Weakening of antiferromagnetism due to frustration on inhomogeneous 2D lattices

TL;DR

This study investigates how frustration introduced by next nearest neighbor interactions weakens antiferromagnetic order in inhomogeneous 2D lattices, revealing site-dependent effects on local order parameters.

Contribution

It demonstrates the impact of frustration on antiferromagnetic order in inhomogeneous 2D lattices using linear spin wave theory, including decorated square lattices and quasiperiodic tilings.

Findings

Local order parameters decrease with increased frustration

Site-dependent rate of order parameter reduction

Frustration effects vary with lattice type

Abstract

This paper discusses the ground state of quantum spins interacting via Heisenberg antiferromagnetic exchange, in two dimensional lattices having several different local environments. In unfrustrated lattices, when a N\'eel type order exists, quantum fluctuations lead to an inhomogeneous order parameter. I consider the effects of adding frustration to such a system by including next nearest neighbor antiferromagnetic interactions. Within linear spin wave theory, it is found that as the frustration parameter increases, the local order parameters decrease at a rate that depends on the type of sites involved in the frustrated loops. The examples of a decorated square lattice system, and a quasiperiodic tiling are considered.