  Excitations in a spin ice behave as magnetic monopoles, and their population
and 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 spin
ice, but its dynamics are three-orders of magnitude faster than the canonical
spin ice Dy$_2$Ti$_2$O$_7$. In this letter we use diffuse neutron scattering to
show that both CdEr$_2$Se$_4$ and CdEr$_2$S$_4$ support a dipolar spin ice
state -- the host phase for a Coulomb gas of emergent magnetic monopoles. These
Coulomb gases have similar parameters to that in Dy$_2$Ti$_2$O$_7$, i.e. dilute
and uncorrelated, so cannot provide three-orders faster dynamics through a
larger monopole population alone. We investigate the monopole dynamics using ac
susceptometry and neutron spin echo spectroscopy, and verify the crystal
electric field Hamiltonian of the Er$^{3+}$ ions using inelastic neutron
scattering. A quantitative calculation of the monopole hopping rate using our
Coulomb gas and crystal electric field parameters shows that the fast dynamics
in 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 alternative
spin ice ground states and dynamics, with equilibration possible at much lower
temperatures than the rare earth pyrochlore examples.
