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

Abstract

We present low-temperature volume thermal expansion, $\ensuremath{\beta}$, 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, $\ensuremath{\beta}$ shows a more singular temperature dependence than $C$, and thus the Gr\"uneisen ratio $\ensuremath{\Gamma}\ensuremath{\propto}\ensuremath{\beta}/C$ diverges as $T\ensuremath{\rightarrow}0$. 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.