  Theories based on the coupling between spin fluctuations and fermionic
quasiparticles are among the leading contenders to explain the origin of
high-temperature superconductivity, but estimates of the strength of this
interaction differ widely. Here we analyze the charge- and spin-excitation
spectra determined by angle-resolved photoemission and inelastic neutron
scattering, respectively, on the same crystals of the high-temperature
superconductor YBa2Cu3O6.6. We show that a self-consistent description of both
spectra can be obtained by adjusting a single parameter, the spin-fermion
coupling constant. In particular, we find a quantitative link between two
spectral features that have been established as universal for the cuprates,
namely high-energy spin excitations and "kinks" in the fermionic band
dispersions along the nodal direction. The superconducting transition
temperature computed with this coupling constant exceeds 150 K, demonstrating
that spin fluctuations have sufficient strength to mediate high-temperature
superconductivity.
