  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.
