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

## TL;DR

This study investigates the electronic structure of BaCoO₃, revealing a low-spin 3d⁵ state, significant spin-orbit coupling, and crystal field effects that influence its magnetic and electronic properties, including potential orbital ordering.

## Contribution

It provides a detailed spectroscopic analysis showing the low-spin state, the role of spin-orbit coupling, and the influence of crystal fields on BaCoO₃'s electronic and magnetic behavior, suggesting possible orbital ordering.

## Key findings

- Co ions are in a low-spin 3d⁵ state.
- BaCoO₃ is a negative charge transfer Mott insulator.
- Crystal field effects influence orbital occupancy and magnetism.

## Abstract

We have studied the electronic structure of BaCoO$_3$ using soft x-ray absorption spectroscopy at the Co-$L_{2,3}$ and O-$K$ edges, magnetic circular dichroism at the Co-$L_{2,3}$ edges, as well as valence band hard x-ray photoelectron spectroscopy. The quantitative analysis of the spectra established 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. The spin-orbit coupling plays also an important role for the magnetism of the system. At the same time, a trigonal crystal field is present with sufficient strength to bring the 3$d^5$ ion away from the $J_{eff} = 1/2$ state. The sign of 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 consists of chains of face-sharing CoO$_6$ octahedra. Moreover, with one hole residing in the $e_g^{\pi}$, the presence of an orbital moment and strong magneto-crystalline anisotropy can be understood. Yet, we also infer that crystal fields with lower symmetry must be present to reproduce the measured orbital moment quantitatively, thereby suggesting the possibility for orbital ordering to occur in BaCoO$_3$.