Scaling ansatz for the ac magnetic response in two-dimensional spin ice

A theory for frequency-dependent magnetic susceptibility chi ( omega ) is developed for thermally activated magnetic monopoles in a two-dimensional (2D) spin ice. By modeling the system in the vicinity of the ground-state manifold as a 2D Coulomb gas with an entropic interaction, and then as a 2D sine-Gordon model, we have shown that the susceptibility has a scaling form chi ( omega )/ chi (0) = [scriptF] ( omega / omega sub(1)), where the characteristic frequency omega sub(1) is related to a charge correlation length between diffusively moving monopoles, and to the principal-breather excitation. The dynamical scaling is universal and applicable not only for kagome ice, but also for superfluid and superconducting films and generic 2D ices possibly including the artificial spin ice.