  With a combined ab initio density functional and model Hamiltonian approach
we establish that in the recently discovered multiferroic phase of the
manganite Sr$_{1/2}$Ba$_{1/2}$MnO$_{3}$ the polar distortion of Mn and O ions
is stabilized via enhanced in-plane Mn-O hybridizations. The magnetic
superexchange interaction is very sensitive to the polar bond-bending
distortion, and we find that this dependence directly causes a strong
magnetoelectric coupling. This novel mechanism for multiferroicity is
consistent with the experimentally observed reduced ferroelectric polarization
upon the onset of magnetic ordering.
