  When spin ice systems undergo a sudden thermal quench, they have been shown
to enter long-lived metastable states where the monopole excitations form
so-called noncontractible pairs [Phys. Rev. Lett. 104, 107201 (2010)]. While
the nature of these states is well understood, the dynamical mechanisms
underpinning their formation remain largely unexplored and are the subject of
this study. We find that the long-range tail of the Coulomb interactions
between monopoles plays a central role by suppressing the monopole-assisted
decay of noncontractible pairs with respect to monopole-antimonopole
annihilation. In conjunction with low final quench temperatures, where the
system enters a nonhydrodynamic regime in which the monopoles effectively move
at terminal velocity in the direction of the local force acting on them, the
interactions lead to a metastable plateau that persists in the thermodynamic
limit. This is a remarkable phenomenon, reminiscent of jamming and some
instances of glassiness: A transient modification of the short-time dynamics of
the system allows it to enter a metastable state whose lifetime can easily be
astronomically large at (experimentally relevant) low temperatures. We
demonstrate this using Monte Carlo simulations and mean field population
dynamics theory, and we provide an analytical understanding of the mechanisms
at play. When the interactions between monopoles are truncated to finite range,
the metastable plateau reduces to a finite size effect. We derive the finite
size scaling behaviour of the density of noncontractible pairs in the
metastable plateau for both short- and long-range interactions, and discuss the
experimental implications of our results.
