Insights into the Spin Dynamics of Mononuclear Cerium(III) Single-Molecule Magnets

Four novel CeIII mononuclear complexes of formulas [Ce(ntfa)3(MeOH)2] (1), [Ce(ntfa)3(5,5′-Me2bipy)] (2), [Ce(ntfa)3(terpy)] (3), and [Ce(ntfa)3(bipy)2] (4), where ntfa = 4,4,4-trifluoro-1-(naphthalen-2-yl)butane-1,3-dionato, 5,5′-Me2bipy = 5,5′-dimethyl-2,2′-dipyridyl, terpy = 2,2′:6′,2″-terpyridine, and bipy = 2,2′-bipyridine, have been synthesized and structurally characterized with CeIII displaying coordination numbers of 8, 8, 9, and 10, respectively. Magnetic measurements indicate that all the complexes show a field-induced single-ion magnet behavior under a small applied dc field. The magnetic analysis shows the relevance of the different spin relaxation mechanisms in the magnetic relaxation of the CeIII compounds, with special emphasis on the local-mode process. Multiconfigurational calculations were also performed to get more information on the axiality of the compounds.


■ INTRODUCTION
Single-molecule magnets (SMMs) are molecules that have the capability to behave as small magnets. 1,2 These molecules exhibit slow relaxation of the magnetization due to their intrinsic magnetic anisotropy, the property of the molecule that provides to its spin a preference to be oriented in a specific direction. Since their discovery, 3 they have received great attention due to their possible application as data storage devices, 4 in spintronics, 5,6 and as spin qubits in quantum computing. 7−9 Initially, the efforts were focused on transition metal compounds, until the discovery of a mononuclear Tb III double-decker complex, [TbPc 2 ] − ·TBA + [Pc = phthalocyanine and TBA + = N(C 4 H 9 ) 4 + ], in 2003 by Ishikawa et al., which exhibited a SMM behavior. 10 The isolation of this compound opened new avenues for the preparation of a plethora of mono and polynuclear SMM lanthanide (Ln) complexes with the aim of achieving high blocking temperatures (T B ) and high energy barriers (U eff ) for magnetization reversal. 11−16 The large magnetic anisotropy usually observed in Ln III metal ions is a result of the large unquenched orbital angular momentum and spin−orbit coupling. 17,18 In contrast to what is usually observed in transition metal complexes, the spin−orbit coupling in lanthanide complexes is generally larger than the crystal field, and as a result, they are better described through the spin−orbit coupled term J. In the design of SMMs, Tb III , Dy III , and Er III lanthanide ions were extensively used because of their large number of unpaired electrons (large angular momentum, J = L + S) and large magnetic anisotropy, which can also be enhanced with the appropriate choice of the ligand field, as proposed by Rinehart and Long. 19 Indeed, a literature search on lanthanide-based SMMs shows that more than 99% of articles on this subject are related to mono-and poly-nuclear complexes of the three mentioned metal ions, with Dy III being the most popular, 12,20−22 probably because the most promising results are usually presented by dysprosium compounds. Examples are the highest blocking temperature (T B = 80 K) reported for the mononuclear Dy III compound [(Cp i Pr 5 )Dy-(Cp*)][B(C 6 F 5 ) 4 ], where Cp i Pr 5 = penta-iso-propylcyclopentadienyl and Cp* = pentamethylcyclopentadienyl, 23 and the larger coercive magnetic field, 14 T, observed for [(Cp i Pr 5 ) 2 Dy 2 I 3 ] at temperatures as high as 60 K. 24 However, the less studied lanthanide ions, the heavy ones such as Ho III , Tm III , and Yb III and the lighter Ce III and Nd III ions, can also form lanthanide-based SMMs and exhibit different applications, as highlighted by the recently published reviews by Pointillart et al. 25 and Borah and Murugavel. 26 Among them, Ce is the most abundant and inexpensive rare earth element, its natural isotopes do not possess a nuclear spin, and it has been used as a dopant instead of Dy III to improve the magnetic properties of one of the strongest existing permanent magnets, Nd 2 Fe 14 B. 27 Although the Ce III ion has only one unpaired electron, 4f 1 , magnetic relaxation can also be observed because spin−orbit coupling can create non-negligible magneto-anisotropy. The expected ground state for the oblate Ce III (L = 3 and S = 1/2) is 2 F 5/2 , which contributes to its significant magnetic anisotropy. To the best of our knowledge, a total of 11 mononuclear Ce III -based SMMs were found, six of them monometallic and five where the Ce III is accompanied by other diamagnetic d transition metal ions (d-Ce III ). These compounds are collected in Table  1.
