Magnetic analog of the isotope effect in cuprates

Abstract

We present extensive magnetic measurements of the $({\mathrm{Ca}}_{x}{\mathrm{La}}_{1\ensuremath{-}x})({\mathrm{Ba}}_{1.75\ensuremath{-}x}{\mathrm{La}}_{0.25+x}){\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ system with its four different families $(x)$ having a ${T}_{c}^{\mathit{max}}(x)$ 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 ${T}_{c}=cJ{n}_{s}$ for all families, where $c\ensuremath{\sim}1$, $J$ is the in-plane Heisenberg exchange, and ${n}_{s}$ is the superconducting carrier density. This relates cuprate superconductivity to magnetism in the same sense that phonon-mediated superconductivity is related to atomic mass.