Critical speeding-up in the magnetoelectric response of spin-ice near its monopole liquid-gas transition.

Competing interactions in the so-called spin-ice compounds stabilize a frustrated ground state with finite zero-point entropy and, interestingly, emergent magnetic monopole excitations. The properties of these monopoles are at the focus of recent research with particular emphasis on their quantum dynamics. It is predicted that each monopole also possesses an electric dipole moment, which allows to investigate their dynamics via the dielectric function ε(ν). Here we report on broadband spectroscopic measurements of ε(ν) in Dy2Ti2O7 down to temperatures of 200 mK with a specific focus on the critical end point present for a magnetic field along the crystallographic [111] direction. Clear critical signatures are revealed in the dielectric response when, similarly as in the liquid-gas transition, the density of monopoles changes in a critical manner. The dielectric relaxation time τ exhibits a critical speeding-up with a significant enhancement of 1/τ as the temperature is lowered towards the critical temperature. Besides demonstrating the magnetoelectric character of the emergent monopole excitations, our results corroborate the unique critical dynamics near the monopole condensation transition.