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Hunting Majorana Fermions in Kitaev Magnets

T0 review · 3 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper argues that in Kitaev magnets, spins split into two kinds of fractional quasiparticles at two well-separated temperatures, and that the half-quantized thermal Hall plateau in α-RuCl3 identifies the Majorana fermions.

desk verdict A reliable, unusually candid review of Kitaev magnets whose multi-probe case for Majorana fractionalization is solid — only the Sec. 5.8 thermal Hall 'strong evidence' conclusion overshoots. read the letter →

arxiv 1909.02234 v2 pith:4UQ4TKJA submitted 2019-09-05 cond-mat.str-el

Yukitoshi Motome , Joji Nasu This is my paper · ORCID
classification cond-mat.str-el
keywords KitaevmodelquantumspinliquidMajoranafermionsthermalfractionalizationα-RuCl3HallconductivityZ2fluxhoneycomblattice
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 is a review that aims to establish thermal fractionalization as the organizing principle of finite-temperature Kitaev magnets: a spin-1/2 degree of freedom splits into itinerant Majorana fermions and localized $Z_2$ fluxes whose energy scales are so different that they show up as two separate temperatures, $T_H$ and $T_L$, in thermodynamic and dynamical observables. It argues that this two-step fractionalization accounts for the specific heat, entropy, neutron scattering, NMR, Raman, and thermal transport data in candidate materials, most importantly α-RuCl3. If the picture is right, the half-quantized thermal Hall plateau seen in the field-induced paramagnetic state of α-RuCl3 is direct evidence that the heat carriers are charge-neutral Majorana fermions carrying half the degrees of freedom of an electron, and that a topological quantum spin liquid has been reached. The review's final claim is that this plateau offers strong evidence of a Kitaev-type quantum spin liquid with a gapped excitation in the field-induced paramagnetic state.

What carries the argument

The load-bearing object is the Majorana representation of the Kitaev model: a Jordan-Wigner transformation rewrites each spin-1/2 in terms of itinerant Majorana fermions $\gamma$ coupled to conserved $Z_2$ bond variables $\eta$, equivalently plaquette fluxes $W_p$. Because the bond variables are conserved, the ground state is exact and finite-temperature simulations can sample the $\eta$ configurations as classical variables with sign-free quantum Monte Carlo, which is what exposes the two crossovers at $T_H$ and $T_L$. The second load-bearing element is the weak-field perturbation theory: a magnetic field generates imaginary second-neighbor Majorana hopping, formally equivalent to a Majorana-fermion Chern insulator, which opens a topological gap with chiral edge modes and is the origin of the half-quantized thermal Hall response.

What would settle it

Measure $\kappa_{xy}/T$ in α-RuCl3 in the field-induced paramagnetic state down to temperatures well below the estimated flux-gap scale of about 1 K, while separately extracting the phonon thermal Hall contribution from a nonmagnetic structural analog: if the plateau persists below that scale, or if its magnitude tracks the phonon mean free path or changes with isotopic substitution, the half-quantized signal cannot be assigned to chiral Majorana edge modes.

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Extended reading notes

Core claim

The central claim is that the Kitaev honeycomb model is not merely exactly solvable at zero temperature: its finite-temperature physics is governed by thermal fractionalization, in which the entropy $\ln 2$ per spin is released in two roughly equal steps. The first step occurs at $T_H$, set by the Fermi degeneracy of complex fermions built from itinerant Majorana fermions, and the second at $T_L$, set by the excitation gap of localized $Z_2$ fluxes. Between the two crossovers the system is a fractional paramagnet, a 'Majorana metal' with $T$-linear specific heat, saturated static spin correlations, and growing dynamical correlations. In a magnetic field the itinerant Majorana sector acquires a topological gap via imaginary second-neighbor hopping, producing chiral Majorana edge modes and a thermal Hall conductivity divided by temperature that approaches half the integer quantum Hall value, $\kappa_{xy}/T \to \pi/12$. The review argues that the observed plateau in α-RuCl3 in a narrow field window is the key evidence that the field-induced paramagnet is a Kitaev-type quantum spin liquid with gapped excitations.

Load-bearing premise

The argument stands on the assumption that α-RuCl3 in the field-induced paramagnetic state is well described by the isotropic honeycomb Kitaev model, so that the half-quantized thermal Hall plateau is carried by chiral Majorana edge modes rather than by phonons or by non-Kitaev exchange interactions.

