Anomalous Reduction of the Lorenz Ratio at the Quantum Critical Point in YbAgGe

We report measurements of the electrical and thermal transport on the hexagonal heavy-fermion metal YbAgGe for temperatures $T\ge 40\mathrm{mK}$ and in magnetic fields $H\parallel ab$ up to 14 T. This distorted kagome-lattice system displays a series of magnetic states and a quantum critical point at $H_c=4.5\mathrm{T}$. The Lorenz ratio $L(T)/L_0$ displays a marked reduction only close to $H_c$. A $T$-linear contribution below 120 mK, present at all different fields, allows us to extrapolate the Lorenz ratio towards $T=0$. At the critical field this yields $L/L_0=0.92\pm 0.03$, suggesting a violation of the Wiedemann-Franz law due to strong inelastic scattering.

Figure 1

Schematic $T\mathrm{\text{−}}H$ phase diagram of YbAgGe for $H\parallel ab$, summarizing earlier measurements [19]. Below 4.5 T, commensurate AF order forms in phase $a$, then changes to incommensurate AF order in phase $b$, and finally returns back to commensurate AF order in $c$ [21, 22]. A sign change of the thermal expansion coefficient ($\alpha$) appears near the border between the regions $c$ and $d$. Electrical resistivity $\rho (T)$ varies as $T^n$ with $n\simeq 1$ in region $d$, $1<n<2$ in $e$, and $n=2$ in region $f$ [18]. The red circle indicates the position of the presumed quantum critical end point at $H_c=4.5\mathrm{T}$.

Figure 2

Temperature dependence of the electrical resistivity $\rho (T)$ of YbAgGe along the $c$ direction at various magnetic fields $H\parallel ab$.

Figure 3

Temperature dependence of the thermal conductivity divided by temperature $\kappa (T)/T$ of YbAgGe at different magnetic fields.

Figure 4

Temperature dependence of the normalized Lorenz ratio $L(T)/L_0=\kappa \rho /(L_{0}T)$ for various different magnetic fields. The solid lines indicate linear fits to the data. Error bars at data points represent the statistical scattering whereas those at the lines near absolute zero temperature indicate the systematic error for the extrapolated Lorenz ratio arising from the finite width of the contacts.