Experimental determination of superexchange energy from two-hole spectra

We follow the evolution of Copper and Oxygen two-hole excitations, in optimally doped (Ca$_{x}$La$_{1-x}$)(Ba$_{1.75-x}$La$_{0.25+x} $)Cu$_{3}$O$_{y}$ for $x=0.1$ and $x=0.4$. The spectra have contributions from band states as well as a localized multiplet structure. From their identification, we determine the intrashell Coulomb interaction $U$ for Oxygen and Copper sites. These results allow us to estimate the atomic superexchange coupling $J$ suggesting a positive correlation between the maximal superconducting critical temperature $T_\text{C}^{max}$ and $J$.