Field-Induced Single-Molecule Magnets of Dysprosium Involving Quinone Derivatives

: The coordination reaction of the [Dy(hfac) 3 (H 2 O) 2 ] units (hfac − = 1,1,1,5,5,5- hexaﬂu-oroacetylacetonate) with the two quinone-based derivatives 4,7-di-tert-butyl-2-(3,5-di-tert-butyl-4-oxocyclohexa-2,5-dien-1-ylidene)benzo[d][1,3]dithiole-5,6-dione ( L 1 ) and 7,8-dithiabicyclo[4.2.0]octa-1,5-diene-3,4-dione,2,5bis(1,1-dimethylethyl) ( L 2 ) led respectively to the complexes [Dy(hfac) 3 (H 2 O)( L 1 )] ( 1 ) and [Dy(hfac) 3 (H 2 O) ( L 2 )] · (C 6 H 14 )(CH 2 Cl 2 ) ( 2 ) · (C 6 H 14 )(CH 2 Cl 2 ). X-ray structures on single crystal of 1 and 2 · (C 6 H 14 )(CH 2 Cl 2 ) revealed the coordination of the Dy III on the bischelating oxygenated quinone site and the formation of dimeric species through hydrogen bonds. Ac magnetic measurements highlighted ﬁeld-induced single-molecule magnet behavior with magnetic relaxation through a Raman process.


Introduction
The design of the coordination surrounding of magneto-active ions is a challenging task; a choice of o-quinone-like dioxolenes for this purpose seems to be promising for several reasons: (i) o-dioxolenes possess a redox activity, their oxidation state may be changed directly in the coordination sphere of the metal ion [1][2][3]. Organic radical semiquinone form is often associated to transition metal to design complexes displaying chemical and physical properties, such as valence tautomerism [4], photo-and thermo-mechanical effects [5]. o-Quinone-like dioxolenes in quinone, semiquinone [6][7][8][9] or catecholate [10][11][12] oxidation states have been associated with lanthanide ions to generate luminescence [13] and single-molecule magnet (SMM) behavior [14][15][16], as well as magnetic or optical switching [17][18][19][20]. It is worth mentioning that SMM behavior is associated to the observation of slow magnetic relaxation at the molecular scale, leading to the opening of a hysteresis loop at low temperature. The recent discovery of organometallic complexes of dysprosium with high blocking temperature [21][22][23][24] make them potential candidates for high density data storage; (ii) due to chelating ability, o-dioxolenes form stable complexes with almost all metals; (iii) o-quinone may be modified with various additional redox-active, free radical bearing or coordination-capable functional fragments to provide possibilities for the switching of the redox and/or magnetic state of the molecule [25].
The interest for metal dithiolenes emerged due to their potential applications in molecular conductors and superconductors [26]. Moreover, they have been recently employed to study electronic spin decoherence for quantum computation [27][28][29].
In the present paper, the reaction between L 1 or L 2 in presence of [Dy(hfac)3(H2O)2] led to the coordination on the 1,2-quinone site (regioselectively in case of L 2 ) without reduction of it. Magnetic properties of the resulting [Dy(hfac)3(H2O)(L 1 )] (1) and [Dy(hfac)3(H2O)(L 2 )]⋅(C6H14)(CH2Cl2) (2)⋅(C6H14)(CH2Cl2) complexes are investigated. Chart 1. Molecular structure of L 1 and L 2 ligands. [1,3]dithiole-5,6-dione (L 1 ). This ligand was recently reported by some of us [30]. The IR and NMR data are given in SI. In order to have an optimal structural comparison between the free L 1 quinone and the corresponding coordination complex (1), its X-ray structure was determined at 150 K on dark purple single crystals obtained from n-hexane-ether solution on cooling. A quick description is given in the following lines. L 1 crystallized in the tetragonal space group P-4 (N°81) ( Figure S1 and Table S1). The asymmetric unit is composed of one almost planar organic molecule of L 1 . The three C=O distances range from 1.197(3) to 1.233(4) Å, which is consistent with a double bond character. Alternated bond lengths distribution in the dioxolene ring of L 1 is also typical of sterically hindered o-quinones. Thus, the single crystal X-ray structure confirmed the quinone form of L 1 at 150 K. The crystal packing of L 1 revealed a stacking of the molecules along the c axis; nevertheless, the bulky tert-butyl groups prevented any strong π-π interaction. Thus, the cohesion of the crystal is mainly guaranteed through short S1⋅⋅⋅O1 (3.246 Å) and S2⋅⋅⋅O2 (3.300 Å) contacts. One could remark that to optimize the overlap between the π orbitals of the oxygen and sulfur atoms, the quinone fragment is not planar (Figure 1).
