Generalized Kibble-Zurek mechanism for annealing dynamics of pyrochlore spin ice

Spin ices are novel magnetic systems that are characterized by a disordered, yet highly correlated, low-temperature phase and quasi-particles which carry a net magnetic charge. These emergent magnetic monopoles are fractionalized excitations, which can be viewed as the high-dimensional analogue of kinks in the 1D ferromagnetic Ising model. Indeed, spin-ice systems share many unusual features with the Ising chain, such as the lack of a finite-temperature phase transition and an emergent critical point at the zero-temperature limit. Moreover, the critical behaviors of spin ices and Ising chain are peculiar in that the correlation length follows an exponential divergence as T goes to zero, instead of the power-law behavior as in conventional continuous phase transition. Here we study the nonequilibrium dynamics of kagome and pyrochlore spin ices under a slow cooling protocol and investigate the dependence of residual monopole densities on the annealing rate. We show that the kagome ice does not exhibit scaling behavior in the slow cooling limit. On the other hand, thanks to the topological nature of monopoles in pyrochlore spin ice, its annealing dynamics is well described by a generalized Kibble-Zurek mechanism.