Diagonal superexchange in a simple square CuO2 lattice

Many microscopic models with the interaction between the next-nearest neighbors as a key parameter for cuprate physics have inspired us to study the diagonal superexchange interaction in a CuO₂ layer. Our investigation shows that models with extended hopping provide a correct representation of magnetic interactions only in a hypothetical square CuO₂ layer, where the diagonal superexchange interaction with the next-nearest neighbors always has an antiferromagnetic (AFM) nature. The conclusions are based on the symmetry prohibition on the ferromagnetic contribution to the diagonal superexchange between the next-nearest neighbors for a simple square CuO₂ layer rather than for a real CuO₂ 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.