In the present paper, the reaction between L 1 or L 2 in presence of [Dy(hfac) 3

Results and Discussion
2.1. X-ray Structures 4,7-di-tert-butyl-2-(3,5-di-tert-butyl-4-oxocyclohexa-2,5-dien-1-ylidene)benzo[d] [1,3]dithiole-5,6-dione (L 1 ). This ligand was recently reported by some of us [30]. The IR and NMR data are given in SI. In order to have an optimal structural comparison between the free L 1 quinone and the corresponding coordination complex (1), its X-ray structure was determined at 150 K on dark purple single crystals obtained from n-hexane-ether solution on cooling. A quick description is given in the following lines. L 1 crystallized in the tetragonal space group P-4 (N • 81) ( Figure S1 and Table S1). The asymmetric unit is composed of one almost planar organic molecule of L 1 . The three C=O distances range from 1.197(3) to 1.233(4) Å, which is consistent with a double bond character. Alternated bond lengths distribution in the dioxolene ring of L 1 is also typical of sterically hindered o-quinones. Thus, the single crystal X-ray structure confirmed the quinone form of L 1 at 150 K. The crystal packing of L 1 revealed a stacking of the molecules along the c axis; nevertheless, the bulky tert-butyl groups prevented any strong π-π interaction. Thus, the cohesion of the crystal is mainly guaranteed through short S1···O1 (3.246 Å) and S2···O2 (3.300 Å) contacts. One could remark that to optimize the overlap between the π orbitals of the oxygen and sulfur atoms, the quinone fragment is not planar (Figure 1).
[Dy(hfac) 3 (Table S1) and an ORTEP view of the asymmetric unit is depicted in Figure S1. The latter is composed of one complex of formula [Dy(hfac) 3 (H 2 O)(L 1 )] (Figure 1a). The mononuclear species is formed by coordination of the bischelating quinone fragment to the Dy III metal center. The quinone character is confirmed by the two C16 = O7 (1.240(5) Å) and C21 = O8 (1.236(5) Å) bond lengths. The dioxolene ring of the ligand in 1 also retains an alternated (non-aromatic) distribution of bond lengths. The coordination sphere of the Dy III is filled by three bischelating hfac − anions and one water molecule. The arrangement of the L 1 , the three hfac − anions and the coordinated water molecule formed a polyhedron, having a C 4v spherical capped square antiprism as the closest ideal symmetry (Table S2). The deviations from the ideal symmetries are calculated using the SHAPE software [35].
Magnetochemistry 2021, 7, x FOR PEER REVIEW 3 of 13 distribution of bond lengths. The coordination sphere of the Dy III is filled by three bischelating hfacanions and one water molecule. The arrangement of the L 1 , the three hfacanions and the coordinated water molecule formed a polyhedron, having a C4v spherical capped square antiprism as the closest ideal symmetry (Table S2). The deviations from the ideal symmetries are calculated using the SHAPE software [35]. The coordination to the [Dy(hfac)3(H2O)] unit makes similar short S⋅⋅⋅O contacts like those observed for the X-ray structure of the free L 1 ligand impossible. Consequently, the arrangement of the quinone changed with carbonyl groups on either side of the plane formed by the six-membered ring of the quinone. The crystal packing revealed the formation of a dimeric structure through hydrogen bonds thanks to the coordinated water molecule. Five short O⋅⋅⋅O contacts ranging from 2.873 Å to 2.965 Å have been identified, leading to a Dy⋅⋅⋅Dy intermolecular distance of 5.981 Å (Figure 1b). The shortest intermolecular Dy⋅⋅⋅Dy distance not involved in a dimer was measured at 10.579 Å.
