Ultralow-Temperature Thermal Conductivity of the Kitaev Honeycomb Magnet $\alpha \text{−}{\mathrm{RuCl}}_3$ across the Field-Induced Phase Transition

Recently, there have been increasingly hot debates on whether there exists a quantum spin liquid in the Kitaev honeycomb magnet $\alpha$-${\mathrm{RuCl}}_3$ in a high magnetic field. To investigate this issue, we perform ultralow-temperature thermal conductivity measurements on single crystals of $\alpha$-${\mathrm{RuCl}}_3$ down to 80 mK and up to 9 T. Our experiments clearly show a field-induced phase transition occurring at ${\mu }_0{H}_c\approx 7.5\mathrm{T}$, above which the magnetic order is completely suppressed. The minimum of thermal conductivity at 7.5 T is attributed to the strong scattering of phonons by magnetic fluctuations. Most importantly, above 7.5 T, we do not observe any significant contribution of thermal conductivity from gapless magnetic excitations, which puts a strong constraint on the nature of the high-field phase of $\alpha$-${\mathrm{RuCl}}_3$.

Figure 1

(a) Illustration of edge-sharing ${\mathrm{RuCl}}_6$ octahedra that give rise to a dominant Kitaev exchange interactions in $\alpha$-${\mathrm{RuCl}}_3$ [36]. (b) The $ab$-plane structure of $\alpha$-${\mathrm{RuCl}}_3$, where edge-sharing ${\mathrm{RuCl}}_6$ octahedra form a honeycomb network. (c) Room-temperature x-ray diffraction pattern from the large natural surface of the $\alpha$-${\mathrm{RuCl}}_3$ single crystal. Only ($00l$) Bragg peaks show up, indicating that the large natural surface is the $ab$ plane. Inset: the optical image of a typical $\alpha$-${\mathrm{RuCl}}_3$ single crystal. (d) Temperature dependence of the magnetic susceptibility at ${\mu }_{0}H=0.1\mathrm{T}\parallel$ $ab$ and the specific heat in zero field for the $\alpha$-${\mathrm{RuCl}}_3$ single crystal.

Figure 2

(a) Temperature dependence of inverse magnetic susceptibility for the $\alpha$-${\mathrm{RuCl}}_3$ single crystal in a magnetic field ${\mu }_{0}H=0.1\mathrm{T}$ applied both parallel and perpendicular to the $ab$ plane. The black lines are fits to the Curie-Weiss law. (b) The magnetic susceptibility of the $\alpha$-${\mathrm{RuCl}}_3$ single crystal in various magnetic fields up to 9 T ($H\parallel$ $ab$). (c) A schematic $T\text{−}H$ phase diagram for $\alpha$-${\mathrm{RuCl}}_3$, where $T_N$ is obtained from the kink in the $\chi (T)$ curve. The zigzag magnetic order disappears at a critical field ${\mu }_0{H}_c\sim 7.5\mathrm{T}$.

Figure 3

(a) and (b) The in-plane thermal conductivity of the $\alpha$-${\mathrm{RuCl}}_3$ single crystal in zero and finite magnetic fields. (c) Field dependence of the $\kappa /T$ at $T=0.2$, 0.3, 0.4, and 0.6 K, respectively. For all curves, the $\kappa /T$ first increases slightly for ${\mu }_{0}H<4\mathrm{T}$, then drops rapidly until 7.5 T, followed by a sharp increase. The minimum $\kappa /T$ at $\sim 7.5\mathrm{T}$ corresponds to $H_c$, where the zigzag magnetic order disappears.

Figure 4

(a) The thermal conductivity data of the $\alpha$-${\mathrm{RuCl}}_3$ single crystal in the zigzag magnetic order (${\mu }_{0}H=0\mathrm{T}$) and the high-field phase (${\mu }_{0}H=8.5\mathrm{T}$). Lines are fits to $\kappa /T={\kappa }_0/T+b{T}^{\alpha -1}$ for $T<0.4\mathrm{K}$. (b) Field dependence of the residual linear term ${\kappa }_0/T$. These values of ${\kappa }_0/T$ are virtually zero, indicating the absence of gapless fermionic magnetic excitations.