Editorial extensions

If this is right

  • Specific heat and entropy in a Kitaev magnet should show two broad anomalies at $T_H$ and $T_L$, with entropy released in two roughly half-$\ln 2$ steps; the high-temperature step should survive even where magnetic order hides the low-temperature one.
  • Between $T_H$ and $T_L$ the material is a fractional paramagnet or Majorana metal: the specific heat is $T$-linear, static spin correlations saturate, and dynamical correlations grow, producing a broad peak in the NMR relaxation rate $1/T_1$.
  • Inelastic neutron scattering should show a weakly $q$-dependent high-energy continuum persisting above the magnetic ordering temperature, together with a quasi-elastic response that develops a gap below $T_L$ when the $Z_2$ fluxes freeze.
  • Raman scattering intensity should follow a fermionic $(1-f)^2$ temperature dependence rather than the bosonic $n+1$ form, identifying pair creation of Majorana fermions in an insulator.
  • In an applied magnetic field, the thermal Hall conductivity divided by temperature should approach $\pi/12$ at low temperature in the field-induced paramagnetic state, and the plateau should appear in the field window where magnetic order is suppressed.

Reading between the lines

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

  • A direct test of the phonon background would be to measure the thermal Hall conductivity in a nonmagnetic structural analog of α-RuCl3 with a similar phonon spectrum: if a comparable half-quantized plateau appears, phonon Hall physics rather than Majorana edge modes would explain the signal, since the review itself notes that phonons dominate the longitudinal thermal conductivity.
  • Because the review acknowledges that the theoretical temperature dependence of $\kappa_{xy}/T$ differs qualitatively from experiment, the actual gap that protects the topological state may be set by non-Kitaev exchange terms such as the symmetric off-diagonal $\Gamma$ interaction rather than by the pure Kitaev flux gap; systematic measurements of the plateau versus field angle and sample stacking
  • If thermal fractionalization is a general mechanism, three-dimensional Kitaev candidates should show a flux-loop proliferation transition, a 'gas-liquid' transition in the spin degrees of freedom, rather than the two-dimensional crossover; low-temperature specific heat measurements on three-dimensional iridates in fields that suppress their magnetic order could test this prediction.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. This review article by Motome and Nasu surveys the theoretical and experimental status of Kitaev magnets, with a focus on finite-temperature signatures of fractionalized Majorana fermions and Z2 fluxes. The central concept is 'thermal fractionalization': in the exactly solvable honeycomb Kitaev model, two distinct quasiparticle species (itinerant Majorana fermions and localized fluxes) have widely separated energy scales, producing two crossovers at temperatures TH and TL and a 'fractional paramagnetic' regime in between. The review develops the Majorana-based numerical techniques (QMC, CDMFT, CTQMC) used to compute thermodynamic and dynamical properties, and compares the results with experimental data for Na2IrO3, α-Li2IrO3, and α-RuCl3 across specific heat, entropy, susceptibility, neutron scattering, NMR, thermal conductivity, Raman scattering, and thermal Hall conductivity. The paper concludes in Section 5.8 that the observation of a half-quantized κxy/T plateau in α-RuCl3 offers strong evidence of a Kitaev-type quantum spin liquid with gapped Majorana excitations and chiral edge modes.

Significance. If its central claims hold, this review is a valuable and wide-ranging synthesis. The theoretical machinery is well established: the Kitaev model is exactly solvable via Lieb's theorem and Majorana representations, and the numerical methods described in the Appendix (sign-free Majorana QMC, CDMFT, CTQMC) are state-of-the-art. The strength of the review is its careful, self-critical treatment of thermodynamic comparisons: Section 5.1 explicitly states that specific heat and susceptibility agreement alone are not strong evidence, and Section 5.8 acknowledges several caveats. The paper also offers falsifiable predictions: the T-linear specific heat, the dichotomy between static and dynamic spin correlations, and the two crossovers. These features make the review a useful reference for the field. However, the force of the 'hunting Majoranas' narrative depends on the thermal Hall evidence, and that is exactly where the review's claim is strongest relative to the evidence it presents.

