Classical Heisenberg and planar spin models on the windmill lattice

TL;DR

This study explores the classical Heisenberg and XY spin models on the windmill lattice, revealing a complex phase diagram with various collinear, coplanar, and non-coplanar phases through combined computational and analytical methods.

Contribution

It provides the first complete ground state phase diagram of these models on the windmill lattice, including exact phase energies and insights into their rich phenomenology.

Findings

Identified multiple collinear, coplanar, and non-coplanar phases.

Determined exact energies of all phases.

Mapped the complete ground state phase diagram.

Abstract

We investigate the classical Heisenberg and planar (XY) models on the windmill lattice. The windmill lattice is formed out of two widely occurring lattice geometries: a triangular lattice is coupled to its dual honeycomb lattice. Using a combination of iterative minimization, heat-bath Monte Carlo simulations and analytical calculations, we determine the complete ground state phase diagram of both models and find the exact energies of the phases. The phase diagram shows a rich phenomenology due to competing interactions and hosts, in addition to collinear and various coplanar phases, also intricate non-coplanar phases. We briefly outline different paths to an experimental realization of these spin models. Our extensive study provides a starting point for the investigation of quantum and thermal fluctuation effects.