates, since the tilt-angle and critical-field-difference formulas depend only on the honeycomb bond symmetry, not on the specific electronic structure.
  • A sharp testable prediction follows from the paper's classical spiral analysis: the pitch of IC1 and IC2 helices is independent of $J$ and $J_3$, so measuring the ordering wavevector under uniaxial strain, doping, or varying interlayer coupling would discriminate this model from alternatives with significant further-neighbor anisotropy.
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

3 major / 5 minor

Summary. The paper proposes a staged constraint strategy for the effective J-K-Γ-Γ'-J3 honeycomb model of α-RuCl3. Using three experimental inputs—the out-of-plane zigzag tilt angle, the high-field ESR/THz gap, and the in-plane critical-field difference—the authors derive a bounded region for the anisotropic exchanges, K∈[-10.0,-4.4] meV, Γ∈[3.2,5.0] meV, Γ'∈[1.8,2.85] meV, with Γ+2Γ'∈[7.5,10] meV. They then construct LT, ED, and DMRG phase diagrams for representative parameter points, identify the incommensurate phases as counter-rotating helical states, and show that one complete parameter set, Point ⋆, reproduces the measured critical fields and magnetization curve without fitting those data. The paper also promotes a crystallographic-frame parametrization (XXZ-J±±-Jz±) that makes the resulting model hierarchy and its consistency with prior estimates transparent.

Significance. If the bounded parameter region is robust, this is an important contribution to a long-standing controversy. The paper's main strengths are its extensive use of complementary methods (LT, ED, DMRG), the explicit falsifiable predictions (weak renormalization of ΔHc, the nature of the IC phases), and the demonstration that DMRG can resolve incommensurate helical order on honeycomb cylinders. The independent reproduction of the magnetization curve, with parameters fixed before comparison, is particularly convincing. The proposed crystallographic parametrization is a genuinely useful organizing tool and the systematic re-analysis of prior parameter sets in Tables I and II is valuable. However, the central quantitative claim—the precise boundaries of the allowed parameter region—rests on quasiclassical formulas whose quantum corrections are verified at only a few representative points, and at least one verification is internally inconsistent with the stated physical range. The framework is sound, but the boundary claims need additional numerical support or honest error bars before they can be taken as definitive.

major comments (3)
  1. [Sec. IV B 2 and Sec. II A 3] The ΔHc constraint is verified by DMRG for a single parameter set, Point ⋆, where the authors themselves describe the near-exact match as 'somewhat fortuitous.' This does not establish that the ratio of quantum renormalization of Hc(a) and Hc(b) stays near unity throughout the proposed volume in Figs. 6 and 7, in particular near the ΔHc=1.5 T boundary that sets the Γ'/Γ strip. Since the critical fields are renormalized by about 40% at the verified point, a modest differential correction would shift the boundary and change the quoted ranges. I request DMRG or ED checks at Points A and B, or a quantitative estimate of the spread of the renormalization factor across the accepted region.
  2. [Sec. IV B 1 and Sec. II A 1] The DMRG tilt-angle verification contradicts the stated physical range: Point A has a bare tilt of 32° but a renormalized tilt of 29.4°, below the 30° lower bound used to define the allowed α window and to set the K-range. The text claims the renormalized angles remain 'safely within the physical range,' which is not true for Point A. This shows that quantum corrections to the tilt are not uniformly small across the proposed region, so the bare-tilt constraint as applied in Eqs. (4) and (5) can shift the boundaries of the K interval. The authors should either recompute the boundaries using a quantum-corrected tilt criterion or explicitly justify why a 0.6° violation at one representative point is acceptable.
  3. [Sec. II A 2, Eq. (7) and Fig. 5] The upper bound Γ+2Γ' ≤ 10 meV is based on the plausibility statement that it 'would be very hard to justify' larger values, not on a quantitative calculation. The lower bound is supported by the downward-renormalization argument, but the upper bound is load-bearing for the final ranges in Table I and for the representative points. Since the ED verification in Sec. IV B 3 is performed only for Γtot=9 meV, it does not test the upper bound. Please provide a numerical estimate of the high-field ESR gap renormalization as a function of Γtot, or explicitly label this boundary as heuristic and show how the parameter ranges in Figs. 6 and 7 change if the upper bound is relaxed or tightened.
minor comments (5)
  1. [General notation] The notation for the ESR-gap combination is inconsistent: 'Γ+2Γ′', 'Γtot', and 'Γ tot' are all used. Define the symbol once and use it consistently.
  2. [Eq. (4) and Sec. II A 1] The sign convention for the tilt angle α and its relation to the experimentally measured moment direction is not stated; the text mentions possible differences but does not quantify them, which makes the 30°–37° window difficult to interpret.
  3. [Sec. II A 3] The 'falsifiable prediction' regarding ΔHc would be more useful if stated with a quantitative acceptance criterion before comparison, rather than as a qualitative expectation.
  4. [Table I] Several compiled parameter sets have no listed Γ′ value; it would help to state explicitly what value was assumed when computing α, Γ+2Γ′, and ΔHc for those rows.
  5. [Sec. IV C and Fig. 19] The Van Vleck subtraction procedure is described briefly; a more explicit statement of the slope-extraction range and its uncertainty would strengthen the comparison with the DMRG magnetization curve.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the parameter ranges come from external experimental constraints, and the DMRG/ED checks are independent numerical evaluations rather than algebraic restatements of those constraints.

full rationale

The claimed parameter ranges are obtained by inverse modeling: three independent experimental observables (the zigzag tilt angle, the high-field ESR gap, and the critical-field difference) are inserted into quasiclassical formulas (4), (7), (8), and (9) to carve out the allowed {K, Γ, Γ′} region. The experimental inputs are external to the paper, and the formulas are parameter-free mappings from model parameters to observables; they do not themselves contain the target ranges. The DMRG and ED checks in Sec. IV are genuine numerical evaluations of the quantum model at representative points: the tilt angle, the two critical fields, their difference, and the ESR excitation are recomputed from the Hamiltonian rather than read off from the constraint equations, so the agreement is not an algebraic identity. The magnetization comparison in Sec. IV C is an external benchmark not used in the parameter selection beyond the already-quoted critical-field range and g-factor choice. The main caveat is that verification is performed at a small number of representative points rather than over the entire accepted volume; the Point A tilt check (29.4°) even falls slightly below the 30° lower boundary, and the ΔHc renormalization ratio could vary across the region. These are robustness and generalization concerns, not circularity, because the checks could in principle have failed. Self-citations to Ref. [46] supply the quasiclassical expressions and the positive-Γ′ concept, but those are independently checkable and are here tested against unbiased numerics, so they do not make the derivation circular. Overall, the central claim has independent empirical and numerical content.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim is a parameter-space statement built on top of the effective model and quasiclassical formulas. The model parameters are fitted to experimental observables rather than derived, so the contribution is the constraint logic plus the numerical verification. The only genuinely new classifications are the incommensurate phases, which rest on DMRG and LT agreement rather than on new microscopic entities.

