Bulk magnetoelectricity in the hexagonal manganites and ferrites

Improper ferroelectricity (trimerization) in the hexagonal manganites RMnO3 leads to a network of coupled structural and magnetic vortices that induce domain wall magnetoelectricity and magnetization (M), neither of which, however, occurs in the bulk. Here we combine first-principles calculations, group-theoretic techniques and microscopic spin models to show how the trimerization not only induces a polarization (P) but also a bulk M and bulk magnetoelectric (ME) effect. This results in the existence of a bulk linear ME vortex structure or a bulk ME coupling such that if P reverses so does M. To measure the predicted ME vortex, we suggest RMnO3 under large magnetic field. We suggest a family of materials, the hexagonal RFeO3 ferrites, also display the predicted phenomena in their ground state.