  We present a first-principles study on the interface between perovskite
ferroelectrics (PbTiO3) and conducting magnetic manganites La_{1-x}Sr_xMnO3. We
show that by switching the ferroelectric polarization, additional carriers are
accumulated or depleted at the interfacial region of the manganite and that
this change in carrier density can modify the magnetic spin configuration of
the interfacial Mn, which is consistent with the experimentally observed
anomalously large change in the magnetization. We also describe an unexpected
purely interfacial phenomenon whereby the ferroelectric polarization of the
interfacial region changes the magnetic energetics --- a degree of freedom not
present in bulk manganites. Theoretically, we show the the ground-state
magnetic structure depends sensitively on the precise choice of Hubbard $U$
parameter within the widely-used DFT+U class of exchange correlation
functionals. We provide a simple Ising-like model that explains the evolution
of the magnetic structure with U in tandem with a discussion of various
different ways in which one might try to choose an appropriate U parameter.