free parameters (6)
  • K (Kitaev exchange) = -10.0 to -4.4 meV; Point 0: -7.567
    Constrained by tilt angle and Delta-Hc ranges; not derived from first principles.
  • Gamma (off-diagonal exchange) = 3.2 to 5.0 meV; Point 0: 4.276
    Constrained by ESR gap and Delta-Hc ranges.
  • Gamma-prime (off-diagonal exchange) = 1.8 to 2.85 meV; Point 0: 2.362
    Required positive and sizable by the ESR gap combination Gamma+2Gamma-prime and Delta-Hc.
  • J and J3 isotropic exchanges = Point-star: J = -4.75 meV, J3 = 3.4 meV
    Chosen within the allowed J-J3 strip from the critical-field constraint; explicitly non-unique.
  • g-factors = ga = gb = 2.5; magnetization check: gb = 2.3
    Taken from prior literature to convert field to energy; not fitted in this work.
  • Constraint windows (alpha, Delta-Hc, Gamma-tot) = alpha 30-37 degrees, Delta-Hc 0-1.5 T, Gamma+2Gamma-prime 7.5-10 meV
    Hand-set ranges around experimental values, including a heuristic upper bound for Gamma-tot.
assumptions (6)
  • domain assumption The effective spin model is the nearest-neighbor K-J-Gamma-Gamma-prime plus third-neighbor J3 Hamiltonian (Eq. 1).
    The paper assumes this five-parameter model captures the low-energy physics of alpha-RuCl3 and absorbs further-neighbor anisotropy.
  • domain assumption The exchange matrix on each nearest-neighbor bond has exactly the four symmetry-allowed terms K, J, Gamma, Gamma-prime (Eq. 2).
    Derived from honeycomb lattice symmetry in prior literature (Refs. 57, 58, 14); not re-derived here.
  • domain assumption Quasiclassical expressions for tan 2alpha (Eq. 4), the ESR gap (Eq. 7), and the critical fields (Eqs. 8 and 9) are accurate for S=1/2 up to controlled quantum corrections.
    These formulas map measured tilt, ESR shift, and Delta-Hc onto parameter bounds; DMRG checks are done only at three representative points.
  • domain assumption Interplane couplings are small and mostly isotropic, so they only renormalize J+3J3 and do not affect Delta-Hc.
    Discussion in Sec. II A 3; the paper notes that 3D couplings of about 0.5 meV exist and might require a re-evaluation (Sec. VI).
  • ad hoc to paper Luttinger-Tisza solutions that violate the local spin-length constraint can still correctly describe the incommensurate phases if confirmed by DMRG.
    Stated in Sec. III A 1 and Appendix B as a 'blessing in disguise'; supported by DMRG agreement but not a theorem.
  • domain assumption The experimental values alpha approx 32-35 degrees, Delta-Hc approx 0.8 T, and the ESR/THz high-field data are accurate and representative of the 2D model.
    External data from Refs. 26, 29, 69, 82, 83, 106, and 107 are used without error bars in deriving the region.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Saga of $\alpha$-RuCl$_3$: Parameters, Models, and Phase Diagrams." pith.science (2026). https://pith.science/paper/5EZMVM3W

@misc{pith2026250208698,
  author       = {Pith},
  title        = {Pith review of: The Saga of $\alpha$-RuCl$_3$: Parameters, Models, and Phase Diagrams},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5EZMVM3W}},
  note         = {Machine review of arXiv:2502.08698}
}
abstract

RuCl$_3$ was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the $_{44}$Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form $\alpha$-RuCl$_3$ rose to exceptional prominence. This "re-discovery" of $\alpha$-RuCl$_3$ has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of $\alpha$-RuCl$_3$, and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the non-trivial physical properties of this material. These constraints allow one to focus on the relevant region of the multi-dimensional phase diagram of the $\alpha$-RuCl$_3$ model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the $\alpha$-RuCl$_3$ parameter space using quasi-classical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization group methods, demonstrating a remarkably c... (arxiv cutoff; for the rest, see the paper)

Figures

Figures reproduced from arXiv: 2502.08698 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Ru [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Polar phase diagram of the model ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (22 more)
Figure 5
Figure 5. Figure 5: FIG. 5. ESR [ [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The projection of the [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Same as Figs [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. The [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: (b). It is the same data from Ref. [92], but in the crystallographic parametrization of the XXZ–J±±–Jz± model (3). One can see all the aspects of the physical pa￾rameter space of α-RuCl3 that are discussed in Sec. II B 2 above: leading J1(1 − ∆) that is followed by Jz…
Figure 12
Figure 12. Figure 12: FIG. 12. Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: , all prior works with no exception suggest an easy￾plane character of the ferromagnetic nearest-neighbor ex￾change in their α-RuCl3 modeling, showing |∆| < 1. In retrospect, the strongly easy-plane character of the model (3) is one of the most direct arguments that t…
Figure 14
Figure 14. Figure 14: FIG. 14. The [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. The [PITH_FULL_IMAGE:figures/full_fig_p016_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Polar phase diagrams of the model ( [PITH_FULL_IMAGE:figures/full_fig_p018_16.png]
Figure 17
Figure 17. Figure 17: (b) shows the same for the field perpendicular to the bond, a(x ′ )-direction. To compare the results for the two field directions fairly, we kept the same XC cylinder for H(a) , but used a tilted direction of the field to have it perpendicular to the bond, with the s…
Figure 18
Figure 18. Figure 18: FIG. 18. The intensity map of [PITH_FULL_IMAGE:figures/full_fig_p021_18.png]
Figure 19
Figure 19. Figure 19: FIG. 19. Upper curve is the ordered moment extracted from [PITH_FULL_IMAGE:figures/full_fig_p022_19.png]
Figure 20
Figure 20. Figure 20: FIG. 20. (a) The 32 [PITH_FULL_IMAGE:figures/full_fig_p023_20.png]
Figure 21
Figure 21. Figure 21: (c) as ℓ≈7.85a, which corresponds to the incom￾mensurate |Q| ≈ 0.19 r.l.u. [reciprocal lattice vector is G= (4π/3a, 0)]. Before moving on to the next non-scan, we note, for the record, that the DMRG non-scan in the XC cylinder in [PITH_FULL_IMAGE:figures/full_fig_p02…
Figure 22
Figure 22. Figure 22: FIG. 22. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p025_22.png]
Figure 23
Figure 23. Figure 23: FIG. 23. (a) and (b) The 32 [PITH_FULL_IMAGE:figures/full_fig_p026_23.png]
Figure 24
Figure 24. Figure 24: FIG. 24. (a) The 24-site cluster used in the ED calculations; the outer bonds visualize its periodicity. (b) The allowed momenta [PITH_FULL_IMAGE:figures/full_fig_p031_24.png]
Figure 25
Figure 25. Figure 25: FIG. 25. (a) Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p032_25.png]
Figure 26
Figure 26. Figure 26: FIG. 26. The intensity map of [PITH_FULL_IMAGE:figures/full_fig_p033_26.png]
Figure 27
Figure 27. Figure 27: FIG. 27. Polar phase diagram of the model ( [PITH_FULL_IMAGE:figures/full_fig_p034_27.png]
Figure 28
Figure 28. Figure 28: FIG. 28. Phase diagram of the model ( [PITH_FULL_IMAGE:figures/full_fig_p035_28.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Anyon polarons as a window into the competing phases of the Kitaev-Gamma-Gamma' model

    cond-mat.str-el 2025-08 conditional novelty 7.0 of 10

    From the gap closings of anyons, the authors map the K-Γ-Γ' phase diagram and predict a magnetically ordered quantum spin liquid for the antiferromagnetic Kitaev model with negative Γ.

