2.1 General

Unless stated otherwise, all reactions were conducted in oven-dried glassware in aerobic conditions, with the reagents purchased commercially and used without further purification. The ligand H₂L was prepared as previously described [7].

2.2 Preparation of complexes

2.3 Physical measurements

Elemental analyses were carried out at the “Centro de Instrumentación Científica” (University of Granada) on a Fisons-Carlo Erba analyser model EA 1108. The IR spectra on powdered samples were recorded with a ThermoNicolet IR200FTIR by using KBr pellets. Magnetisation and variable temperature (2–300 K) magnetic susceptibility measurements on polycrystalline samples were carried out with a Quantum Design SQUID MPMS XL-5 device operating at different magnetic fields. The experimental susceptibilities were corrected for the diamagnetism of the constituent atoms by using Pascal's tables.

2.4 Single-crystal structure determination

Suitable crystals of 1-12 were mounted on a glass fibre and used for data collection. For compounds 1-3 and 6-7, data were collected with a dual source Oxford Diffraction SuperNova diffractometer equipped with an Atlas CCD detector and an Oxford Cryosystems low temperature device operating at 100 K and using Mo-K_α radiation. Semi-empirical (multi-scan) absorption corrections were applied using Crysalis Pro [8]. For compounds 4 and 5 data were collected with a Bruker AXS APEX CCD area detector equipped with graphite monochromated Mo-K_α radiation (λ = 0.71073 Å) by applying the ω-scan method. Lorentz-polarization and empirical absorption corrections were applied. Crystallographic data for compounds 8-12 were collected with a Nonius-Kappa CCD area-detector diffractometer using graphite monochromatised Mo-K_α radiation (λ = 0.71073 Å). The data were collected by ϕ and ω rotation scans and processed with the DENZO-SMN v0.93.0 software package [9]. Empirical absorption corrections were performed with SADABS [10]. The structures were solved by direct methods by using the program SIR-97 [11] or SHELXS97 [12] and refined with full-matrix least-squares calculations on F² using SHELXS97 [12]. Figures were drawn with ORTEP-3 for DIAMOND 3.0 [13]. For all compounds the heavy atoms were refined anisotropically. All hydrogen atoms were included at the calculated distances with fixed displacement parameters from their host atoms. Final R(F), wR(F²) and goodness of fit agreement factors, details on the data collection and analysis can be found in Table S2. Selected bond lengths and angles are given in Table S3 for compounds 1-7 and S4 for compounds 8-12. CCDC-866939-866950 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data request.cif.

2.5 Computational details

To consider the neighborhood influence of the Dy^III and the Co^II cations on the g axis of the Co^II and Dy^III atoms, respectively, but with the aim to simplify the calculation, two models have been built up. One, where the Dy^III atom has been substituted by a closed-shell lanthanide such as La^III, and the other one, where the Co^II atom has been substituted by a closed-shell transition metal such as Zn^II.

All calculations have been performed with the MOLCAS 7.2 package [14]. MOLCAS ANO-RCC basis set has been used for all the atoms, with the exception of La^III and Zn^II which have been treated with an embedding model potentials (AIMP) [15]. The following contractions were used: Dy [9s8p6d4f3g2h]; Co [6s5p4d2f]; O [4s3p1d]; N [4s3p1d]; C [3s2p] and H [2s].

To compute the g axis for the Dy^III cation a complete active space self-consisting field (CASSCF) calculation has been performed with an (9,7) active space and 21 sextets, 128 quadruplets and 130 doublets have been mixed into the restricted active space state interaction (RASSI-SO) procedure. For the g axis of the Co^II cation an (7,5) active space CASSCF calculation has been performed and 10 quadruplets and 35 doublets have been mixed through the RASSI-SO procedure.

Finally, the g axis values were extracted form MOLCAS output (CASSCF/RASSI calculations) by using the SINGLE_ANISO computer code [16].

