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 t (=1/2 pi f) vs T-f 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): tau = tau(0) exp[Ea/kB(T-f - T-0)] and to the Power Law (PL): tau = tau(0)* [(T-f - TSG)/T-SG](-z nu). Both of these laws have three fitting parameters each, leaving a degree of uncertainty since the magnitudes of the evaluated parameters tau(0), E-a/k(B), tau(0)*, and z. depend strongly on the choice of T-0 and T-SG. Here, we report an optimized procedure for the analysis of tau vs T-f data on seventeen SG systems for which we could extract such data from published sources. In this optimized method, the data of tau vs T-f are fit by varying T-0 in the linear plots of Ln tau vs 1/(T-f - T-0) for the VFL and by varying T-SG in the linear plot of Ln tau vs Ln (T-f - T-SG)/T-SG for the PL until optimum fits are obtained. The analysis of the associated magnitudes of tau(0), E-a/k(B), tau(0)*, and z. for these optimum values of T-0 and T-SG shows that the magnitudes of tau(0)*, tau(0), and z. fail to provide a clear distinction between canonical and cluster SG. However, new results emerge showing Ea/(kBT0) < 1 in canonical SG, whereas E-a/(k(B)T(0)) >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 E-a/(k(B)T(0)) similar to 1 is desired along with testing of these criteria in other SG systems. (c) 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).