  2. Dynamical Response of the Kitaev Spin Liquid under Third-Nearest-Neighbor Heisenberg Interaction

    cond-mat.str-el 2026-03 conditional novelty 6.0 of 10

    J3 induces soft paramagnon modes coexisting with a Majorana continuum; they condense at a common critical |J3| for FM and AFM Kitaev models related by T4 duality, while Raman response separates matter-fermion and viso...

  3. An integrated theoretical and numerical approach to understand modern experiments on quantum magnetism

    cond-mat.str-el 2026-04 unverdicted novelty 3.0 of 10

    Integrated theory-numerics-experiment collaboration has already clarified key quantum-magnet models and materials, and is required to resolve remaining spin-liquid candidates.

Reference graph

Works this paper leans on

163 extracted references · 69 canonical work pages · cited by 3 Pith papers

  1. [1]

    combined

    L T formalism The most general lattice Hamiltonian with binary in- teractions of the classical spins is given by H = X ⟨ij⟩ ST i ˆJijSj , (B3) where the lattice indices i and j run over all sites of the lattice, ⟨ij⟩ denotes the corresponding bonds, and the 3 × 3 exchange matrix depends only on ri − rj because of the translational invariance. To capitaliz...

  2. [2]

    20(a), a different state is realized, for which we found the “rotated” YC orientation of the cylinders to be optimal

    IC2 For J3 = 1.5 meV, the point in the proximity of the FM-IC phase boundary, see Fig. 20(a), a different state is realized, for which we found the “rotated” YC orientation of the cylinders to be optimal. In Fig. 22(a), the 6 ×24 YC cylinder is shown, with the same color-coding for the spins according to their sublattices as in Fig. 21(a), but spin are no...

  3. [3]

    Comparison with LT and classical spiral ansatz The IC phases were found as potentially proximate to the α-RuCl3 parameter space using the LT approach and verified with ED and DMRG. In order to show the almost unnatural closeness of the agreement of the LT and DMRG results, we per- formed additional checks of the IC states within the LT approach for the re...

  4. [4]

    Our Figures 23(a) and 23(b) provide the 1D scans through the phase diagram for the Point A in Fig

    Point A, more phases, more helices Here we provide some additional DMRG analysis of the phase diagram for the Point A anisotropic parameter set in order to reinforce the earlier findings, expose addi- tional phases, and verify the ubiquity of the IC states. Our Figures 23(a) and 23(b) provide the 1D scans through the phase diagram for the Point A in Fig. ...

  5. [5]

    no,” or “maybe,

    IC summary The puzzling incommensurate phases in the phase di- agram of α-RuCl3 are enigmas no more. The IC1 and IC2 phases were identified in Sec. III as proximate to the parameter space relevant to α-RuCl3, see Figs. 14, 15, and 16. They were discussed as vitally important to the understanding of their possible effects onto the α-RuCl3 properties. They ...

  6. [6]

    The couplings that are of interest for the model (1) concern the first- and the third-nearest neighbors, providing connections only between the A and B sublattices, see Fig

    Application to the J1–∆–J±±–Jz±–J3 and K–J–Γ–Γ′–J3 honeycomb lattice models The honeycomb lattice considered in this work is bipar- tite with the same spin length on each site. The couplings that are of interest for the model (1) concern the first- and the third-nearest neighbors, providing connections only between the A and B sublattices, see Fig. 1. Wit...

  7. [7]

    Cartesian ED phase diagrams To obtain the phase diagrams for the Point 0, A, and B sets in Figs. 14(b), 15(b), and 3, respectively, ED sweeps where carried out in the horizontal (fixed J3, varying J) and vertical (fixed J, varying J3) directions, with a dis- cretization step of 0.01 meV within the depicted range of the phase diagrams. In Fig. 24(c), posit...

  8. [8]

    III B is shown in Fig

    Polar ED phase diagram The polar ED phase diagram of the JXY 1 –Jz±–J3 model discussed in Sec. III B is shown in Fig. 16(b). It is ob- tained using the grid of the radial, polar, and spiral sweeps, with the summary of them shown in Fig. 25(a). Each dot corresponds to a maximum in the Gaussian or Lorentzian fit of the −∂2E0/∂X 2, with X = {θ, φ} and the co...

    2000

Show all 163 references
  1. [9]

    The correlation functions (C1) can be calculated nu- merically using ED in finite clusters, such as the one dis- cussed in this work; see also Refs

    Dynamical spin-spin correlation function The dynamical spin-spin correlation function S µν(q, ω) = 1 2π Z ∞ −∞ eiωt⟨Sµ −q(t)Sν q(0)⟩ dt , (C1) can be related to various forms of dynamical structure factors, which are the subjects of ESR and INS spectro- scopic experiments. The...

  2. [10]

    Paramount Pictures, Every story needs a hero , in “Rango” (2011)

    2011

  3. [11]

    Hilleringmann, Silicon Semiconductor Technology (Springer Vieweg Wiesbaden, 2023)

    U. Hilleringmann, Silicon Semiconductor Technology (Springer Vieweg Wiesbaden, 2023)

    2023

  4. [12]

    Cherepanov, I

    V. Cherepanov, I. Kolokolov, and V. L’vov, The saga of YIG: Spectra, thermodynamics, interaction and re- laxation of magnons in a complex magnet, Phys. Rep. 229, 81 (1993)

    1993

  5. [13]

    A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009)

    2009

  6. [14]

    Savary and L

    L. Savary and L. Balents, Quantum spin liquids: a re- view, Rep. Prog. Phys. 80, 016502 (2017)

    2017

  7. [15]

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

    2017

  8. [16]

    M. R. Norman, Colloquium: Herbertsmithite and the search for the quantum spin liquid, Rev. Mod. Phys. 88, 041002 (2016), and references therein

    2016

  9. [17]

    P. W. Anderson, Resonating valence bonds: A new kind of insulator?, Mater. Res. Bull. 8, 153 (1973)

    1973

  10. [18]

    Zorko, M

    A. Zorko, M. Herak, M. Gomilˇ sek, J. van Tol, M. Vel´ azquez, P. Khuntia, F. Bert, and P. Mendels, Symmetry reduction in the quantum kagome antiferro- magnet herbertsmithite, Phys. Rev. Lett. 118, 017202 (2017)

    2017

  11. [19]

    Claus, Fortsetzung der Untersuchung des Plat- inr¨ uckstandes, nebst vorl¨ aufiger Ank¨ undigung eines neuen Metalles, J

    C. Claus, Fortsetzung der Untersuchung des Plat- inr¨ uckstandes, nebst vorl¨ aufiger Ank¨ undigung eines neuen Metalles, J. Prak. Chem. 34, 420 (1845)

  12. [20]

    Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics 321, 2 (2006)

    A. Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics 321, 2 (2006)

    2006

  13. [21]

