Magnetoelectricity in multiferroic hexaferrites as understood by crystal symmetry analyses

Two multiferroic hexaferrites Y-type Ba0.5Sr1.5Zn2(Fe0.92Al0.08)(12)O-22 and Z-type Ba0.52Sr2.48CO2Fe24O41 have been reported to show giant electric field control of magnetization and small magnetic field control of drastic change of polarization, i.e., giant magnetoelectric (ME) effects up to room temperature. However, it is still a mystery that their ME properties are quite different in many aspects even though they have very similar transverse cone spin configurations. Here, we report the comparative investigation of angle-dependent ME effects in two compounds. When the external H is rotated clockwise by 360 degrees, the in-plane P vector is rotated clockwise by 360 degrees in the Y-type hexaferrite and counterclockwise by 720 degrees in the Z-type hexaferrite. These contrasting ME effects can only be explained with a new symmetry-based spin model and tensor analysis. Our new approach reveals that the faster and opposite rotation of the P vector in the Z-type hexaferrite is associated with the lack of the space inversion in one of the magnetic blocks. Moreover, such a peculiar crystal symmetry also results in contrasting microscopic origins for the spin-driven ME behaviors; only the inverse DM interaction is responsible for the Y-type hexaferrite while additional p-d hybridization becomes more important in the Z-type hexaferrite. This work demonstrates the importance of the crystal symmetry in the determination of ME properties in the hexaferrites and provides a fundamental framework for understanding and applying the ME properties in other spin-driven multiferroics.