  We investigate the possibility of controlling the magnetic phase transition
of the heterointerface between a half-doped manganite
La$_{0.5}$Ca$_{0.5}$MnO$_{3}$ and a multiferroic BiFeO$_{3}$ through
magnetoelectric coupling. Using macroscopic magnetometry and element-selective
x-ray magnetic circular dichroism at the Mn and Fe \emph{L}-edges, we discover
that the ferroelectric polarization of BFO controls simultaneously the
magnetization of BFO and LCMO. X-ray absorption spectra at oxygen \emph{K}-edge
and linear dichroism at Mn \emph{L}-edge suggest that the interfacial coupling
is mainly derived from the superexchange between Mn and Fe \emph{t}$_{2g}$
spins. The combination of x-ray absorption spectroscopy and mean field theory
calculations reveals that the \emph{d}-electron modulation of Mn cations
changes the magnetic coupling in LCMO, which controls the enhanced canted
moments of interfacial BFO via the interfacial coupling. Our results
demonstrate that the competition between ferromagnetic and antiferromagnetic
instability can be modulated by an electric field at the heterointerface,
providing another pathway for the electrical field control of magnetism.