major comments (3)
  1. [Sec. 5.8 and Fig. 46] The concluding sentence of Section 5.8 asserts that the half-quantized κxy/T plateau 'offers strong evidence of the Kitaev-type QSL with a gapped excitation in the field-induced PM state.' This is an overclaim relative to the evidence documented in the same section. The review itself notes two crucial caveats: (i) the longitudinal thermal conductivity κxx at low T is dominated by phonons (Ref. 197), and (ii) phonon magnetothermal effects alone can produce quantized thermal Hall plateaus in insulating systems with no topological spin carriers (Refs. 198-199). The manuscript neither provides a quantitative estimate of the phonon contribution to κxy in α-RuCl3 nor describes a control experiment or subtraction procedure that isolates a Majorana contribution. Without that separation, the plateau is not uniquely diagnostic of chiral Majorana edge modes. The authors should either temper the conclusion to describe the plateau as suggestive but not yet conclusive evidence, or add a quantitative discussion of why phonon contributions can be excluded in this material.
  2. [Sec. 5.8, Fig. 44 vs. Fig. 46] The quantitative mismatch between the theoretical and experimental T dependences of κxy/T is acknowledged but its implication for the strength of the claim is not fully weighed. In Fig. 44, the theoretical curve for the weak-field effective model approaches the half-quantized value only well below TL ≈ 0.012J (about 1 K for J ≈ 100 K), whereas the experimental data in Fig. 46 saturate below about 5 K and show an overshoot above π/12. The manuscript attributes these discrepancies to the weak-field perturbation approximation and possible non-Kitaev interactions, but this admission undercuts the claim that the experimental plateau is a quantitative confirmation of the Kitaev prediction. The review should state more clearly that the observed effect is qualitatively consistent with the Kitaev scenario but the quantitative connection is not established, and that a beyond-perturbation theory is needed before the plateau can be interpreted as a smoking-gun signature.
  3. [Sec. 5.4 and Sec. 5.8] The load-bearing premise for interpreting the α-RuCl3 experiments is that the field-induced paramagnetic state is well described by the isotropic honeycomb Kitaev model. The review itself documents deviations from this premise: the star-shaped low-energy neutron scattering intensity (Sec. 5.4), the magnetic anisotropy (Sec. 5.3), and the presence of non-Kitaev (Heisenberg, Γ, Γ′) interactions (Sec. 2.8). While the review discusses these as future issues, the strength of the final conclusion in Section 5.8 does not reflect this documented uncertainty. The authors should explicitly calibrate the strength of the evidence for the Kitaev identification in the field-induced state against the known deviations from the idealized model.
minor comments (3)
  1. [Sec. 5.8 (paragraph before Fig. 44)] The text refers to 'the Kobo formula'; this should read 'the Kubo formula'.
  2. [Fig. 44 caption] The phrase 'half quantizated value' contains a typo; it should be 'half-quantized value'.
  3. [Ref. 61] The year in the reference for E. H. Lieb is given as '2994'; it should be '1994'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: finite-temperature predictions and the half-quantized thermal-Hall plateau follow from explicit Kitaev-model calculations and exact results, not from fitted inputs or self-referential definitions.

full rationale

The review's central claims are anchored to Kitaev's exact ground-state solution and Lieb's theorem, to explicit Majorana-based QMC/CDMFT/CTQMC methods described in the Appendix, and to external experimental measurements. The two crossovers TH and TL are read off from computed specific-heat and entropy data (Figs. 15 and 17), and their attribution to itinerant Majorana fermions versus localized Z2 fluxes is checked through separate, independently defined observables Kx and <Wp> (Fig. 16), rather than being imposed by construction. The half-quantized value of kappa_xy/T follows from the band topology of the effective field-perturbed Hamiltonian (Eqs. 13 and 23; Fig. 44) and is not fitted to the alpha-RuCl3 data; in fact, the review explicitly concedes that 'the T dependence of kappa_xy/T is different from the theoretical results in Fig. 44 both quantitatively and qualitatively.' The phonon alternative is also acknowledged: 'Another caveat is the contribution from phonons. The large value of the longitudinal thermal conductivity kappa_xx at low T suggests the dominant phonon contribution... The possibility of the observation of quantized kappa_xy even in such a situation was theoretically discussed.' Thus the Sec. 5.8 conclusion is an interpretation of external experimental data, not a reduction of the prediction to its inputs. The paper does rely heavily on the authors' own numerical work (Refs. 37-44) and on experiments on which they are co-authors (Refs. 194 and 195), but the numerical methods are reproduced in the Appendix and the experimental results are external; no load-bearing step reduces to an unverified self-citation. The main weakness is inferential overreach in calling the plateau 'strong evidence' despite the phonon caveat, but that is a correctness or overclaim concern, not circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The review's key quantitative results are exact or numerically controlled within the Kitaev model, but the leap from model to material is made by assuming alpha-RuCl3 is a proximate Kitaev system with negligible phonon contribution to the thermal Hall signal.

