How Correlations and Spin–Orbit Coupling Work within Extended Orbitals of Transition-Metal Tetrahedra of 4d/5d Lacunar Spinels

Spin–orbit quartet ground states are associated with rich phenomenology, ranging from multipolar phases in f1 rare-earth borides to magnetism emerging through covalency and vibronic couplings in d1 transition-metal compounds. The latter effect has been studied since the 1960s on t2g1 octahedral ML6 units in both molecular complexes and extended solid-state lattices. Here we analyze the Jeff = 3/2 quartet ground state of larger cubane-like M4L4 entities in lacunar spinels, composed of transition-metal (M) tetrahedra caged by chalcogenide ligands (L). These represent a unique platform where spin–orbit coupling acts on molecular-like, delocalized t2 orbitals. Using quantum chemical methods, we pin down the interplay of spin–orbit couplings in such a setting and many-body physics related to other molecular-like single-electron levels, both below and above the reference t21. We provide a different interpretation of resonant inelastic X-ray scattering data on GaTa4Se8 and, by comparing magnetic susceptibility data with calculated g factors, valuable insights into the important role of vibronic couplings.