Six-Coordinate Ln ( III ) Complexes with Various Coordination Geometries Showing Distinct Magnetic Properties

The syntheses, structural characterization, and magnetic properties of three lanthanide complexes with formulas [Ln(L)3] (Ln = Dy (1Dy); Er (1Er)); and [Dy(L)2] (2Dy) were reported. Complexes 1Dy and 1Er are isostructural with the metal ion in distorted trigonal-prismatic coordination geometry, but exhibit distinct magnetic properties due to the different shapes of electron density for DyIII (oblate) and ErIII (prolate) ions. Complex 1Dy shows obvious SMM behavior under a zero direct current (dc) field with an effective energy barrier of 31.4 K, while complex 1Er only features SMM behavior under a 400 Oe external field with an effective energy barrier of 23.96 K. In stark contrast, complex 2Dy with the octahedral geometry only exhibits the frequency dependence of alternating current (ac) susceptibility signals without χ′′ peaks under a zero dc field.


Introduction
Single-molecule magnets (SMMs), with the individual molecules acting as tiny magnets, are the most appealing candidates to develop memory devices with ultra-high density and spintronic devices [1][2][3][4][5][6].The realization of those potential applications firstly depends on the high magnetic blocking temperature (T B ) and large effective energy barrier (U eff ), which have attracted the interests of chemists, physicists, and theorists [7][8][9].The effective energy barrier (also called the anisotropy barrier, ∆E) is the potential barrier hampering the reversal of the magnetization.For polynuclear transition metal SMMs, such as Mn 12 [10] and Mn 4 [11], the anisotropy barrier can be expressed as ∆E = DS 2 or D(S 2 − 1/4) for integer and half-integer spins, in which D is the axial zero-field splitting parameter and S is the spin of ground state.The magnetic blocking temperature (T B ) can refer to the highest temperature at which the M(H) hysteresis loop is observed.It is worth noting that T B strongly depends on the field-sweep rate.Usually, a complex with a high anisotropy barrier will not have a guaranteed high blocking temperature, which may be attributed to the fast quantum tunneling of magnetizations.Up to now, the records of blocking temperature and effective energy barrier have been achieved by the complex {[(Cp ttt ) 2 Dy][B(C 6 F 5 ) 4 ]} (Cp ttt = 1,2,4-tri(tertbutyl)cyclopentadienide) [12,13], as reported by the Layfield and Mills groups, with T B = 60 K and U eff = 1837 K, in which the value of U eff is higher by more than a factor of 30 than that of the Mn 12 [10], the first SMM with U eff = 61 K.The remarkable SMM properties of {[(Cp ttt ) 2 Dy][B(C 6 F 5 ) 4 ]} should mainly benefit from a perfectly axial crystal field realized by the bis(cyclopentadienyl) ligand, which demonstrates that the coordination environment of lanthanide ions plays a critical role in designing and modifying the SMMs, with the exception of complex N 2 3− -Ln 2 [14,15], where strong lanthanide-radical magnetic exchange coupling hinders zero-field fast relaxation pathways, and the asymmetric Dy 2 (ovph) 2 [16,17] with the Ising exchange interaction between Dy III ions, which efficiently suppresses fast QTM [18].
Considering the various coordination geometries and numbers of lanthanide complexes, choosing the particular coordination geometry is of vital importance in order to obtain better SMMs.For Dy III ions with the oblate-shaped electron density, a crystal field in which the ligand electron density is concentrated above and below the equatorial plane is desired to enhance the magnetic anisotropy [19].Furthermore, this kind of crystal field could lead to a highly efficient dysprosium SIM (single-ion magnet), such as D 4d [20][21][22] or D 5h [23][24][25].Moreover, the low-coordinate lanthanide complexes are superior at controlling the coordinated environment and understanding the magneto-structural relationship [26][27][28][29][30].
SIMs with six-coordination geometries are still rare in the previously reported Ln-based complexes, compared with other SIMs with high coordination numbers [31,32].Recently, Gao and co-workers reported that the complex [(L CO )Dy(N * ) 2 ] (L CO  2 ) 3 (HPz = pyrazole) [34] and Dy(Bc Me ) 3 ([Bc Me ] − = dihydrobis(methylimidazolyl)borate) [35] both exhibit only field-or dilution-induced slow relaxation of magnetization, in which cases the averaged bond distances of Dy-N and Dy-C are 2.477 and 2.577 Å, respectively.Those cases have demonstrated that the occurrence of SIMs' properties not only depends on the coordination geometry, but also on the strong axial-ligand field.In contrast, the six-coordinate Ln-based complexes possessing octahedral geometries show no SIM properties under a zero dc field, such as {(H 2 O)[Ln(NA) 2 ]•H 2 O} n (H 2 NA = 5-hydroxynicotinic acid) [28] and [36], which can be attributed to the fact that the cubic O h symmetry does not have second-order uniaxial anisotropy parameter B 0 2 [37][38][39].Herein, we report three six-coordinate lanthanide complexes, [Ln(L 1 Complexes 1Ln present the distorted trigonal-prismatic coordination geometry, while complex 2Dy shows distorted octahedral coordination geometry.The ac susceptibility data reveal the SIM behavior of 1Dy under a zero dc field, but the field-induced SIM behavior of 1Er.Without exception, complex 2Dy only shows the frequency dependence of ac signals without χ" peaks under a zero dc field, as reported previously [28,40].Therefore, this series of complexes sheds light on the magneto-structural correlation of six-coordinate complexes with different geometries.Importantly, complex 1Dy is the second SIM with trigonal-prismatic coordination geometry in the absence of an external field. SMMs, with the exception of complex N2 3− -Ln2 [14,15], where strong lanthanide-radical magnetic exchange coupling hinders zero-field fast relaxation pathways, and the asymmetric Dy2(ovph)2 [16,17] with the Ising exchange interaction between Dy III ions, which efficiently suppresses fast QTM [18].
Considering the various coordination geometries and numbers of lanthanide complexes, choosing the particular coordination geometry is of vital importance in order to obtain better SMMs.For Dy III ions with the oblate-shaped electron density, a crystal field in which the ligand electron density is concentrated above and below the equatorial plane is desired to enhance the magnetic anisotropy [19].Furthermore, this kind of crystal field could lead to a highly efficient dysprosium SIM (single-ion magnet), such as D4d [20][21][22] or D5h [23][24][25].Moreover, the low-coordinate lanthanide complexes are superior at controlling the coordinated environment and understanding the magnetostructural relationship [26][27][28][29][30].

