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arXiv:1802.00545 · Physical review. B./Physical review. B

Effective model with strong Kitaev interactions for α−RuCl3

Takafumi Suzuki, Sei-ichiro Suga

Published Apr 25, 2018• 41 citations
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Abstract

We use an exact numerical diagonalization method to calculate the dynamical spin structure factors of three ab initio models and one ab initio guided model for a honeycomb-lattice magnet $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the $\mathrm{\ensuremath{\Gamma}}$ point in the dynamical spin structure factors increases with increasing nearest-neighbor spin correlation. In addition, we find that the four models fail to explain heat-capacity measurements whereas two of the four models succeed in explaining inelastic-neutron-scattering experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function increases. However, the peak temperature in heat capacity is too low in comparison with that observed experimentally. To address these discrepancies, we propose an effective model that includes strong ferromagnetic Kitaev coupling, and we show that this model quantitatively reproduces both inelastic-neutron-scattering experiments and heat-capacity measurements. To further examine the adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra, which reproduces the experimental results: the spin-gapped excitation survives up to an onset field where the magnetic order disappears and the response in the high-field region is almost linear. Based on these numerical results, we argue that the low-energy magnetic excitation in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between nearest-neighbor pairs, rather than by the strong Kitaev interactions.

DOI
10.1103/physrevb.97.134424

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We use an exact numerical diagonalization method to calculate the dynamical spin structure factors of three ab initio models and one ab initio guided model for a honeycomb-lattice magnet \ensuremathα\ensuremath-RuCl3\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}\ensuremathα\ensuremath-RuCl3​. We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the \ensuremathΓ\mathrm{\ensuremath{\Gamma}}\ensuremathΓ point in the dynamical spin structure factors increases with increasing nearest-neighbor spin correlation. In addition, we find that the four models fail to explain heat-capacity measurements whereas two of the four models succeed in explaining inelastic-neutron-scattering experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function increases. However, the peak temperature in heat capacity is too low in comparison with that observed experimentally. To address these discrepancies, we propose an effective model that includes strong ferromagnetic Kitaev coupling, and we show that this model quantitatively reproduces both inelastic-neutron-scattering experiments and heat-capacity measurements. To further examine the adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra, which reproduces the experimental results: the spin-gapped excitation survives up to an onset field where the magnetic order disappears and the response in the high-field region is almost linear. Based on these numerical results, we argue that the low-energy magnetic excitation in \ensuremathα\ensuremath-RuCl3\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}\ensuremathα\ensuremath-RuCl3​ is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between nearest-neighbor pairs, rather than by the strong Kitaev interactions.
Possible effective model with strong Kitaev interaction for α\alphaα-RuCl3{\rm RuCl_3}RuCl3​
We calculate dynamical spin structure factors (DSFs) of three ab-initio models and one ab-initio-guided model for a honeycomb-lattice magnet α\alphaα-RuCl3_33​ with an exact numerical diagonalization method. We also calculate temperature dependences of the heat capacity, the nearest-neighbor (NN) spin-spin correlation function, and the static spin structure factor by employing thermal pure quantum states. From the obtained results for the four effective models, we find that, even when the magnetic order appears at a low temperature, the intensity at the Γ\GammaΓ point in the DSFs grows as the NN spin correlation grows. In addition, we find that the four models fail in explaining the features of both the inelastic-neutron-scattering experiments and the heat capacity measurements. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function grows. However, the peak temperatures in the heat capacity are too low in comparison with the observed values in the experiments. Thus, we propose an effective model with the strong ferromagnetic Kitaev coupling. We show that the proposed model quantitatively reproduces the above two experimental features. To discuss the further adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra. We find that the proposed model successfully reproduces the experimental results: the spin-gapped excitation surviving up to an onset field where the magnetic order disappears and the almost linear response in the high field region. From the obtained numerical results, we argue that the feature of the low-energy magnetic excitation in α\alphaα-RuCl3_33​ is mainly characterized by the other interactions rather than the most dominant Kitaev interactions such as the off-diagonal interactions on the nearest-neighbor pairs.
Honeycomb-lattice magnet α-RuCl 3 is considered to be a potential candidate of realizing Kitaev spin liquid, although this material undergoes a phase transition to the zigzag magnetically ordered state at T N ∼ 7 K. Quite recently, inelastic neutron-scattering experiments using single crystal α-RuCl 3 have unveiled characteristic dynamical properties. We calculate dynamical spin structure factors of three ab-initio models for α-RuCl 3 with an exact numerical diagonalization method. We also calculate temperature dependences of the specific heat by employing thermal pure quantum states. We compare our numerical results with the experiments and discuss characteristics obtained by using three ab-initio models.
Abstract What is the correct low-energy spin Hamiltonian description of α\alphaα α -RuCl 3_{3}3​ 3 ? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of α\alphaα α -RuCl 3_{3}3​ 3 . In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in the magnetic specific heat, while overestimating the magnon energy at the zone center. In contrast, other models reproduce important features of the INS data, but do not adequately describe the magnetic specific heat. To address this discrepancy we propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.
We calculate polarized terahertz (THz) spectra of two effective models for a honeycomb-lattice magnet α-RuCl3 by using a numerical exact-diagonalization method. One of the two models is the ab initio model proposed in H.-S. Kim and H.-Y. Kee [Phys. Rev. B 93, 155143 (2016)] and the other is the large-|K| model that we have proposed by an empirical way in order to explain experimental results for α-RuCl3. We discuss the magnetic-field dependence of the lowest-excitation mode in the polarized THz spectra for the two models. We find that the energy gap of the lowest-excitation mode in both models does not close and increases almost linearly above the critical field, where the zigzag order is suppressed. From the obtained results, we point out that the low-energy excitation is mainly governed not by the Kitaev interaction but by the Heisenberg interaction and the off-diagonal interactions.
It is known that α-RuCl3 has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on α-RuCl3 single crystals to explore the scattering continuum around the Γ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that, while the spin-wave excitations around the M point vanish above the transition temperature T N, the pure magnetic continuous excitations around the Γ point are robust against temperature. Furthermore, by calculating the dynamical spin-spin correlation function using the cluster perturbation theory, we derive magnetic dispersion spectra based on the K–Γ model, which involves with a ferromagnetic Kitaev interaction of –7.2 meV and an off-diagonal interaction of 5.6 meV. We find this model can reproduce not only the spin-wave excitation spectra around the M point, but also the non-spin-wave continuous magnetic excitations around the Γ point. These results provide evidence for the existence of fractional excitations around the Γ point originating from the Kitaev QSL state, and further support the validity of the K–Γ model as the effective minimal spin model to describe α-RuCl3.
Using quantum chemistry calculations we shed fresh light on the electronic structure and magnetic properties of RuCl3, a proposed realization of the honeycomb Kitaev spin model. It is found that the nearest-neighbor Kitaev exchange K is weaker than in 5d5 Ir oxides but still larger than other effective spin couplings. The electronic-structure computations also indicate a ferromagnetic K in the halide, which is supported by a detailed analysis of the field-dependent magnetization. From exact-diagonalization calculations for extended Kitaev-Heisenberg Hamiltonians we additionally find that a transition from zigzag order to a spin-liquid ground state can be induced in RuCl3 with external magnetic field.