Finally, the dimers of 1 were organized in a parallel way along the b axis, while the quinone derivatives L 1 were organized in an orthogonal way with the neighboring L 1 (Figure 1c). Such arrangement allowed the carbonyl group involving the O10 atom to point towards the two sulfur atoms of the neighboring molecule leading to O10⋅⋅⋅S1 and O10⋅⋅⋅S2 distances of 3.934 Å and 3.536 Å ( Figure S2).  Figures S3 and S4. The bischelating dioxolene site in a quinone form is coordinated to the [Dy(hfac)3(H2O)] unit, in agreement with the oxophilic character of the lanthanide ion, in contrast with what was observed for the bischelating dithiolene coordination site, which is coordinated to the soft Pd II [34]. The quinone form of L 2 was confirmed by the C=O bond lengths, ranging from 1.064 Å to 1.417 Å (average distance of 1.230 Å). The coordination sphere of the Dy III is filled with three bischelating hfacanions and one water molecule. The deviations from the ideal symmetries for each The coordination to the [Dy(hfac) 3 (H 2 O)] unit makes similar short S···O contacts like those observed for the X-ray structure of the free L 1 ligand impossible. Consequently, the arrangement of the quinone changed with carbonyl groups on either side of the plane formed by the six-membered ring of the quinone. The crystal packing revealed the formation of a dimeric structure through hydrogen bonds thanks to the coordinated water molecule. Five short O···O contacts ranging from 2.873 Å to 2.965 Å have been identified, leading to a Dy···Dy intermolecular distance of 5.981 Å (Figure 1b). The shortest intermolecular Dy···Dy distance not involved in a dimer was measured at 10.579 Å.
Finally, the dimers of 1 were organized in a parallel way along the b axis, while the quinone derivatives L 1 were organized in an orthogonal way with the neighboring L 1 (Figure 1c). Such arrangement allowed the carbonyl group involving the O10 atom to point towards the two sulfur atoms of the neighboring molecule leading to O10···S1 and O10···S2 distances of 3.934 Å and 3.536 Å ( Figure S2).
[Dy(hfac) 3 . The coordination reaction of the tris(1,1,1,5,5,5-hexafluoroacetylacetonate)bis(aqueous)Dy III ([Dy(hfac) 3 in CH 2 Cl 2 led to the formation of the complexes [Dy(hfac) 3 (H 2 O)(L 2 )]·(C 6 H 14 )(CH 2 Cl 2 ) ((2)·(C 6 H 14 )(CH 2 Cl 2 )). 2·(C 6 H 14 )(CH 2 Cl 2 ) crystallized in the monoclinic space group P2 1 ( Table S1). The asymmetric unit is composed of eight molecules [Dy(hfac) 3 Figure 2a) and its ORTEP view is shown in Figures S3 and S4. The bischelating dioxolene site in a quinone form is coordinated to the [Dy(hfac) 3 (H 2 O)] unit, in agreement with the oxophilic character of the lanthanide ion, in contrast with what was observed for the bischelating dithiolene coordination site, which is coordinated to the soft Pd II [34]. The quinone form of L 2 was confirmed by the C=O bond lengths, ranging from 1.064 Å to 1.417 Å (average distance of 1.230 Å). The coordination sphere of the Dy III is filled with three bischelating hfac − anions and one water molecule. The deviations from the ideal symmetries for each Dy III surrounding are calculated using the SHAPE software (Table S3) [35]. The eight coordination polyhedron symmetries corresponding to the eight crystallographically independent dysprosium can be classified into two groups, with Dy1, Dy2 and Dy5 adopting a D 3h spherical tricapped trigonal prism, while the five others adopted a C 4v spherical capped square antiprism. Since one water molecule coordinated to the Dy III is present, the formation of dimers through hydrogen bonds is observed (Figure 2b). For each dimer, three short O···O contacts ranging from 2.653 Å to 3.039 Å have been identified, leading to an average Dy···Dy intermolecular distance of 5.868 Å. The shortest intermolecular Dy···Dy distance not involved in a dimer was measured at 9.657 Å. H···F and F···F contacts ensured the cohesion between the different dimers ( Figure S5). Dy III surrounding are calculated using the SHAPE software (Table S3) [35]. The eight coordination polyhedron symmetries corresponding