Crystallography
Single-crystal X-ray diffraction investigation revealed that complexes 1Dy, 1Er (Figure 1), and 2Dy (Figure 2) crystallize in the triclinic P1 space group with Z = 2, in which complexes 1Dy and 1Er are isostructural.Herein, the crystal structure of 1Dy is described representatively.Details of the crystallographic data and the structure solution of three complexes are summarized in Table 1.Selected bond distances and angles are listed in Table S1 (see Supplementary Materials).The asymmetric unit of 1Dy contains one Dy III ion with a [N 3 O 3 ] coordination environment, which comes from three [L 1 ] − ligands.The coordination geometry around the Dy III ion is similar to the trigonal-prismatic geometry, which has been proven by the SHAPE 2.1 software [41][42][43], revealing that the Dy III ion is located in a distorted trigonal prism with a deviation of 2.36 from the ideal D 3h symmetry (Table S2, Supplementary Materials).The up and down basal planes are constructed by atoms O1, O3, and N3 and O2, N1, and N2, respectively, in which the θ angle between the two planes is 13.12 • (Figure S1 The formula and the formula weight of 2Dy do not include the squeezed solvents.

Magnetic Properties
The variable-temperature magnetic susceptibility data of complexes 1Dy, 1Er, and 2Dy were collected on the polycrystalline samples under an applied magnetic field of 1 kOe.At room temperature, the χMT values (Figure 3) of 1Dy, 1Er, and 2Dy are 13.77, 11.38, and 13.21 cm 3 •K•mol −1 , respectively, which are slightly lower than the expected value for free Dy III (14.17 cm 3 •K•mol −1 ) and Er III (11.48 cm 3 •K•mol −1 ) ions.As the temperature decreased, the χMT products decrease slowly down to 2 K, reaching values of 11.60 and 11.15 cm 3 •K•mol −1 for 1Dy and 2Dy, respectively.For complex 1Er, upon cooling, the χMT products slightly decrease over the range of 300-100 K, followed by an obvious decrease until 2 K with a minimum of 7.99 cm 3 •K•mol −1 .The decrease of χMT values can be attributed to the Stark level splitting of lanthanide ions with large unquenched orbital moment.The

Magnetic Properties
The variable-temperature magnetic susceptibility data of complexes 1Dy, 1Er, and 2Dy were collected on the polycrystalline samples under an applied magnetic field of 1 kOe.At room temperature, the χMT values (Figure 3) of 1Dy, 1Er, and 2Dy are 13.77, 11.38, and 13.21 cm 3 •K•mol −1 , respectively, which are slightly lower than the expected value for free Dy III (14.17 cm 3 •K•mol −1 ) and Er III (11.48 cm 3 •K•mol −1 ) ions.As the temperature decreased, the χMT products decrease slowly down to 2 K, reaching values of 11.60 and 11.15 cm 3 •K•mol −1 for 1Dy and 2Dy, respectively.For complex 1Er, upon cooling, the χMT products slightly decrease over the range of 300-100 K, followed by an obvious decrease until 2 K with a minimum of 7.99 cm 3 •K•mol −1 .The decrease of χMT values can be attributed to the Stark level splitting of lanthanide ions with large unquenched orbital moment.The

