Dipolar-octupolar correlations and hierarchy of exchange interactions in Ce${}_2$Hf${}_2$O${}_7$

High-resolution neutron spectroscopy on Ce${}_2$Hf${}_2$O${}_7$ reveals a correlated state characterized by distinct dipolar scattering signals – quasi-elastic and inelastic contributions consistent with photon' and spinon’ excitations in quantum spin ice. These signals coexist with weak octupolar scattering. Fits of thermodynamic data using numerical methods indicate a dominant octupolar exchange, $J_x$ or $J_y$, with substantial dipolar $J_z$ and minute dipole-octupole $J_{xz}$ couplings. The $J_{xz}$ value is corroborated by an independent fit of the neutron scattering amplitude balance between dipolar and octupolar photon' contributions, highlighting its importance to understand neutron scattering results in this family. Ce$_2$Hf$_2$O$_7$ enriches the landscape of dipole-octupole pyrochlore physics, and reveals a quantum multipolar liquid’ where hybrid correlations involve multiple terms in moment series expansion, opening questions on their intertwining and hierarchy in quantum phases.