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

## TL;DR

This study demonstrates that CdEr₂X₄ (X=Se, S) exhibits dipolar spin ice states with significantly faster monopole hopping rates than traditional spin ices, enabling new insights into spin ice dynamics and ground states.

## Contribution

The paper reveals that CdEr₂X₄ supports dipolar spin ice states with ultra-fast monopole hopping, distinct from known spin ices, and provides a detailed analysis of the underlying mechanisms.

## Key findings

- CdEr₂X₄ exhibits dipolar spin ice states with Pauling entropy.
- Monopole hopping rates in CdEr₂X₄ are three orders of magnitude faster than in Dy₂Ti₂O₇.
- Fast dynamics are primarily due to rapid monopole hopping, not increased monopole population.

## Abstract

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.