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 phenomenolo 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 ML6 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 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 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 GaTa4Se8 and, by comparing magnetic susceptibility data with calculated g factors, valuable insights into the important role of vibronic couplings.