Complex Transport and Magnetism in Inhomogeneous Mixed Valence Ce$_3$Ir$_4$Ge$_{13}$

We report the discovery of Ce$_3$Ir$_4$Ge$_{13}$, a new Remeika phase compound with a complex array of structural, electronic, and magnetic properties. Our single crystal x-ray diffraction measurements show that Ce$_3$Ir$_4$Ge$_{13}$ forms in the tetragonally distorted $I4_1/amd$ space group. The electrical resistivity is almost temperature independent over three decades in temperature, from 0.4 K to 400 K, while the Hall coefficient measurements are consistent with a low-carrier semimetal. Magnetic susceptibility measurements reveal an effective moment of $\mu^{\text{exp}}_{\text{eff}} = 1.87 \mu_B$/Ce, suggesting that this material has a mixture of magnetic Ce$^{3+}$ and non-magnetic Ce$^{4+}$. Upon cooling, Ce$_3$Ir$_4$Ge$_{13}$ first enters a short range magnetically ordered state below $T_{\text{SRO}}=10$ K, marked by a deviation from Curie-Weiss behavior in susceptibility and a broad field-independent heat capacity anomaly. At lower temperatures, we observe a second, sharper peak in the heat capacity at $T^* = 1.7$ K, concurrent with a splitting of the field-cooled and zero-field-cooled susceptibilities. A small resistivity drop at $T^*$ suggests a loss of spin disorder scattering consistent with a magnetic ordering or spin freezing transition. Ce$_3$Ir$_4$Ge$_{13}$ is therefore a rare example of an inhomogeneous mixed valence compound with a complex array of thermodynamic and transport properties.