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.