In the synthesis of the Ce III complexes shown above, different ligands have been employed. The β-diketone ligands in combination with polypyridine derivatives have been strongly emerged into this area. 41−43 Besides the variety, typically two categories of complexes were produced when Ln III ions are coordinated with the anionic β-diketone ligands, the neutral complexes in the 1:3 stoichiometric ratio or the anionic complexes in the 1:4 ratio. 41 In the field of molecular magnetism, since the discovery of mononuclear [Dy-(acac) 3 (H 2 O) 2 ] (acac = acetylacetonate) behaving as an SMM, 42 most of the research of Ln III /β-diketonate has been focused on Dy III ions. In the case of octa-coordinated complexes, a square antiprism (D 4d ) symmetry was most likely constructed, a geometry that can be beneficial for the maximization of magnetic anisotropy with the appropriate ligand field. The same symmetry was also generated when the Ln III ions and β-diketonate with different substituents are combined with auxiliary N-donors polypyridyl ligands. This strategy was employed to yield mononuclear Dy III SMMs with a D 4d symmetry with the aim of obtaining magnetostructural correlations regarding electronic effects and intermolecular interactions. 43−47 This approach was successfully used by some of us to synthesize several pyridyl adducts, [Ln III (βdiketonate) 3 (NN)], where NN = polypyridyl ligands, 48−50 in which the corresponding mononuclear pyridyl adducts of Nd III showed an SMM behavior. 50 Regarding Ce III complexes displaying an SMM behavior (Table 1), the only pyridyl adduct with a β-diketonate ligand was the mononuclear octacoordinated [Ce(fdh) 3 (bpy)] compound. 31 Therefore, this study was undertaken to synthesize some polypyridyl adducts of Ce III −Hntfa complexes and investigate their magnetic properties and SMM behavior.

(terpy)] (3).
[Ce(ntfa) 3 (MeOH) 2 ] (151 mg, 0.15 mmol) was dissolved in 15 mL of ethanol/acetone (3:1), and 2,2′:6′,2″terpyridine (39 mg, 0.17 mmol) was dissolved in 15 mL of ethanol/ acetone (3:1). The two solutions were combined and stirred for approximately for 3 h at 70°C. The mixture was filtered off and allow to crystallize at room temperature. After 2 days, the orange crystals, which were separated, were collected by filtration and dried in air (yield: 66 mg, 37.5%). Anal. Calcd. for C 57  [Ce(ntfa) 3   Single-Crystal Structural Determination. Suitable single crystals of complexes 1−4 were selected by use of a polarizing microscope and mounted on an Bruker-AXS APEX CCD diffractometer. Data collection of X-ray single-crystal data was performed at 100(2) K by use of Mo-Kα radiation (λ = 0.71073 Å), and the data were subsequently processed (Lp, and absorption corrections; APEX and SADABS). 51 The structures were solved and refined using the SHELX package (direct methods; full-matrix leastsquares on F 2 ). 52 Anisotropic displacement parameters were applied for all non-hydrogen atoms. The hydrogen atoms were located from difference Fourier maps, assigned with isotropic displacement factors, and included in the final refinement cycles by use of geometrical constraints. Other programs, Mercury, 53 Olex, 54 and Platon, 55 were also employed. Main parameters, data, and refinement details are collected in Table 2.
Magnetic Measurements. A Quantum Design MPMS XL SQUID magnetometer was employed. Data were collected for powder microcrystalline samples or for crushed polycrystalline samples of complexes 1−4 in a gelatin capsule, whose purity and structural integrity were analyzed by powder X-ray diffraction (Figures S1−S4). dc susceptibility measurements were acquired between 2 and 300 K and under an external magnetic field of 0.3 T. For the capsule and holder, blank measurements were performed, and their diamagnetic contributions were corrected. Diamagnetic corrections of the complexes were estimated from Pascal tables. 56 Alternated current (ac) susceptibility measurements were carried out by applying an oscillating ac field of 4 Oe with ac frequencies between 1 and 1500 Hz at different temperatures and dc applied fields indicated in the text.
