THEORY OF SPIN DYNAMICS IN HIGH-T-C SUPERCONDUCTORS

We analyze the spectrum of magnetic excitations as observed by neutron diffraction and NMR experiments in YBa2Cu3O6+x, in the frame of the single-band t-t'-J model in which the next-nearest neighbor hopping term has been introduced in order to fit the shape of the Fermi surface revealed in photoemission. Within the slave-boson approach, we have as well examined the d-wave superconducting state, and the singlet-RVB phase appropriate to describe the normal state of heavily doped systems. Our calculations show a smooth evolution of the spectrum from one phase to the other, with the existence of a spin-gap in the frequency dependence of chi ''(Q, omega) The value of the threshold of excitations E(G) is found to increase with doping, while the characteristic temperature scale T-m at which the spin-gap opens, exhibits a regular decrease, reaching T-c only in the overdoped regime. This very typical combined variation of E(G) and T-m with doping results of strong-correlation has its effect in the presence of a realistic band structure. We point out the presence of a resonance in the omega-dependence of chi ''(Q, omega) in good agreement with the neutron diffraction results obtained at x = 0.92 and x = 1.0. This resonance is interpreted as a dynamical Kohn anomaly of the second kind in the Cooper channel. Finally, we examine the q-dependence of the dynamical susceptibility allowing to study the magnetic correlation length xi as a function of doping, frequency and temperature.