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 $J$.