High-field thermal transport properties of the Kitaev quantum magnet $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$: Evidence for low-energy excitations beyond the critical field

We investigate the phononic in-plane longitudinal low-temperature thermal conductivity ${\kappa }_{ab}$ of the Kitaev quantum magnet $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ for large in-plane magnetic fields up to 33 T. Our data reveal, for fields larger than the critical field $B_c\approx 8\mathrm{T}$, at which the magnetic order is suppressed, a dramatic increase of ${\kappa }_{ab}$ at all temperatures investigated. The analysis of our data shows that the phonons are not only strongly scattered by a magnetic mode at relatively large energy which scales roughly linearly with the magnetic field, but also by a small-energy mode which emerges near $B_c$ with a square-root-like field dependence. While the former is in striking agreement with recent spin-wave theory (SWT) results of the magnetic excitation spectrum at the $\mathrm{\Gamma }$ point, the energy of the latter is too small to be compatible with the SWT-expected magnon gap at the $M$ point, despite the matching field dependence. Therefore, an alternative scenario based on phonon scattering off the thermal excitation of random-singlet states is proposed.

Figure 1

Temperature dependence of the longitudinal heat conductivity ${\kappa }_{ab}$ of $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ parallel to the honeycomb layers in zero and high in-plane magnetic fields. Data for $10\le B\le 16\mathrm{T}$ were taken at IFW Dresden (squares), data for the same sample, $B=0$ and $B\ge 18\mathrm{T}$ at HFML (circles). The temperature scale is logarithmic; dashed lines are guides to the eye.

Figure 2

(a),(b) Magnetic field-dependent data of the longitudinal heat conductivity ${\kappa }_{ab}$ of $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ parallel to the honeycomb layers at constant $T$. The data of sample 1 were taken at IFW Dresden (open squares) as well as at HFML (open circles); sample 2 was measured at HFML (open triangles). (a) At $B\gtrsim B_c$, ${\kappa }_{ab}$ increases strongly at all temperatures measured. (b) Semilogarithmic plot of the low-$T$ data—a substantial field dependence up to the highest field is visible down to the lowest temperatures, as discussed in the main text. (c) Illustration of the expected relative field dependencies ${\kappa }_{\mathrm{rel}}=[{\kappa }_{ab}\left(B\right)-{\kappa }_{ab}\left(10\mathrm{T}\right)]/{\kappa }_{ab}\left(10\mathrm{T}\right)$ at three distinct temperature regimes (see text) for a model comprising one characteristic magnetic scattering mode of energy $\mathrm{\Delta }$. Details on the calculations are specified in the Appendix.

Figure 3

(a) Temperature dependence of ${\kappa }_{ab}$ of $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ (open symbols, sample 1) for $T\gtrsim 8\mathrm{K}$ with fits to the two-mode model. The inset shows the field dependence of the obtained energy scales $\hslash {\omega }_0\left(B\right)$ (red) and $\hslash {\omega }_1\left(B\right)$ (green, scaled for better visibility). The square-root fit to the low-energy excitation's energy is indicated by the dashed line. Open squares are the literature data for $\hslash {\omega }_0\left(B\right)$, reproduced from Ref. [30]. (b) Low-temperature magnetic field dependence of ${\kappa }_{ab}$ (open symbols, sample 2); lines are fits as described in the text.

Figure 4

Field dependence of $\hslash {\omega }_1\left(B\right)$ (green circles) and multiple fits thereof according to Eq. (A4).