Abstract
Spin-orbit entanglement in 5d-based transition metal oxides (TMOs) has been identified as a
route to a host of unconventional physical states including quantum spin liquids, Weyl semimetals,
and axion insulators1,2. Yet despite intense interest, no clear rules have emerged for the treatment
of spin-orbit coupling (SOC) in 5d TMOs outside of idealised LS or jj coupling paradigms. This is
exemplified in 5d3 oxides in which an orbitally-quenched singlet ground state is anticipated3,4, yet
SOC is manifest in the observed magnetic properties5–9. Here we solve this long-outstanding puzzle
by revealing that the electronic ground state of Os5+ 5d3 ions is an unquenched J = 3/2 state.
Resonant inelastic x-ray scattering (RIXS) in Ca3LiOsO6 and Ba2YOsO6 exposes a SOC-controlled
splitting of the t2g manifold. The results are successfully described using an intermediate-coupling
framework in which oxygen hybridisation promotes the breakdown of the orbital singlet. This
framework opens the door to realistic treatment of SOC across a range of 5d TMOs beyond the
5d3 case.
