Dynamics of relaxor ferroelectrics
Abstract
We study a dynamic model of relaxor ferroelectrics based on the spherical randombondrandomfield model and the Langevin equations of motion written in the representation of eigenstates of the random interaction matrix. The solution to these equations is obtained in the longtime limit where the system reaches an equilibrium state in the presence of random local electric fields. The complex dynamic linear and thirdorder nonlinear susceptibilities χ_{1}(ω) and χ_{3}(ω), respectively, are calculated as functions of frequency and temperature. In analogy with the static case, the dynamic model predicts a narrow frequency dependent peak in χ_{3}(T,ω), which mimics a transition into a glasslike state, but a real transition never occurs in the case of nonzero random fields. A freezing transition can be described by introducing the empirical VogelFulcher (VF) behavior of the relaxation time τ in the equations of motion, with the VF temperature T_{0} playing the role of the freezing temperature T_{f}. The scaled thirdorder nonlinear susceptibility a'_{3}(T,ω)=χ¯'_{3}(ω)/χ¯'_{1}(3ω)χ¯'_{1}(ω)^{3}, where the bar denotes a statistical average over T_{0}, shows a crossover from paraelectriclike to glasslike behavior in the quasistatic regime above T_{f}. The shape of χ¯_{1}(ω) and χ¯_{3}(ω)and thus of a'_{3}(T,ω)depends crucially on the probability distribution of τ. It is shown that for a linear distribution of VF temperatures T_{0}, a'_{3}(T,ω) has a peak near T_{f} and shows a strong frequency dispersion in the lowtemperature region.
 Publication:

Physical Review B
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevB.63.054203
 arXiv:
 arXiv:condmat/0010022
 Bibcode:
 2001PhRvB..63e4203P
 Keywords:

 64.70.Pf;
 77.22.d;
 77.84.Dy;
 Glass transitions;
 Dielectric properties of solids and liquids;
 Niobates titanates tantalates PZT ceramics etc.;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 15 pages, Revtex plus 5 eps figures