I will discuss the magnetism in the high-Tc cuprates as predicted theoretically and observed experimentally (neutrons) and I will analyse the role of the spin fluctuations in the anomalies of the electronic properties in the hole-doped and electron-doped cuprates. Firstly : we show that magnetic properties of the metallic and superconducting states are quite asymmetric with respect to the nature of the doping, hole- or electron- one. The spin dynamics in the former case is characterised by the collective resonance mode (spin exciton) with a remarkable downward dispersion while in the latter case there are commensurate spin excitations of the relaxational type characterised by an extremely narrow q-width and by an extremely low spin gap. This is a consequence of the existence in 2D fermion system on a square lattice of the two topological quantum critical points located on the opposite sides of zero doping and on the other hand of the presence of strong electron correlations. These spin fluctuations play a remarkable role for the electronic properties: In the normal state they break up some parts of the Fermi surface, the effect that results in anomalies of various electronic properties namely in the anomalies observed by ARPES and tunnelling. For the superconductivity they play a double role : to create an attractive interaction between electrons and to destroy (to certain degree) these electrons. As a result spin fluctuations are pair breaking or pair mediating depending on parameters : energy, doping, etc. We study in details the SC state appearing due to the collective resonance mode: the symmetry of the order parameter, the density of states, the electron spectral functions. We study also the doping dependence of the superfluid density and of the SC gap and we show that they vary with doping in a different manner. The study is done based on self-consistent dynamic equations (generalisation of the Eliashberg equations for phonons and isotropic electrons to the case of spin fluctuations and anisotropic electrons)
Laboratoire Léon Brillouin