A magnetic analog of the isotope effect in cuprates

Since the discovery of superconductivity in the cuprates, it has been speculated that their pairing mechanism is due to magnetic interactions. However, this was never proven. Such a proof would require an experiment similar to the isotope effect in metallic superconductors, namely, a measurement of T$_{c}$ versus the in-plane super-exchange J, with no other structural changes. We have done this experiment using the (Ca$_{x}$La$_{1-x})$(Ba$_{1.75-x}$La$_{0.25+x})$Cu$_{3}$O$_{y}$ system with its 4 different families having different T$_{c}^{max}$. For each family, we measured the N\'{e}el Temperature T$_{N}$, the anisotropies of the magnetic interactions, the spin glass temperature T$_{g}$ of underdoped samples, and, of course, T$_{c}$ from under to overdoped compounds. These properties were determined using the zero field muon spin resonance ($\mu $SR) technique, where one injects polarized muons into the sample and measures the time evolution of their spin polarization. Our measurements allow us to demonstrate that T$_{c}^{max}$J$_{f}^{-1}$=const where f is a family index, and to prove experimentally that pairing in the cuprates stems from magnetic interactions.