Weak Coupling Approach to Magnetic Fluctuations in Layered Cuprates

NMR and inelastic neutron scattering data on the layered cuprates are analyzed within an RPA-like approach. This weak coupling model used for calculating the magnetic susceptibility is described and its results for the susceptibility are compared with those of Monte Carlo simulations. In the normal state, the calculated temperature dependences of the copper and the oxygen relaxation rates are in satisfactory agreement with the experimental data. It is shown, within a similar approach, that in the superconducting state the Knight shift data are in support of an s-wave gap symmetry, while the data on the nuclear relaxation rate can be better fit with a d-wave gap. Weak coupling results for the transverse nuclear relaxation rate of copper in YBa_2 Cu_3O_7 and the spin-fluctuation spectral function of the two-dimensional Hubbard model are also presented. Finally, the dynamics of the magnetic correlations are investigated in real space within the same scheme.