Paramagnons and high-temperature superconductivity in mercury-based cuprates.

We present a comparative study of magnetic excitations in the first two Ruddlesden-Popper members of the Hg-family of high-temperature superconducting cuprates, which are chemically nearly identical and have the highest critical temperature ($T_\mathrm{c}$) among all cuprate families. Our inelastic photon scattering experiments reveal that the two compounds' paramagnon spectra are nearly identical apart from an energy scale factor of $\sim130\%$ that matches the ratio of $T_\mathrm{c}$'s, as expected in magnetic Cooper pairing theories. By relating our observations to other cuprates, we infer that the strength of magnetic interactions determines how high $T_\mathrm{c}$ can reach. Our finding can be viewed as a magnetic analogue of the isotope effect, thus firmly supporting models of magnetically mediated high-temperature superconductivity.