LAUSR

By means of density functional theory plus dynamical mean-field theory (DFT $+$ DMFT) calculations and resonant inelastic x-ray scattering (RIXS) experiments, we investigate the high-pressure phases of the spin-orbit-coupled ${J}_{\mathrm{eff}}=3/2$ insulator ${\mathrm{GaTa}}_{4}{\mathrm{Se}}_{8}$. Its metallic phase, derived from the Mott state by applying pressure, is found to carry ${J}_{\mathrm{eff}}=3/2$ moments. The characteristic excitation peak in the RIXS spectrum maintains its destructive quantum interference of ${J}_{\mathrm{eff}}$ at the Ta ${L}_{2}$ edge up to 10.4 GPa. Our exact diagonalization-based DFT $+$ DMFT calculations including spin-orbit coupling also reveal that the ${J}_{\mathrm{eff}}=3/2$ character can be clearly identified under high pressure. These results establish the intriguing nature of the correlated metallic magnetic phase, which represents the first confirmed example of ${J}_{\mathrm{eff}}=3/2$ moments residing in a metal. They also indicate that the pressure-induced superconductivity is likely unconventional and influenced by these ${J}_{\mathrm{eff}}=3/2$ moments. Based on a self-energy analysis, we furthermore propose the possibility of doping-induced superconductivity related to a spin-freezing crossover.