SPIN EXCITATIONS OF 2-DIMENSIONAL-LATTICE ELECTRONS - DISCUSSION OF NEUTRON-SCATTERING AND NMR EXPERIMENTS IN HIGH-T(C) SUPERCONDUCTORS

The spin-excitation spectrum as observed in neutron-diffraction and NMR experiments in YBa2Cu3O6+x is theoretically examined in the weak-coupling limit of a two-dimensional Hubbard lattice model in which the next-nearest-neighbor hopping term t' is considered in order to fit the shape of the Fermi surface observed in angle-resolved-photoemission experiments. The presence of a Van Hove singularity in the density of states at omega = 4t', no longer centered at the center of the band if t' not-equal 0, leads to correct predictions for the variation of the Knight shift with doping when compared to experiments. As long as pairing effects are not included, the frequency dependence of chi''(Q, omega) at T = 0 has no gap for the current regime of interest (4t' < mu < 0), but instead presents a typical double-cusp structure that we discuss. In the presence of d-wave pairing, it is shown how the spectrum of excitations gains four additional superconducting ellipses around the nodes of excitations. Consequently at T = 0, chi''(Q, omega) exhibits a resonance superimposed on a gap structure which bears striking resemblance with the neutron results reported by Rossat-Mignod et al. [Physica B 169, 58 (1991)] in YBa2Cu3O6.92. The resonance is analyzed as a Kohn anomaly of the second kind in the Cooper channel. The value of the threshold E(G) evolves between two different regimes as the chemical potential goes from 0 to 4t', associated with two different scales for the temperature at which the spin gap fills up. Finally, the Knight shift is calculated showing a Yosida-like law with a linear T dependence at very low temperatures as expected for axial superconductivity in two dimensions.