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By means of neutron powder diffraction, we investigated the effect of thepolar Bi$^{3+}$ ion on the magnetic ordering of the Mn$^{3+}$ ions inBiMn$_3$Mn$_4$O$_{12}$, the counterpart with \textit{quadruple} perovskitestructure of the \textit{simple} perovskite BiMnO$_3$. The data are consistentwith a \textit{noncentrosymmetric} spacegroup $Im$ which contrasts the\textit{centrosymmetric} one $I2/m$ previously reported for the isovalent andisomorphic compound LaMn$_3$Mn$_4$O$_{12}$, which gives evidence of aBi$^{3+}$-induced polarization of the lattice. At low temperature, the twoMn$^{3+}$ sublattices of the $A'$ and $B$ sites order antiferromagnetically(AFM) in an independent manner at 25 and 55 K, similarly to the case ofLaMn$_3$Mn$_4$O$_{12}$. However, both magnetic structures ofBiMn$_3$Mn$_4$O$_{12}$ radically differ from those of LaMn$_3$Mn$_4$O$_{12}$.In BiMn$_3$Mn$_4$O$_{12}$ the moments $\textbf{M}_{A'}$ of the $A'$ sites forman anti-body AFM structure, whilst the moments \textbf{M}$_{B}$ of the $B$sites result from a large and \textit{uniform} modulation $\pm\textbf{M}_{B,b}$ along the b-axis of the moments \textbf{M}$_{B,ac}$ in the$ac$-plane. The modulation is strikingly correlated with the displacements ofthe Mn$^{3+}$ ions induced by the Bi$^{3+}$ ions. Our analysis unveils a strongmagnetoelastic coupling between the internal strain created by the Bi$^{3+}$ions and the moment of the Mn$^{3+}$ ions in the $B$ sites. This is ascribed tothe high symmetry of the oxygen sites and to the absence of oxygen defects, twocharacteristics of quadruple perovskites not found in simple ones, whichprevent the release of the Bi$^{3+}$-induced strain through distortions ordisorder. This demonstrates the possibility of a large magnetoelectric couplingin proper ferroelectrics and suggests a novel concept of internal strainengineering for multiferroics design.

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