Magnetic Properties
The variable-temperature magnetic susceptibility data of complexes 1Dy, 1Er, and 2Dy were collected on the polycrystalline samples under an applied magnetic field of 1 kOe.At room temperature, the χ M T values (Figure 3) of 1Dy, 1Er, and 2Dy are 13.77, 11.38, and 13.21 cm 3 •K•mol −1 , respectively, which are slightly lower than the expected value for free Dy III (14.17 cm 3 •K•mol −1 ) and Er III (11.48 cm 3 •K•mol −1 ) ions.As the temperature decreased, the χ M T products decrease slowly down to 2 K, reaching values of 11.60 and 11.15 cm 3 •K•mol −1 for 1Dy and 2Dy, respectively.
For complex 1Er, upon cooling, the χ M T products slightly decrease over the range of 300-100 K, followed by an obvious decrease until 2 K with a minimum of 7.99 cm 3 •K•mol −1 .The decrease of χ M T values can be attributed to the Stark level splitting of lanthanide ions with large unquenched orbital moment.The field-dependent magnetizations for complexes 1Dy and 2Dy show the same tendency (Figures S6 and S8, Supplementary Materials), as observed in most dysprosium complexes reported [44].The magnetizations increase rapidly up to a field of 10 kOe, followed by an almost constant rise to 70 kOe, reaching values of 5.57 and 4.91 µ B at 1.9 K for 1Dy and 2Dy, respectively.However, a residual slope for complex 1Er (Figure S7, Supplementary Materials) is observed even at high field, and the magnetization finally reaches a value of 5.07 µ B at 1.9 K.The non-saturation of the field-dependent magnetizations at high field (70 kOe) for three complexes reveal the presence of magnetic anisotropy caused by the crystal-field effects and/or low-lying excited states.S8, Supplementary Materials), as observed in most dysprosium complexes reported [44].The magnetizations increase rapidly up to a field of 10 kOe, followed by an almost constant rise to 70 kOe, reaching values of 5.57 and 4.91 μB at 1.9 K for 1Dy and 2Dy, respectively.However, a residual slope for complex 1Er (Figure S7, Supplementary Materials) is observed even at high field, and the magnetization finally reaches a value of 5.07 μB at 1.9 K.The non-saturation of the field-dependent magnetizations at high field (70 kOe) for three complexes reveal the presence of magnetic anisotropy caused by the crystal-field effects and/or low-lying excited states.Alternating current susceptibility measurements were also conducted for three complexes under zero and 400 Oe dc field to further probe the dynamics of magnetization.In the absence of an applied dc field, both in-phase (χ′) and out-of-phase (χ′′) ac susceptibilities for complex 1Dy exhibit frequency (Figure 4) and temperature (Figure S9, Supplementary Materials) dependency.However, no maximum peaks of temperature dependence of the out-of-phase (χ′′) signal are observed in the range of 1-1488 Hz, which may be caused by the quantum tunneling of the magnetization (QTM), as also indicated by strong temperature-independent peaks below 9 K showed in Figure 4. To evaluate the effective barrier of magnetic relaxation, the relaxation times (τ) were extracted from the plot χ″ versus υ using the Debye model [45].The τ versus T −1 plot (Figure 5) shows a crossover from a linear increase of thermally activated to a temperature independent regime of QTM, which suggests the presence of more than one relaxation pathway.The plot was fitted using Equation (1), yielding effective energy barriers Ueff of 31.40K with a τ0 = 3.56 × 10 −4 s, where the τ −1 QTM, AH 2 T, CT n , and τ0 −1 exp(−Ueff/kBT) represent quantum tunneling, direct, Raman, and Orbach relaxation processes, respectively.For complex 1Dy, the direct process is excluded since the corresponding contribution is nullified at zero dc field.Other parameters obtained from the fitting are given in Table S3 (see Supplementary Materials).Alternating current susceptibility measurements were also conducted for three complexes under zero and 400 Oe dc field to further probe the dynamics of magnetization.In the absence of an applied dc field, both in-phase (χ ) and out-of-phase (χ ) ac susceptibilities for complex 1Dy exhibit frequency (Figure 