Coupled magnetic and ferroelectric excitations in PbFe_{1/2}Nb_{1/2}O₃

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.