free parameters (2)
  • Kitaev coupling J (material-dependent energy scale) = J ~ 100-300 K for iridates, J ~ 8-10 meV for alpha-RuCl3
    Used to convert dimensionless T/J results to absolute temperatures for experimental comparison; values are inputs from prior literature, not derived in this paper.
  • Effective magnetic field h_tilde = 0.012-0.048 J in Fig. 44
    Coupling strength of the third-order perturbation term in the magnetic field; chosen for illustration, not fit to experiments.
assumptions (4)
  • standard math Lieb's theorem determines the flux-free ground state for cases with at least two equal Kitaev couplings (Sec. 2.4).
    The review relies on this theorem to assert the QSL ground state in the symmetric cases.
  • standard math The spin model is exactly mapped to noninteracting Majorana fermions coupled to Z2 fluxes through the Majorana/Jordan-Wigner representation (Sec. 2.3).
    This mapping is the foundation of all finite-T numerical methods.
  • domain assumption Z2 variables can be treated as classical c-numbers for quantum Monte Carlo sampling, and the sign problem is absent at zero field (Sec. 2.6 and Appendix A.1).
    The sign-free QMC is central to all thermodynamics results; it fails in a magnetic field, so the field-dependent results rely on the effective perturbation model.
  • domain assumption Candidate materials, especially alpha-RuCl3, are described by the isotropic Kitaev model with small non-Kitaev perturbations in the temperature and field range of interest (Sec. 5).
    The entire comparison of signatures with experiments depends on this mapping.

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Cite this review

Pith. "Pith review of Hunting Majorana Fermions in Kitaev Magnets." pith.science (2026). https://pith.science/paper/4UQ4TKJA

@misc{pith2026190902234,
  author       = {Pith},
  title        = {Pith review of: Hunting Majorana Fermions in Kitaev Magnets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4UQ4TKJA}},
  note         = {Machine review of arXiv:1909.02234}
}
read the original abstract

A Majorana fermion is a fermionic particle that is its own antiparticle. Since the theoretical discovery in 1937, the exotic particle has long been searched in particle physics. In the last few decades, however, it has attracted renewed interest in condensed matter physics, where it can be realized as an elementary excitation (quasiparticle) in quantum states of matter. In this review, we discuss another platform for Majorana fermions, the quantum spin liquid, in which interacting magnetic moments remain disordered down to the lowest temperature under strong quantum fluctuations. They are characterized by topological entanglement and fractional excitations, whose possible application to topological quantum computation is recently discussed intensively. As a prime candidate for such exotic states, we here focus on the Kitaev magnets, a subgroup of the spin-orbit Mott insulators. After a brief overview of the Kitaev model and the fractionalization of spins in the exact ground state, we review recent explosive development in this rapidly growing field, with a focus on numerical solutions of the Kitaev model at finite temperatures and the comparison with experiments. The key concept is thermal fractionalization --- two types of fractional excitations manifest themselves at largely different temperatures. This leads to distinct thermodynamics and spin dynamics in a variety of experimentally measurable quantities. We discuss such peculiar behaviors as the signatures of fractional quasiparticles, in careful comparison with the available experimental data for the candidate materials of the Kitaev magnets. Our review gives an overview of the current status of the identification of Majorana fermions in the Kitaev magnets, which would serve as a basis for further experimental and theoretical studies toward the manipulation of the exotic particles for topological quantum computation.

Figures

Figures reproduced from arXiv: 1909.02234 by the authors.

