Picometer atomic displacements behind ferroelectricity in the commensurate low-temperature phase in multiferroic ${\mathrm{YMn}}_2{\mathrm{O}}_5$

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 $Pbam\left(55\right)$ 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 $Pb{2}_{1}m$, 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 $P_S=(1.3\pm 0.4)\mathrm{mC}{\mathrm{m}}^{-2}$, which is in good agreement with our measured value $P_S=(0.88\pm 0.06)\mathrm{mC}{\mathrm{m}}^{-2}$. 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.

Figure 1

Room temperature P phase of ${\mathrm{YMn}}_2{\mathrm{O}}_5$ with space group $Pbam\left(55\right)$.

Figure 2

Overview of the four low-temperature phase transitions of ${\mathrm{YMn}}_2{\mathrm{O}}_5$.

Figure 3

General procedure of the structure solution within this paper. Left: Identification of sensitive reflections. Those reflections are characterized by a structure factor approaching zero and a respective local minimum of the energy dependent Bragg intensity, which provides orders of magnitude contrast. Middle: Refinement of the structural parameters based on the experimental data (black dots), in particular within the vicinity of the local energy minimum. The relevant dynamic and static atomic displacement parameters are determined by refining the sensitive reflections simultaneously. Even minuscule displacements can be revealed (gray, tabulated structure; red, refined fit). Right: Final model of the structure with subpicometer resolution of the atomic positions.

Figure 4

Temperature-dependent polarization at different electric fields. The lightly colored areas indicate the error level, which mainly originates from the accuracy of the used electrometer. All measured polarizations are similar within the error range. The polarization is equivalently pronounced also without electric field as well as with opposite poling, even above the coercive field strength of $2.2\mathrm{k}\mathrm{V}\mathrm{c}{\mathrm{m}}^{-1}$. An appearance of a measurable polarization below theoretical $T_{\text{CM}}$ is clearly visible. We determine the phase transition temperature at $T=(36\pm 2)\mathrm{K}$.

Figure 5

Electrical setup used for the experiment (a) at beamline BM28 (ESRF) with a closed cycle cryostat and (b) at beamline P23 (DESY) with a $\mathrm{He}$ flow cryostat.

Figure 6

Experimental and simulated RSD spectra above $T_{\text{CM}}$ for selected reflections (Refl.): The initial structure from Kagomiya et al. [47] (gray, ${\chi }^2=1.6\times {10}^{-4}$), the best fits using isotropic ADPs (green, ${\chi }^2=5.4\times {10}^{-5}$), those using anisotropic ADPs (cyan, ${\chi }^2=3.8\times {10}^{-5}$), as well as the best fits using anisotropic ADPs and static displacements (red, ${\chi }^2=8.5\times {10}^{-6}$) are shown in comparison.

Figure 7

Visualization of the static atomic displacements based on ICSD No. 165870 [47], before (grayish balls) and after refinement of the P phase (colored balls), in two different projections. The main improvement in the P phase structure concerns the position of the oxygen atom.

Figure 8

Simulation of RSD spectra of the refined CM phase (red) in comparison to the best refinement of the P phase (gray), as well as the experimental data below the phase transition temperature. With the additional degrees of freedom in space group $Pb{2}_{1}m$ the reduced ${\chi }^2$ has improved to $1.96\times {10}^{-5}$ from $3.3\times {10}^{-4}$ for the unrefined parameters from the P phase. The simulated RSD spectra of the CM phase show in particular an improved concordance with the most sensitive region of the intensity minimum.

Figure 9

Visualization of the static atomic displacements (colored balls) of the CM phase in comparison to those of the P phase (gray) in two different projections. Remarkable is in particular the most prominent movement of ${\mathrm{Mn}}^{3+}$ ions outside of the pyramid's basal plane.

Figure 10

The resulting polarization in the CM phase of ${\mathrm{YMn}}_2{\mathrm{O}}_5$ due to structural displacements is visualized exemplarily by the Mn vectorial contributions (black arrows). The main contribution originates in particular from the displacement of the ${\mathrm{Mn}}^{3+}$ ions with respect to the surrounding $\mathrm{O}$ pyramid.

Figure 11

Bärnighausen-like tree of YMO with space group $Pbam\left(55\right)$. The diagram shows the symmetry transitions involving two steps with respect to maximal subgroups (translationsgleich, klassengleich, and isomorph) as listed and labeled in the International Tables [103]. In addition to the space group name, the boxes list the permutation and multiplicity of the lattice vectors. Inappropriate multiplicities are marked in red. The background color of the box shows whether the corresponding point group is polar (blue) or nonpolar (red). In total, all those space groups are crossed out that are nonpolar or have a wrong multiplicity of the lattice vectors.

Figure 12

(a) Schematic of the sample setup. The sample is mounted on an electrically insulating sapphire plate and aligned such that an electric field is applied in the $b$ direction (the coordinate system marks the sample orientation). (b) The entire sample holder mounted at the end of the cold finger of the cryostat for electric characterization. The sapphire was placed onto a ceramic plate and the electrodes on sapphire have been connected to the sample holder by copper wires to the circuit leading outside the cryostat.

Figure 13

Calculation of the rocking curve of the 004 reflection with dynamical theory (green) in comparison to experimental data (black). The diffraction data reflect a mosaic crystal.

Figure 14

Comparison of the RSD spectra measured at $50\mathrm{K}$ (black) and 30 or $25\mathrm{K}$ (orange). The energy dependencies above and below the phase transition change only slightly.