Thermopower Evidence for an Abrupt Fermi Surface Change at the Quantum Critical Point of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$

We present low-temperature thermopower results, $S(T)$, on the heavy-fermion compound ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ in the vicinity of its field-induced quantum critical point (QCP). At $B=0$, a logarithmic increase of $-S(T)/T$ between 1 and 0.1 K reveals strong non-Fermi-liquid behavior. A pronounced downturn of $-S(T)/T$ below $T_{\max }=0.1\mathrm{K}$ and a sign change from negative to positive $S(T)$ values at $T_0\approx 30\mathrm{mK}$ are observed on the low-field side of the Kondo breakdown crossover line $T^{*}(B)$. In the field-induced, heavy Landau-Fermi-liquid regime, $S(T)/T$ assumes constant, negative values below $T_{\mathrm{LFL}}$. A pronounced crossover in the $-S(B)/T$ isotherms at $T^{*}(B)$ sharpens with decreasing $T$ and seems to evolve toward a steplike function for $T\to 0$. This is attributed to an abrupt change of the Fermi volume upon crossing the unconventional QCP of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$.

Figure 1

(a) Low-temperature thermopower $S(T)$ of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ for small fields $0\le B\le 0.1\mathrm{T}$ on a linear $T$ scale. The $S(T)$ curves are shifted by $\Delta S=-0.6\mu \mathrm{V}/\mathrm{K}$ for clarity. A sign change from negative to positive appears at $T_0\approx 30\mathrm{mK}$ at $B<B_c$. The positions of $T_N$ deduced from $\rho (T)$ results are marked by arrows. The dashed line represents $S=\alpha T$ indicating LFL behavior at $B=0.1\mathrm{T}$. (b) Negative thermopower divided by temperature, $-S(T)/T$, in a semilogarithmic plot. The dashed lines indicate constant $-S(T)/T$ below the NFL-LFL crossover temperature, $T_{\mathrm{LFL}}$. Inset: $-S(T)/T$ vs $T$ at $B=0$. A pronounced anomaly at $T_{\max }\approx 0.1\mathrm{K}$ occurs well above $T_N$. The solid line represents a logarithmic increase of $-S(T)/T$ upon cooling.

Figure 2

Field dependence of the initial slope of the thermopower, $-{\alpha }_0=-S(T)/T$, and of the Sommerfeld coefficient ${\gamma }_0$ [25], as a function of ($B-B_c$). Inset: Field dependence of the Néel temperature $T_N$, the NFL-LFL crossover temperature $T_{\mathrm{LFL}}$, as well as of the temperatures of the sign change $T_0$ and the maximum $T_{\max }$ in $-S(T)/T$. $T_N$ was derived from $\rho (T)$ results on the same sample and $T_{\mathrm{LFL}}$ either from $\rho (T)$ (onset of $\Delta \rho \propto T^2$, circles) or from $S(T)$ measurements (onset of $S\propto T$, diamonds). $T_N(B)$ and $T_{\mathrm{LFL}}(B)$ extrapolate to a critical field $B_c=64\mathrm{mT}$. The crossover line $T^{*}(B)$ was taken from 3 and scaled to $B_c$ of the particular sample. $q$ denotes the ratio of $S/T$ and $c_p/T$.

Figure 3

$-S/T$ vs $B$ isotherms for different temperatures. The arrows mark the positions of $T^{*}(B)$ [3]. The solid lines are guides to the eye.