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.

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• Electronic structure
• Magnetism
• Pressure effects
• Spin-orbit coupling
• Superconductivity
• Magnetic systems
• Mott insulators
• Spinels
• Superconductors
• Unconventional superconductors
• DFT+DMFT
• Exact solutions for many-body systems
• Fermi liquid theory
• First-principles calculations
• Hard x-ray photoelectron spectroscopy
• Pressure techniques
• X-ray scattering