Magnetic anisotropies and general on--site Coulomb interactions in the cuprates

TL;DR

This paper derives anisotropic superexchange interactions in undoped cuprates from a Hubbard model, including general on-site Coulomb interactions, and predicts anisotropy consistent with experiments.

Contribution

It extends previous calculations to include the most general on-site Coulomb interactions in a Hubbard model for cuprates.

Findings

Predicted easy-plane anisotropy in tetragonal cuprates.

Results agree with experimental anisotropy values.

Provided estimates for small in-plane anisotropy.

Abstract

This paper derives the anisotropic superexchange interactions from a Hubbard model for excitations within the copper 3d band and the oxygen 2p band of the undoped insulating cuprates. We extend the recent calculation of Yildirim et al. [Phys. Rev. B {\bf VV}, pp, 1995] in order to include the most general on--site Coulomb interactions (including those which involve more than two orbitals) when two holes occupy the same site. Our general results apply when the oxygen ions surrounding the copper ions form an octahedron which has tetragonal symmetry (but may be rotated as in lanthanum cuprate). For the tetragonal cuprates we obtain an easy--plane anisotropy in good agreement with experimental values. We predict the magnitude of the small in--plane aniso