Title: Deviation from the dipole-ice model in the new spinel spin-ice candidate, MgEr$_2$Se$_4$,
Abstract: 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 underexplored 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 neutron
inelastic scattering confirms that the moments have perfect Ising character,
and further identifies the ground state Kramers doublet as having
dipole-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 T$\rightarrow$0 K, but again falls short of the full
Pauling expectation for DSI, unless significant disorder is added. We show that
these observations are fully in-line with what is recently reported for
CdEr$_2$Se$_4$, and point to the importance of quantum fluctuations in these
materials.