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 Jeff=3/2 insulator GaTa4Se8. Its metallic phase, derived from the Mott state by applying pressure, is found to carry Jeff=3/2 moments. The characteristic excitation peak in the RIXS spectrum maintains its destructive quantum interference of Jeff at the Ta L2 edge up to 10.4 GPa. Our exact diagonalization-based DFT + DMFT calculations including spin-orbit coupling also reveal that the Jeff=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 Jeff=3/2 moments residing in a metal. They also indicate that the pressure-induced superconductivity is likely unconventional and influenced by these Jeff=3/2 moments. Based on a self-energy analysis, we furthermore propose the possibility of doping-induced superconductivity related to a spin-freezing crossover.
