Thermal Conductivity through the Quantum Critical Point in ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ at Very Low Temperature

The thermal conductivity of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ has been measured down to very low temperatures under field in the basal plane. An additional channel for heat transport appears below 30 mK, both in the antiferromagnetic and paramagnetic states, respectively, below and above the critical field suppressing the magnetic order. This excludes antiferromagnetic magnons as the origin of this additional contribution to thermal conductivity. Moreover, this low temperature contribution prevails a definite conclusion on the validity or violation of the Wiedemann-Franz law at the field-induced quantum critical point.

Figure 1

Electrical resistivity (full squares) and thermal resistivity (open circles) of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ at 0 T (in black) and at 70 mT, close to $H_c$ (in red) at low temperature. Clear anomalies are observed in zero field at $T_N$, and a new channel for heat transport appears below 30 mK (see text). Inset: Normalized ratio $L(T)/L_0$ in the whole temperature range at 0 T and 70 mT.

Figure 2

Ratio $L(T)/L_0$ at low temperatures below $1\mathrm{T}$. The dashed lines are the extrapolation to $L(0)=0.97L_0$ when $T>30\mathrm{mK}$. Inset: $L(T)/L_0$ at higher fields, which also extrapolates to 0.97 at low temperature.

Figure 3

Comparison of the electronic thermal conductivity using the expression (1) with $\alpha =1$ and $\alpha =2.2$. The latter value was chosen to optimize the low temperature contribution of ${\kappa }_{\text{qp}}$.