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We report on the non-equilibrium monopole dynamics in the classical spin iceDy$_2$Ti$_2$O$_7$ detected by means of high-resolution magnetostrictionmeasurements. Significant lattice changes occur at the transition from thekagome-ice to the saturated-ice phase, visible in the longitudinal andtransverse magnetostriction. A hysteresis opening at temperatures below 0.6 Ksuggests a first-order transition between the kagome and saturated state.Extremely slow lattice relaxations, triggered by changes of the magnetic field,were observed. These lattice-relaxation effects result from non-equilibriummonopole formation or annihilation processes. The relaxation times extractedfrom our experiment are in good agreement with theoretical predictions withdecay constants of the order of $10{^4}$ s at 0.3 K.

Extremely slow non-equilibrium monopole dynamics in classical spin ice