Nonlinear Magnetoelectric Effect in Magnetically Disordered Relaxor Ferroelectrics

The nonlinear magnetoelectric effect in a relaxor ferroelectric, which is randomly diluted by a (ferro) magnetic compound, is investigated on the basis of a phenomenological Landau-type free energy model. It is assumed that macroscopic electrostrictive and magnetostrictive deformations give rise to fourth-order magnetoelectric terms in the free energy functional. On a mesoscopic scale this implies that the local electric field inside a polar nanoregion (PNR), which is temperature (T) dependent, is modified both by the applied electric field E and magnetic field H. The dielectric relaxation time is shown to obey a modified Vogel-Fulcher relation and diverges on a critical surface in the E, H, T space.