Absence of true critical exponents in relaxor ferroelectrics: the case for defect dynamics

It is argued that the large discrepancy (x2 in strontium barium niobate SBN) between experimental values from different kinds of experiment for the critical exponent beta describing the temperature evolution of the order parameter in relaxors such as SBN arises from the fact that such ferroelectric systems, assumed to be [3D] random field Ising models by Kleemann et al (2002 Europhys. Lett. 57 14), are not in thermal equilibrium. These arguments are illustrated primarily in SBN61-SrxBa1-xNb2O6:Ce with x = 0.61 and Ce = ca. 0.7%. An alternative model of Levanyuk and Sigov for defect-dominated dynamics is invoked. The inferred dimensionality of domain walls is also addressed, and the possibility of a d = 5/2 universality class controlled by domain dimensionality is considered as an alternative to defect dynamics; inter alia, four sets of d = 5/2 exponents (with beta = 1/2, 1/3, and 1/4) satisfy all known scaling and hyperscaling equalities. The present results support the scepticism about SBN critical exponents emphasized by Chao et al (2005 Phys. Rev. B 72 134105).