Magnetic critical dynamics and monopole clustering of pyrochlore spin ice

Spin-ice materials such as Ho2Ti2O7 and Dy2Ti2O7 are a class of geometrically frustrated ferromagnets that retain an extensive residual entropy even at very low temperatures. Importantly, the elementary dipole excitations fractionalize into magnetic monopoles in these compounds. Indeed, the field-induced first-order transition in spin-ice compounds can be understood as a monopole liquid-gas transition. Despite extensive studies on magnetic monopole dynamics at low magnetic field, the kinetics of the liquid-gas transition and the particular role played by monopoles have not been thoroughly investigated. Here we present extensive numerical simulations to investigate the structural as well as dynamical properties of monopoles in the vicinity of the field-induced first-order transition. Our results relate the critical magnetic dynamics to the percolation of magnetic monopoles in the monopole gas phase. Interestingly, we show that similar percolating clusters consisting of bound monopole hole pairs also appear in the dense monopole liquid phase.