In this article, we performed symmetry analysis of perovskite-based multiferroics: bismuth ferrite (BiFeO3)-like, orthochromites (RCrO3), and Ruddlesden-Popper perovskites (Ca3Mn2O7-like), being the typical representatives of multiferroics of the trigonal, orthorhombic, and tetragonal crystal families, and we explored the effect of crystallographic distortions on magnetoelectric properties. We determined the principal order parameters for each of the considered structures and obtained their invariant combinations consistent with the particular symmetry. This approach allowed us to analyze the features of the magnetoelectric effect observed during structural phase transitions in BixR1-xFeO3 compounds and to show that the rare-earth sublattice has an impact on the linear magnetoelectric effect allowed by the symmetry of the new structure. It was shown that the magnetoelectric properties of orthochromites are attributed to the couplings between the magnetic and electric dipole moments arising near Cr3+ ions due to distortions linked with rotations and deformations of the CrO6 octahedra. For the first time, such a symmetry consideration was implemented in the analysis of the Ruddlesden-Popper structures, which demonstrates the possibility of realizing the magnetoelectric effect in the Ruddlesden-Popper phases containing magnetically active cations, and allows the estimation of the conditions required for its optimization.
Keywords: crystal lattices; keyword multiferroics; magnetoelectric effect; perovskites; symmetry.