Order and thermalized dynamics in Heisenberg-like square and Kagom\'e spin ices

TL;DR

This paper investigates the thermodynamic and ordering properties of Heisenberg-like spin ice models on Kagomé and square lattices using dynamic simulations, revealing challenges in achieving order due to geometric frustration.

Contribution

It introduces a Heisenberg-like dipolar spin ice model on Kagomé and square lattices and analyzes its thermodynamics and order parameters through Langevin dynamics.

Findings

Slow cooling does not produce a well-ordered state.

Long-range dipolar interactions influence the system's thermodynamics.

Proposals are made to reduce frustration and promote local order.

Abstract

Thermodynamic properties of a spin ice model on a Kagom\'e 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 Kagom\'e 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. Some suggestions are proposed for the alleviation of the geometric frustration effects and for the generation of local order in the low temperature regime.