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 f 1 rare-earth borides to magnetism emerging through covalency and vibronic couplings in d 1 transition-metal compounds. The latter effect has been studied since the 1960s on t 2g 1 octahedral ML 6 units in both molecular complexes and extended solid-state lattices. Here we analyze the J eff = 3/2 quartet ground state of larger cubane-like M 4 L 4 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 t 2 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 t 2 1 . We provide a different interpretation of resonant inelastic X-ray scattering data on GaTa 4 Se 8 and, by comparing magnetic susceptibility data with calculated g factors, valuable insights into the important role of vibronic couplings.