Spin-orbit coupling in a half-filled t2g shell: The case of 5d3 K2ReCl6

The half-filled ${t}_2g$ shell of the ${t}_2g³$ configuration usually, in $LS$ coupling, hosts a $S=3/2$ ground state with quenched orbital moment. This state is not Jahn-Teller active. Sufficiently large spin-orbit coupling $\ensuremath{\zeta}$ has been predicted to change this picture by mixing in orbital moment, giving rise to a sizable Jahn-Teller distortion. In $5{d}³\phantom{\rule{4pt}{0ex}}{\mathrm{K}}₂{\mathrm{ReCl}}₆$ we study the electronic excitations using resonant inelastic x-ray scattering and optical spectroscopy. We observe on-site intra-${t}_2g$ excitations below 2 eV and corresponding overtones with two intra-${t}_2g$ excitations on adjacent sites, the Mott gap at 2.7 eV, ${t}_2g$-to-${e}_g$ excitations above 3 eV, and charge-transfer excitations at still higher energy. The intra-${t}_2g$ excitation energies are a sensitive measure of $\ensuremath{\zeta}$ and Hund's coupling ${J}_{\mathrm{H}}$. The sizable value of $\ensuremath{\zeta}\ensuremath{\approx}0.29\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ places ${\mathrm{K}}₂{\mathrm{ReCl}}₆$ into the intermediate coupling regime, but $\ensuremath{\zeta}/{J}_{\mathrm{H}}\ensuremath{\approx}0.6$ is not sufficiently large to drive a pronounced Jahn-Teller effect. We discuss the ground state wave function in a Kanamori picture and find that the $S=3/2$ multiplet still carries about 97% of the weight. However, the finite admixture of orbital moment allows for subtle effects. We discuss small temperature-induced changes of the optical data and find evidence for a lowering of the ground state by about 3 meV below the structural phase transitions.