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

It is argued that the large discrepancy ( × 2 in strontium barium niobate SBN) between experimental values from different kinds of experiment for the critical exponent β 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—Sr x Ba 1− x Nb 2 O 6 :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 β = 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).