Effective model with strong Kitaev interactions for $\alpha$-${\rm RuCl_3}$

TL;DR

This study uses numerical methods to analyze models of $ ext{RuCl}_3$, finding that a strong ferromagnetic Kitaev interaction model best explains experimental data, highlighting the importance of off-diagonal and weak Heisenberg interactions.

Contribution

The paper introduces an effective model with strong ferromagnetic Kitaev interactions that accurately reproduces experimental observations of $ ext{RuCl}_3$.

Findings

The proposed model matches inelastic neutron scattering data.

The model reproduces heat capacity measurements.

Low-energy excitations are mainly due to off-diagonal and weak Heisenberg interactions.

Abstract

We use an exact numerical diagonalization method to calculate the dynamical spin structure factors (DSFs) of three ab-initio models and one ab-initio-guided model for a honeycomb-lattice magnet $\alpha$-RuCl$_3$. We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor (NN) 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 $\Gamma$ point in the DSFs increases with increasing NN 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 (INS) experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the NN 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 INS 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 $\alpha$-RuCl$_3$ is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between NN pairs, rather than by the strong Kitaev interactions.