Computational Details. Ab initio calculations were performed using the OpenMolcas package, 57  . The CASSCF method was used to calculate the spin-free state energies of the compounds, and the spin−orbit coupling was included perturbatively in the second step by using the restricted active space state interaction (RASSI) method. 61 Due to the large ionic character of the Ln−O and Ln−N bonds, dynamic correlation contributions are not essential, which was also demonstrated for Ce complexes, 38 and CASPT2 calculations were not performed. In the CASSCF calculation, a (1,7) active space was used considering the seven doublets. The SINGLE_ANISO module, as implemented in Open-Molcas, was employed for the evaluation of the direction and magnitude of the magnetic moments of the final states. 62,63 Also, the probability of transition between different states has been estimated by the calculation of the matrix elements of the transition magnetic moments. Additionally, experimental geometries were optimized, and vibrational frequencies were calculated using the Gaussian09 D01 code 64 with the B3LYP functional 65 using the Stuttgart pseudo/basis set 66 for Ce and a TZV basis set 67   Inorganic Chemistry pubs.acs.org/IC Article molecular structures were determined by single-crystal X-ray crystallography. In addition, the purity of the microcrystalline solids was characterized by PXRD ( Figures S1−S4, Supporting Information). The IR spectra of the complexes revealed their characteristic coordination feature, where the strong vibrational band observed at around 1610 cm −1 for 1−3 complexes and at 1632 cm −1 in the case of 4 is typically assigned to the stretching frequency, ν(C�O), of the coordinated carbonyl group of ntfa. Crystal Structures. Each Ce III center in the monomeric neutral complexes 1−4 is ligated by six oxygen donor atoms of three β-diketonato ligand anions (ntfa) (Figure 1). A CN of 8 around Ce1 in 1 is completed by oxygen atoms of two terminal methanol molecules and in 2 by two N-donor atoms of the chelating 5,5′-dimethylbipyridine molecule. Selected distances and angles are collected in Table 3. The Ce−N/O bond distances in 1 and 2 are in the range from 2.398(2) to 2.671(3) Å. The CeO 6 N 3 "chromophore" around the two crystallographic independent Ce III centers in 3 is formed by ligation of one terpy chelating ligand, achieving a CN of 9 around the central Ce III ion. The two crystallographic independent molecules in 3 differ mainly in the opposite "head-to-tail" arrangement of one diketo anion (i.e., that with O5 and O6 bonded to Ce1 compared to that with O11 and O12 bonded to Aside from the observed different coordination, the coligands also favor or avoid different intermolecular interactions. The pyridyl rings form interplanar angles with their mean planes of 14.9 and 5.6°for the two bipy molecules Despite the gradual increase at a high field, no saturation of the magnetization is observed, which indicates significant anisotropy. In order to study the dynamic magnetic properties and the possible SMM behavior, ac magnetic susceptibility measurements with variable values of the field, temperature, and frequency were recorded for compounds 1−4 under the same conditions, as depicted in Figure 3. Without the application of an external dc field, none of these compounds exhibited dependence of the out-of-phase (χ M ″) signal with frequency and temperature, although a small signal seems to start for 2. This fact suggests that the relaxation of the magnetization under these conditions occurs through fast QTM. The application of a dc magnetic field of only 25 Oe is enough to suppress the QTM for 2−4, and a clear maximum appears in the χ M ″ component. In the case of 1, a slightly larger field is needed, 50 Oe. The need of a larger dc field for 1 might be correlated with the shorter Ce···Ce distance, 5.536 Å (vs  In all the compounds, upon increasing the applied dc field, the maximum first moves to smaller frequencies, indicating slower relaxation times (τ); then, the maximum position appears in similar frequency values for a range of fields and then finally moves to larger frequencies. Although the general tendencies can be relatively similar, compound 1 covers a large range of frequencies and has the slower τ, followed by 4, 2, and 3.
