Deviation from the dipole-ice model in the new spinel spin-ice candidate, MgEr$_2$Se$_4$

In spin ice research, small variations in structure or interactions drive a multitude of different behaviors, yet the collection of known materials relies heavily on the `227 pyrochlore structure. Here, we present thermodynamic, structural and inelastic neutron scattering data on a new spin-ice material, MgEr$_2$Se$_4$, which contributes to the relatively under-explored family of rare-earth spinel chalcogenides. X-ray and neutron diffraction confirm a normal spinel structure, and places Er$^{3+}$ moments on an ideal pyrochlore sublattice. Measurement of crystal electric field excitations with inelastic neutron scattering confirms that the moments have perfect Ising character, and further identifies the ground state Kramers doublet as having dipolar-octupolar form with a significant multipolar character. Heat capacity and magnetic neutron diffuse scattering have ice-like features, but are inconsistent with Monte Carlo simulations of the nearest-neighbor and next-nearest-neighbor dipolar spin-ice (DSI) models. A significant remnant entropy is observed as $Trightarrow0$~K, but again falls short of the full Pauling expectation for DSI, unless significant disorder is added. We show that these observations are fully in-line with what is recently reported for CdEr$_2$Se$_4$, and point to the importance of quantum fluctuations in these materials.