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

Abstract

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.

Observation of cluster spin glass behavior in thermally decomposed nanocrystalline Sn0.5Fe0.5O2−δ

“…Assuming the cluster's size to be related to their coupling strength, the ratio of E a / k B and T 0 is used as a measure of coupling/clustering strength among the dynamic entities that freeze at T f . E a /( k B T 0 ) < 1 signifies the strong coupling between the magnetic entities while E a /( k B T 0 ) > 1 indicates the weak coupling 68,74 In our case, E a / k B ∼ 10 T 0 , suggests a weak coupling among the clusters and E a /( k B T 0 ) > 1 had been observed in cluster SG systems 75,76 which is consistent with our system. In view of the above observations, the cluster spin glass state of Sn 0.5 Fe 0.5 O 2− δ at low temperatures results due to the competing AFM and FM interactions.…”

“…For canonical SG: τ 0 = 10 −12 –10 −13 s; for conventional spin glass: τ 0 = 10 −10 –10 −13 s ( zv = 4–12) while τ 0 = 10 −7 –10 −10 s for cluster spin glass. 70–73,75,76 Therefore, Sn 0.5 Fe 0.5 O 2− δ is a cluster spin glass at low temperatures.…”