The in-plane thermal conductivity $\kappa$ and electrical resistivity $\rho$ of the heavy-fermion metal ${\text{YbRh}}_2$${\text{Si}}_2$ were measured down to 50 mK for magnetic fields $H$ parallel and perpendicular to the tetragonal $c$ axis, through the field-tuned quantum critical point $H_c$, at which antiferromagnetic order ends. The thermal and electrical resistivities, $w\equiv L_{0}T/\kappa$ and $\rho$, show a linear temperature dependence below 1 K, typical of the non-Fermi-liquid behavior found near antiferromagnetic quantum critical points, but this dependence does not persist down to $T=0$. Below a characteristic temperature $T^{☆}\simeq 0.35$ K, which depends weakly on $H$, $w\left(T\right)$ and $\rho \left(T\right)$ both deviate downward and converge as $T\to 0$. We propose that $T^{☆}$ marks the onset of short-range magnetic correlations, persisting beyond $H_c$. By comparing samples of different purity, we conclude that the Wiedemann-Franz law holds in ${\text{YbRh}}_2$${\text{Si}}_2$, even at $H_c$, implying that no fundamental breakdown of quasiparticle behavior occurs in this material. The overall phenomenology of heat and charge transport in ${\text{YbRh}}_2$${\text{Si}}_2$ is similar to that observed in the heavy-fermion metal ${\text{CeCoIn}}_5$, near its own field-tuned quantum critical point.

• Received 24 September 2013
• Revised 17 December 2013

DOI:https://doi.org/10.1103/PhysRevB.89.045130