Divergence of the Grüneisen Ratio at Quantum Critical Points in Heavy Fermion Metals

We present low-temperature volume thermal expansion, $\beta$, and specific heat, $C$, measurements on high-quality single crystals of ${\mathrm{C}\mathrm{e}\mathrm{N}\mathrm{i}}_2{\mathrm{G}\mathrm{e}}_2$ and ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2({\mathrm{S}\mathrm{i}}_{0.95}{\mathrm{G}\mathrm{e}}_{0.05}{)}_2$ which are located very near to quantum critical points. For both systems, $\beta$ shows a more singular temperature dependence than $C$, and thus the Grüneisen ratio $\Gamma \propto \beta /C$ diverges as $T\to 0$. For ${\mathrm{C}\mathrm{e}\mathrm{N}\mathrm{i}}_2{\mathrm{G}\mathrm{e}}_2$, our results are in accordance with the spin-density wave (SDW) scenario for three-dimensional critical spin fluctuations. By contrast, the observed singularity in ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2({\mathrm{S}\mathrm{i}}_{0.95}{\mathrm{G}\mathrm{e}}_{0.05}{)}_2$ cannot be explained by the itinerant SDW theory but is qualitatively consistent with a locally quantum critical picture.