4) and temperature (Figure S9, Supplementary Materials) dependency.However, no maximum peaks of temperature dependence of the out-of-phase (χ ) signal are observed in the range of 1-1488 Hz, which may be caused by the quantum tunneling of the magnetization (QTM), as also indicated by strong temperature-independent peaks below 9 K showed in Figure 4. To evaluate the effective barrier of magnetic relaxation, the relaxation times (τ) were extracted from the plot χ versus υ using the Debye model [45].The τ versus T −1 plot (Figure 5) shows a crossover from a linear increase of thermally activated to a temperature independent regime of QTM, which suggests the presence of more than one relaxation pathway.The plot was fitted using Equation (1), yielding effective energy barriers U eff of 31.40K with a τ 0 = 3.56 × 10 −4 s, where the τ −1 QTM , AH 2 T, CT n , and τ −1 0 exp(−U eff /k B T) represent quantum tunneling, direct, Raman, and Orbach relaxation processes, respectively.For complex 1Dy, the direct process is excluded since the corresponding contribution is nullified at zero dc field.Other parameters obtained from the fitting are given in Table S3 (see Supplementary Materials).For complex 1Er, no out-of-phase (χ″) signals (Figure S10, Supplementary Materials) were observed above 1.9 K at 997 Hz, which may be attributed to the fast quantum tunneling of the magnetization at zero dc field.The rather different magnetic behaviors of 1Dy and 1Er are correlated with the axial ligand field of trigonal-prismatic coordination geometry, as Dy III is oblate and Er III is prolate [19].In order to suppress the QTM process, the ac magnetic susceptibility measurements were also performed under a dc field (Figure S11, Supplementary Materials).The non-zero frequency-and temperature-dependent χ' and χ″ signals (Figures 4 and S12, Supplementary Materials) were observed at low temperature, indicating the field-induced SMM behavior.The relaxation times (τ) of 1Er were extracted from the plot χ″ versus υ using the Debye model.The τ versus T −1 plot (Figure 5), showing a smooth increase as the temperature was lowered, corroborates that the QTM is suppressed to a certain extent.The plot was fitted using Equation ( 1), yielding effective energy barriers Ueff of 23.96 K with a τ0 = 5.46 × 10 −8 s, and other parameters are listed in Table S3 (see Supplementary Materials).To avoid overparametrization, the direct process is canceled.
The Cole-Cole plots (Figure 6) of 1Dy and 1Er both show an asymmetrical semicircular shape, which can be fitted by the generalized Debye model [45], giving a series of α parameters below 0.11 from 1.9 to 13 K for 1Dy and 0.13 from 1.9 to 3.7 K for 1Er, respectively, which indicates a narrow distribution of the relaxation time for both complexes.
For complex 2Dy, both in-phase (χ′) and out-of-phase (χ′′) ac susceptibilities exhibited frequency (Figure 4) and temperature (Figure S13, Supplementary Materials) dependency under a zero dc field, indicative of slow relaxation of magnetization.However, no peaks of χ′′ were observed, indicating the presence of fast QTM relaxation.For complex 1Er, no out-of-phase (χ″) signals (Figure S10, Supplementary Materials) were observed above 1.9 K at 997 Hz, which may be attributed to the fast quantum tunneling of the magnetization at zero dc field.The rather different magnetic behaviors of 1Dy and 1Er are correlated with the axial ligand field of trigonal-prismatic coordination geometry, as Dy III is oblate and Er III is prolate [19].In order to suppress the QTM process, the ac magnetic susceptibility measurements were also performed under a dc field (Figure S11, Supplementary Materials).The non-zero frequency-and temperature-dependent χ' and χ″ signals (Figures 4 and S12, Supplementary Materials) were observed at low temperature, indicating the field-induced SMM behavior.The relaxation times (τ) of 1Er were extracted from the plot χ″ versus υ using the Debye model.The τ versus T −1 plot (Figure 5), showing a smooth increase as the temperature was lowered, corroborates that the QTM is suppressed to a certain extent.The plot was fitted using Equation (1), yielding effective energy barriers Ueff of 23.96 K with a τ0 = 5.46 × 10 −8 s, and other parameters are listed in Table S3 (see Supplementary Materials).To avoid overparametrization, the direct process is canceled.
