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A phenomenological spin-fluctuation analysis (Ref. 1), based upon inelasticneutron scattering (INS) and angular resolved photoemission spectroscopy(ARPES) data for ${\rm YBCO}_{6.6}(T_c=61K)$, is used to calculate thefunctional derivative of the d-wave eigenvalue $\lambda_d$ of the linearizedgap equation with respect to the imaginary part of the spin susceptibility$\chi''(q,\omega)$ at 70K. For temperatures near $T_c$, the variation of $T_c$with respect to $\chi''(q,\omega)$ is proportional to this functionalderivative. Based on this, we discuss how different parts of the $q$ and$\omega$ dependent spin-fluctuation spectrum of YBCO$_{6.6}$ contribute to$T_c$.

Dependence of $T_c$ on the $q-\omega$ structure of the spin-fluctuation spectrum