    K. Hyde, E. Hooper, J. Waters, and J. Fletcher, α- and β-ruthenium trichloride, J. Less Common Metals 8, 428 (1965)

    1965

  14. [22]

    J. M. Fletcher, W. E. Gardner, A. C. Fox, and G. Top- ping, X-ray, infrared, and magnetic studies of α- and β-ruthenium trichloride, J. Chem. Soc. A , 1038 (1967)

    1967

  15. [23]

    S. M. Winter, A. A. Tsirlin, M. Daghofer, J. van den Brink, Y. Singh, P. Gegenwart, and R. R. Valent ´ ı, Mod- els and Materials for Generalized Kitaev Magnetism, J. Phys.: Condens. Matter 29, 493002 (2017), and refer- ences therein

    2017

  16. [24]

    Binotto, I

    L. Binotto, I. Pollini, and G. Spinolo, Optical and trans- port properties of the magnetic semiconductor α-RuCl3, Phys. Status Solidi B 44, 245 (1971)

    1971

  17. [25]

    Rojas and G

    S. Rojas and G. Spinolo, Hall effect in α-RuCl3, Solid State Commun. 48, 349 (1983)

    1983

  18. [26]

    Pollini, Electronic properties of the narrow-band ma- terial α-RuCl3, Phys

    I. Pollini, Electronic properties of the narrow-band ma- terial α-RuCl3, Phys. Rev. B 53, 12769 (1996)

    1996

  19. [27]

    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

  20. [28]

    McGuire, Crystal and magnetic structures in lay- ered, transition metal dihalides and trihalides, Crystals 7, 121 (2017)

    M. McGuire, Crystal and magnetic structures in lay- ered, transition metal dihalides and trihalides, Crystals 7, 121 (2017)

    2017

  21. [29]

    Kobayashi, T

    Y. Kobayashi, T. Okada, K. Asai, M. Katada, H. Sano, and F. Ambe, M¨ ossbauer Spectroscopy and Magnetiza- tion Studies of α- and β-RuCl3, Inorg. Chem. 31, 4570 (1992)

    1992

  22. [30]

    J. A. Sears, M. Songvilay, K. W. Plumb, J. P. Clancy, Y. Qiu, Y. Zhao, D. Parshall, and Y.-J. Kim, Magnetic order in α-RuCl3: A honeycomb-lattice quantum mag- net with strong spin-orbit coupling, Phys. Rev. B 91, 144420 (2015)

    2015

  23. [31]

    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

  24. [32]

    K. I. Kugel’ and D. I. Khomskii, The Jahn-Teller ef- fect and magnetism: transition metal compounds, Sov. Phys. Usp. 25, 231 (1982)

    1982

  25. [33]

    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

  26. [34]

    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

  27. [35]

    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

  28. [36]

    L. J. Sandilands, Y. Tian, K. W. Plumb, Y.-J. Kim, and K. S. Burch, Scattering Continuum and Possible Fractionalized Excitations in α-RuCl3, Phys. Rev. Lett. 114, 147201 (2015)

    2015

  29. [37]

    Banerjee, C

    A. Banerjee, C. A. Bridges, J.-Q. Yan, A. A. Aczel, L. Li, M. B. Stone, G. E. Granroth, M. D. Lumsden, Y. Yiu, J. Knolle, S. Bhattacharjee, D. L. Kovrizhin, R. Moessner, D. A. Tennant, D. G. Mandrus, and S. E. Nagler, Proximate Kitaev quantum spin liquid be- haviour in a honey...

    2016

  30. [38]

    A. N. Ponomaryov, E. Schulze, J. Wosnitza, P. Lampen- Kelley, A. Banerjee, J.-Q. Yan, C. A. Bridges, D. G. Mandrus, S. E. Nagler, A. K. Kolezhuk, and S. A. Zvya- gin, Unconventional spin dynamics in the honeycomb- lattice material α-RuCl3: High-field electron spin reso- nance ...

    2017

  31. [39]

    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, Neutron scattering in the proximate quantum spin liquid α-RuCl3, Science 356, 1055 (2017)

    2017

  32. [40]

    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, Excitations in the field-induced quantum spin l...

    2018

  33. [41]

    Yokoi, S

    T. Yokoi, S. Ma, Y. Kasahara, S. Kasahara, T. Shibauchi, N. Kurita, H. Tanaka, J. Nasu, Y. Mo- tome, C. Hickey, S. Trebst, and Y. Matsuda, Half- integer quantized anomalous thermal Hall effect in the Kitaev material candidate α-RuCl3, Science 373, 568 (2021)

    2021

  34. [42]

    Kasahara, T

    Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Mo- 37 tome, T. Shibauchi, and Y. Matsuda, Majorana quanti- zation and half-integer thermal quantum Hall effect in a Kitaev spin liquid, Nature 559, 227 (2018)

    2018

  35. [43]

    Kasahara, K

    Y. Kasahara, K. Sugii, T. Ohnishi, M. Shimozawa, M. Yamashita, N. Kurita, H. Tanaka, J. Nasu, Y. Mo- tome, T. Shibauchi, and Y. Matsuda, Unusual Thermal Hall Effect in a Kitaev Spin Liquid Candidate α-RuCl3, Phys. Rev. Lett. 120, 217205 (2018)

    2018

  36. [44]

    Czajka, T

    P. Czajka, T. Gao, M. Hirschberger, P. Lampen-Kelley, A. Banerjee, J. Yan, D. G. Mandrus, S. E. Nagler, and N. P. Ong, Oscillations of the thermal conductivity in the spin-liquid state of α-RuCl3, Nat. Phys. 17, 915 (2021)

    2021

  37. [45]

    M. Ye, G. B. Hal´ asz, L. Savary, and L. Balents, Quanti- zation of the Thermal Hall Conductivity at Small Hall Angles, Phys. Rev. Lett. 121, 147201 (2018)

    2018

  38. [46]

    Vinkler-Aviv and A

    Y. Vinkler-Aviv and A. Rosch, Approximately Quan- tized Thermal Hall Effect of Chiral Liquids Coupled to Phonons, Phys. Rev. X 8, 031032 (2018)

    2018

  39. [47]

    J. A. N. Bruin, R. R. Claus, Y. Matsumoto, N. Kurita, H. Tanaka, and H. Takagi, Robustness of the thermal Hall effect close to half-quantization in α-RuCl3, Nat. Phys. 18, 401 (2022)

    2022

  40. [48]

    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

  41. [49]

    D. A. S. Kaib, S. M. Winter, and R. Valent ´ ı, Kitaev hon- eycomb models in magnetic fields: Dynamical response and dual models, Phys. Rev. B 100, 144445 (2019)

    2019

  42. [50]

    Hermanns, I

    M. Hermanns, I. Kimchi, and J. Knolle, Physics of the Kitaev Model: Fractionalization, Dynamic Correla- tions, and Material Connections, Annu. Rev. Condens. Matter Phys. 9, 17 (2018)

    2018

  43. [51]

    Motome and J

    Y. Motome and J. Nasu, Hunting Majorana Fermions in Kitaev Magnets, J. Phys. Soc. Jpn. 89, 012002 (2020)

    2020

  44. [52]

