  Entanglement of spin and orbital degrees of freedom drives the formation of
novel quantum and topological physical states. Discovering new spin-orbit
entangled ground states and emergent phases of matter requires both
experimentally probing the relevant energy scales and applying suitable
theoretical models. Here we report resonant inelastic x-ray scattering
measurements of the transition metal oxides Ca$_3$LiOsO$_6$ and Ba$_2$YOsO$_6$.
We invoke an intermediate coupling approach that incorporates both spin-orbit
coupling and electron-electron interactions on an even footing and reveal 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.
