AC susceptibility measurements of clusters
1–
3 were performed to explore their dynamic magnetic properties at indicated frequencies under zero DC field and a 3 Oe AC field at 2 K. As shown in Figs. S21 (Supporting information), the out-of-phase susceptibilities (
χ") of clusters
2 and
3 exhibit temperature dependence at 100–1500 Hz, but no significant peaks are observed due to the quantum tunneling effect. The in-phase susceptibilities (
χ') and the out-of-phase susceptibilities (
χ") of cluster
1 exhibit obvious temperature dependence, and the out-of-phase susceptibilities (
χ") have obvious peaks at 0.1–1500 Hz. The AC magnetic susceptibility of cluster
1 was further tested at the specified temperatures in the frequency range of 0.1–1000 Hz under zero DC field and a 3 Oe AC field.
Figs. 3a and
b show the frequency dependence plots of
χ' and
χ''. A series of single frequency-dependent peaks were observed between 2 K and 9 K, indicating the SMM behavior of cluster
1. The Cole-Cole plots were fitted using the generalized Debye model (
Fig. 3c). The large
α values under zero DC field indicates the presence of multiple relaxation processes (Table S10 in Supporting information) [
54]. The ln
τ vs.
T−1 plots are almost linear when
T > 7 K, which can be fitted by considering only the Orbach relaxation process using Arrhenius' law (
τ =
τ0exp(
Ueff/
kBT)). The obtained parameters are
Ueff/
kB = 43.68 K and
τ0=1.4 × 10
−6 s, which is consistent with the reported ranges for other SMMs (10
−6–10
−11 s). However, when
T < 7 K, the ln
τ vs.
T−1 plots deviate from linearity, indicating the presence of other magnetic relaxation processes. Combining the Obrach and quantum tunneling of magnetization (QTM) relaxation processes using the equation
τ−1 =
τ0−1 exp(−
Ueff/
kBT) +
τQTM−1 gives the best fit (
R2 = 0.99865), where
τQTM is the rate of QTM. The fit gives
τ0 = 6.4 × 10
−7 s,
τQTM = 6.0 × 10
−3 s, and
Ueff/
kB= 50.24 K (
Fig. 3d). To slow relaxation, the AC magnetic susceptibilities were measured under specific DC fields at 2 K. Under DC fields from 1000 Oe to 4000 Oe, the out-of-phase AC signal values increased significantly compared to those at 0 Oe (Fig. S22 in Supporting information), indicating that QTM is suppressed. Simultaneously, the frequency corresponding to the peak of the AC signal effectively decreases after applying the field and remains stable above 2500 Oe (Fig. S23 in Supporting information). The AC susceptibilities of cluster
1 were measured under an optimal 2500 Oe DC field. The temperature-dependent and frequency-dependent out-of-phase susceptibilities (
χ") are significantly higher than that at zero field. The peak frequency is lower, and the peak temperature is slightly higher under the same frequency conditions. The Cole-Cole plot obtained by fitting the same generalized Debye model shows a semicircular shape (
Fig. 4 and Fig. S24 in Supporting information). Similarly, the ln
τ vs.
T−1 plot is almost linear in the high-temperature region; considering only the Orbach relaxation process fitted according to Arrhenius' law:
Ueff/
kB = 64.55 K, and
τ0 = 1.7 × 10
−7 s. In the low-temperature region, the ln
τ vs.
T−1 plot deviates from linearity. As shown in
Fig. 4d, combining the Obrach, direct and Raman relaxation processes using the equation
τ−1 =
τ0−1exp(-
Ueff/
kBT) + A
T + C
Tn, results in
τ0 = 9.3 × 10
−8s,
Ueff/
kB = 80.21 K, A = 1.97 K
−1 s
−1, C = 1.51 × 10
−3 s
−1 K
−n, n = 6.6 (
R2 = 0.99762). If the QTM relaxation process is also considered, the fitted
τQTM = −8.05 × 10
14 s, suggesting that QTM can be considered completely suppressed at 2500 Oe [
33,
55].