Relation between cuprate superconductivity and magnetism: A Raman study of (CaLa)(BaLa)$_{2}$Cu$_{3}$O$_{y}$

We present an investigation of charge-compensated antiferromagnetic (Ca$_{x}$La$_{1-x}$)(Ba$_{1.75-x}$La$_{0.25+x}$)Cu$_{3}$O$_{y}$ single crystals using Raman scattering as well as muon spin rotation. In this system the parameter $x$ controls the Cu-O-Cu superexchange interaction via bond distances and buckling angles. The oxygen content $y$ controls the charge doping. In the absence of doping the two-magnon peak position is directly proportional to the superexchange strength $J$. We find that both $x$ and $y$ affect the peak position considerably. The N\'{e}el temperature determined from muon spin rotation on the same samples independently confirms the strong dependence of the magnetic interaction on $x$ and $y$. We find a considerable increase in the maximum superconducting transition temperature $T_{c}^{max}$ with $J$. This is strong evidence of the importance of orbital overlap to superconductivity in this family of cuprates.