Magnetically induced electronic ferroelectricity in half-doped manganites

Using a joint approach of density functional theory and model calculations, we demonstrate that a prototypical charge ordered half-doped manganite, La${}_{1\mathrm{/}2}$Ca${}_{1\mathrm{/}2}$MnO${}_3$ is multiferroic. The combination of a peculiar charge-orbital ordering and a tendency to form spin dimers breaks inversion symmetry, leads to a ferroelectric ground-state with a polarization up to several $\mu C\mathrm{/}c{m}^2$. The presence of improper ferroelectricity does not depend on hotly debated structural details of this material: in the Zener-polaron structure we find a similar dramatic ferroelectric response with a large polarization of purely magnetic origin.