Tuning Perpendicular Magnetic Anisotropy Compatible with Hybrid Improper Ferroelectricity via a Geometrical Route

Achieving effective manipulation of perpendicular magnetic anisotropy within the coupling of ferroelectricity remains an intricate challenge, yet it is crucial in the electric-field control of the excitation and propagation of magnonic spin-polarization currents. Perpendicularly magnetized structures are normally inhibited to varying degrees in a polarization switching path due to the intrinsic chemical incompatibility of electronic mechanisms for single-phase multiferroics. Here, we demonstrate a geometrically coupling strategy of oxygen octahedral distortions to regulate hybrid improper ferroelectricity and perpendicular magnetic anisotropy coupled in double-perovskite superlattice films. The geometrical ferroic mechanisms lead to a coexistence of strong ferromagnetism and room-temperature ferroelectricity, particularly with a perpendicularly magnetized structure. Based on the perturbation theory and Arrott-Noakes equation, it is revealed that such magnetic anisotropy originates from spin-orbit coupling and is regulated by the crystal-field splitting from Jahn-Teller distortion in a stable mean-field exchange model, compatible with polarization changes. Our Letter provides a geometrical route to design and regulate the coupling ferroic orders of perpendicular magnetic anisotropy and ferroelectricity.