    Trebst and C

    S. Trebst and C. Hickey, Kitaev materials, Phys. Rep. 950, 1 (2022)

    2022

  45. [53]

    Rousochatzakis, N

    I. Rousochatzakis, N. B. Perkins, Q. Luo, and H.-Y. Kee, Beyond Kitaev physics in strong spin-orbit coupled magnets, Rep. Prog. Phys. 87, 026502 (2024)

    2024

  46. [54]

    Matsuda, T

    Y. Matsuda, T. Shibauchi, and H.-Y. Kee, Kitaev Quantum Spin Liquids (2025), arXiv:2501.05608 [cond- mat.str-el]

    2025

  47. [55]

    P. A. Maksimov and A. L. Chernyshev, Rethinking α- RuCl3, Phys. Rev. Res. 2, 033011 (2020), and references therein

    2020

  48. [56]

    C. Balz, P. Lampen-Kelley, A. Banerjee, J. Yan, Z. Lu, X. Hu, S. M. Yadav, Y. Takano, Y. Liu, D. A. Tennant, M. D. Lumsden, D. Mandrus, and S. E. Nagler, Finite field regime for a quantum spin liquid inα-RuCl3, Phys. Rev. B 100, 060405 (2019)

    2019

  49. [57]

    R. L. Smit, S. Keupert, O. Tsyplyatyev, P. A. Maksi- mov, A. L. Chernyshev, and P. Kopietz, Magnon damp- ing in the zigzag phase of the kitaev-heisenberg-Γ model on a honeycomb lattice, Phys. Rev. B 101, 054424 (2020)

    2020

  50. [58]

    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

  51. [59]

    L. Chen, E. Lefran¸ cois, A. Vallipuram, Q. Barth´ elemy, A. Ataei, W. Yao, Y. Li, and L. Taillefer, Planar thermal Hall effect from phonons in a Kitaev candidate material, Nat. Commun. 15, 3513 (2024)

    2024

  52. [60]

    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

  53. [61]

    Li and S

    S. Li and S. Okamoto, Thermal Hall effect in the Kitaev- Heisenberg system with spin-phonon coupling, Phys. Rev. B 106, 024413 (2022)

    2022

  54. [62]

    J. A. N. Bruin, R. R. Claus, Y. Matsumoto, J. Nuss, S. Laha, B. V. Lotsch, N. Kurita, H. Tanaka, and H. Takagi, Origin of oscillatory structures in the magne- tothermal conductivity of the putative Kitaev magnet α-RuCl3, APL Materials 10, 090703 (2022)

    2022

  55. [63]

    Mangeolle, L

    L. Mangeolle, L. Balents, and L. Savary, Phonon Ther- mal Hall Conductivity from Scattering with Collective Fluctuations, Phys. Rev. X 12, 041031 (2022)

    2022

  56. [64]

    S. Li, H. Yan, and A. H. Nevidomskyy, Magnons, Phonons, and Thermal Hall Effect in Candidate Ki- taev Magnet α-RuCl3 (2023), arXiv:2301.07401 [cond- mat.str-el]

    2023 arXiv

  57. [65]

    Dhakal, D

    R. Dhakal, D. A. S. Kaib, S. Biswas, R. Valent ´ ı, and S. M. Winter, Spin-Phonon Coupling in Transi- tion Metal Insulators II: Spin-Orbital Moments, Chi- ral Phonons and Application to α-RuCl3 (2024), arXiv:2407.00660 [cond-mat.str-el]

    2024 arXiv

  58. [66]

    J. G. Rau and H.-Y. Kee, Trigonal distortion in the hon- eycomb iridates: Proximity of zigzag and spiral phases in Na2IrO3 (2014), arXiv:1408.4811 [cond-mat.str-el]

    2014 arXiv

  59. [67]

    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

  60. [68]

    S. M. Winter, Magnetic couplings in edge-sharing high- spin d7 compounds, J. Phys. Mater. 5, 045003 (2022)

    2022

  61. [69]

    L. P. Regnault and J. Rossat-Mignod, Phase Transi- tions in Quasi Two-Dimensional Planar Magnets, in Magnetic Properties of Layered Transition Metal Com- pounds, edited by L. J. de Jongh (Springer Netherlands, Dordrecht, 1990) pp. 271–321

    1990

  62. [70]

    J. Nasu, J. Knolle, D. L. Kovrizhin, Y. Motome, and R. Moessner, Fermionic response from fractionalization in an insulating two-dimensional magnet, Nat. Phys.12, 912 (2016)

    2016

  63. [71]

    Do, S.-Y

    S.-H. Do, S.-Y. Park, J. Yoshitake, J. Nasu, Y. Motome, Y.-S. Kwon, D. T. Adroja, D. J. Voneshen, K. Kim, T.- H. Jang, J.-H. Park, K.-Y. Choi, and S. Ji, Majorana fermions in the Kitaev quantum spin system α-RuCl3, Nat. Phys. 13, 1079 (2017)

    2017

  64. [72]

    Rousochatzakis, J

    I. Rousochatzakis, J. Reuther, R. Thomale, S. Rachel, and N. B. Perkins, Phase Diagram and Quantum Order by Disorder in the Kitaev K 1–K2 Honeycomb Magnet, Phys. Rev. X 5, 041035 (2015)

    2015

  65. [73]

    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, Sci. Rep. 6, 1 (2016)

    2016

  66. [74]

    H.-S. Kim, V. V. Shankar, A. Catuneanu, and H.-Y. Kee, Kitaev magnetism in honeycomb RuCl 3 with in- termediate spin-orbit coupling, Phys. Rev. B91, 241110 (2015)

    2015

  67. [75]

    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

  68. [76]

    S. M. Winter, K. Riedl, D. Kaib, R. Coldea, and R. Va- 38 lent ´ ı, Probingα-RuCl3 Beyond Magnetic Order: Effects of Temperature and Magnetic Field, Phys. Rev. Lett. 120, 077203 (2018)

    2018

  69. [77]

    Janssen, E

    L. Janssen, E. C. Andrade, and M. Vojta, Magnetiza- tion processes of zigzag states on the honeycomb lattice: Identifying spin models for α-RuCl3 and Na2IrO3, Phys. Rev. B 96, 064430 (2017)

    2017

  70. [78]

    C. Balz, L. Janssen, P. Lampen-Kelley, A. Baner- jee, Y. H. Liu, J.-Q. Yan, D. G. Mandrus, M. Vo- jta, and S. E. Nagler, Field-induced intermediate or- dered phase and anisotropic interlayer interactions in α-RuCl3, Phys. Rev. B 103, 174417 (2021)

    2021

  71. [79]

    Lampen-Kelley, S

    P. Lampen-Kelley, S. Rachel, J. Reuther, J.-Q. Yan, A. Banerjee, C. A. Bridges, H. B. Cao, S. E. Na- gler, and D. Mandrus, Anisotropic susceptibilities in the honeycomb Kitaev system α-RuCl3, Phys. Rev. B 98, 100403(R) (2018)

    2018

  72. [80]

    Kim and H.-Y

    H.-S. Kim and H.-Y. Kee, Crystal structure and mag- netism in α-RuCl3: An ab initio study, Phys. Rev. B 93, 155143 (2016)

