Critical magneto-electric dynamics of pyrochlore spin ice

Spin-ice materials such as Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$ are a class of geometrically frustrated ferromagnets that retain an extensive residual entropy even at very low temperatures. Magnetic ions in these materials form a three-dimensional network of corner-sharing tetrahedra. Spins in the disordered yet highly correlated ground states obey the two-in-two-out ice rules in every tetrahedra, similar to the Bernal-Fowler rules in water ice. More importantly, topological defects that violate the ice-rules, i.e. 3-in-1-out or 1-in-3-out tetrahedra, behave as emergent magnetic monopoles. Recently, it has been shown that these emergent monopoles also possess an electric dipole moment~[1]. This observation opens the possibility of monitoring and even controlling the spin dynamics with an electric field. Here we present a detailed numerical investigation of the magneto-electric dynamics of spin-ice systems using extensive Monte Carlo simulations. Our results shed light on the recent experiment~[2] in spin-ice Dy$_2$Ti$_2$O$_7$ that shows a critical speeding up of dielectric relaxation near the monopole liquid-gas transition.

[1] D. I. Khomskii, Nat. Commun. {\bf 3}, 904 (2012).

[2] C. P. Grams, M. Valldor, M. Garst, and J. Hemberger, Nat. Commun. {\bf 5}, 4853 (2014).