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Multiferroics are of interest for memory and logic device applications, as the coupling between ferroelectric and magnetic properties enables the dynamic interaction between these order parameters. Here, we report an approach to control and switch local ferromagnetism with an electric field using multiferroics. We use two types of electromagnetic coupling phenomenon that are manifested in heterostructures consisting of a ferromagnet in intimate contact with the multiferroic BiFeO₃. The first is an internal, magnetoelectric coupling between antiferromagnetism and ferroelectricity in the BiFeO₃ film that leads to electric-field control of the antiferromagnetic order. The second is based on exchange interactions at the interface between a ferromagnet (Co_0.9Fe_0.1) and the antiferromagnet. We have discovered a one-to-one mapping of the ferroelectric and ferromagnetic domains, mediated by the colinear coupling …