  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 Malozemoff's 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.
