Magnetic moment suppression in Ba3CoRu2O9: hybridization effect

An unusual orbital state was recently proposed to explain the magnetic and transport properties of Ba${}_3$CoRu${}_2$O${}_9$ [Phys. Rev. B. {\bf 85}, 041201 (2012)]. We show that this state contradicts to the first Hund’s rule and does not realize in the system under consideration because of a too small crystal-field splitting in the $t_{2g}$ shell. A strong suppression of the local magnetic moment in Ba${}_3$CoRu${}_2$O${}_9$ is attributed to a strong hybridization between the Ru 4$d$ and O 2$p$ states.