Comment on “Charge order inFe2OBO3: AnLSDA+Ustudy”

In a recently published paper [Phys. Rev. B 72, 014407 (2005)], Leonov et al. present an $\mathrm{LSDA}+\mathrm{U}$ study of the low temperature monoclinic structure of the iron oxoborate $\left({\mathrm{Fe}}_2{\mathrm{OBO}}_3\right)$. They report on ${\mathrm{Fe}}^{2+}\text{−}{\mathrm{Fe}}^{3+}$ charge ordering without taking into account recent resonant x-ray scattering experiments, which demonstrate the lack of charge ordering in a closely related oxide such as ${\mathrm{Fe}}_3{\mathrm{O}}_4$. They propose that the charge ordering occurs between equivalent crystallographic sites. First, this result, apart from surprising, is at odds with basic concepts in condensed matter. Second, we argue on the reliability of this theoretical approach, showing that a strong discrepancy is obtained for the calculated total and $d$-projected charges at Fe atoms with formally the same valence state and local environment between two closed related compounds, ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and ${\mathrm{Fe}}_2{\mathrm{OBO}}_3$, using the same theoretical method. Finally, we reconsider the reported theoretical calculations on the basis of a rigorous definition of the concepts of charge and orbital ordering and we show that ${\mathrm{Fe}}_2{\mathrm{OBO}}_3$ does not show charge ordering.