Figure 1
Figure 1. (Color online) Schematic picture of the Kitaev model defined on a honeycomb structure with three kinds of interactions Jx, Jy, and Jz on the x, y, and z bonds, respectively. a1 and a2 are the primitive translation vectors and r labels the unit cell including the z bond. The Cartesian coordinate axes (a, b, c) are also shown. fermionic nature is clearly identified in a wide-T range. Fi￾nally, in Sec. 5.8, a direct ev… view at source ↗
Figure 2
Figure 2. (Color online) (a) Energy scheme of the atomic d-orbital states oc￾cupied by five electrons in the presence of the cubic crystalline electric field (CEF) and the spin-orbit coupling (SOC). (b) Pictorial representation of the jeff = 1/2 Kramers doublet in Eq. (7). (c) Schematic picture of the lattice structure with edge-sharing ligand octahedra (left), and two kinds of the ex￾change processes by the indirect d-p-d ho… view at source ↗
Figure 3
Figure 3. (Color online) Schematic picture of the one-dimensional chains consisting of the x and y bonds, which are shown by the thick blue and green lines, respectively. The honeycomb structure in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (39 more)
Figure 4
Figure 4. Figure 4: (Color online) Representations of the Z2 flux Wp for a plaquette p by using (a) the spin operators σ µ˜ j at the six vertices [Eq. (17)] and (b) the Z2 variables ηr on the two z bonds [Eq. (18)]. is transformed into H = Jx 4 X hr 0 ,w;r,bix (ar 0 ,w − a † r 0 ,w )(ar,b…
Figure 5
Figure 5. Figure 5: (Color online) Schematic figures of the Kitaev model in (a) the spin representation in Eq. (4) and (b) the Majorana representation in Eq. (13). The arrows in (a) represent the spins Si . In (b), the itinerant Majorana fermions γi are represented by the pink spheres, an…
Figure 6
Figure 6. Figure 6: (Color online) Configurations {Wp} for the states (a) S z i |Ψi and (b) S y j |Ψi, where |Ψi represents the flux-free state. S µ i flips two Wp on both sides of the µ bond connected to the site i. As the states with different {Wp} are orthogonal to each other, hΨ|S z i…
Figure 7
Figure 7. Figure 7: (Color online) Dispersion relations of the complex fermion band in the first Brillouin zone and the density of states D0(ω) for the flux-free state at several sets of the exchange parameters with |Jx| + |Jy| + |Jz | = 3. The inset of (d) shows the extended plot of the …
Figure 8
Figure 8. Figure 8: (Color online) (a) Excitation gap in the itinerant fermion band in the flux-free ground state, ∆γ, on the plane of |Jx| + |Jy| + |Jz | = 3. The cyan dot at the center stands for the isotropic point and the dotted lines represent the boundaries between the gapless and g…
Figure 9
Figure 9. Figure 9: (a)]. Note that {Wp} and {ηr} remain conserved within the perturbation theory since the flux configurations are iden￾tical between the initial and final states by definition. By using the Majorana representation in Sec. 2.3, Eq. (22) is written in the form H0 = − ih˜ 8…
Figure 10
Figure 10. Figure 10: (Color online) (a) Dispersion relation of the complex fermion band in the first Brillouin zone for the isotropic case Jx = Jy = Jz = J with the effective magnetic field h˜ = 0.05J. The inset shows the extended plot of the gapped dispersion around the K point. (b) Corr…
Figure 11
Figure 11. Figure 11: (Color online) Gaps in the itinerant fermion band, ∆γ, and for the flux excitation, ∆f , as functions of the effective magnetic field h˜ in the isotropic case Jx = Jy = Jz = J. The same plot is found in the Supplemental Material for Ref. 44. Thus, while the fermionic …
Figure 12
Figure 12. Figure 12: ). There are two distinct features in this thermal Hall effect by the Majorana fermions. One is that the thermal Hall conductivity divided by T is predicted to be quantized at half of that for the integer quantum Hall state.27) This is because each Majorana fermion ca…
Figure 13
Figure 13. Figure 13: (Color online) Phase diagram of the Kitaev-Heisenberg model with J/JHeis = 2 tan ϕ obtained by the exact diagonalization of the 24-site cluster, where J and JHeis are the Kitaev and Heisenberg exchange constants, respectively. Reprinted with permission from Ref. 80 c …
