Internal-strain mediated coupling between polar Bi and magnetic Mn ions in the defect-free quadruple-perovskite BiMn$_3$Mn$_4$O$_{12}$

By means of neutron powder diffraction, we investigated the effect of the polar Bi$^{3+}$ ion on the magnetic ordering of the Mn$^{3+}$ ions in BiMn$_3$Mn$_4$O$_{12}$, the counterpart with \textit{quadruple} perovskite structure of the \textit{simple} perovskite BiMnO$_3$. The data are consistent with a \textit{noncentrosymmetric} spacegroup $Im$ which contrasts the \textit{centrosymmetric} one $I2/m$ previously reported for the isovalent and isomorphic compound LaMn$_3$Mn$_4$O$_{12}$, which gives evidence of a Bi$^{3+}$-induced polarization of the lattice. At low temperature, the two Mn$^{3+}$ sublattices of the $A'$ and $B$ sites order antiferromagnetically (AFM) in an independent manner …