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We report the synthesis of powder and single-crystal samples of the ceriumpyrohafnate and their characterization using neutron diffraction,thermogravimetry and X-ray absorption spectroscopy. We evaluate the amount ofnon-magnetic Ce$^{4+}$ defects and use this result to interpret the spectrum ofcrystal-electric field transitions observed using inelastic neutron scattering.The analysis of these single-ion transitions indicates the dipole-octupolenature of the ground state doublet and a significant degree of spin-latticecoupling. The single-ion properties calculated from the crystal-electric fieldparameters obtained spectroscopically are in good agreement with bulk magneticsusceptibility data down to about 1 K. Below this temperature, the behavior ofthe magnetic susceptibility indicates a correlated regime without showing anysign of magnetic long-range order or freezing down to 0.08 K. We conclude thatCe$_2$Hf$_2$O$_{7}$ is another candidate to investigate exotic correlatedstates of quantum matter such as the octupolar quantum spin ice recently arguedto exist in the isostructural compounds Ce$_2$Sn$_2$O$_7$ andCe$_2$Zr$_2$O$_7$.

Crystal-field states and defect levels in candidate quantum spin ice Ce$_{2}$Hf$_{2}$O$_{7}$