Picometer atomic displacements behind ferroelectricity in the commensurate low-temperature phase in multiferroic YMn2O5

Multiferroics are rare materials that exhibit an interaction of ferroelectricity and magnetism. One such multiferroic material is the $\mathrm{Mn}$-based mullite ${\mathrm{YMn}}₂{\mathrm{O}}₅$. ${\mathrm{YMn}}₂{\mathrm{O}}₅$ undergoes several low-temperature phases, and the origin of ferroelectricity in the commensurate phase remains open. Changes in the Mn spin configuration are believed to be the main driving force, which can be induced by magnetostriction caused by symmetric exchange, the antisymmetric inverse Dzyaloshinskii-Moriya interaction, or a combination of both. These mechanisms are accompanied by specific displacements of ions in the structure. The space group $Pbam\phantom{\rule{0.16em}{0ex}}(55)$ of the paraelectric phase does not allow polar displacements. Moreover, conventional structure analysis has been unsuccessful in refining the charge structure in a lower symmetric phase due to its limited sensitivity in resolving the expected positional displacements. To shed light on this controversial discussion, our goal was to resolve potential ionic displacements within a polar space group by employing the new resonantly suppressed diffraction method, which is highly sensitive to minuscule structural changes in the (sub)picometer range. In this paper, we present the first refined structure model of the commensurate phase in ${\mathrm{YMn}}₂{\mathrm{O}}₅$ using the lower symmetric space group $Pb{2}₁m$, allowing polarization in the $b$ direction. We observed a significant displacement of the Mn ions and the partial structure of oxygen, resulting in a calculated spontaneous polarization ${P}_S=(1.3\ifmmode\pm\else\textpm\fi{}0.4)\phantom{\rule{0.16em}{0ex}}\mathrm{mC}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}2}$, which is in good agreement with our measured value ${P}_S=(0.88\ifmmode\pm\else\textpm\fi{}0.06)\phantom{\rule{0.16em}{0ex}}\mathrm{mC}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}2}$. Importantly, we confirm that ${P}_S$ predominantly arises from an ionic contribution induced by magnetostriction. These results hold great interest not only for all multiferroic Mn-based mullites, but also for other multiferroic materials where ferroelectricity arises from their magnetic order. Furthermore, a precise understanding of the ionic movement induced by magnetism will aid in the material tuning process to enhance or create multiferroic properties.