The Cole-Cole plots (Figure 6) of 1Dy and 1Er both show an asymmetrical semicircular shape, which can be fitted by the generalized Debye model [45], giving a series of α parameters below 0.11 from 1.9 to 13 K for 1Dy and 0.13 from 1.9 to 3.7 K for 1Er, respectively, which indicates a narrow distribution of the relaxation time for both complexes.
For complex 2Dy, both in-phase (χ′) and out-of-phase (χ′′) ac susceptibilities exhibited frequency (Figure 4) and temperature (Figure S13, Supplementary Materials) dependency under a zero dc field, indicative of slow relaxation of magnetization.However, no peaks of χ′′ were observed, indicating the presence of fast QTM relaxation.For complex 1Er, no out-of-phase (χ ) signals (Figure S10, Supplementary Materials) were observed above 1.9 K at 997 Hz, which may be attributed to the fast quantum tunneling of the magnetization at zero dc field.The rather different magnetic behaviors of 1Dy and 1Er are correlated with the axial ligand field of trigonal-prismatic coordination geometry, as Dy III is oblate and Er III is prolate [19].In order to suppress the QTM process, the ac magnetic susceptibility measurements were also performed under a dc field (Figure S11, Supplementary Materials).The non-zero frequency-and temperature-dependent χ and χ signals (Figure 4 and Figure S12, Supplementary Materials) were observed at low temperature, indicating the field-induced SMM behavior.The relaxation times (τ) of 1Er were extracted from the plot χ versus υ using the Debye model.The τ versus T −1 plot (Figure 5), showing a smooth increase as the temperature was lowered, corroborates that the QTM is suppressed to a certain extent.The plot was fitted using Equation (1), yielding effective energy barriers U eff of 23.96 K with a τ 0 = 5.46 × 10 −8 s, and other parameters are listed in Table S3 (see Supplementary Materials).To avoid overparametrization, the direct process is canceled.
The Cole-Cole plots (Figure 6) of 1Dy and 1Er both show an asymmetrical semicircular shape, which can be fitted by the generalized Debye model [45], giving a series of α parameters below 0.11 from 1.9 to 13 K for 1Dy and 0.13 from 1.9 to 3.7 K for 1Er, respectively, which indicates a narrow distribution of the relaxation time for both complexes.
For complex 2Dy, both in-phase (χ ) and out-of-phase (χ ) ac susceptibilities exhibited frequency (Figure 4) and temperature (Figure S13, Supplementary Materials) dependency under a zero dc field, indicative of slow relaxation of magnetization.However, no peaks of χ were observed, indicating the presence of fast QTM relaxation.Compared with 1Ln with trigonal-prismatic geometry, the six-coordinated 2Dy with octahedral geometry demonstrates inferior magnetic properties, verifying that the coordination geometry around lanthanide ions directly affects the SMM performance.The closer the distribution of the ligands to spherical symmetry, such as the environment of cubic symmetry (octahedron, etc.), the smaller the crystal-field (CF) splitting [46].Therefore, the trigonal prismatic geometry can improve a relatively axial ligand field compared with the octahedron, which means that the six-coordinated lanthanide-based complexes, especially dysprosium complexes, located in trigonal-prismatic geometry are more likely to show SMM behavior in principle, which coincides with our experimental results.In order to further explore the magnetic properties of these two six-coordinate Dy-based complexes, the Magellan program [47] was used to calculate the magnetic anisotropy axes of complex 1Dy (Figure 7).The results reveal that the orientation of the magnetic axis of complex 1Dy is found to be almost collinear to Dy-O2 with an angle of 3.707°.Apparently, the negative charges on the O atoms are much larger than those on the N atoms for 1Dy, where it is more capable of stabilizing the ground doublet.As the