    2016

  73. [81]

    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

  74. [82]

    Y. S. Hou, H. J. Xiang, and X. G. Gong, Unveiling mag- netic interactions of ruthenium trichloride via constrain- ing direction of orbital moments: Potential routes to re- alize a quantum spin liquid, Phys. Rev. B 96, 054410 (2017)

    2017

  75. [83]

    Wang, Z.-Y

    W. Wang, Z.-Y. Dong, S.-L. Yu, and J.-X. Li, Theo- retical investigation of magnetic dynamics in α-RuCl3, Phys. Rev. B 96, 115103 (2017)

    2017

  76. [84]

    Eichstaedt, Y

    C. Eichstaedt, Y. Zhang, P. Laurell, S. Okamoto, A. G. Eguiluz, and T. Berlijn, Deriving models for the Kitaev spin-liquid candidate material α-RuCl3 from first prin- ciples, Phys. Rev. B 100, 075110 (2019)

    2019

  77. [85]

    K. Ran, J. Wang, W. Wang, Z.-Y. Dong, X. Ren, S. Bao, S. Li, Z. Ma, Y. Gan, Y. Zhang, J. T. Park, G. Deng, S. Danilkin, S.-L. Yu, J.-X. Li, and J. Wen, Spin-Wave Excitations Evidencing the Kitaev Interaction in Sin- gle Crystalline α-RuCl3, Phys. Rev. Lett. 118, 107203 (2017)

    2017

  78. [86]

    S. M. Winter, K. Riedl, P. A. Maksimov, A. L. Cherny- shev, A. Honecker, and R. Valent ´ ı, Breakdown of magnons in a strongly spin-orbital coupled magnet, Nat. Commun. 8, 1152 (2017)

    2017

  79. [87]

    Suzuki and S

    T. Suzuki and S. Suga, Effective model with strong Ki- taev interactions for α-RuCl3, Phys. Rev. B 97, 134424 (2018)

    2018

  80. [88]

    Cookmeyer and J

    J. Cookmeyer and J. E. Moore, Spin-wave analysis of the low-temperature thermal Hall effect in the candidate Kitaev spin liquid α-RuCl3, Phys. Rev. B 98, 060412 (2018)

    2018

  81. [89]

    L. Wu, A. Little, E. E. Aldape, D. Rees, E. Thewalt, P. Lampen-Kelley, A. Banerjee, C. A. Bridges, J.-Q. Yan, D. Boone, S. Patankar, D. Goldhaber-Gordon, D. Mandrus, S. E. Nagler, E. Altman, and J. Oren- stein, Field evolution of magnons in α-RuCl3 by high- resolution polarize...

    2018

  82. [90]

    I. O. Ozel, C. A. Belvin, E. Baldini, I. Kimchi, S. Do, K.-Y. Choi, and N. Gedik, Magnetic field-dependent low-energy magnon dynamics in α-RuCl3, Phys. Rev. B 100, 085108 (2019)

    2019

  83. [91]

    Sahasrabudhe, D

    A. Sahasrabudhe, D. A. S. Kaib, S. Reschke, R. Ger- man, T. C. Koethe, J. Buhot, D. Kamenskyi, C. Hickey, P. Becker, V. Tsurkan, A. Loidl, S. H. Do, K. Y. Choi, M. Gr¨ uninger, S. M. Winter, Z. Wang, R. Valent ´ ı, and P. H. M. van Loosdrecht, High-field quantum disordered sta...

    2020

  84. [92]

    J. A. Sears, L. E. Chern, S. Kim, P. J. Bereciartua, S. Francoual, Y. B. Kim, and Y.-J. Kim, Ferromag- netic Kitaev interaction and the origin of large magnetic anisotropy in α-RuCl3, Nat. Phys. 16, 837 (2020)

    2020

  85. [93]

    Laurell and S

    P. Laurell and S. Okamoto, Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate α-RuCl3, npj Quantum Mater. 5, 2 (2020)

    2020

  86. [94]

    Suzuki, H

    H. Suzuki, H. Liu, J. Bertinshaw, K. Ueda, H. Kim, S. Laha, D. Weber, Z. Yang, L. Wang, H. Takahashi, K. F´ ursich, M. Minola, B. V. Lotsch, B. J. Kim, H. Yavas, M. Daghofer, J. Chaloupka, G. Khaliullin, H. Gretarsson, and B. Keimer, Proximate ferromagnetic state in the Kitaev...

    2021

  87. [95]

    D. A. S. Kaib, S. Biswas, K. Riedl, S. M. Winter, and R. Valent ´ ı, Magnetoelastic coupling and effects of uni- axial strain in α-RuCl3 from first principles, Phys. Rev. B 103, L140402 (2021)

    2021

  88. [96]

    E. C. Andrade, L. Janssen, and M. Vojta, Susceptibil- ity anisotropy and its disorder evolution in models for Kitaev materials, Phys. Rev. B 102, 115160 (2020)

    2020

  89. [97]

    Janssen, S

    L. Janssen, S. Koch, and M. Vojta, Magnon dispersion and dynamic spin response in three-dimensional spin models for α-RuCl3, Phys. Rev. B 101, 174444 (2020)

    2020

  90. [98]

    Li, H.-K

    H. Li, H.-K. Zhang, J. Wang, H.-Q. Wu, Y. Gao, D.- W. Qu, Z.-X. Liu, S.-S. Gong, and W. Li, Identification of magnetic interactions and high-field quantum spin liquid in α-RuCl3, Nat. Commun. 12, 4007 (2021)

    2021

  91. [99]

    K. Ran, J. Wang, S. Bao, Z. Cai, Y. Shangguan, Z. Ma, W. Wang, Z.-Y. Dong, P. Cerm´ ak, A. Schneidewind, S. Meng, Z. Lu, S.-L. Yu, J.-X. Li, and J. Wen, Evi- dence for Magnetic Fractional Excitations in a Kitaev Quantum-Spin-Liquid Candidate α-RuCl3, Chin. Phys. Lett. 39, 0275...

    2022

  92. [100]

    A. M. Samarakoon, P. Laurell, C. Balz, A. Baner- jee, P. Lampen-Kelley, D. Mandrus, S. E. Nagler, S. Okamoto, and D. A. Tennant, Extraction of inter- action parameters for α-RuCl3 from neutron data using machine learning, Phys. Rev. Res. 4, L022061 (2022)

    2022

  93. [101]

    H. Liu, J. Chaloupka, and G. Khaliullin, Exchange in- teractions in d5 Kitaev materials: From Na 2IrO3 to α- RuCl3, Phys. Rev. B 105, 214411 (2022)

    2022

  94. [102]

    N. Rao, K. Liu, M. Machaczek, and L. Pollet, Machine- learned phase diagrams of generalized Kitaev honey- comb magnets, Phys. Rev. Res. 3, 033223 (2021)

    2021

  95. [103]

    D. A. S. Kaib, K. Riedl, A. Razpopov, Y. Li, S. Backes, I. I. Mazin, and R. Valent ´ ı, Electronic and magnetic properties of the RuX 3 (X=Cl, Br, I) family: two siblings–and a cousin?, npj Quantum Mater. 7, 75 (2022)

