We have investigated the longitudinal thermal conductivity of $alpha$-RuCl$_{3}$, the magnetic state of which is considered to be proximate to a Kitaev honeycomb model, along with the spin susceptibility and magnetic specific heat. We found that the temperature dependence of the thermal conductivity exhibits an additional peak around 100 K, which is well above the phonon peak temperature ($sim$ 50 K). The higher-temperature peak position is comparable to the temperature scale of the Kitaev couplings rather than the Neel temperatures below 15 K. The additional heat conduction was observed for all five samples used in this study, and was found to be rather immune to a structural phase transition of $alpha$-RuCl$_{3}$, which suggests its different origin from phonons. Combined with experimental results of the magnetic specific heat, our transport measurement suggests strongly that the higher-temperature peak in the thermal conductivity is attributed to itinerant spin excitations associated with the Kitaev couplings of $alpha$-RuCl$_{3}$. A kinetic approximation of the magnetic thermal conductivity yields a mean free path of $sim$ 20 nm at 100 K, which is well longer than the nearest Ru-Ru distance ($sim$ 3 AA), suggesting the long-distance coherent propagation of magnetic excitations driven by the Kitaev couplings.
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