ground-state wave function of complex [(L CO )Dy(N * )2] [33] featuring similar trigonal-prismatic coordination geometry around Dy III ion with complex 1Dy shows a dominant MJ = ±15/2 doublet, the magnetic axis orientation might prefer the negative charge dense direction for the Dy III ion with the oblate shaped electron density of <±15/2> doublet.Herein, the calculation was based on an electrostatic model, and a further quantitative evaluation of the anisotropy axis through ab initio calculation is definitely needed.Compared with 1Ln with trigonal-prismatic geometry, the six-coordinated 2Dy with octahedral geometry demonstrates inferior magnetic properties, verifying that the coordination geometry around lanthanide ions directly affects the SMM performance.The closer the distribution of the ligands to spherical symmetry, such as the environment of cubic symmetry (octahedron, etc.), the smaller the crystal-field (CF) splitting [46].Therefore, the trigonal prismatic geometry can improve a relatively axial ligand field compared with the octahedron, which means that the six-coordinated lanthanide-based complexes, especially dysprosium complexes, located in trigonal-prismatic geometry are more likely to show SMM behavior in principle, which coincides with our experimental results.In order to further explore the magnetic properties of these two six-coordinate Dy-based complexes, the Magellan program [47] was used to calculate the magnetic anisotropy axes of complex 1Dy (Figure 7).The results reveal that the orientation of the magnetic axis of complex 1Dy is found to be almost collinear to Dy-O2 with an angle of 3.707 • .Apparently, the negative charges on the O atoms are much larger than those on the N atoms for 1Dy, where it is more capable of stabilizing the ground doublet.As the ground-state wave function of complex [(L CO )Dy(N*) 2 ] [33] featuring similar trigonal-prismatic coordination geometry around Dy III ion with complex 1Dy shows a dominant M J = ±15/2 doublet, the magnetic axis orientation might prefer the negative charge dense direction for the Dy III ion with the oblate shaped electron density of <±15/2> doublet.Herein, the calculation was based on an electrostatic model, and a further quantitative evaluation of the anisotropy axis through ab initio calculation is definitely needed.Compared with 1Ln with trigonal-prismatic geometry, the six-coordinated 2Dy with octahedral geometry demonstrates inferior magnetic properties, verifying that the coordination geometry around lanthanide ions directly affects the SMM performance.The closer the distribution of the ligands to spherical symmetry, such as the environment of cubic symmetry (octahedron, etc.), the smaller the crystal-field (CF) splitting [46].Therefore, the trigonal prismatic geometry can improve a relatively axial ligand field compared with the octahedron, which means that the six-coordinated lanthanide-based complexes, especially dysprosium complexes, located in trigonal-prismatic geometry are more likely to show SMM behavior in principle, which coincides with our experimental results.In order to further explore the magnetic properties of these two six-coordinate Dy-based complexes, the Magellan program [47] was used to calculate the magnetic anisotropy axes of complex 1Dy (Figure 7).The results reveal that the orientation of the magnetic axis of complex 1Dy is found to be almost collinear to Dy-O2 with an angle of 3.707°.Apparently, the negative charges on the O atoms are much larger than those on the N atoms for 1Dy, where it is more capable of stabilizing the ground doublet.As the ground-state wave function of complex [(L CO )Dy(N * )2] [33] featuring similar trigonal-prismatic coordination geometry around Dy III ion with complex 1Dy shows a dominant MJ = ±15/2 doublet, the magnetic axis orientation might prefer the negative charge dense direction for the Dy III ion with the oblate shaped electron density of <±15/2> doublet.Herein, the calculation was based on an electrostatic model, and a further quantitative evaluation of the anisotropy axis through ab initio calculation is definitely needed.

