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Excitations in a spin ice behave as magnetic monopoles, and their populationand mobility control the dynamics of a spin ice at low temperature.CdEr$_2$Se$_4$ is reported to have the Pauling entropy characteristic of a spinice, but its dynamics are three-orders of magnitude faster than the canonicalspin ice Dy$_2$Ti$_2$O$_7$. In this letter we use diffuse neutron scattering toshow that both CdEr$_2$Se$_4$ and CdEr$_2$S$_4$ support a dipolar spin icestate -- the host phase for a Coulomb gas of emergent magnetic monopoles. TheseCoulomb gases have similar parameters to that in Dy$_2$Ti$_2$O$_7$, i.e. diluteand uncorrelated, so cannot provide three-orders faster dynamics through alarger monopole population alone. We investigate the monopole dynamics using acsusceptometry and neutron spin echo spectroscopy, and verify the crystalelectric field Hamiltonian of the Er$^{3+}$ ions using inelastic neutronscattering. A quantitative calculation of the monopole hopping rate using ourCoulomb gas and crystal electric field parameters shows that the fast dynamicsin CdEr$_2$X$_4$ (X = Se, S) are primarily due to much faster monopole hopping.Our work suggests that CdEr$_2$X$_4$ offer the possibility to study alternativespin ice ground states and dynamics, with equilibration possible at much lowertemperatures than the rare earth pyrochlore examples.

Dipolar spin ice states with fast monopole hopping rate in CdEr$_2$X$_4$ (X = Se, S)