Magnetic analog of the isotope effect in cuprates

We present extensive magnetic measurements of the (CaₓLa_1-x)(Ba_1.75-xLa0.25+x)Cu₃Oy system with its four different families $(x)$ having a Tcᵐᵃˣ(x) variation of 28% and minimal structural changes. For each family, we measured the N\'eel temperature, the anisotropies of the magnetic interactions, and the spin-glass temperature. Our results exhibit a universal relation Tc=cJnₛ for all families, where c~1, J is the in-plane Heisenberg exchange, and nₛ is the superconducting carrier density. This relates cuprate superconductivity to magnetism in the same sense that phonon-mediated superconductivity is related to atomic mass.