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

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.

11 pages, 9 figures, accepted for publication in Physical Review Letters