Individual and cooperative superexchange enhancement in cuprates

It is now widely accepted that the antiferromagnetic coupling within high temperature superconductors strongly exhibits a profound correlation with the upper limit of superconducting transition temperature these materials can reach. Thus, accurately calculating the positive and negative mechanisms that influence magnetic coupling in specific materials is crucial for the exploration of superconductivity at higher temperatures. Nevertheless, it is notoriously difficult to establish a complete description of electron correlations employing ab initio theories because of the large number of orbitals involved. In this study, we tackle the challenge of achieving high-level ab initio wave function theory calculations, which allow an explicit treatment of electron correlations associated with a large number of high-energy orbitals. We elucidate the atomic-shell-wise contributions to the superexchange coupling in the lanthanum cuprate, including individual effects of high-energy orbitals (Cu 4d, 5d, 4f, 5p) and cooperative effects between the core and these high-energy orbitals. Specifically, the prominent contributions from Cu 4d, 5d, 4f and 5p give rise to a rich collection of previously unexamined superexchange channels. We propose a p-d-f model to universally account for the contributions of high-energy orbitals at copper sites. Our calculations and physical rationalizations offer a more robust theoretical foundation for investigating cuprate-type high-temperature superconductors.