Large crystal-symmetry-induced magnetoelectric coupling in the quadruple perovskite BiMn$_3$Mn$_4$O$_{12}$

The remarkable properties of manganese oxides $A$MnO$_3$ with perovskite structure, such as the colossal magnetoresistance and the multiferroicity, arise from peculiar charge, spin and orbital orderings of the Mn \textit{e$_g$} electrons driven by cooperative Jahn-Teller distortions of the MnO$_6$ octahedra. Mastering these orderings remains a challenge owing to local structural distortions and electronic inhomogeneities enhanced by chemical substitutions and oxygen defects. We show that these difficulties are absent in \textit{quadruple} perovskites $A$Mn$_3$Mn$_4$O$_{12}$. These compounds share with \textit{simple} perovskites $A$MnO$_3$ a similar pseudo-cubic network of corner-sharing MnO$_6$ octahedra and similar electronic properties associated with the Mn$^{3+}$ and Mn$^{4+}$ ions. However, they display smaller distortions thanks to the higher crystal symmetry an no defects. For $A$=Bi, by means of neutron powder diffraction we give direct crystallographic evidence of a large coupling between the electric dipole of the 6s lone pair of Bi$^{3+}$ and the magnetic structure of the Mn$^{3+}$ ions, which provides a hint for enhancing the magnetoelectric coupling in proper ferroelectrics in view of multiferroic applications.