  Obtaining strong magnetoelectric couplings in bulk materials and
heterostructures is an ongoing challenge. We demonstrate that manganite
heterostructures of the form ${\rm
(Insulator)/(LaMnO_3)_n/(CaMnO_3)_n/(Insulator)}$ show strong multiferroicity
in magnetic manganites where ferroelectric polarization is realized by charges
leaking from ${\rm LaMnO_3}$ to ${\rm CaMnO_3}$ due to repulsion. Here, an
effective nearest-neighbor electron-electron (electron-hole) repulsion
(attraction) is generated by cooperative electron-phonon interaction. Double
exchange, when a particle virtually hops to its unoccupied neighboring site and
back, produces magnetic polarons that polarize antiferromagnetic regions. Thus
a striking giant magnetoelectric effect ensues when an external electrical
field enhances the electron leakage across the interface.
