Hybrid Local-Order Mechanism for Inversion Symmetry Breaking

TL;DR

This study uses Monte Carlo simulations to show how combining local order mechanisms can break inversion symmetry and induce polarization, providing insights into ferroelectric materials like BaTiO3.

Contribution

It introduces a simple model combining Kitaev-like and steric interactions that together induce spontaneous polarization through local order intersection.

Findings

Local interactions alone do not cause symmetry breaking.

Two separate local orders lead to hidden transitions.

Their intersection results in a polarized ground state.

Abstract

Using classical Monte Carlo simulations, we study a simple statistical mechanical model of relevance to the emergence of polarisation from local displacements on the square and cubic lattices. Our model contains two key ingredients: a Kitaev-like orientation-dependent interaction between nearest neighbours, and a steric term that acts between next-nearest neighbours. Taken by themselves, each of these two ingredients is incapable of driving long-range symmetry breaking, despite the presence of a broad feature in the corresponding heat capacity functions. Instead each component results in a "hidden" transition on cooling to a manifold of degenerate states, the two manifolds are different in the sense that they reflect distinct types of local order. Remarkably, their intersection---\emph{i.e.} the ground state when both interaction terms are included in the Hamiltonian---supports a spontaneous polarisation. In this way, our study demonstrates how local ordering mechanisms might be combined to break global inversion symmetry in a manner conceptually similar to that operating in the "hybrid" improper ferroelectrics. We discuss the relevance of our analysis to the emergence of spontaneous polarisation in well-studied ferroelectrics such as BaTiO$_3$ and KNbO$_3$.