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First-principles calculations are presented for the layered perovskiteCa$_3$Mn$_2$O$_7$. The results reveal a rich set of coupled structural,magnetic and polar domains in which oxygen octahedron rotations induceferroelectricity, magnetoelectricity and weak-ferromagnetism. The key point isthat the rotation distortion is a combination of two non-polar modes withdifferent symmetries. We use the term "hybrid" improper ferroelectricity todescribe this phenomenon and discuss how control over magnetism is achievedthrough these functional antiferrodistortive octahedron rotations.

Hybrid Improper Ferroelectricity: A Mechanism for Controllable Magnetization-Polarization Coupling