Conclusions
In summary, we have synthesized and characterized three Ln-based mononuclear complexes, 1Dy, 1Er, and 2Dy, which show distinct magnetic properties.In complexes 1Dy and 1Er, the trigonal-prismatic coordination geometry provides an axial ligand field, which is in favor of the oblate Dy III ion rather than the prolate Er III ion; therefore, 1Dy exhibits the better magnetic properties with U eff = 31.4K under a zero dc field.1Er shows field-induced SIM properties with U eff = 23.96K under a 400 Oe dc field.Complex 2Dy with the O h symmetry only displays the frequency dependence of ac signals without χ peaks under the zero dc field, indicating the presence of fast QTM relaxation.For six-coordinate dysprosium complexes, the trigonal-prismatic coordination geometry is much more favorable to designing effective SIMs.

Supplementary Materials:
The following are available online at www.mdpi.com/2304-6740/6/1/16/s1.Cif and Checkcif files.Table S1: Selected bond distances [Å] and angles [ • ] for complexes 1Dy, 1Er, and 2Dy.Table S2: Lanthanide geometry analysis by SHAPE software for 1Dy, 1Er, and 2Dy.Table S3: Best-fit parameters for the Arrhenius plots of 1Dy and 1Er.S6: Molar magnetization (M) versus field (H) for complex 1Dy at 1.9, 3.0, and 5.0 K. Figure S7: Molar magnetization (M) versus field (H) for complex 1Er at 1.9, 3.0, and 5.0 K. Figure S8: Molar magnetization (M) versus field (H) for complex 2Dy at 1.9, 3.0, and 5.0 K. Figure S9: Temperature dependent in phase (χ ) and out of phase (χ ) ac susceptibilities for complexes 1Dy at indicated frequencies under a zero dc field.Figure S10: Temperature dependence in phase (χ ) and out of phase (χ ) ac susceptibilities for complexes 1Er under zero dc field.Figure S11: The field dependence of the out-of-phase signals of 1Er and 2Dy on applied dc field strength at 1.9 K and 997 Hz. Figure S12: Temperature dependent in phase (χ ) and out of phase (χ ) ac susceptibilities for complexes 1Er under a 400 Oe dc field.Figure S13: Temperature dependent in phase (χ ) and out of phase (χ ) ac susceptibilities for complexes 2Dy under a zero dc field.

