The 134-type $A$-site ordered ${\mathrm{LaMn}}_3{\mathrm{Cr}}_4{\mathrm{O}}_{12}$, that belongs to the family of $A{A}_3^{\prime }{B}_4{\mathrm{O}}_{12}$ perovskites, with cubic structure and magnetically driven improper polarization is puzzling because the conventional mechanisms leading to the creation of polarization in type-II multiferroics do not apply. By symmetry analysis and first-principles simulations, we discover an original and previously overlooked energetic term that naturally explains the origin of improper polarization in ${\mathrm{LaMn}}_3{\mathrm{Cr}}_4{\mathrm{O}}_{12}$. In addition, we demonstrate the existence of three other energetic invariants in $A{A}_3^{\prime }{B}_4{\mathrm{O}}_{12}$ perovskites, for which other physical quantities (such as oxygen tiltings or shear strain) mediate the interaction between $G$-type antiferromagnetic vectors to create and even enhance improper polarization.

中文翻译：

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134型AA3'B4O12钙钛矿中铁电不当

134型 $\mathrm{一种}$现场订购 ${\mathrm{镧锰}}_3{铬}_4{\mathrm{Ø}}_{12}$，属于 $\mathrm{一种}{\mathrm{一种}}_3^{\prime }{乙}_4{\mathrm{Ø}}_{12}$具有立方结构和磁性驱动的不正确极化的钙钛矿令人困惑，因为不适用导致II型多铁磁化产生极化的常规机制。通过对称性分析和第一性原理模拟，我们发现了一个原始的，以前被忽视的高能术语，自然地解释了极化不当的根源。${\mathrm{镧锰}}_3{铬}_4{\mathrm{Ø}}_{12}$。此外，我们证明了存在其他三个能量不变量$\mathrm{一种}{\mathrm{一种}}_3^{\prime }{乙}_4{\mathrm{Ø}}_{12}$ 钙钛矿，其他物理量（例如氧气倾斜或剪切应变）介导的钙钛矿 $G$型反铁磁载体来产生甚至增强不正确的极化。