  We demonstrate that a new tool, a model independent numerical Eliashberg
inversion of the optical self-energy, based on maximum entropy considerations
can be used to extract the magnetic excitation spectra of
high-transition-temperature superconductors. In Bi-2212 we explicitly show that
the magnetic mode that dominates the self-energy at low temperatures directly
evolves out of a smooth transfer of spectral weight to the mode from the
continuum just above it. This redistribution starts already at 200 K in
optimally doped materials but is much weaker in overdoped samples. This
provides evidence for the magnetic origin of the superconductivity and presents
a challenge to theories of the spin susceptibility and to neutron scattering
experiments in high-temperature superconductors.
