On the nature of antiferromagnetism in the CuO

Recent results regarding electron- and hole-doped CuO2 planes can be rather easily explained by the marked covalency of CuO bonding, suggesting a band picture of long and short range antiferromagnetism. The maxima of superconductive Tc versus doping can be related to the crossing by the Fermi level of the edges of the pseudogap due to antiferromagnetic short range order (bonding edge for hole-doping, antibonding for electron-doping). The symmetry of the superconductive gap can be related to the Bragg scattering of electronic Bloch states near the edges of the antiferromagnetism (AF) pseudogap. Assuming a standard phonon coupling, one then predicts for commensurate AF a pure $d_{x^2-y^2}$ symmetry for the superconductive gap for underdoped samples and $d_{x^2-y^2}$ symmetry plus an imaginary contribution of s or dxy symmetry contribution increasing linearly with overdoping. This seems in agreement with recent measurements of gap symmetry for YBCO, but should be more fully tested, especially for electron-doped samples. Incommensurate AF, as in LSCO, is not considered here. The simple Hartree-Fock band approximation used could no doubt be made more realistic by specific inclusion of electron correlations and by a better description of the AF short range order. This weak atomic repulsion U model, standard in transitional metals, is complementary to the strong U models usually assumed in oxides. It considers specifically the possible effects, in doped samples, of a short range AF which could be slowly dynamical or static, possibly including in that case recent evidences of nanostructures of two different phases