Revisit of the Vögel-Fulcher freezing in lead magnesium niobate relaxors

The Vögel-Fulcher (VF) equation ω= ω₀ exp [- E_a / k_B (T_m - T_f)] was frequently used to describe the dielectric relaxation of relaxor ferroelectrics where ω is the probe frequency at the peak temperature T_m of either the real or imaginary parts of the dielectric constant. We revisited this relation in a typical relaxor lead magnesium niobate and found that the parameters obtained were not physically meaningful. Meaningful results can only be obtained by fitting the VF relation on the characteristic relaxation time τ_c, whose temperature dependence can be obtained from the Cole-Cole model. The freezing temperature we obtained is 230 K, below which τ_c becomes temperature independent.