We present a comprehensive structural study of the charge-orbital ordering and magnetic phase transitions observed in the $A$-site ordered $\mathrm{SmBa}{\mathrm{Mn}}_2{\mathrm{O}}_6$ perovskite combining synchrotron radiation x-ray powder diffraction and symmetry-adapted modes analysis. In $\mathrm{SmBa}{\mathrm{Mn}}_2{\mathrm{O}}_6$, successive phase transitions in charge, spin, and lattice degrees of freedom take place with decreasing temperature at $T_{\mathrm{CO}1}\approx 380\mathrm{K}, T_{\mathrm{CO}2}\approx 190\mathrm{K}$, and $T_{\mathrm{N}}\approx 250\mathrm{K}$. The main difference between the two charge-ordered phases concerns the stacking sequence along the $c$ axis, which is double for the high temperature charge-ordered phase and has led to controversy in the literature. We show that both charge-ordered phases are pseudosymmetric with respect to the ideal undistorted tetragonal structure of $A$-site ordered $R\mathrm{Ba}{\mathrm{Mn}}_2{\mathrm{O}}_6$ perovskites and lead to two nonequivalent Mn sites. However, the charge segregation stabilizes at about $0.35e^{-}$ in the low temperature charge-ordered phase, clearly below the nominal separation of one charge unit between ${\mathrm{Mn}}^{3+}$ and ${\mathrm{Mn}}^{4+}$ and undergoes a prominent increase in the high temperature charge-ordered phase when warming above $\approx 250\mathrm{K}$. The two Mn sites are anisotropic in both charge-ordered phases but the analysis of the active modes discloses that only the low temperature charge-ordered phase displays a Jahn-Teller-like distortion for one of the Mn sites. In addition, this low temperature charge-ordered phase has polar symmetry compatible with ferroelectricity along the $a$ axis.

中文翻译：

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A位有序SmBaMn2O6钙钛矿中扭曲极性/非极性结构的对称模式分析

我们对电荷轨道排序和磁相变进行了全面的结构研究。 $\mathrm{一种}$- 现场订购 $\mathrm{斯巴达}{锰}_2{\mathrm{哦}}_6$钙钛矿结合同步辐射X射线粉末衍射和对称适应模式分析。在$\mathrm{斯巴达}{锰}_2{\mathrm{哦}}_6$，随着温度的降低，电荷、自旋和晶格自由度的连续相变发生在 ${吨}_{\mathrm{二氧化碳}1}\approx 380\mathrm{钾}, {吨}_{\mathrm{二氧化碳}2}\approx 190\mathrm{钾}$， 和 ${吨}_{\mathrm{N}}\approx 250\mathrm{钾}$. 两个电荷有序相之间的主要区别涉及沿$C$轴，这是高温电荷有序相的两倍，并在文献中引起了争议。我们表明，相对于理想的无畸变四方结构，两个电荷有序相都是伪对称的$\mathrm{一种}$- 现场订购 $\mathrm{电阻}巴{锰}_2{\mathrm{哦}}_6$钙钛矿并导致两个不等价的 Mn 位点。然而，电荷分离稳定在大约$0.35{\mathrm{电子}}^{-}$ 在低温电荷有序阶段，明显低于一个电荷单元之间的标称间隔 ${锰}^{3+}$ 和 ${锰}^{4+}$ 并且当升温到高于温度时，高温电荷有序相显着增加 $\approx 250\mathrm{钾}$. 两个 Mn 位点在两个电荷有序相中都是各向异性的，但对活性模式的分析表明，对于其中一个 Mn 位点，只有低温电荷有序相显示类似 Jahn-Teller 的畸变。此外，这种低温电荷有序相具有与铁电性相容的极性对称性$\mathrm{一种}$ 轴。