  A neutron scattering investigation of the magnetoelectric coupling in
PbFe_{1/2}Nb_{1/2}O_{3} (PFN) has been undertaken. Ferroelectric order occurs
below 400 K, as evidenced by the softening with temperature and subsequent
recovery of the zone center transverse optic phonon mode energy (\hbar
\Omega_{0}). Over the same temperature range, magnetic correlations become
resolution limited on a terahertz energy scale. In contrast to the behavior of
nonmagnetic disordered ferroelectrics (namely Pb(Mg,Zn)_{1/3}Nb_{2/3}O_{3}), we
report the observation of a strong deviation from linearity in the temperature
dependence of (\hbar \Omega_{0})^{2}. This deviation is compensated by a
corresponding change in the energy scale of the magnetic excitations, as probed
through the first moment of the inelastic response. The coupling between the
short-range ferroelectric and antiferromagnetic correlations is consistent with
calculations showing that the ferroelectricity is driven by the displacement of
the body centered iron site, illustrating the multiferroic nature of magnetic
lead based relaxors in the dynamical regime.