to the eight crystallographically independent dysprosium can be classified into two groups, with Dy1, Dy2 and Dy5 adopting a D3h spherical tricapped trigonal prism, while the five others adopted a C4v spherical capped square antiprism. Since one water molecule coordinated to the Dy III is present, the formation of dimers through hydrogen bonds is observed (Figure 2b). For each dimer, three short O⋅⋅⋅O contacts ranging from 2.653 Å to 3.039 Å have been identified, leading to an average Dy⋅⋅⋅Dy intermolecular distance of 5.868 Å. The shortest intermolecular Dy⋅⋅⋅Dy distance not involved in a dimer was measured at 9.657 Å. H⋅⋅⋅F and F⋅⋅⋅F contacts ensured the cohesion between the different dimers ( Figure S5). One could remark that even if both X-ray structures of 1 and 2⋅(C6H14)(CH2Cl2) involved similar dimerization of the complexes through hydrogen bond due to the remaining coordinated water molecules, a slight structural difference could be noticed. Indeed, the dimer of 1 involved both Ow⋅⋅⋅Ow (2.954 Å) and Ow⋅⋅⋅Ohfac (average distance of 2.919 Å) short contacts, while in 2⋅(C6H14)(CH2Cl2), only Ow⋅⋅⋅Ohfac (average distance of 2.835 Å) are involved. Previous systems, published by some of us, already showed that the coordination of the quinone-tetrathiafulvalene-quinone triad [14] or quinone-(extended-TTF)-quinone triad [17] to the [Dy(hfac)3] unit led to the observation of a remaining coordinated water molecule and such dimerization through Ow⋅⋅⋅Ohfac short contacts only. In others words, 1 is the only system showing Ow⋅⋅⋅Ow short contact susceptible to induce difference in the magnetic behavior. One could remark that even if both X-ray structures of 1 and 2·(C 6 H 14 )(CH 2 Cl 2 ) involved similar dimerization of the complexes through hydrogen bond due to the remaining coordinated water molecules, a slight structural difference could be noticed. Indeed, the dimer of 1 involved both O w ···O w (2.954 Å) and O w ···O hfac (average distance of 2.919 Å) short contacts, while in 2·(C 6 H 14 )(CH 2 Cl 2 ), only O w ···O hfac (average distance of 2.835 Å) are involved. Previous systems, published by some of us, already showed that the coordination of the quinone-tetrathiafulvalene-quinone triad [14] or quinone-(extended-TTF)quinone triad [17] to the [Dy(hfac) 3 ] unit led to the observation of a remaining coordinated water molecule and such dimerization through O w ···O hfac short contacts only. In others words, 1 is the only system showing O w ···O w short contact susceptible to induce difference in the magnetic behavior.

Static Magnetic Measurements
The magnetic susceptibility (χ M ) was measured for both 1 and 2 compounds in the temperature range of 2-300 K and their thermal dependence of the χ M T products is depicted in Figure 3. The experimental room temperature values for 1 and 2 are respectively 13.62 cm 3 ·K·mol −1 and 13.77 cm 3 ·K·mol −1 , in agreement with the expected value consider-ing one isolated Dy III ion ( 6 H 15/2 ground state multiplet) (14.17 cm 3 ·K·mol −1 ) [32]. When decreasing the temperature, χ M T products decrease monotonically down to 8.61 cm 3 ·K·mol −1 for 1 and 10.28 cm 3 ·K·mol −1 for 2. Such magnetic behavior is attributed to the thermal depopulation of the M J states and antiferromagnetic dipolar interactions. Indeed, some of us demonstrated that the formation of dimer through hydrogen bonds led to antiferromagnetic interactions up to -0.65 cm −1 between the two Dy III ions [17]. In such a situation, the observed χ M T value at 2 K is close to 10 cm 3 ·K·mol −1 , which is in agreement with the observed value for 2, while a lower value is observed for 1. Such a low value might be attributed to stronger antiferromagnetic interaction in 1 than in 2 and previously reported examples [14,17], because the O w ···O w contact is the shortest one. Considering that the dipolar interaction is proportional to 1/r 3 (where r 3 is the distance between the two spin carriers), it is reasonable to consider that the inter-dimer dipolar interaction would be negligible compared to the intra-dimer dipolar interaction.

