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We have studied the electronic structure of BaCoO$_3$ using soft x-rayabsorption spectroscopy at the Co-$L_{2,3}$ and O-$K$ edges, magnetic circulardichroism at the Co-$L_{2,3}$ edges, as well as valence band hard x-rayphotoelectron spectroscopy. The quantitative analysis of the spectraestablished that the Co ions are in the formal low-spin tetravalent 3$d^5$state and that the system is a negative charge transfer Mott insulator. Thespin-orbit coupling plays also an important role for the magnetism of thesystem. At the same time, a trigonal crystal field is present with sufficientstrength to bring the 3$d^5$ ion away from the $J_{eff} = 1/2$ state. The signof this crystal field is such that the $a_{1g}$ orbital is doubly occupied,explaining the absence of a Peierl's transition in this system which consistsof chains of face-sharing CoO$_6$ octahedra. Moreover, with one hole residingin the $e_g^{\pi}$, the presence of an orbital moment and strongmagneto-crystalline anisotropy can be understood. Yet, we also infer thatcrystal fields with lower symmetry must be present to reproduce the measuredorbital moment quantitatively, thereby suggesting the possibility for orbitalordering to occur in BaCoO$_3$.

Spin-orbit coupling and crystal-field distortions for a low-spin $3d^5$ state in BaCoO$_{3}$