3.1 Crystal structures

Complexes 1 and 4 are isostructural, crystallizing in the triclinic P-1 space group. Their structures are made of two almost identical dinuclear [Co(μ-L)(μ-Ac)Ln(NO₃)₂] molecules, in which the Ln^III and Co^II ions are bridged by two phenoxo groups of the L²⁻ ligand and one syn-syn acetate anion. These complexes are isostructural to those previously reported by us for the Ni^IIDy^III analogue [7]. Complexes 2, 3, and 5 are also isostructural but they crystallize in the monoclinic P21/n space group and their structure is very similar to those of 1 and 4 but having only one crystallographically independent Co^IILn^III molecule. The structure of 1 is given as an example in Fig. 1.

Within the dinuclear [Co(μ-L)(μ-Ac)Ln(NO₃)₂] molecules, the Co^II ion exhibits a slightly distorted fac-CoN₃O₃ octahedral coordination environment. The distortion mainly takes place along the three-fold axis passing through the N₃ and O₃ faces of the octahedron. In fact, the calculation of the degree of distortion of the Co^II coordination polyhedron with respect to an ideal six-vertex polyhedra, by using the continuous shape measure theory and SHAPE software [18], led to shape measures relative to the octahedron (OC-6) and trigonal prism (TPR-6) with values of ∼1.7 and ∼10, respectively, for the isostructural complexes 1 and 4 and with values of ∼2.8 and ∼8.4 for the isostructural complexes 2, 3 and 5. The shape measures relative to other reference polyhedra are significantly larger and therefore the CoN₃O₃ coordination spheres of complexes 1-5 are found in the OC-6 ↔ TPR-6 deformation pathway close to the octahedral geometry (∼77% for 1 and 4 and ∼70% for 2, 3 and 5). In all these complexes, the corresponding Ln^III ion exhibits a rather asymmetric LnO₉ coordination sphere, which is comprised of two phenoxo bridging oxygen atoms, two methoxy oxygen atoms, one oxygen atom from the acetate bridging group and four oxygen atoms belonging to two bidentate nitrate anions, with Ln-O bond distances in the range 2.28–2.51 Å.

The average Ln-O_phenoxo bond distances within each series of isostructural compounds 1 and 4, and 2, 3 and 5, respectively, steadily decrease from Gd^III to Er^III with a concomitant decrease of the average Co-Ln and Ln-O_acetate bond distances, due to the lanthanide contraction.

The Co(O_phenoxo)₂Ln bridging fragment is rather asymmetric as there are two non-equivalent Ln-O_phenoxo and Co-O_phenoxo bond distances, as well as two different Co-O-Ln bridging angles (∼7° of difference). It is interesting to note that in complexes 1-5 the coordination of the syn-syn bridging acetate group induces the folding of the M(μ-O₂)Ln bridging fragment, with hinge angles (the dihedral angle between the O-Co-O and O-Ln-O planes) that are close to 22°. In each series of isostructural compounds, the hinge angle increases with decreasing Ln^III size, as expected.

The reaction of the H₂L ligand with Co(NO₃)₃·6H₂O and subsequently with Ln(NO₃)₃·6H₂O (Ln^III = Gd and Tb) led to two isostructural double-phenoxo-bridged dinuclear complexes [Co(H₂O)(μ-L)Ln(NO₃)₃] (Gd (6) and Tb (7)) (Fig. 2).

Although diphenoxo-nitrate triply-bridged Ni-Ln complexes have been observed for the smaller Ln^III ions (from Tb^III to Er^III) [19], the Tb^III ion is not able to form the triple-bridged complex. It seems that the combined effect of the Ln^III and M^II sizes plays an important role in the adoption of the triply-bridged structure. Thus when the size of the metal ion increases, the tension of the nitrate bridging ligand becomes larger and, from definite values of the size of the metal ions, the formation of the nitrate bridge is unfavourable. Therefore, subtle changes in the size of the M^II ion on going from Ni^II to Co^II may be responsible for the presence of only a double-phenoxo bridge in 7. The absence of the nitrate bridging group in 6 and 7 allows the structure to be more planar (hinge angles of 3.7° and 1.5°, respectively) and the bridging fragment more symmetric (the two Ln-O-Co angles of the bridging fragment are very close to each other with values of ∼109°) than in the case of complexes 1-5. The planarity of the structure gives rise to an increase in the Co-Ln distance with respect to those observed in 1-5. In addition, the Ln coordination sphere, which is rather asymmetric regarding the Ln-O bond distances, expands from LnO₉ to LnO₁₀. It should be noted that the sixth position of the Co^II is saturated by the coordination of a water molecule, leading to a CoN₃O₃ octahedral coordination sphere that is more distorted toward trigonal prismatic that those of compounds 1-5. In particular, shape measures relative to the octahedron (OC-6) and trigonal prism (TPR-6) were 2.30 and 9.38 for 6 (73.9% of octahedral geometry) and 2.95 and 11.28, for 7 (81.3% of octahedral geometry).

