Order and thermalized dynamics in Heisenberg-like square and Kagomé spin ices.

Thermodynamic properties of a spin ice model on a Kagomé lattice are obtained from dynamic simulations and compared with properties in square lattice spin ice. The model assumes three-component Heisenberg-like dipoles of an array of planar magnetic islands situated on a Kagomé lattice. Ising variables are avoided. The island dipoles interact via long-range dipolar interactions and are restricted in their motion due to local shape anisotropies. We define various order parameters and obtain them and thermodynamic properties from the dynamics of the system via a Langevin equation, solved by the Heun algorithm. Generally, a slow cooling from high to low temperature does not lead to a particular state of order, even for a set of coupling parameters that gives well thermalized states and dynamics. At very low temperature, however, square ice is more likely to reach states near the ground state than Kagomé ice, for the same island coupling parameters.