Open Access

Thorben Petersen, Lilian Prodan, Korbinian Geirhos, Hiroyuki Nakamura, István Kézsmárki, Liviu Hozoi

• The lacunar-spinel chalcogenides exhibit magnetic centers in the form of transition-metal tetrahedra. On the basis of density-functional computations, the electronic ground state of an Mo413+ tetrahedron has been postulated as single-configuration a12 e4 t25, where a1, e, and t2 are symmetry-adapted linear combinations of single-site Mo t2g atomic orbitals. Here we unveil the many-body tetramer wave-function: we show that sizable correlations yield a weight of only 62% for the a12 e4 t25 configuration. While spin–orbit coupling within the peculiar valence orbital manifold is still effective, the expectation value of the spin–orbit operator and the g factors deviate from figures describing nominal t5 jeff = 1/2 moments. As such, our data documents the dressing of a spin–orbit jeff = 1/2 object with intra-tetramer excitations. Our results on the internal degrees of freedom of these magnetic moments provide a solid theoretical starting point in addressing the intriguing phase transitionsThe lacunar-spinel chalcogenides exhibit magnetic centers in the form of transition-metal tetrahedra. On the basis of density-functional computations, the electronic ground state of an Mo413+ tetrahedron has been postulated as single-configuration a12 e4 t25, where a1, e, and t2 are symmetry-adapted linear combinations of single-site Mo t2g atomic orbitals. Here we unveil the many-body tetramer wave-function: we show that sizable correlations yield a weight of only 62% for the a12 e4 t25 configuration. While spin–orbit coupling within the peculiar valence orbital manifold is still effective, the expectation value of the spin–orbit operator and the g factors deviate from figures describing nominal t5 jeff = 1/2 moments. As such, our data documents the dressing of a spin–orbit jeff = 1/2 object with intra-tetramer excitations. Our results on the internal degrees of freedom of these magnetic moments provide a solid theoretical starting point in addressing the intriguing phase transitions observed at low temperatures in these materials.…