We have combined neutron scattering and piezoresponse force microscopy to study the relation between the exchange bias observed in CoFeB/BiFeO3 heterostructures and the multiferroic domain structure of the BiFeO3 films. We show that the exchange field scales with the inverse of the ferroelectric and antiferromagnetic domain size, as expected from Malozemoffs model of exchange bias extended to multiferroics. Accordingly, polarized neutron reflectometry reveals the presence of uncompensated spins in the BiFeO3 film at the interface with the CoFeB. In view of these results we discuss possible strategies to switch the magnetization of a ferromagnet by an electric field using BiFeO3.
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