Figure 14
Figure 14. Figure 14: (Color online) Schematic phase diagrams while changing temperature T, magnetic field, and non-Kitaev interactions for the cases with (a) FM and (b) AFM Kitaev couplings. The yellow circle at the origin represents the exact QSL ground state for the Kitaev model. When a…
Figure 16
Figure 16. Figure 16: (Color online) T dependences of (a) the measure of the kinetic energy of itinerant Majorana fermions, Kx, and (b) the thermal average of the Z2 flux, hWpi. Note that Kx = − 2 3 E = 4hS x i S x j i for the isotropic case. The data for L = 12 were taken from Ref. 38. Th…
Figure 17
Figure 17. Figure 17: (Color online) Contour plot of the entropy per site normalized by ln 2 as functions of T and Jz with Jx = Jy = (3 − Jz)/2 for the L = 12 cluster. The solid and dashed curves represent ζGγ and 1 2 ζ∆f , respectively, where Gγ and ∆f are the COM of the fermion DOS for t…
Figure 19
Figure 19. Figure 19: (Color online) (a) T dependence of the fermion DOS D(ω) for the L = 12 cluster. See also [PITH_FULL_IMAGE:figures/full_fig_p014_19.png]
Figure 20
Figure 20. Figure 20: (Color online) Plot of the data in [PITH_FULL_IMAGE:figures/full_fig_p014_20.png]
Figure 21
Figure 21. Figure 21: (Color online) Schematic picture of the triangle-honeycomb struc￾ture. The two sets of Kitaev couplings are also shown. taev coupling, (Jx, Jy, Jz) and (J 0 x , J 0 y , J 0 z ), for the two types of NN bonds, intra-triangle and inter-triangle ones, respectively (see …
Figure 22
Figure 22. Figure 22: (Color online) Finite-T phase diagram of the triangle-honeycomb Kitaev model with (J, J 0 ) = 4(cos α,sin α) obtained by the Majorana-based QMC simulations. Reprinted with permission from Ref. 98 c (2015) the American Physical Society. T Cv (b) (a)S / ln 2 α/π = 0.4 α…
Figure 23
Figure 23. Figure 23: (Color online) T dependences of (a) the specific heat and (b) the entropy per site in the triangle-honeycomb Kitaev model with (J, J 0 ) = 4(cos α,sin α). The horizontal dotted lines in (b) denote 1/3, 1/2, and 2/3 of ln 2. Reprinted with permission from Ref. 98 c (20…
Figure 25
Figure 25. Figure 25: (Color online) T dependences of (a) the specific heat and (b) the entropy per site for the 3D Kitaev model on the hyperhoneycomb lattice with isotropic coupling Jx = Jy = Jz = J. The data are obtained by the Majorana￾based QMC simulations for the clusters with N = 4L …
Figure 26
Figure 26. Figure 26: (Color online) Finite-T phase diagrams for (a) the 3D and (b) 2D Kitaev toric code with the FM Ising interaction Jxx. λB is the coupling con￾stant in the toric code. TCP in (a) and QCP in (b) denote the tricritical point and the quantum critical point, respectively. R…
Figure 27
Figure 27. Figure 27: (Color online) Schematic finite-T phase diagrams of the Kitaev models for (a) the 2D cases like the honeycomb case in Sec. 3.1, (b) the 3D cases like the hyperhoneycomb case in Sec. 3.3.1, and (c) the 2D and 3D cases like the triangle-honeycomb case in Sec. 3.2 and th…
Figure 28
Figure 28. Figure 28: (Color online) Schematic pictures of (a) the hyper- and (b) stripy￾honeycomb structures with edge-sharing octahedra, which are realized in β￾and γ-Li2IrO3, respectively. stacking faults show rather high TN; the lowest TN = 6.5 K was reported for a single crystal with …
Figure 30
Figure 30. Figure 30: (Color online) (a) Real part of the optical conductivity obtained for α-RuCl3 at several T. The inset shows the low-energy detail around the peak α; the data for 100, 200, and 300 K are offset for clarity. (b) T dependence of the spectral weight of the peak α in (a) i…
Figure 29
Figure 29. Figure 29: (Color online) T dependences of the specific heat (Cmag) and en￾tropy (S mag) for (a) Na2IrO3, (b) α-Li2Ir3, and (c) α-RuCl3. In (c), the spe￾cific heat divided by T is plotted. The magnetic contributions are extracted by subtracting the data for the nonmagnetic compo…
Figure 31