Static Magnetic Measurements
The magnetic susceptibility (χM) was measured for both 1 and 2 compounds in the temperature range of 2-300 K and their thermal dependence of the χMT products is de picted in Figure 3. The experimental room temperature values for 1 and 2 are respectively 13.62 cm 3 ·K·mol −1 and 13.77 cm 3 ·K·mol −1 , in agreement with the expected value consider ing one isolated Dy III ion ( 6 H15/2 ground state multiplet) (14.17 cm 3 ·K·mol −1 ) [32]. When decreasing the temperature, χMT products decrease monotonically down to 8.61 cm 3 ·K·mol −1 for 1 and 10.28 cm 3 ·K·mol −1 for 2. Such magnetic behavior is attributed to the thermal depopulation of the MJ states and antiferromagnetic dipolar interactions. Indeed some of us demonstrated that the formation of dimer through hydrogen bonds led to an tiferromagnetic interactions up to -0.65 cm −1 between the two Dy III ions [17]. In such a situation, the observed χMT value at 2 K is close to 10 cm 3 ·K·mol −1 , which is in agreemen with the observed value for 2, while a lower value is observed for 1. Such a low value might be attributed to stronger antiferromagnetic interaction in 1 than in 2 and previously reported examples [14,17], because the Ow⋅⋅⋅Ow contact is the shortest one. Considering that the dipolar interaction is proportional to 1/r 3 (where r 3 is the distance between the two spin carriers), it is reasonable to consider that the inter-dimer dipolar interaction would be negligible compared to the intra-dimer dipolar interaction. Figure 3. Temperature dependence of χMT for 1 (blue) and 2 (black) between 2 and 300 K. In inset, the field variations of the magnetization at 2 K for 1 (blue) and 2 (black) between 0 and 50 kOe.
The measured magnetizations at 50 kOe are 5.46 μB for 1 and 5.24 μB for 2 far from the expected saturated value of 10 μB, due to the magnetic anisotropy of the systems (inse of Figure 3) [36]. The two magnetizations at 2 K showed significant differences, i.e., slower increase at low field for 1 than for 2, in agreement with possible stronger antiferromag netic interaction in 1 than in 2. Moreover, the slope of the magnetization at higher fields might also suggest a different composition of the ground state. Thus, the nature of the M ground doublet state could also play a role in the χMT low value for 1.

Dynamic Magnetic Measurements
The high magnetic moment and the strong magnetic anisotropy of the Dy III ion in an O9 surrounding could be suitable parameters to observe a slow relaxation of its magneti zation [14,17]. The molar ac magnetic susceptibility (χM) was measured for both com pounds 1 and 2 in order to study the dynamic magnetic properties. No out-of-phase signa (χM″) was detected in zero magnetic field in the frequency range 1-1000 Hz for 1 ( Figure  S6) and the reason is usually imputed to a fast magnetic relaxation through a quantum . Temperature dependence of χ M T for 1 (blue) and 2 (black) between 2 and 300 K. In inset, the field variations of the magnetization at 2 K for 1 (blue) and 2 (black) between 0 and 50 kOe.
The measured magnetizations at 50 kOe are 5.46 µ B for 1 and 5.24 µ B for 2 far from the expected saturated value of 10 µ B , due to the magnetic anisotropy of the systems (inset of Figure 3) [36]. The two magnetizations at 2 K showed significant differences, i.e., slower increase at low field for 1 than for 2, in agreement with possible stronger antiferromagnetic interaction in 1 than in 2. Moreover, the slope of the magnetization at higher fields might also suggest a different composition of the ground state. Thus, the nature of the M J ground doublet state could also play a role in the χ M T low value for 1.

Dynamic Magnetic Measurements
The high magnetic moment and the strong magnetic anisotropy of the Dy III ion in an O9 surrounding could be suitable parameters to observe a slow relaxation of its magnetization [14,17]. The molar ac magnetic susceptibility (χ M ) was measured for both compounds 1 and 2 in order to study the dynamic magnetic properties. No out-of-phase signal (χ M ") was detected in zero magnetic field in the frequency range 1-1000 Hz for 1 ( Figure S6) and the reason is usually imputed to a fast magnetic relaxation through a quantum tunneling of the magnetization (QTM). The latter can be cancelled, applying a dc magnetic field, as shown in Figure S6. The field dependence of the magnetic susceptibility revealed that a good compromise for the applied magnetic field value is 1600 Oe. Under such an applied field, 1 highlighted a frequency dependence of the magnetic susceptibility ( Figure S7). An extended Debye model [37,38] was used to extract the temperature dependence of the relaxation time, fitting simultaneously both χ M and χ M " ( Figure S8 and Table S4), which are depicted in Figure 4. possible contributing processes is given in the following Equation (1):  (1) with the different relaxation rates standing for the Orbach, the Raman, the QTM (quantum tunneling of the magnetization), and the direct processes, respectively; and the different parameters (τ0, Δ, τTI, n, C and A) are found by fitting the experimental data, whereas m exponent is supposed to be tabulated and known values. Since no high-frequency shift for the maxima of the out-of phase contribution was observed under an applied magnetic field, direct spin-phonon relaxation process was discarded. The relaxation time of the magnetization (τ) can be fitted using the thermally dependent Raman process only (τ −1 = CT n ). The best fit was obtained with the following parameters: C = 175(19) s −1 K −n and n = 1.95 (11) (Figures 4 and S9). The presence of both acoustic and optical phonons could induce the observation of n values between 2 and 7 [39][40][41], instead of the expected n value of 9 for Kramers ions [42]. It is worth noticing that the slow relaxation fraction is low (about 25% of the sample susceptibility) at 2 K. The non-relaxing fraction was extracted from the extrapolation of the normalized Argand plot to the x-axis at a given temperature ( Figure S10). Thus, the field dependence of the magnetic susceptibility was checked at higher frequency ( Figure S6), showing that a non-zero contribution is present at a higher frequency than 10,000 Hz.
