Spin-orbit coupling in a half-filled $t_{2g}$ shell: the case of $5d^3$ K${}_2$ReCl${}_6$

Abstract

The half-filled $t_{2g}$ shell of the $t_{2g}^3$ 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 $\hat{I}\P$ has been predicted to change this picture by mixing in orbital moment, giving rise to a sizable Jahn-Teller distortion. In $5d^3$ K${}_2$ReCl${}_6$ we study the electronic excitations using resonant inelastic x-ray scattering (RIXS) 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 $\hat{I}\P$ and Hund's coupling $J_H$. The sizable value of $\hat{I}\P \approx$ 0.29 eV places K${}_2$ReCl${}_6$ into the intermediate coupling regime, but $\hat{I}\P /J_H\approx 0.6$ is not sufficiently large to drive a pronounced Jahn-Teller effect. We discuss the ground state wavefunction 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.

16 pages, 14 figures