Hybrid improper ferroelectricity: a mechanism for controllable polarization-magnetization coupling.

First-principles calculations are presented for the layered perovskite Ca3Mn2O7. The results reveal a rich set of coupled structural, magnetic, and polar domains in which oxygen octahedron rotations induce ferroelectricity, magnetoelectricity, and weak ferromagnetism. The key point is that the rotation distortion is a combination of two nonpolar modes with different symmetries. We use the term "hybrid" improper ferroelectricity to describe this phenomenon and discuss how control over magnetism is achieved through these functional antiferrodistortive octahedron rotations.