Spin-Orbit Coupling Controlled J=3/2 Electronic Ground State in 5d^{3} Oxides

Entanglement of spin and orbital degrees of freedom drives the formation of novel quantum and topological physical states. Here we report resonant inelastic x-ray scattering measurements of the transition metal oxides Ca_{3}LiOsO_{6} and Ba_{2}YOsO_{6}, which reveals a dramatic spitting of the t_{2g} manifold. We invoke an intermediate coupling approach that incorporates both spin-orbit coupling and electron-electron interactions on an even footing and reveal that the ground state of 5d^{3}-based compounds, which has remained elusive in previously applied models, is a novel spin-orbit entangled J=3/2 electronic ground state. This work reveals the hidden diversity of spin-orbit controlled ground states in 5d systems and introduces a new arena in the search for spin-orbit controlled phases of matter.