To study the possibility of a slow magnetic relaxation, the ac susceptibility measurements for

**1**–

**5** were performed at 1.8 K with a dc magnetic field in the range of 0–0.3 T. The out-of-phase ac susceptibility (

χ_{M}″) signals for all five complexes in the absence of an applied field did not present any apparent peaks in the available frequency (

ν) range. As expected for the eight-coordinated triangular dodecahedral geometry of the two Ln

^{III} centers, an approximate

D_{2d} symmetry was observed. This led to the crystal field parameters

B^{0}_{2},

B^{0}_{4},

B^{4}_{4},

B^{0}_{6}, and

B^{4}_{6}, wherein

B^{4}_{4} and

B^{4}_{6} are the off-diagonal components. The existence of these off-diagonal crystal field parameters strongly suggests the mixing of the ground

M_{J} states. Furthermore, the Ln

^{III} centers in

**1**–

**5** comprise isotopes that display a nuclear spin, resulting in the nuclear hyperfine interaction effect [

33,

34,

35,

36,

37]. Additionally, the intra- and/or intermolecular separations between the Ln

^{III} centers suggests the presence of dipolar interactions [

10,

11,

12,

13,

14,

15,

16,

17,

18]. These contributions lead to the absence of a slow magnetic relaxation under a zero applied dc field, thereby allowing the quantum tunneling of the magnetization. In such cases, the application of a dc field can suppress and break up the quantum tunneling, caused by nuclear hyperfine couplings, dipolar interactions, and transverse fields from the off-diagonal crystal field splittings, and reveal the slow relaxation of the magnetization. However, under small static dc magnetic fields, frequency-dependent non-zero

χ_{M}″ signals were only clearly observed for the Kramers ions in complexes

**4** and

**5** (

Figure 3,

Figures S2 and S3). For these two complexes, each

χ_{M}″ peak maximum shifted to a lower frequency with an increasing applied dc field ≤0.1 T. A further increase in the applied dc field resulted in the maximum

χ_{M}″ shifting to a higher frequency. Notably,

**4** and

**5** also presents another minor magnetic relaxation process at higher dc fields (

Figure 3), which may arise from thermally assisted quantum tunneling [

10,

11,

12,

13,

14,

15,

16,

17,

18]. The dc field dependence of the low temperature relaxation times (

τ = 1/2π

ν) for

**4** and

**5** was extracted at each of these fields by fitting

ν versus

χ_{M}’ and

χ_{M}″ and the Argand plots [

38,

39] (

χ_{M}’ versus

χ_{M}″) using a generalized Debye model [

40]. The values determined for

**4** and

**5** are listed in

Tables S2 and S3 and plotted in

Figure S3. The two magnetic relaxation processes of the direct and quantum relaxation pathways were elucidated by fitting the variable-field magnetic relaxation data of

**4** and

**5** using Equation (1) [

10,

11,

12,

13,

14,

15,

16,

17,

18]:

where the first and second terms represent the respective direct and quantum tunneling pathways. Moreover, because of the presence of Kramers ions, the power index

m = 4 was used for the direct process. The best fits, based on Equation (1), are presented as solid black lines in

Figure 3 and are summarized in

Table 4. These results imply that the dipolar interactions and/or off-diagonal crystal fields support quantum tunneling at low magnetic dc fields. On the other hand, due to the presence of spin-active nuclei, single-phonon direct relaxation dominates at high dc fields. In addition, the optimum dc field for

**4** and

**5** was determined as ~0.1 T.

Subsequently, ac susceptibility measurements were performed under an applied dc field of 0.1 T in the temperature range of 1.8–10 K (

Figure 4), where the optimum dc magnetic field for

**4** and

**5** was determined as 0.1 T (variable-field magnetic relaxation data; vide supra,

Figure 3). The temperature dependences of the magnetic relaxation times for

**4** and

**5** were extracted in the temperature range of 1.8–5.0 K by fitting

ν versus

χ_{M}’ and

χ_{M}″ and the Argand plots using a generalized Debye model (

Figure 4 and

Figure 5, and

Tables S4 and S5, respectively). The Argand plots for

**4** and

**5** comprised one semicircle with small

α parameters in the ranges of 0.08–0.42 (4) and of 0.02–0.18 (5).

Arrhenius fits of the temperature-dependent relaxation time afford the thermally activated barriers Δ

_{eff} = 26.0 cm

^{−1} (

τ_{0} = 1.79 × 10

^{−9} s) for

**4** and 21.5 cm

^{−1} for

**5** (

τ_{0} = 2.81 × 10

^{−8} s). The extracted

τ_{0} values fall within the typical range of Ln

^{III}-based single-molecule and single-ion magnets [

10,

11,

12,

13,

14,

15,

16,

17,

18]. As the temperature decreases, the plots of

τ versus 1/

T for

**4** and

**5** become gradually nonlinear (

Figure 6). Such behavior suggests the coexistence of multiple magnetic relaxation pathways, which is caused by energy transfer from the spin to the lattice; this is known as the spin-lattice relaxation [

10,

11,

12,

13,

14,

15,

16,

17,

18]. Hence, the variable temperature relaxation times for

**4** and

**5** were analyzed in terms of their spin-lattice relaxation (Equation (3)):

where the first, second, third, and fourth terms represent the direct, quantum tunneling, Orbach, and Raman relaxation processes, respectively [

10,

11,

12,

13,

14,

15,

16,

17,

18]. Since the temperature dependence of the

τ data was collected at the optimum dc field of 0.1 T, the direct and quantum tunneling contributions should be excluded. Therefore, the overall

τ versus 1/

T data for

**4** and

**5** can only be fit with the Orbach and Raman contributions. The best fits, presented as solid black lines, are illustrated in

Figure 6 and

Figure S5, while their best-fit parameters are listed in

Table 5. The calculated

m values are smaller than the ideal value of

m = 9 for the Kramers ions, suggesting that these Raman-like relaxations are attributed to acoustic and optical vibrations [

10,

11,

12,

13,

14,

15,

16,

17,

18].