Optimized analysis of the AC magnetic susceptibility data in several spin-glass systems using the Vogel–Fulcher and Power laws

In spin-glasses (SG), the relaxation time τ (=1/2πf) vs Tf data at the peak position Tf in the temperature variation of the ac magnetic susceptibilities at different frequencies f is often fit to the Vogel–Fulcher Law (VFL): τ = τ0 exp[Ea/kB(Tf − T0)] and to the Power Law (PL): τ = τ0* [(Tf−TSG)/TSG]−zυ. Both of these laws have three fitting parameters each, leaving a degree of uncertainty since the magnitudes of the evaluated parameters τ0, Ea/kB, τ0*, and zυ depend strongly on the choice of T0 and TSG. Here, we report an optimized procedure for the analysis of τ vs Tf data on seventeen SG systems for which we could extract such data from published sources. In this optimized method, the data of τ vs Tf are fit by varying T0 in the linear plots of Ln τ vs 1/(Tf − T0) for the VFL and by varying TSG in the linear plot of Ln τ vs Ln (Tf − TSG)/TSG for the PL until optimum fits are obtained. The analysis of the associated magnitudes of τ0, Ea/kB,τ0*, and zυ for these optimum values of T0 and TSG shows that the magnitudes of τ0*, τ0, and zυ fail to provide a clear distinction between canonical and cluster SG. However, new results emerge showing Ea/(kBT0) < 1 in canonical SG, whereas Ea/(kBT0) >1 for cluster SG systems, and the optimized T0 < optimized TSG in all cases. Although some interpretation of these new results is presented, a more rigorous theoretical justification of the boundary near Ea/(kBT0) ∼ 1 is desired along with testing of these criteria in other SG systems.