In case of 2, an out-of phase component of the magnetic susceptibility was observed without applied magnetic field (Figures 5 and S11) at 2 K. Two contributions can be observed at 100 Hz and higher than 10,000 Hz. Application of a dc field induced a shift of the two χM'' contributions at lower frequency. The value of 1200 Oe was selected as the The full formula for the relaxation rate of the magnetization as a sum of the different possible contributing processes is given in the following Equation (1): with the different relaxation rates standing for the Orbach, the Raman, the QTM (quantum tunneling of the magnetization), and the direct processes, respectively; and the different parameters (τ 0 , ∆, τ TI , n, C and A) are found by fitting the experimental data, whereas m exponent is supposed to be tabulated and known values. Since no high-frequency shift for the maxima of the out-of phase contribution was observed under an applied magnetic field, direct spin-phonon relaxation process was discarded. The relaxation time of the magnetization (τ) can be fitted using the thermally dependent Raman process only (τ −1 = CT n ). The best fit was obtained with the following parameters: C = 175(19) s −1 K −n and n = 1.95 (11) (Figure 4 and Figure S9). The presence of both acoustic and optical phonons could induce the observation of n values between 2 and 7 [39][40][41], instead of the expected n value of 9 for Kramers ions [42]. It is worth noticing that the slow relaxation fraction is low (about 25% of the sample susceptibility) at 2 K. The non-relaxing fraction was extracted from the extrapolation of the normalized Argand plot to the x-axis at a given temperature ( Figure S10). Thus, the field dependence of the magnetic susceptibility was checked at higher frequency ( Figure S6), showing that a non-zero contribution is present at a higher frequency than 10,000 Hz.
In case of 2, an out-of phase component of the magnetic susceptibility was observed without applied magnetic field ( Figure 5 and Figure S11) at 2 K. Two contributions can be observed at 100 Hz and higher than 10,000 Hz. Application of a dc field induced a shift of the two χ M " contributions at lower frequency. The value of 1200 Oe was selected as the optimal field. Under the 1200 Oe applied field, a frequency dependence of the magnetic susceptibility was observed ( Figure 5 and Figure S12).
Magnetochemistry 2021, 7, x FOR PEER REVIEW optimal field. Under the 1200 Oe applied field, a frequency dependence of the m susceptibility was observed (Figures 5 and S12). At 2 K, a single signal was observed centered at 80 Hz, while when increa temperature, a second contribution localized at a lower frequency appeared in th imental frequency windows. The temperature dependence of the relaxation time two contributions of the magnetic susceptibility was extracted, fitting simultaneo and χM″ with a modified extended Debye model ( Figure S14 and Table S5). The re time of the magnetization (τ) for the two high frequency (HF) and low frequen contributions can be fitted using the thermally dependent Raman process only (τ − Figure 5. (Above) field dependence of the out-of-phase contribution of the magnetic susceptibility between 0 and 4000 Oe at 2 K for 2. (Below) Frequency dependence of the out-of-phase contribution of the magnetic susceptibility between 2 and 9 K under an applied field of 1200 Oe. At 2 K, a single signal was observed centered at 80 Hz, while when increasing the temperature, a second contribution localized at a lower frequency appeared in the experimental frequency windows. The temperature dependence of the relaxation time for the two contributions of the magnetic susceptibility was extracted, fitting simultaneously χ M and χ M " with a modified extended Debye model ( Figure S14 and Table S5). The relaxation time of the magnetization (τ) for the two high frequency (HF) and low frequency (LF) contributions can be fitted using the thermally dependent Raman process only (τ −1 = CT n ).