Figure 1 .
Figure 1.The molecular structures of complexes 1Dy (left) and 1Er (right).The dashed green lines represent the basal planes.Hydrogen atoms have been omitted for clarity.

Figure 2 .
Figure 2. The molecular structure of complex 2Dy.The dashed green lines represent the equatorial plane.Hydrogen atoms have been omitted for clarity.

Figure 1 .Figure 1 .
Figure 1.The molecular structures of complexes 1Dy (left) and 1Er (right).The dashed green lines represent the basal planes.Hydrogen atoms have been omitted for clarity.

Figure 2 .
Figure 2. The molecular structure of complex 2Dy.The dashed green lines represent the equatorial plane.Hydrogen atoms have been omitted for clarity.

Figure 2 .
Figure 2. The molecular structure of complex 2Dy.The dashed green lines represent the equatorial plane.Hydrogen atoms have been omitted for clarity.
magnetizations for complexes 1Dy and 2Dy show the same tendency (Figures S6 and

Figure 3 .
Figure 3. Plots of the χMT versus T for 1Dy, 1Er and 2Dy in an applied field of 1 kOe.

Figure 3 .
Figure 3. Plots of the χ M T versus T for 1Dy, 1Er and 2Dy in an applied field of 1 kOe.

Figure 5 .
Figure 5. Plots of τ versus T −1 for 1Dy (left) and 1Er (right), respectively.The red lines correspond to the best fits, and the blue line corresponds to the Orbach process.

Figure 5 .
Figure 5. Plots of τ versus T −1 for 1Dy (left) and 1Er (right), respectively.The red lines correspond to the best fits, and the blue line corresponds to the Orbach process.

Figure 5 .
Figure 5. Plots of τ versus T −1 for 1Dy (left) and 1Er (right), respectively.The red lines correspond to the best fits, and the blue line corresponds to the Orbach process.

Figure 6 .
Figure 6.Cole-Cole plots for 1Dy (left) and 1Er (right) at the indicated temperature; the solid lines correspond to the best fits.

Figure 7 .
Figure 7. Ground-state magnetic anisotropy of complexes 1Dy.The green lines represent the orientations of the anisotropy axes for Dy III ion (charges for the calculation: Dy + 3; O − 1; other 0), as calculated by the electrostatic model.

Figure 6 .
Figure 6.Cole-Cole plots for 1Dy (left) and 1Er (right) at the indicated temperature; the solid lines correspond to the best fits.

Figure 6 .
Figure 6.Cole-Cole plots for 1Dy (left) and 1Er (right) at the indicated temperature; the solid lines correspond to the best fits.

Figure 7 .
Figure 7. Ground-state magnetic anisotropy of complexes 1Dy.The green lines represent the orientations of the anisotropy axes for Dy III ion (charges for the calculation: Dy + 3; O − 1; other 0), as calculated by the electrostatic model.

Figure 7 .
Figure 7. Ground-state magnetic anisotropy of complexes 1Dy.The green lines represent the orientations of the anisotropy axes for Dy III ion (charges for the calculation: Dy + 3; O − 1; other 0), as calculated by the electrostatic model.
Figure S1: X-ray structures of complexes 1Dy.The green planes represent the coordination planes with labeled dihedral angle (θ).Solvents and hydrogen atoms have been omitted for clarity.
Figure S2: Packing diagram of 2 viewed along the c-axis.
Figure S3: X-ray structures of complexes 1Er.The green planes represent the coordination planes with labeled dihedral angle (θ).Solvents and hydrogen atoms have been omitted for clarity.Figure S4: Packing diagram of 1Er viewed along the c-axis.
Figure S5: Packing diagram of 2Dy viewed along the c-axis.

Table 1 .
Crystallographic data and structure refinement details of complexes 1Dy, 1Er, and 2Dy.