Anisotropic nonlinear dielectric response of relaxor ferroelectrics

The anisotropy of the nonlinear static dielectric response of inorganic relaxor ferroelectrics of lead magnesium niobate (PMN) type is studied in the framework of the spherical random bond-random field model. Assuming that the shape of a polar nanoregion (PNR) and thus its dipole moment is modified by the action of homogeneous lattice strains, the anisotropic part of the interaction between the PNRs is derived. This interaction is bilinear in the electric field as well as in the order parameter field components, and gives rise to an effective field-dependent interaction strength, which depends both on the magnitude and the direction of the electric field. In addition to the isotropic intrinsic nonlinearity of the system studied earlier, we thus obtain an anisotropic part of the nonlinear response. By comparing the results with the experimental data of Tagantsev and Glazounov [Appl. Phys. Lett. 74, 1910 (1999)] for PMN we calculate the temperature dependence of the anharmonicity coefficients in the effective free energy of the system.