  Using polarized neutron reflectometry (PNR), we observe an induced
magnetization of 75$\pm$ 25 kA/m at 10 K in a La$_{0.7}$Sr$_{0.3}$MnO$_3$
(LSMO)/BiFeO$_3$ superlattice extending from the interface through several
atomic layers of the BiFeO$_3$ (BFO). The induced magnetization in BFO is
explained by density functional theory, where the size of bandgap of BFO plays
an important role. Considering a classical exchange field between the LSMO and
BFO layers, we further show that magnetization is expected to extend throughout
the BFO, which provides a theoretical explanation for the results of the
neutron scattering experiment.