Figure 31. Figure 31: (Color online) T dependence of the magnetic susceptibility for the honeycomb Kitaev model with isotropic coupling Jx = Jy = Jz = J obtained by combining the Majorana-based QMC and CTQMC methods. (a) and (b) correspond to the cases with FM and AFM Kitaev coupling, resp…
Figure 32
Figure 32. Figure 32 [PITH_FULL_IMAGE:figures/full_fig_p022_32.png]
Figure 33
Figure 33. Figure 33: (Color online) Dynamical spin structure factor S (q, ω) calculated for the honeycomb Kitaev model with isotropic coupling Jx = Jy = Jz = J for both cases with FM and AFM Kitaev coupling: (a) at T = 0 and (b) for finite T. The finite-T results are obtained by combining…
Figure 34
Figure 34. Figure 34 [PITH_FULL_IMAGE:figures/full_fig_p024_34.png]
Figure 35
Figure 35. Figure 35: (Color online) Comparison of the dynamical spin structure factors between experiment and theory. (a) and (c) show the experimental data for single crystals of α-RuCl3, and (b) and (d) are the theoretical results for the honeycomb Kitaev model with isotropic FM couplin…
Figure 36
Figure 36. Figure 36: (Color online) Inelastic neutron scattering spectra measured for a powder sample of α-RuCl3 at (a) 15 K and 0 T, (b) 2 K and 8 T, and (c) 2 K and 0 T. (d) displays the magnetic phase diagram determined by the T dependence of the magnetic susceptibility shown in the in…
Figure 37
Figure 37. Figure 37: (Color online) T dependence of the NMR relaxation rate 1/T1 for the honeycomb Kitaev model with isotropic coupling Jx = Jy = Jz = J in the zero-field limit. The results are obtained by a combined technique of the Majorana-based QMC and CTQMC methods.41) (a) and (b) di…
Figure 38
Figure 38. Figure 38: In the low-field region for . 9 T where the magnetic ordering takes place at low T, 1/T1 grows gradually while de￾creasing T, and shows a sharp anomaly at the critical tempera￾ture TN, followed by a rapid decrease below TN. On the other hand, in the higher-field regio…
Figure 39
Figure 39. Figure 39: (Color online) (a) T dependence of the thermal conductivity κ for α-RuCl3 and (b) the data after the subtraction of the contributions from phonons. #1-#5 denote different samples. (c) T dependence of the magnetic specific heat Cmag. The inset of (c) shows the T depend…
Figure 38
Figure 38. Figure 38: (Color online) T dependences of the NMR relaxation rate 1/T1 for α-RuCl3. In (a) and (b), the magnetic field is applied along the direction parallel to the electric field gradient at a Cl ion, while in (c), it is tilted from the c axis by the angle θ with fixed magnit…
Figure 41
Figure 41. Figure 41: (Color online) Intensity of the Raman scattering spectrum calcu￾lated for the exact QSL ground state of the honeycomb Kitaev model with isotropic coupling. Note that the energy scale is four-times different, as in [PITH_FULL_IMAGE:figures/full_fig_p028_41.png]
Figure 42
Figure 42. Figure 42: (Color online) (a) Raman scattering intensity measured for α￾RuCl3 at 5 K. (b) Magnetic contributions of the Raman intensity for several T. (c) T dependence of the magnetic Raman intensity integrated between 2.5 and 12.5 meV. The solid and dashed lines represent the f…
Figure 44
Figure 44. Figure 44: (Color online) T dependence of the thermal Hall conductivity κxy divided by T calculated for the effective model for the Kitaev model in a magnetic field derived by the perturbation theory [Eqs (13) and (23)]. h˜ rep￾resents the magnitude of the effective magnetic fie…
Figure 47
Figure 47. Figure 47: summarizes the field-T phase diagram elaborated by the experiments. In the field region between ∼ 7 T and ∼ 9 T after the magnetic order is suppressed (red area in [PITH_FULL_IMAGE:figures/full_fig_p031_47.png]
Figure 46
Figure 46. Figure 46: (Color online) (a) T dependence of κxy/T for α-RuCl3 in a mag￾netic field tilted from the c axis to the a axis by the angle θ. The horizontal dashed line represents the half quantization value. The inset displays the data in a wider-T range. (b) Field dependences of κ…

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Works this paper leans on

257 extracted references · 71 canonical work pages

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