To also analyze the dependence of χ M ″ on temperature, the same external dc field was selected for all the complexes. In this case, 200 Oe was selected as a compromise for all the compounds, being the one where in general the maximum of χ M ″ had a larger value and the relaxation time was larger. The temperature dependence of χ M ″ with frequency shows the typical SMM behavior. The maximum in the out-of-phase component of the susceptibility appears between 10 and 1000 Hz depending on the compound and moves to larger frequencies when the temperature is increased.
In order to analyze the spin dynamics of these Ce III compounds, the Cole−Cole plots were fitted to a Debye function using the CCfit package ( Figures S9−S24), and  (Tables S1−S8). The α values are in general small, indicating a relatively narrow distribution of relaxation times. In general, maximum values (0.18, 0.13, 0.24, and 0.26 for 1, 2, 3, and 4, respectively) are obtained at larger fields or smaller temperatures. The spin−lattice relaxation rate τ parameter can be employed to analyze the spin relaxation mechanism by analyzing the dependence of τ −1 with T and the applied external field, which follows eq 1 The terms in eq 1 refer to direct, QTM, Raman, local-mode, and Orbach relaxation mechanisms, in the given order. The Raman term is a field-dependent term using the Brons−van Vleck equation, it has a coefficient field-dependent (d represents zero-field relaxation, e is related with paramagnetic center concentration, and the f parameter reports the effect of the external field in suppressing the spin relaxation) and also the typical exponential dependence with the temperature. The Orbach processes are not considered because the ab initio calculations (see the next section) show that the first excited state (250−300 cm −1 ) is much higher in energy than the obtained energy barrier using the last term of eq 1 (around 10−20 cm −1 ). In fact, for all the reported systems (Table 1), the energy barrier oscillates between 15 and 32 cm −1 , while none of the calculated systems have an excited state so close in energy. To analyze the dependence of τ −1 with T and field, we first focus on the field dependence because despite the presence of several mechanisms, usually one of them (among the three first terms of eq 1, which are the ones having field dependence) is the predominant in each part of the curve.
As represented in Figure 4, at low external fields, the tunneling mechanism is responsible of the fast τ −1 decay. For intermediate field values, the field-dependent Raman mechanism is the main contribution, whereas at high field values, the direct mechanism becomes predominant due to the H 4 dependence (see Figure 4). Hence, each region can be independently fitted with the corresponding term (see eq 2), and these parameters are the starting point for the fitting of the whole set.
The dependence with the temperature can be fitted using eq 3, where the three field-dependent constants are those determined using the fitted parameters from eq 2, and thus, there are only three parameters to be fit (n, C, and ω). Despite the lower number of parameters, the temperature dependence is more complicated because the last two terms containing these three parameters have a very similar numerical dependence, and both can be predominant at high temperatures. However, for 1, the field dependence values indicate a relatively small τ −1 value in the predominant Raman region (around 0.2−0.4 T in Figure 4 left). This fact results in a very small contribution of this Raman term in the temperature dependence; thus, the temperature dependence is basically due to the local mode (see Figure 4 right). The fit of the temperature dependence curve using eq 3 resulted in the final values of the n exponent of the Raman term being n = 2.98 and the two parameters of the local-mode relaxation being C = 1.23 × 10 9 s −1 and ω = 46.4 K (32.2 cm −1 ).
The analysis of the density functional theory (DFT) vibrational frequencies for 1 allows us to identify two modes at 24.3 and 25.0 cm −1 (close to the fitted local-mode value of 32.2 cm −1 ) as those with largest reduced mass, indicating a large contribution of the lanthanide atom. A spin-phonon calculation corresponding to such vibrational modes would verify their participation in the spin relaxation, but it is out of the scope of the paper.
