Antiferromagnetism and crystal field effects in superconducting copper oxides

Some modified perovskites (mixed oxydes of copper, rare earths, and alkaline earths) show a high superconducting transition temperature Tc. They seem to be antiferromagnetic insulators when stoechiometric. We show here that the De Gennes model, with two degenerate orbitals per copper atom, has an antiferromagnetic ground state only if crystal fields are included (either in the site energies or in the hopping integrals). If not, the intraatomic exchange coupling JH - leading to Hund's rule - imposes a ferromagnetic ground state. We show that antiferromagnetism prevails even when the crystal field is much smaller than JH