The best fits were obtained with C = 3.93(69) s −1 K −n and n = 6.81 (16) and C = 1.44(27) s −1 K −n and n = 7.78(11) (Figure 6 and Figure S9) for the HF and LF contributions, respectively. The slow magnetic relaxation fraction represents the main part of the sample (about 90% of the sample) ( Figure S14). One could be tempted to attribute the HF and LF contributions to the magnetic relaxation of the Dy III in C 4v and D 3h coordination environment regarding the intensity ratio.
The compounds 1 and 2 displayed a magnetic relaxation mainly through a pure Raman process (Figure 4, Figure 6 and Figure S9), which could be justified by the applied magnetic field (cancelling of the QTM), the moderate value of the field (the direct process is not the fastest magnetic relaxation process) and the low temperature range at which the relaxation times are extracted (below 10 K), leading to a negligible Orbach contribution. Recently, several Dy III -based SMMs displaying pure Raman magnetic relaxation under moderate applied field in the low temperature range have been reported [43][44][45][46][47][48][49]. For some of the reported example in Table 1, an Orbach process can be involved in the magnetic relaxation in the high temperature range, in which an out-of-phase contribution of the magnetic susceptibility was measured. The variation of the dynamic parameters could be attributed to the nature of the surrounding, symmetry of the coordination sphere, as well as the nature of the matrix (crystal packing) and they cannot be easily compared.
between 0 and 4000 Oe at 2 K for 2. (below) Frequency dependence of the out-of-phase contribution of the magnetic susceptibility between 2 and 9 K under an applied field of 1200 Oe. At 2 K, a single signal was observed centered at 80 Hz, while when increasing the temperature, a second contribution localized at a lower frequency appeared in the exper imental frequency windows. The temperature dependence of the relaxation time for the two contributions of the magnetic susceptibility was extracted, fitting simultaneously χM and χM″ with a modified extended Debye model ( Figure S14 and Table S5). The relaxation time of the magnetization (τ) for the two high frequency (HF) and low frequency (LF contributions can be fitted using the thermally dependent Raman process only (τ −1 = CT n ) Figure 6. Temperature variation of the relaxation time for 2 for high frequency (gray spots) and low frequency (black spots) contributions in the temperature range of 2-9 K with the best fitted curves with Raman processes (red lines) (see text for details).

Synthesis. General Procedures and Materials
The precursor [Dy(hfac) 3 3 (H 2 O) 2 ] (0.02 mmol) were dissolved in 10 mL of CH 2 Cl 2 and then added to a pink-purple solution of 10 mL of CH 2 Cl 2 containing 10.0 mg of L 1 (0.02 mmol). The resulting solution changed color from purple to green when adding the Dy III salt. After 20 min of stirring, 20 mL of n-hexane were layered at room temperature. Suitable deep green single crystals of 1 suitable for X-ray diffraction study were obtained by slow diffusion, followed by a slow evaporation in the dark. Yield (determined from isolated single crystals) 21.8 mg (84%). Anal. Calcd (%) for C 44  ] (0.02 mmol) were dissolved in 10 mL of CH 2 Cl 2 and then added to a violet solution of 10 mL of CH 2 Cl 2 containing 5.6 mg of L 2 (0.02 mmol). The resulting solution changed color from violet to green when adding the Dy III salt. After 15 min of stirring, 20 mL of n-hexane were layered at room temperature. Suitable deep green single crystals of (2)·(C 6 H 14 )(CH 2 Cl 2 ) for X-ray diffraction study were obtained by slow diffusion followed by a slow evaporation in the dark. Yield (determined from isolated single crystals) 12.8 mg (59%). Anal. Calcd (%) for C 29

Crystallography
Single crystals of L 1 , 1 and 2·(C 6 H 14 )(CH 2 Cl 2 ) were mounted on a D8 VENTURE Bruker-AXS diffractometer for data collection (MoK α radiation source, λ = 0.71073 Å), from the diffractometric center X (CDIFX), University of Rennes 1, France (Table S1). SHELXT program [51] was used to solve the structures with a direct method and refinements were done with the SHELXL-14/7 program [52] using a full matrix least-squares method on F 2 . It is worth to notice that the bad quality of the obtained single crystal does not allowed a high level of refinement. Moreover, 2 contains large solvent accessible voids in which residual peak of diffraction were observed and SQUEEZE procedure of PLATON [53] was performed. Residual electronic density and the volume of voids are in agreement with 8 n-hexane and 8 dichloromethane molecules per asymetric unit. CCDC number is 2,039,846-2,039,848 for compounds L 1 , 1 and 2·(C 6 H 14 )(CH 2 Cl 2 ), respectively.

