Unusual Phonon Heat Transport in $\alpha \text{−}{\mathrm{RuCl}}_3$: Strong Spin-Phonon Scattering and Field-Induced Spin Gap

The honeycomb Kitaev-Heisenberg model is a source of a quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. Here we unveil the highly unusual low-temperature heat conductivity $\kappa$ of $\alpha \text{−}{\mathrm{RuCl}}_3$, a prime candidate for realizing such physics: beyond a magnetic field of $B_c\approx 7.5\mathrm{T}$, $\kappa$ increases by about one order of magnitude, both for in-plane as well as out-of-plane transport. This clarifies the unusual magnetic field dependence unambiguously to be the result of severe scattering of phonons off putative Kitaev-Heisenberg excitations in combination with a drastic field-induced change of the magnetic excitation spectrum. In particular, an unexpected, large energy gap arises, which increases linearly with the magnetic field, reaching remarkable $\hslash {\omega }_0/k_B\approx 50\mathrm{K}$ at 18 T.

Figure 1

$T$ dependence of the heat conductivity of $\alpha \text{−}{\mathrm{RuCl}}_3$ at zero magnetic field and at $B=16\mathrm{T}$. The heat current was aligned (a) parallel to the $ab$ direction for sample I (${\kappa }_{ab}$) and (b) perpendicular to it for sample II (${\kappa }_c$). In both cases, the field was applied parallel to the $ab$ planes and perpendicular to the heat current. The onset of long-range magnetic order at $T_N\approx 7\mathrm{K}$ and the structural transition at $T_s\approx 155\mathrm{K}$ are indicated.

Figure 2

$B$ and $T$ dependence of the heat conductivity of $\alpha \text{−}{\mathrm{RuCl}}_3$ (sample I) with the heat current and the magnetic field $B$ parallel to the $ab$ planes. (a) Isothermal field-dependent heat conductivity ${\kappa }_{ab}(B)$ for selected $T$. (b) ${\kappa }_{ab}(T)$ for $B>7.5\mathrm{T}$, measured in steps of 0.5 T.

Figure 3

False-color representation of the $T$ derivative $\partial {\kappa }_{ab}(T,B)/\partial T$ (sample I) together with the gap energy $\hslash {\omega }_0/k_B$ (solid squares) extracted from the phononic fits. The color scale is in units of $\mathrm{W}/{\mathrm{K}}^2\mathrm{m}$. The left ordinate shows the temperature $T$ of the measurement, while the right ordinate shows $\hslash {\omega }_0/k_B$. Note that for $B\le 12\mathrm{T}$, an unambiguous extraction of ${\omega }_0$ cannot be obtained from fitting ${\kappa }_{ab}(T)$, because the $T_{\min }$ is too close to the lower limit of the measurement range. Nevertheless, good fits to the data are obtained if ${\omega }_0(B)$ for $B>12\mathrm{T}$ is extrapolated towards smaller fields (open squares) and subsequently used to fit ${\kappa }_{ab}(T)$ at the corresponding fields (see the Supplemental Material [27]). These extrapolated ${\omega }_0$’s should be regarded as an upper limit only. The data can be described similarly well with a somewhat smaller ${\omega }_0(B)$ (dotted line).

Figure 4

${\kappa }_{ab}$ data of sample I (solid circles) and fits (solid lines) to the Callaway model for selected magnetic fields. The fits have been obtained by incorporating magnetic scattering of the phonons (see the Supplemental Material [27]). Inset: ${\kappa }_{ab}$ data of sample I (solid circles) at zero field as compared to the hypothetical phononic heat conductivity described by the model if the magnetic scattering mechanism is switched off (dashed line). This highlights that the magnetic scattering affects the phonon heat conductivity in a very large temperature range, where the field-induced changes occur essentially at $T<50\mathrm{K}$.