Complexes 8-12 are isotructural and their structure consists of centrosymmetric tetranuclear molecules [Co(μ-L)(μ-N(CN)₂)Ln(NO₃)₂]₂ and four methanol molecules of crystallization. Within each tetranuclear Co₂Ln₂ molecule, two dinuclear cationic fragments [Co(μ-L)Ln(NO₃)₂]⁺ are connected by two 1,5-dicyanamide bridging ligands in a “head to tail” arrangement (Fig. 3).

The cobalt(II) ions exhibit distorted octahedral CoN₄O₂ coordination spheres with shape measures relative to the octahedron (OC-6) and trigonal prism (TPR-6) of ∼2.30 and ∼9.8, respectively, and are found in the OC-6 ↔ TPR-6 deformation pathway, close to octahedral geometry (∼75%). The coordination of the dicyanamide bridging ligand to the lanthanide ion leads to a LnO₈N coordination sphere, which, as in the dinuclear complexes 1-7, is rather asymmetric regarding the Ln-O bond distances (Table S3). As expected for the lanthanide contraction, the Ln-N, Ln···Co and the average Ln-O_phenoxo bond distances decrease with decreasing Ln^III ionic radii on going from Gd^III to Er^III. The bridging fragment is asymmetric but the difference between the two Ln-O-Co angles is only ∼3°, whereas the hinge angle is ∼7.5°. When the Ln-O-Co and hinge angles are compared for complexes 1-12, one realizes that the bridging fragment becomes more symmetrical (smaller difference between each couple of Ln-O and Co-O bond distances and Ln-O-Co angles) as its planarity increases (smaller hinge angles).

Complexes 1-5 are devoid of any hydrogen bond interactions. However, compound 6 exhibits both intermolecular and intramolecular hydrogen bond interactions. Neighbouring centrosymmetrically related molecules are held together by two pairs of complementary hydrogen bonds involving either the coordinated water molecules and a coordinated nitrate anion (donor-acceptor distance of 2.878 Å) or the water molecule of crystallization and one coordinated nitrate anion (donor-acceptor distances of 2.692 Å and 2.995 Å). Both types of interactions lead to a chain of hydrogen bonded dinuclear Gd^III-Co^II molecules that extend along the c axis (Fig. S2). In addition, there exists an intramolecular hydrogen bond involving the coordinated water molecule and a coordinated nitrate anion of the same dinuclear molecule (donor-acceptor distance of 2.898 Å). In complex 7, two centrosymmetrically neighbouring molecules are connected by hydrogen bonds involving the crystallization methanol molecules and one of the coordinated nitrate anions (donor-acceptor distance of 2.988 Å). Besides this, there exists a hydrogen bond involving the coordinated methanol molecule and a coordinated nitrate anion of the same dinuclear molecule (donor-acceptor distance of 2.845 Å). In complexes 8-12, there are hydrogen bond interactions between the crystallization methanol molecules (with O···O distances in the range 2.561–2.705 Å) and between one of these molecules and one of the coordinated nitrate anions of the tetranuclear Co₂Ln₂ molecules (donor-acceptor distance of 2.810 Å). However, the hydrogen bonds do not connect two different Co₂Ln₂ tetranuclear molecules (Fig. S2).

3.2 Magnetic properties

The temperature dependence of χ_MT for complexes 1-7 (χ_M is the molar magnetic susceptibility per CoLn unit) and 8-12 (χ_M being the molar magnetic susceptibility per Co₂Ln₂ unit) were measured in an applied magnetic field of 0.5 T and are displayed in Fig. 4 (complexes 1-3 and 6-7), Fig. 5 (complexes 4 and 5) and Fig. 6 (complexes 8-12).

