Universal relaxor polarization in (formula presented) and related materials

The dielectric permittivity ε at frequencies from (formula presented) to (formula presented) is studied in perovskite (formula presented) relaxor ferroelectric ceramics of different compositions (formula presented) 0.25, and 0, which exhibit, below the temperature of the diffuse (formula presented) maximum (formula presented) a tetragonal ferroelectric, a rhombohedral ferroelectric, and a nonergodic relaxor phase, respectively. The universal relaxor dispersion previously observed at temperatures near and above (formula presented) in the ceramics of (formula presented) is also found to exist in other compositions. This dispersion is described by the fractional power dependence of the real and imaginary parts of susceptibility on frequency, (formula presented) The real part of the universal relaxor susceptibility (formula presented) is only a comparatively small fraction of the total permittivity (formula presented) but (formula presented) is the dominant contribution to the losses in a wide frequency-temperature range above (formula presented) In the high-temperature phase a divergent temperature behavior is observed, (formula presented) and (formula presented) with (formula presented) and (formula presented) for all the three compositions studied. The universal relaxor susceptibility is attributed to the polarization of polar nanoregions, which are inherent in the relaxor ferroelectrics. A microscopic model of this polarization is proposed, according to which the dipole moments of some “free” unit cells inside the polar nanoregion can freely choose several different directions, while the direction of the total moment of the nanoregion remains the same. The ensemble of interacting polar nanoregions is described in terms of a standard spherical model, which predicts the quadratic divergence of susceptibility above the critical temperature, in agreement with the experimental results.