MAGNETIC ANISOTROPIES AND GENERAL ON-SITE COULOMB INTERACTIONS IN THECUPRATES

This paper derives the anisotropic superexchange interactions from a H ubbard model for excitations within the copper 3d band and the oxygen 2p band of the undoped insulating cuprates. We extend the recent calcu lation of Yildirim et al. [Phys. Rev. B 52, 10 239 (1995)] in order to include the most general on-site Coulomb interactions (including thos e 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 ob tain an easy-plane anisotropy in good agreement with experimental valu es. We predict the magnitude of the small in-plane anisotropy gap in t he spin-wave spectrum of YBa2Cu3O6.