SUPEREXCHANGE ANISOTROPY IN THE CUPRATES

The single-bond superexchange anisotropy resulting from the 2p(sigma) and the 2p(z) orbitals on the ligand ion of the cuprates is analyzed f or a general case in which the oxygen octahedra surrounding each coppe r rotate around a general axis in the CuO2 plane. An extension of Mori ya's calculation shows that when the oxygen orbitals are degenerate, t he single-bond spin interaction is rotationally invariant, contrary to previous claims. When the orbitals are nondegenerate the single-bond Hamiltonian is anisotropic, but the anisotropy is small. The ground st ate of the entire CuO2 plane is found to be completely antiferromagnet ic in the low-temperature tetragonal phase. The weak ferromagnetism of the low-temperature orthorhombic phase is mainly due to the anisotrop y resulting from frustration of the single-bond interactions. These fr ustration effects also generate an anisotropy which dominates that due to the nondegeneracy of the oxygen orbitals. We present explicit resu lts for the weak ferromagnetic moment and for the spin-wave spectrum, as a function of the direction of the octahedra rotation axis.