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We have investigated the longitudinal thermal conductivity of$\alpha$-RuCl$_{3}$, the magnetic state of which is considered to be proximateto a Kitaev honeycomb model, along with the spin susceptibility and magneticspecific heat. We found that the temperature dependence of the thermalconductivity exhibits an additional peak around 100 K, which is well above thephonon peak temperature ($\sim$ 50 K). The higher-temperature peak position iscomparable to the temperature scale of the Kitaev couplings rather than theN\'eel temperatures below 15 K. The additional heat conduction was observed forall five samples used in this study, and was found to be rather immune to astructural phase transition of $\alpha$-RuCl$_{3}$, which suggests itsdifferent origin from phonons. Combined with experimental results of themagnetic specific heat, our transport measurement suggests strongly that thehigher-temperature peak in the thermal conductivity is attributed to itinerantspin excitations associated with the Kitaev couplings of $\alpha$-RuCl$_{3}$. Akinetic approximation of the magnetic thermal conductivity yields a mean freepath of $\sim$ 20 nm at 100 K, which is well longer than the nearest Ru-Rudistance ($\sim$ 3 \AA), suggesting the long-distance coherent propagation ofmagnetic excitations driven by the Kitaev couplings.

Magnetic thermal conductivity far above the N\'eel temperatures in the Kitaev-magnet candidate $\alpha$-RuCl$_{3}$