Frustrated ground states of a generalized XY model and their mapping to non-magnetic structural analogues

TL;DR

This paper explores the complex ground state phases of a generalized XY model on a triangular lattice, revealing how geometrical frustration and competing interactions lead to various ordered states, and maps these findings to structural phases in related chemical systems.

Contribution

It introduces a comprehensive analysis of the ground states of a generalized XY model with higher-order interactions and establishes a novel mapping to non-magnetic structural analogues in chemistry.

Findings

Multiple ordered and quasi-ordered phases identified

Phase behavior depends on the higher harmonic parameter q

Mapping predicts structural phases in bimetalic cyanides

Abstract

Ground state phases of a generalized XY model with magnetic and generalized nematic couplings on a non-bipartite triangular lattice are investigated in the exchange interactions parameter space. We demonstrate that the model displays a number of ordered and quasi-ordered phases as a result of geometrical frustration and/or competition between the magnetic and generalized nematic interactions. The nature and the extent of the respective phases depend on the parameter $q$, characterizing the higher-order harmonics term in the Hamiltonian. Motivated by the recent discovery of the experimental realization of the model with $q=2$ in the seemingly unrelated field of the systems chemistry [A.B. Cairns et al., Nature Chemistry 8, 442 (2016)], the model for $q>2$ is discussed in the context of the prediction of structural phases of a class of bimetalic cyanides based on a mapping between the two systems.