    2022

  96. [104]

    J. G. Rau, E. K.-H. Lee, and H.-Y. Kee, Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Sys- tems: Iridates and Related Materials, Annu. Rev. Con- dens. Matter Phys. 7, 195 (2016)

    2016

  97. [105]

    N. J. Robinson, F. H. L. Essler, I. Cabrera, and R. Coldea, Quasiparticle breakdown in the quasi-one- dimensional Ising ferromagnet CoNb 2O6, Phys. Rev. B 39 90, 174406 (2014)

    2014

  98. [106]

    Y. Li, P. Gegenwart, and A. A. Tsirlin, Spin liquids in geometrically perfect triangular antiferromagnets, J. Phys.: Condens. Matter 32, 224004 (2020)

    2020

  99. [107]

    Coldea, D

    R. Coldea, D. A. Tennant, K. Habicht, P. Smeibidl, C. Wolters, and Z. Tylczynski, Direct Measurement of the Spin Hamiltonian and Observation of Condensa- tion of Magnons in the 2D Frustrated Quantum Magnet Cs2CuCl4, Phys. Rev. Lett. 88, 137203 (2002)

    2002

  100. [108]

    Mourigal, M

    M. Mourigal, M. Enderle, A. Kl¨ opperpieper, J.-S. Caux, A. Stunault, and H. M. Rønnow, Fractional spinon ex- citations in the quantum Heisenberg antiferromagnetic chain, Nat. Phys. 9, 435 (2013)

    2013

  101. [109]

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

    2017

  102. [110]

    K. A. Ross, L. Savary, B. D. Gaulin, and L. Balents, Quantum Excitations in Quantum Spin Ice, Phys. Rev. X 1, 021002 (2011)

    2011

  103. [111]

    J. D. Thompson, P. A. McClarty, D. Prabhakaran, I. Cabrera, T. Guidi, and R. Coldea, Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb 2Ti2O7 in a Magnetic Field, Phys. Rev. Lett. 119, 057203 (2017)

    2017

  104. [112]

    J. G. Rau, R. Moessner, and P. A. McClarty, Magnon interactions in the frustrated pyrochlore ferromagnet Yb2Ti2O7, Phys. Rev. B 100, 104423 (2019)

    2019

  105. [113]

    Woodland, D

    L. Woodland, D. Macdougal, I. M. Cabrera, J. D. Thompson, D. Prabhakaran, R. I. Bewley, and R. Coldea, Tuning the confinement potential between spinons in the Ising chain compound CoNb 2O6 using longitudinal fields and quantitative determination of the microscopic Hamiltonian,...

    2023

  106. [114]

    T. Xie, S. Gozel, J. Xing, N. Zhao, S. M. Av- doshenko, L. Wu, A. S. Sefat, A. L. Chernyshev, A. M. L¨ auchli, A. Podlesnyak, and S. E. Nikitin, Quantum Spin Dynamics Due to Strong Kitaev Interactions in the Triangular-Lattice Antiferromagnet CsCeSe2, Phys. Rev. Lett. 133, 096...

    2024

  107. [115]

    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

  108. [116]

    A. N. Ponomaryov, L. Zviagina, J. Wosnitza, P. Lampen-Kelley, A. Banerjee, J.-Q. Yan, C. A. Bridges, D. G. Mandrus, S. E. Nagler, and S. A. Zvya- gin, Nature of Magnetic Excitations in the High-Field Phase of α-RuCl3, Phys. Rev. Lett. 125, 037202 (2020)

    2020

  109. [117]

    J. M. Luttinger and L. Tisza, Theory of Dipole Interac- tion in Crystals, Phys. Rev. 70, 954 (1946)

    1946

  110. [118]

    D. H. Lyons and T. A. Kaplan, Method for Determin- ing Ground-State Spin Configurations, Phys. Rev. 120, 1580 (1960)

    1960

  111. [119]

    Friedman and J

    Z. Friedman and J. Felsteiner, On the solution of the Luttinger-Tisza problem for magnetic systems, Philos. Mag. 29, 957 (1974)

    1974

  112. [120]

    D. B. Litvin, The Luttinger-Tisza method, Physica 77, 205 (1974)

    1974

  113. [121]

    Niggemann, M

    N. Niggemann, M. Hering, and J. Reuther, Classical spiral spin liquids as a possible route to quantum spin liquids, J. Phys.: Condens. Matter 32, 024001 (2019)

    2019

  114. [122]

    Chaloupka and G

    J. Chaloupka and G. Khaliullin, Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates A2IrO3, Phys. Rev. B 92, 024413 (2015)

    2015

  115. [123]

    P. A. Maksimov and A. L. Chernyshev, Easy-plane anisotropic-exchange magnets on a honeycomb lattice: Quantum effects and dealing with them, Phys. Rev. B 106, 214411 (2022)

    2022

  116. [124]

    P. A. Maksimov, Z. Zhu, S. R. White, and A. L. Cherny- shev, Anisotropic-Exchange Magnets on a Triangular Lattice: Spin Waves, Accidental Degeneracies, and Dual Spin Liquids, Phys. Rev. X 9, 021017 (2019)

    2019

  117. [125]

    J. G. Rau and M. J. P. Gingras, Frustration and anisotropic exchange in ytterbium magnets with edge- shared octahedra, Phys. Rev. B 98, 054408 (2018)

    2018

  118. [126]

    Rastelli, A

    E. Rastelli, A. Tassi, and L. Reatto, Non-simple mag- netic order for simple Hamiltonians, Physica B+C 97, 1 (1979)

    1979

  119. [127]

    Jiang, S

    S. Jiang, S. R. White, and A. L. Chernyshev, Quan- tum phases in the honeycomb-lattice J1–J3 ferro- antiferromagnetic model, Phys. Rev. B 108, L180406 (2023)

    2023

  120. [128]

    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

  121. [129]

    Watanabe, S

    Y. Watanabe, S. Trebst, and C. Hickey, Frustrated Fer- romagnetism of Honeycomb Cobaltates: Incommensu- rate Spirals, Quantum Disordered Phases, and Out- of-Plane Ising Order (2022), arXiv:2212.14053 [cond- mat.str-el]

    2022 arXiv

  122. [130]

    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, Proc. Natl. Acad. Sci. U.S....

