Is magnetism relevant to cuprate superconductivity: lanthanides versus charge compensated 123?

Many theories suggest that the mechanism for cuprate superconductivity is based on super-exchange interaction between electrons. The most obvious test of these theories is a measurement of the correlation between $T_{c}$ and the super-exchange parameter $J$. Alteration of $J$ is achieved by chemical modifications or external pressure. Measurements of $J$ are done with: Neutron scattering, muon spin rotation (muSR), two magnon Raman scattering or resonant inelastic x-ray scattering. However, the experimental data is confusing. A recent Raman study showed an anticorrelation between $T_{c}$ and $J$ in the set of LnBa2Cu3Oy compounds with Ln$=$(La,..Lu,Y) [B.P.P. Mallet \textit{et al.}, Phys. Rev. Lett. 111, 237001 (2013)]. On the other hand, experimental measurements on the charge compensated 123 material (Ca$_{\mathrm{x}}$La$_{\mathrm{1-x}})$(Ba$_{\mathrm{1.75-x}}$La$_{\mathrm{0.25+x}})$Cu3O$_{\mathrm{y}}$ (CLBLCO) inferred an overall positive correlation between $T_{c}$ and $J$ [D.S. Ellis \textit{et al.}, Phys. Rev. B 92, 104507 (2015)]. Thus, the effect of $J$ on $T_{c}$ is not established experimentally. In this talk I will review the experimental situation, mainly from the muSR viewpoint, and shed light on this controversy.