Quantum Criticality in high purity specimens of Ce$_{2}$Rh$_{3}$Ge$_{5}$ and Ce$_{2}$Pt$_{3}$Si$_{5}$

We report results for high purity specimens of the heavy fermion antiferromagnets Ce$_{2}$Rh$_{3}$Ge$_{5}$ and Ce$_{2}$Pt$_{3}$Si$_{5}$, which have similar ordering temperatures: T$_{N} =$ 5.5 K and 6.3 K, respectively, and belong to the same family of materials that includes the pressure-induced superconductor Ce$_{2}$Ni$_{3}$Ge$_{5}$. Our measurements show that the antiferromagnetic state is suppressed to zero temperature at similar magnetic fields (H$_{c} =$ 23 T and 36 T, respectively), suggesting comparable magnetic energy scales in these compounds. In contrast, while the pressure needed to access a quantum critical point (QCP) in Ce$_{2}$Rh$_{3}$Ge$_{5}$ is extremely low (P$_{c}$ $\sim$ 5 kbar), the N\'{e}el temperature for Ce$_{2}$Pt$_{3}$Si$_{5}$ is insensitive to pressures up to 15 kbar. This result implies that although these compounds are markedly similar, the mechanism that drives the QCP in Ce$_{2}$Rh$_{3}$Ge$_{5}$ is not present in Ce$_{2}$Pt$_{3}$Si$_{5}$. We discuss possible differences between these compounds and mechanisms for their quantum criticality with an emphasis on how the shape of the Fermi surface affects their physical properties.