  $Ab$ $initio$ calculations show the presence of a strong magnetoelectric
interfacial coupling in CaMnO$_3$ ultra-thin film grown on a strained BaTiO$_3$
ferroelectric film. This heterostructure presents a polarization driven
magnetic transition from a G-type to an A-type antiferromagnetic structure.
Together with this magnetic transition we find a metallic behaviour at the
interface between these two insulators, where the charge character of the
carriers can be tuned from electrons to holes by switching the electric
polarization direction of the FE film. Besides, the electron gas is
spin-polarized while the hole-gas is not.
