Improper ferroelectricity in 134-type $AA_3'B_4\text{O}_{12}$ perovskites
The 134-type $\textit{A}$-site ordered LaMn 3 Cr 4 O 12 , that belongs to the family of $AA_3'B_4\text{O}_{12}$ 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 in this work, we discover an original and previously overlooked energetic term that naturally explains the origin of improper polarization in LaMn 3 Cr 4 O 12 . In addition, we demonstrate the existence of three other energetic invariants in $AA_3'B_4\text{O}_{12}$ perovskites, for which other physical quantities (such as oxygen tiltings or shear strain) mediate the interaction between $\textit{G}$-type antiferromagnetic vectors to create and even enhance improper polarization.