Resonating holes vs molecular spin-orbit coupled states in group-5 lacunar spinels

The valence electronic structure of magnetic centers is one of the factors that determines the characteristics of a magnet. This may refer to orbital degeneracy, as for j_eff = 1/2 Kitaev magnets, or near-degeneracy, e.g., involving the third and fourth shells in cuprate superconductors. Here we explore the inner structure of magnetic moments in group-5 lacunar spinels, fascinating materials featuring multisite magnetic units in the form of tetrahedral tetramers. Our quantum chemical analysis reveals a very colorful landscape, much richer than the single-electron, single-configuration description applied so far to all group-5 GaM₄X₈ chalcogenides, and clarifies the basic multiorbital correlations on M₄ tetrahedral clusters: while for V strong correlations yield a wave-function that can be well described in terms of four V⁴⁺V³⁺V³⁺V³⁺ resonant valence structures, for Nb and Ta a picture of dressed molecular-orbital j_eff = 3/2 entities is more appropriate. These internal degrees of freedom likely shape vibronic couplings, phase transitions, and the magneto-electric properties in each of these systems.