Diagonal superexchange in a simple square CuO${}_2$ lattice

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.

12 pages, 4 figures