Coupling of the magnetic structure to crystal phase transition in La$_{1-x}$Ba$_{x}$CoO$_{3}$

The addition of charge carriers into the perovskite LaCoO$_{3}$ leads to a ferromagnetic (FM) state that becomes metallic via the double-exchange interaction mechanism. Neutron scattering showed that in La$_{1-x}$Ba$_{x}$CoO$_{3}$, the FM order coexists with an antiferromagnetic (AFM) order that$_{ }$is initially incommensurate and becomes commensurate when $x >$ 0.15. We investigated the magnetic structures of $x $= 0.17 - 0.22 by performing powder neutron diffraction at 10 K. For $x $= 0.17, only the AFM phase is present and can be indexed with a propagation vector of (0, -0.5, 0.5). The Co moments lie in the \textit{ab} plane of the rhombohedral ($R\bar {3}c)$ lattice in the hexagonal setting. With increasing $x$, the FM phase appears with the Co moments pointing along (001)$_{rhomb}$ and becomes dominant. At $x $= 0.22, the AFM order vanishes while the crystal structure transforms from rhombohedral to orthorhombic (Pnma) with the moments pointing along the (001)$_{ortho}$ direction.