Heisenberg-Kitaev model in a magnetic field: 
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 expansion

Cônsoli, Pedro M.; Janssen, Lukas; Vojta, Matthias; Andrade, Eric C.

doi:10.1103/physrevb.102.155134

Cited by 36 publications

(23 citation statements)

References 88 publications

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“…The LSWT is valid up to O(1/S) and can return an unphysical result when the number of magnons is large relative to S. This occurs in the presence of low-lying flat magnon bands where the magnon-magnon interactions cannot be ignored. In such a case the LSWT breaks down and accurate calculation of observables requires a proper accounting of effects beyond the single-magnon picture, which already tend to be significant in noncollinear magnetic orders [61][62][63]. Nevertheless the reduced moment provides a general estimate of the regions of the classical phase space which are most susceptible to a quantum-disordered state [64], and we find that such a phase may be stabilized in the Γ dominant limit with moderate anisotropy.…”

Section: Effects Of Quantum Fluctuationsmentioning

confidence: 86%

Extent of frustration in the classical Kitaev-$Γ$ model via bond anisotropy

Rayyan,

Luo,

Kee

2021

Preprint

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In the pseudospin-1 2 honeycomb Mott insulators with strong spin-orbit coupling, there are two types of bond-dependent exchange interactions named Kitaev (K) and Γ leading to strong frustration. While the ground state of the Kitaev model is a quantum spin liquid with fractionalized excitations, the ground state of Γ model remains controversial. In particular, the phase diagram of KΓ model with ferromagnetic K and antiferromagnetic Γ interactions has been intensively studied because of its relevance to candidate materials such as α-RuCl3. Numerical studies also included the effects of tuning the bond strengths, i.e, z-bond strength different from the other bonds. However, no clear consensus on the overall phase diagram has been reached yet. Here we study the classical KΓ model with the anisotropic bond strength using Monte Carlo simulations to understand the emerging phases out of competition between two frustrated limits. We also address how the anisotropic bond strength affects the phase diagram and strength of quantum fluctuations. We found various large unit cell phases due to the competing frustrations, and analyzed their intrinsic degeneracy based on the symmetry of the Hamiltonian. Using the linear spin wave theory we showed that the anisotropic bond strength enhances quantum fluctuations in the Γ dominant regime where a small reduced moment is observed. The implications of our findings in relation to the quantum model are also discussed.

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Section: Effects Of Quantum Fluctuationsmentioning

confidence: 86%

Extent of frustration in the classical Kitaev-$Γ$ model via bond anisotropy

Rayyan,

Luo,

Kee

2021

Preprint

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“…For all other field orientations, the inhomogeneously canted extensions of the zero-field states compete not only with the polarized state, but also with new symmetry-broken phases that allow more favorable canting mechanisms. This gives rise to complex magnetic orderings and metamagnetic transitions at large S [41][42][43][44].…”

Section: Model and Details Of The Ed Calculationmentioning

confidence: 99%

Stability of ordered and disordered phases in the Heisenberg-Kitaev model in a magnetic field

Cônsoli

Andrade

2022

J. Phys.: Conf. Ser.

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The S = 1/2 Kitaev honeycomb model has attracted significant attention as an exactly solvable example with a quantum spin liquid ground state. In an properly oriented external magnetic field, the system exhibits chiral Majorana edge modes with an associated quantized thermal Hall conductance, and a distinct spin-disordered phase emerges at intermediate field strengths, below the polarized phase. However, since material realizations of Kitaev magnetism invariably display competing exchange interactions, the stability of these exotic phases with respect to additional couplings is a key issue. Here, we report a 24-site exact diagonalization study of the Heisenberg-Kitaev model in a magnetic field applied in the [001] and [111] directions. By mapping the full phase diagram of the model and contrasting the results to recent nonlinear spin-wave calculations, we show that both methods agree well, thus establishing that quantum corrections substantially modify the classical phase diagram. Furthermore, we find that, in a [111] field, the intermediate-field spin-disordered phase is remarkably stable to Heisenberg interactions and may potentially end in a novel quantum tricritical point.

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“…To understand the origin of the magnetic ordering, one has introduced additional interactions such as the Heisenberg and off-diagonal Γ terms in the Kitaev model [18][19][20][21][22][23]. While a lot of efforts have been devoted to clarifying the global phase diagrams of the Kitaev-Heisenberg and Kitaev-Heisenberg-Γ models [23][24][25][26][27][28], the relationship to the candidate materials, in particular, the realistic values of the exchange constants, has been still under debate [29].…”

Section: Introductionmentioning

confidence: 99%

“…Triggered by these experimental results, magnetic-field effects on the Kitaev-related systems have been studied theoretically [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. Moreover, classical phase diagrams of the Kitaev-Heisenberg and Kitaev-Γ models under the magnetic field were obtained by the mean-field (MF) approach and Monte Carlo simulations [25][26][27][28]60]. In the phase diagrams, an applied magnetic field stabilizes various ordered states, including noncollinear and noncoplanar configurations.…”

Section: Introductionmentioning

confidence: 99%

Field-angle dependence of thermal Hall conductivity in a magnetically ordered Kitaev-Heisenberg system

Koyama

Nasu²

2021

Phys. Rev. B

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We study magnetic excitations and thermal Hall effect on the Kitaev-Heisenberg model under magnetic fields. By employing the spin-wave theory for the magnetic orders realized in this model, we examine the topological nature of the spin-wave dispersions and calculate the thermal Hall conductivity. The comprehensive investigations on the field-angle dependence clarify that the thermal Hall conductivity is sensitive to the spin ordered pattern and excitation spectra of magnons; this quantity is enhanced by the noncoplanar spin configurations and small magnon gap in the excitation spectrum. On the other hand, we also find a common feature in the field-angle dependence of the thermal Hall conductivity. It vanishes when the magnetic field is on the planes spanned by the spin axes. We reveal that the behavior is intrinsic to the Kitaev-Heisenberg model in an applied field and demonstrate that the introduction of the off-diagonal spin interaction causes the disappearance of the feature in the thermal Hall conductivity.

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Heisenberg-Kitaev model in a magnetic field: 1/S expansion

Cited by 36 publications

References 88 publications

Extent of frustration in the classical Kitaev-$Γ$ model via bond anisotropy

Extent of frustration in the classical Kitaev-$Γ$ model via bond anisotropy

Stability of ordered and disordered phases in the Heisenberg-Kitaev model in a magnetic field

Field-angle dependence of thermal Hall conductivity in a magnetically ordered Kitaev-Heisenberg system

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