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Possible effective model with strong Kitaev interaction for $\alpha$-${\rm RuCl_3}$

Takafumi Suzuki, Sei-ichiro Suga

Published Feb 2, 2018• 0 citations
OpenAlex

Abstract

We calculate dynamical spin structure factors (DSFs) of three ab-initio models and one ab-initio-guided model for a honeycomb-lattice magnet $\alpha$-RuCl$_3$ 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 $\Gamma$ 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 $\alpha$-RuCl$_3$ 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.

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Semiclassical Routes to the $α$-RuCl$_3$ Scattering Continuum via Model Meta$-$Analysis

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$α$-RuCl$_3$ is a leading material for proximate Kitaev magnetism. We address the origin of the broad, $Γ$-point centered excitation continuum observed by inelastic neutron scattering at elevated temperatures in this compound. Using stochastic Landau-Lifshitz dynamics augmented with quantum-equivalent corrections, we reproduce the temperature-dependent dynamical spin structure factor across both the correlated and conventional paramagnetic regimes. A meta-analysis of 38 published exchange parameter sets identifies those most consistent with the full temperature evolution. A Bayesian optimization procedure is used to derive parameters that capture the low-energy star-like momentum dependence and the overall bandwidth of the continuum. Rescaling temperatures by the Curie--Weiss scale produces a collapse of spectral measures, demonstrating that the high-$T$ dynamics are governed by correlated paramagnetism below $θ_{\mathrm{CW}}$ rather than by the Kitaev crossover to fractionalized excitations. Complementary 24-site exact diagonalization clarifies finite-size systematics at low temperature and the proximity to zigzag/incommensurate ordering. Beyond $α$-RuCl$_3$, our simulation pipeline provides a reproducible, data-driven framework to infer effective spin models in magnets that exhibit broad continua.

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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.
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.
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.
We investigate the dynamical properties of Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​. For five effective models proposed for Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​, we numerically calculate dynamical structure factors (DSFs) with an exact diagonalization method. An effective model obtained from ab initio calculations explains inelastic neutron scattering experiments adequately. We further calculate excitation modes based on linearized spin-wave theory. The spin-wave excitation of the effective models obtained by ab initio calculations disagrees with the low-lying excitation of DSFs. We attribute this discrepancy to the location of Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​ in a parameter space close to the phase boundary with the Kitaev spin-liquid phase.
Semiclassical Routes to the ααα-RuCl3_33​ Scattering Continuum via Model Meta−-−Analysis
ααα-RuCl3_33​ is a leading material for proximate Kitaev magnetism. We address the origin of the broad, ΓΓΓ-point centered excitation continuum observed by inelastic neutron scattering at elevated temperatures in this compound. Using stochastic Landau-Lifshitz dynamics augmented with quantum-equivalent corrections, we reproduce the temperature-dependent dynamical spin structure factor across both the correlated and conventional paramagnetic regimes. A meta-analysis of 38 published exchange parameter sets identifies those most consistent with the full temperature evolution. A Bayesian optimization procedure is used to derive parameters that capture the low-energy star-like momentum dependence and the overall bandwidth of the continuum. Rescaling temperatures by the Curie--Weiss scale produces a collapse of spectral measures, demonstrating that the high-TTT dynamics are governed by correlated paramagnetism below θCWθ_{\mathrm{CW}}θCW​ rather than by the Kitaev crossover to fractionalized excitations. Complementary 24-site exact diagonalization clarifies finite-size systematics at low temperature and the proximity to zigzag/incommensurate ordering. Beyond ααα-RuCl3_33​, our simulation pipeline provides a reproducible, data-driven framework to infer effective spin models in magnets that exhibit broad continua.