Strong electron correlations drive the Mott insulator transition, yet a universal framework to classify Mott insulators by their correlation strength has long been lacking. Cuprates offer a unique platform to study these interactions, but spectroscopic access to a clean half-filled Mott-insulating state has been missing in compounds with the highest superconducting onset temperatures, limiting insights into the link between correlation strength and high-temperature superconductivity.

To fill this gap, we synthesized a pristine half-filled thallium-based cuprate system, Tl₂Ba₅Cu₄O_x (Tl2504), and probed its magnetic excitations using high-resolution resonant inelastic x-ray scattering (RIXS). By modelling the magnon dispersion with a Hubbard-Heisenberg approach, we extract the correlation strength and uncovered a universal relation between electron interaction and magnon zone-boundary dispersion across cuprate systems. Our results further suggest that high-temperature superconductivity in cuprates is optimal at intermediate correlation strength, striking a delicate balance between electron localization and itinerancy.

This work has been published in Communications Materials (Biało, I.^✉, Wang, Q.^✉, Chang J. et al. Magnetic Excitations of a Half-Filled Tl-based Cuprate. https://doi.org/10.1038/s43246-025-01061-1). We are thankful to all collaborators.