Diagonal superexchange in a simple square CuO$_2$ lattice

TL;DR

This paper investigates the nature of diagonal superexchange interactions in a simplified square CuO$_2$ lattice, revealing that extended hopping models predict always antiferromagnetic interactions, with implications for understanding magnetic frustration.

Contribution

It demonstrates that in a simplified model, diagonal superexchange is always antiferromagnetic, highlighting the importance of symmetry and extended hopping in magnetic interaction modeling.

Findings

Diagonal superexchange in the simplified model is always AFM.

Symmetry prohibits FM contribution to diagonal superexchange.

Magnetic frustration is sensitive to square symmetry breaking.

Abstract

Many microscopic models with the interaction between the next-nearest neighbours as a key parameter for cuprate physics have inspired us to study the diagonal superexchange interaction in a CuO$_2$ layer. Our investigation shows that models with extended hopping provide a correct representation of magnetic interactions only in a hypothetical square CuO$_2$ layer, where the diagonal superexchange interaction with the next-nearest neighbors always has the AFM nature. The conclusions are based on the symmetry prohibition on FM contribution to the diagonal superexchange between the next-nearest neighbors for a simple square CuO$_2$ layer rather than for a real CuO$_2$ layer, where diagonal AFM superexchange may be overestimated. We also discuss the reasons for magnetic frustration effects and high sensitivity of spin nanoinhomogeneity to square symmetry breaking.