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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$J_{\rm{eff}}=3/2$ insulator GaTa$_4$Se$_8$. Its metallic phase, derived fromthe Mott state by applying pressure, is found to carry $J_{\rm{eff}}=3/2$moments. The characteristic excitation peak in the RIXS spectrum maintains itsdestructive quantum interference of $J_{\rm{eff}}$ at the Ta $L_2$-edge up to10.4 GPa. Our exact diagonalization based DFT+DMFT calculations includingspin-orbit coupling also reveal that the $J_{\rm{eff}}=3/2$ character can beclearly identified under high pressure. These results establish the intriguingnature of the correlated metallic magnetic phase, which represents the firstconfirmed example of $J_{\rm{eff}}$=3/2 moments residing in a metal. They alsoindicate that the pressure-induced superconductivity is likely unconventionaland influenced by these $J_{\rm{eff}}=3/2$ moments. Based on a self-energyanalysis, we furthermore propose the possibility of doping-inducedsuperconductivity related to a spin-freezing crossover.

Novel $J_{\rm{eff}}$=3/2 Metallic Phase and Unconventional Superconductivity in GaTa$_4$Se$_8$