Field induced phase transition in layered honeycomb spin system $\alpha$-$\textrm{RuCl}_3$ studied by thermal conductivity*

$\alpha$-$\textrm{RuCl}_3$, a quasi –two-dimensional honeycomb lattice is known to be a candidate material to realize the Heisenberg-Kitaev spin model of a highly anisotropic bond-dependent exchange interaction. We investigate in-plane thermal conductivity ($\kappa$) as a function of temperature ($T$) and in-plane applied field ($H$). At $H=0$, the onset of a strong increase in $\kappa$ marks the spontaneous long range ordering temperature, $T_c = 6.5\mathrm{K}$, corresponding to “zigzag” antiferromagnetic ordering. A broad peak appearing below $T_c$ in $\kappa$ was found to be suppressed significantly as $H$ increases up to $\approx 7 \mathrm{T}$, implying the system undergoes a field-induced transition from ordered to a new spin-disordered state analogous to the transverse-field Ising model. Further increasing $H$ above $7.1\mathrm{T}$, the large field seems to begin polarizing spins thus increasing the phonon mean free path, resulting in a significant rise in $\kappa$. This tendency is clearly shown in the field dependence of $\kappa$ below $T_c$, which has a pronounced minimum at $H_{{\mathrm{min}}}=7.1\mathrm{T}$. We will discuss our scaling analysis to characterize this field-induced phase transition and compare to the transverse-field Ising spin system.