The same fitting procedure has been performed for the other two compounds containing bipyridine-type ligands (except for 3 because of the presence of two different molecules in the unit cell), and the results are illustrated in Figure 5  (left) on a static external field at 2.5 K and (right) on the temperature with a 0.02 T external field. The black solid line represents the fit of the experimental data (black dots) with the terms of eqs 2 and 3, respectively. In the inset of the field dependence, green, blue, and red lines correspond to the direct, Raman, and tunneling contributions, respectively. In the temperature dependence (right), green, blue, red, and orange lines correspond to the direct, Raman, tunneling, and local-mode (superposed with the black line) contributions, respectively. Inorganic Chemistry pubs.acs.org/IC Article 10 6 T −2 for the field dependence (eq 2) and n = 8.01, C = 2.83 × 10 5 s −1 , and ω = 13.6 K (9.5 cm −1 ) (eq 3), while for 4, the values are a = 1162 s −1 T −4 K −1 , B 1 = 1177 s −1 , B 2 = 1.02 × 10 5 T −2 , dT n = 209 s −1 , e = 2390 T −2 , and f = 583 T −2 for the field dependence (eq 2) and n = 1.28, C = 6.20 × 10 5 s −1 , and ω = 22.7 K (15.7 cm −1 ) (eq 3). The comparison of the results indicates the following: (i) the importance of tunneling relaxation on these complexes, which can be eliminated with very small external fields. The field needed is smaller for 2 (which starts to show a signal at zero field) and increases for 4 and 1, being larger the field required for 1 than the required for 4. This might be related with the Ce···Ce distances being larger in 2 and 4 than in 1 (5.536 Å in 1, 10.996 in 2, and 9.963 Å in 4) and the different intermolecular interactions (hydrogen bond in 1, one short ring···ring interaction in 2, and two short ring···ring interactions in 4) and packing. Thus, the larger dimethyl bipyridine ligands of 2 adopt a less dense packing, resulting in a smaller dipolar interaction and consequently less efficient tunneling relaxation. (ii) τ −1 is smaller for 1 and 4 at intermediate fields, indicating a less effective Raman spin relaxation for such systems. (iii) The direct term gives larger τ −1 contributions at high fields for 2, followed by 1. (iv) The faster temperature-dependent spin relaxation of 2 is basically due to the two main spin relaxation mechanisms, Raman and local-mode, playing an active role, while in 1 and 4, only the local-mode mechanism is significant, resulting in slower relaxation.
Computational Results. High-level calculations including spin−orbit effects through the RASSI approach (see the Computational Details section) based on the CASSCF methodology have been employed to study the magnetic properties of the reported compounds. Cerium(III) complexes have 4f 1 and 2 F 5/2 ground states. Magnetic susceptibility and magnetization have been simulated and show similar trends to those observed experimentally for compounds 1−4, Figures  S25 and S26. All the systems show an axial anisotropy with a relatively large g z component consistent with an m J = ±5/2 ground state, but the values reveal a contribution of m J = ±3/2 states. The calculated g tensors are collected in Table 4, where the g z values are in the range of 2.9−3.9, while for a perfectly axial Ce III complex, the value is 4.19 (30/7). The calculated g z orientations (see Figure 6) for the four compounds are quite different, and also, the CNs are 8 for 1 and 2, 9 for 3, and 10 for 4. For an m J = ±5/2 ground state, an oblate f electron density is expected with a perpendicular g z orientation.
Basically, there are two criteria that control the g z orientation in order to reduce the metal−ligand electrostatic repulsion: (i) the alignment of g z with the shortest Ce−O bond distances, so the f electron density disc remains perpendicular to that direction, and (ii) the f electron density disc is aligned in the  Figure 6. (left) Calculated ab initio orientations of the g tensor of the ground Kramers doublet. Blue, green, and red arrows represent g z , g y , and g x components, respectively. The atoms abide by the following color code: yellow, cerium; red, oxygen; blue, nitrogen; gray, carbon; and pink, hydrogen. (right) Energies of states as a function of their magnetic moment, Mz, along the main anisotropy axis for the studied systems. The green arrows correspond to the quantum tunneling mechanism of ground and first excited states, while the purple arrow shows the hypothetical Orbach relaxation process. The red arrow indicates the transition between the ground and first Kramers doublets. The values close to the arrows indicate the matrix elements of the transition magnetic moments (above 0.1, an efficient spin relaxation mechanism is expected). , allowing the f electron density disc to remain in the plane where the coordinated methanol molecules are. In the case of 2, the g z is located in a way that the electron density disc avoids all the ligands. For 3, there are two crystallographic independent molecules that differ mainly in the arrangement of one of the diketo anions. For 3b, g z is located in a way that the density disc is in the plane where the terpy is; however, for 3a, the avoidance of the shortest Ce−O bond distances results in the disc being aligned in a not so predictive plane but still where the Ce−L distances are larger. In the case of 4, however, it is clear that the density is located in the plane almost containing both pyridine ligands. Calculated Kramers doublet energies and transition probabilities between the states are represented in Figure 6. The tunneling probability in the ground state shows the smallest values for compounds 2 and 4. This fact agrees with the experimental evidence that 2 starts to show a signal at a zero field. However, for 4, such a behavior is probably hindered by the shorter intermolecular Ce···Ce distances, as already pointed out. The calculated largest tunneling effect in 1 and 3 is also reflected in the experimental field dependence τ −1 curves. A stronger external field is required to suppress such an effect in comparison with 2 and 4 systems. As already remarked, the high first excited energies allow us to rule out the Orbach spin relaxation, taking into account the fact that the fitted barriers with such a mechanism give values of around 20−30 cm −1 .