    2023

  123. [131]

    C. A. Gallegos and A. L. Chernyshev, Magnon interac- tions in the quantum paramagnetic phase of CoNb 2O6, Phys. Rev. B 109, 014424 (2024)

    2024

  124. [132]

    Kubota, H

    Y. Kubota, H. Tanaka, T. Ono, Y. Narumi, and K. Kindo, Successive magnetic phase transitions in α- RuCl3: XY-like frustrated magnet on the honeycomb lattice, Phys. Rev. B 91, 094422 (2015)

    2015

  125. [133]

    P. M. Cˆ onsoli, L. Janssen, M. Vojta, and E. C. Andrade, Heisenberg-Kitaev model in a magnetic field: 1 /S ex- pansion, Phys. Rev. B 102, 155134 (2020)

    2020

  126. [134]

    J. A. Sears, Y. Zhao, Z. Xu, J. W. Lynn, and Y.-J. Kim, Phase diagram of α-RuCl3 in an in-plane magnetic field, Phys. Rev. B 95, 180411 (2017)

    2017

  127. [135]

    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

  128. [136]

    Q. Luo, S. Hu, B. Xi, J. Zhao, and X. Wang, Ground- state phase diagram of an anisotropic spin- 1 2 model on the triangular lattice, Phys. Rev. B 95, 165110 (2017)

    2017

  129. [137]

    Becker, M

    M. Becker, M. Hermanns, B. Bauer, M. Garst, and S. Trebst, Spin-orbit physics ofj = 1 2 Mott insulators on the triangular lattice, Phys. Rev. B 91, 155135 (2015)

    2015

  130. [138]

    I. A. Zaliznyak and M. E. Zhitomirsky, Modification of the classical Heisenberg helimagnet by weak uniaxial anisotropy and magnetic field, JETP 81, 568 (1995)

    1995

  131. [139]

    Kimchi and A

    I. Kimchi and A. Vishwanath, Kitaev-Heisenberg mod- els for iridates on the triangular, hyperkagome, kagome, 40 fcc, and pyrochlore lattices, Phys. Rev. B 89, 014414 (2014)

    2014

  132. [140]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, The itensor software library for tensor network calculations, SciPost Phys. Codebases , 4 (2022)

    2022

  133. [141]

    S. R. White and A. L. Chernyshev, Ne´ el Order in Square and Triangular Lattice Heisenberg Models, Phys. Rev. Lett. 99, 127004 (2007)

    2007

  134. [142]

    Z. Zhu, D. A. Huse, and S. R. White, Weak Plaquette Valence Bond Order in the S = 1/2 Honeycomb J1–J2 Heisenberg Model, Phys. Rev. Lett. 110, 127205 (2013)

    2013

  135. [143]

    Zhu and S

    Z. Zhu and S. R. White, Spin liquid phase of the S = 1 2 J1–J2 Heisenberg model on the triangular lattice, Phys. Rev. B 92, 041105(R) (2015)

    2015

  136. [144]

    Z. Zhu, D. A. Huse, and S. R. White, Unexpected z- Direction Ising Antiferromagnetic Order in a Frustrated Spin-1/2 J1–J2 XY Model on the Honeycomb Lattice, Phys. Rev. Lett. 111, 257201 (2013)

    2013

  137. [145]

    Z. Zhu, P. A. Maksimov, S. R. White, and A. L. Cherny- shev, Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO4, Phys. Rev. Lett. 119, 157201 (2017)

    2017

  138. [146]

    Z. Zhu, P. A. Maksimov, S. R. White, and A. L. Cherny- shev, Topography of Spin Liquids on a Triangular Lat- tice, Phys. Rev. Lett. 120, 207203 (2018)

    2018

  139. [147]

    Jiang, J

    S. Jiang, J. Romh´ anyi, S. R. White, M. E. Zhitomirsky, and A. L. Chernyshev, Where is the Quantum Spin Ne- matic?, Phys. Rev. Lett. 130, 116701 (2023)

    2023

  140. [148]

    Jiang, D

    S. Jiang, D. J. Scalapino, and S. R. White, Ground-state phase diagram of thet-t′-J model, Proc. Natl. Acad. Sci. U.S.A. 118 (2021)

    2021

  141. [149]

    Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral op- erators, J

    C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral op- erators, J. Res. Natl. Bur. Stand. B 45, 255 (1950)

    1950

  142. [150]

    Dagotto, Correlated electrons in high-temperature superconductors, Rev

    E. Dagotto, Correlated electrons in high-temperature superconductors, Rev. Mod. Phys. 66, 763 (1994)

    1994

  143. [151]

    Biffin, R

    A. Biffin, R. D. Johnson, I. Kimchi, R. Morris, A. Bombardi, J. G. Analytis, A. Vishwanath, and R. Coldea, Noncoplanar and Counterrotating Incom- mensurate Magnetic Order Stabilized by Kitaev Interac- tions in γ-Li2IrO3, Phys. Rev. Lett. 113, 197201 (2014)

    2014

  144. [152]

    Biffin, R

    A. Biffin, R. D. Johnson, S. Choi, F. Freund, S. Manni, A. Bombardi, P. Manuel, P. Gegenwart, and R. Coldea, Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in β-Li2IrO3: Full solution via magnetic resonant x-ray diffraction, Phys. Rev. B 90, 205116 (2014)

    2014

  145. [153]

    Kimchi, R

    I. Kimchi, R. Coldea, and A. Vishwanath, Unified the- ory of spiral magnetism in the harmonic-honeycomb iri- dates α, β, and γ-Li2IrO3, Phys. Rev. B 91, 245134 (2015)

    2015

  146. [154]

    S. C. Williams, R. D. Johnson, F. Freund, S. Choi, A. Jesche, I. Kimchi, S. Manni, A. Bombardi, P. Manuel, P. Gegenwart, and R. Coldea, Incommen- surate counterrotating magnetic order stabilized by Ki- taev interactions in the layered honeycomb α−Li2IrO3, Phys. Rev. B 93, 1951...

    2016

  147. [155]

    Kimchi and R

    I. Kimchi and R. Coldea, Spin dynamics of counterrotat- ing Kitaev spirals via duality, Phys. Rev. B 94, 201110 (2016)

    2016

  148. [156]

    Q. Wang, A. de la Torre, J. A. Rodriguez-Rivera, A. A. Podlesnyak, W. Tian, A. A. Aczel, M. Matsuda, P. J. Ryan, J.-W. Kim, J. G. Rau, and K. W. Plumb, Pulling Order Back from the Brink of Disorder: Observation of a Nodal-Line Spin Liquid and Fluctuation Stabilized Order in K ...

    2025

  149. [157]

    M. J. Freiser, Thermal Variation of the Pitch of Helical Spin Configurations, Phys. Rev. 123, 2003 (1961)

    1961

  150. [158]

    Yosida, The Status of the Theories of Magnetic Anisotropy, J

    K. Yosida, The Status of the Theories of Magnetic Anisotropy, J. Appl. Phys. 39, 511 (1968)

    1968

  151. [159]

    Y.-D. Li, X. Wang, and G. Chen, Anisotropic spin model of strong spin-orbit-coupled triangular antiferro- magnets, Phys. Rev. B 94, 035107 (2016)

    2016

  152. [160]

    T. A. Kaplan and N. Menyuk, Spin ordering in three- dimensional crystals with strong competing exchange interactions, Philos. Mag. 87, 3711 (2007)

    2007

  153. [161]

    Sela, H.-C

    E. Sela, H.-C. Jiang, M. H. Gerlach, and S. Trebst, Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model, Phys. Rev. B 90, 035113 (2014)

    2014

  154. [162]

    M. L. Abell, J. P. Braselton, J. A. Rafter, and J. A. Rafter, Statistics with Mathematica , Vol. 1 (Academic Press, 1999)

    1999

  155. [163]

    Mourigal, W

    M. Mourigal, W. T. Fuhrman, A. L. Chernyshev, and M. E. Zhitomirsky, Dynamical structure factor of the triangular-lattice antiferromagnet, Phys. Rev. B 88, 094407 (2013)

    2013

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.