Coupling between magnetic ordering and structural instabilities in perovskite biferroics: A first-principles study

We use first-principles density-functional-theory-based calculations to investigate structural instabilities in the high symmetry cubic perovskite structure of rare-earth ($R=\text{La}$, Y, Lu) and Bi-based biferroic chromites, focusing on $\ensuremath{\Gamma}$ and $R$ point phonons of nonmagnetic, ferromagnetic, and antiferromagnetic states. We find that (a) the structure with $G$-type antiferromagnetic ordering is most stable, (b) the most dominant structural instabilities in these oxides are the ones associated with rotations of oxygen octahedra, and (c) structural instabilities involving changes in Cr-O-Cr bond angle sensitively depend on the changes in magnetic ordering. The dependence of structural instabilities on magnetic ordering can be understood in terms of how superexchange interactions depend on the Cr-O-Cr bond angles and Cr-O bond lengths. We demonstrate how adequate buckling of Cr-O-Cr chains can favor ferromagnetism. Born effective charges calculated by using the Berry phase expression are found to be anomalously large for the $A$ cations, indicating their chemical relevance to ferroelectric distortions.