Physical Measurements
The elemental analyses of the compounds were performed at the Centre Régional de Mesures Physiques de l'Ouest, Rennes. The static susceptibility measurements were performed on solid polycrystalline samples with a Quantum Design MPMS-XL SQUID magnetometer. The following values of magnetic field were used 0.2 kOe, 2 kOe and 10 kOe respectively for the temperature range of 2-20 K, 20-80 K and 80-300 K in order to prevent any saturation effect. The ac magnetic susceptibility measurements were performed on both Quantum Design MPMS-XL SQUID magnetometer (1-1000 Hz frequency range) and Quantum Design PPMS (10-10000 Hz frequency range) system equipped with an AC/DC probe. Immobilized selected and crunched single crystals were employed to realize the magnetic measurements and the latter were all corrected for the diamagnetic contribution as calculated with Pascal's constants.
Supplementary Materials: The following are available online at https://www.mdpi.com/2312 -7481/7/2/24/s1, Scheme S1. Coordination reactions leading to the formation of complexes 1 and 2. Figure S1. ORTEP view of the asymmetric unit for 1. Thermal ellipsoids are drawn at 30% probability. Hydrogen atoms are omitted for clarity. Figure S2. Orthogonal arrangement of two neighboring molecules in the crystal packing of 1. Figure S3. ORTEP view of the asymmetric unit for 2·(C 6 H 14 )(CH 2 Cl 2 ). Thermal ellipsoids are drawn at 30% probability. Hydrogen atoms and solvent molecules of crystallization are omitted for clarity; Figure S4. Crystal packing of 2·(C 6 H 14 )(CH 2 Cl 2 ) showing the alternation between ordered and disordered layers of dimers; Figure S5. Representation of the four dimers constituting the asymmetric unit with H···F (dashed brown lines) and F···F (dashed black lines) contacts; Figure S6. Frequency dependence of χ M ' and χ M " between 0 and 4000 Oe for 1 at 2K in the frequency range of 1-1000 Hz (left) and 100-10000 Hz (right); Figure S7. Frequency dependence of χ M (above) and χ M " (below) between 2 and 7 K at 1600 Oe for 1; Figure  S8. Frequency dependence of the in-phase (χ M ) and out-of-phase (χ M ") components of the ac susceptibility measured on powder at 2 K and 1600 Oe with the best fitted curves (red lines) for 1.; Figure S9. Linear plot of the temperature variation of the relaxation time for 1 in the temperature range of 2-3.5 K (blue spots) and 2 in the temperature range of 2-9 K (blue spots) with the best fitted curve with the modified Arrhenius law (red line); Figure S10. Normalized Argand plot for 1 between 2 and 4 K.; Figure S11. Frequency dependence of χ M ' between 0 and 4000 Oe for 2 at 2 K in the frequency range of 10-10000 Hz.; Figure S12. Frequency dependence of χ M between 2 and 9 K at 1200 Oe for 2; Figure S13. Frequency dependence of the in-phase (χ M ) and out-of-phase (χ M ") components of the ac susceptibility measured on powder at 3.5 K and 1200 Oe with the best fitted curves (red lines) for 2.; Figure S14. Normalized Argand plot for 2 between 2 and 9 K.; Table S1: X-ray crystallographic data of L 1 , 1 and 2; Table S2: SHAPE analysis of the coordination polyhedron around the Dy III center for 1; Table S3: SHAPE analysis of the coordination polyhedra around the Dy III centers for 1 for 2; Table S4: Best fitted parameters (χ T , χ S , τ and α) with the modified extended Debye model for 1 at 1600 Oe in the temperature range 2-3.5 K. Table S5. Best fitted parameters (τ 1 , α 1 , χ 1T , τ 2 , α 2 , χ 2T and χ S ) with the modified extended Debye model for 2 at 1200 Oe in the temperature range 2-9 K.
Author Contributions: K.M., S.N., V.K., B.L. and F.P. performed the organic syntheses and performed the coordination chemistry and crystallizations, V.D. realized the single crystal X-ray diffraction experiments and refined the X-ray structures; O.C. and J.F.G. performed and analyzed the magnetic measurements. V.C. discussed the idea and the results and commented on the manuscript. F.P. and V.K. conceived and designed the experiments and contributed to the writing of the article. All authors have read and agreed to the published version of the manuscript.