Study of Ferroelectric and Magnetic Properties in A₃Fe₂O₇

Hybrid improper ferroelectrics (HIFs) realize switchable polarization through a trilinear coupling among two non-polar octahedral modes—rotation and tilt—and the polar mode. This symmetry-allowed coupling links three order parameters and provides a robust route to functional cross-responses. First-principles theory predicted HIF behavior in n = 2 Ruddlesden–Popper oxides and suggested electric-field control of weak ferromagnetism via reversal of the Dzyaloshinskii–Moriya (DM) vector. Experimentally, HIF has been established in A₃B₂O₇ systems such as Ca₃Ti₂O₇, Ca₃Mn₂O₇, and (Sr_1-xCa_x)₃Sn₂O₇, with coercive fields low enough to enable practical switching. Building on these advances, rare-earth substitution on the A site for magnetic A₃B₂O₇ compounds tunes the Goldschmidt tolerance factor and could drive octahedral rotations/tilts favorable for HIF. We have investigated structural trends versus rare-earth ionic radius and discuss prospects for cross-coupling-enabled multiferroicity in candidate RP ferrites. In this talk, we scrutinize the physical properties of magnetic A₃B₂O₇ Ruddlesden-Popper compounds and discuss possible magnetic hybrid improper ferroelectricity.