Analysis of the resonance peak and magnetic coherence seen in inelastic neutron scattering of cuprate superconductors: a consistent picture with tunneling and conductivity data

Assuming the exchange of antiferromagnetic spin fluctuations as the Cooper pairing mechanism we calculate the doping dependence of the resonance peak seen in inelastic neutron scattering and the magnetic coherence effect. Most importantly, we find that the resonance peak in the magnetic susceptibility, $Im\chi (\mathbf{q},\omega )$, appears {\it only} in the superconducting state, that it scales with $T_c$, and that magnetic coherence is a result of a d-wave order parameter. We further analyze the structure of $Im\chi$ below $T_c$, the position of the peak at ${\omega }_{res}$ and the consequences for photoemission, tunneling spectroscopy and the optical conductivity.