■ CONCLUSIONS
This work describes four new Ce III compounds that behave as field-induced SMMs and increase the scarce family of Ce III SMMs. Three β-diketone ligands, nfta, coordinate the Ce III ions in these compounds, leaving other coordination positions to the solvent or polypyridyl ligands. Depending on the employed coligands, the CN oscillates from 8 to 10, showing the flexibility of the system and the possibilities of tuning it with the appropriate election of the ligand. The magnetic properties are also remarkable, all the complexes show a fieldinduced SMM behavior with a very small applied field needed in order to observe the behavior. Additionally, for 2, a signal starts to appear at the zero field, showing this coordination and election of ligands as a promising one to achieve zero-field Ce III SMMs if the QTM is decreased more. The analysis of the dynamic susceptibility measurements also brings some insights into the relaxation processes involved in the spin relaxation of Ce III SMMs. The examination of the dependence with the field at 2.5 K clearly shows three different areas in the curves where different processes predominate. At low fields, QTM is the dominating process and can be suppressed with the application of very small external fields. The intermediate area is better described by the Raman process, and in the high fields, the direct process predominates. The fitting of the dependence with the temperature was performed using the Raman and local-mode terms and without including the Orbach process because, as shown by the calculations, the first excited state is at a larger energy (250−300 cm −1 ) than that obtained from a fit with an Orbach process (around 10−20 cm −1 ). The results show different contributions of both terms for the complexes, but in all of them, the local-mode term, which is not included routinely yet, cannot be ruled out as it has an important contribution or it can even be the predominant relaxation process. Moreover, we are providing a different explanation for the very low effective energy barriers usually obtained for Ce III SMMs. In addition, DFT results show the presence of vibrational modes with a large contribution of the lanthanide at an energy similar to the obtained ω value, which might be responsible for the spin relaxation. Multiconfigurational calculations, on the other hand, show the axial anisotropy of the complexes with a relatively large g z component, which is oriented in a way that the perpendicular f electron density disc avoids the shortest Ce−O bond distances and is in general in the same plane as that of the longest Ce−L bond distances. The transition probabilities between states show large QTM in general being smaller for 2 and 4 and the relaxation through the Orbach process at more than 250 cm −1 . Nevertheless, the comparison of the studied systems shows the slower relaxation for 4, which is the system with a larger g z component, the one showing a smaller QTM probability, and it also presents a large Ce···Ce distance and smaller dipolar interactions. However, the complex showing smaller QTM is compound 2, which also has a larger Ce···Ce distance and smaller dipolar interactions. It is also worth noting that compound 1, besides the larger QTM, shows slower relaxation than 2 when the external field is applied. Even though in general more examples of Ce III SMMs are needed to further understand and be able to tune the spin relaxation of this type of compounds, through this study, we are increasing this limited family and providing new insights into the understanding of their spin relaxation. ■ ASSOCIATED CONTENT
Powder X-ray diffraction data, crystal packing, main noncovalent interactions found, dynamic magnetic measurements and fits, and additional computational results (calculated susceptibility and magnetization curves and Kramers doublet energies and g tensor components) (PDF)