Let us start with the Co-Gd complexes 1, 6 and 8, whose magnetic properties are easier to analyze. At room temperature, the χ_MT values for 1 and 6 of 11.20 cm³ mol⁻¹ K and 10.68 cm³ mol⁻¹ K are slightly larger than the expected value for non-interacting Co^II (S = 3/2) and Gd^III (S = 7/2) ions (9.750 cm³ mol⁻¹ K with g = 2), which may be due to both the orbital contribution of the Co^II ion with an octahedral geometry and a ⁴T_1g ground term and the ferromagnetic interaction between Co^II and Gd^III ions (see below). On lowering the temperature, the χ_MT for 1 first slowly decreases from room temperature to reach a minimum value of 10.75 K cm³ mol⁻¹ K at 26 K and then shows an abrupt increase to12.40 cm³ mol⁻¹ K at 2 K. The observed high temperature decrease is due to the thermal depopulation of the spin-orbit coupling levels arising from the ⁴T_1g ground term, whereas the increase at low temperature indicates a ferromagnetic interaction between Co^II and Gd^III ions. In the case of 6, the χ_MT product slightly increases from 300 K to 40 K and then increases sharply to14.34 cm³ mol⁻¹ K at 2 K, thus indicating the existence of a ferromagnetic interaction between the Co^II and Gd^III ions. The lack of a decrease in χ_MT in the high temperature region [due to the spin-orbit coupling effect of the Co^II ion] suggests that the ferromagnetic coupling in 6 is stronger than in 1. At room temperature, the χ_MT value for complex 8 of 23.05 cm³ mol⁻¹ K is larger than that expected for two isolated Co^II and two isolated Gd^III ions with g = 2 (19.5 cm³ mol⁻¹ K), which, as in the cases of 1 and 6, is due to both the spin-orbit coupling effect of the Co^II ion and the ferromagnetic interaction between Co^II and Gd^III ions. This ferromagnetic interaction is, like in 6, responsible for the steady increase of the χ_MT product from room temperature to 29.82 cm³ mol⁻¹ K at 2 K. It has been previously shown that the cobalt(II) orbital contribution is significantly quenched when its coordination sphere deviates from the ideal octahedral geometry [6c]. In such cases there is no appreciable decrease of the χ_MT in the high temperature region and the cobalt(II) ions almost follows the Curie law. In agreement with this, compounds 6 and 8, which have coordination spheres that are more distorted from octahedral to trigonal prismatic than compound in 1, show a steady increase in χ_MT from room temperature. Conversely, complex 1 with a less distorted octahedral geometry clearly exhibits the effect of spin-orbit coupling at high temperature. In view of these considerations the magnetic susceptibility data of compounds 6 and 8 can be analyzed using an isotropic Hamiltonian. Nevertheless, we stress that the magnetic parameters derived from this Hamiltonian can only be viewed as an approximation. The data for compound 1 were analyzed by considering that below 30 K only the lowest Kramer doublet of the Co^II ion with an effective spin S_eff = 1/2 is thermally populated. This effective spin is related with the real spin by a factor of 5/3 and therefore the Hamiltonian describing the magnetic exchange interaction between Gd^III and Co^II ions is:

From this Hamiltonian, the molar magnetic susceptibility is calculated to be:

The magnetization isotherm of 1 at 2 K (Fig. S3) reaches a value of 9.28 μ_B at 5 T, which is close to that expected for a Co^II ion with S_eff = 1/2 and g = 4.3 and a Gd^III ion with S = 7/2 and g = 2.0 of 9.15 μ_B. The experimental magnetization data fall above the Brillouin curve for a pair of non-interacting Co^II (S_eff = 1/2) and Gd^III ions, thus confirming the existence of a ferromagnetic interaction between these metal ions in the compound.

The magnetic properties of complexes 6 and 8, which present distorted octahedral coordination environments and apparently small orbital contributions, can be analyzed by means of isotropic Hamiltonians. In the case of 6, the isotropic Hamiltonian takes the form:

The best set of parameters obtained from the fitting of the experimental data to the above equation is J = +0.69(1) cm⁻¹, g = 2.090(1) and zJ′ = −0.008(4) cm⁻¹. The magnetic exchange coupling for compound 6 should be stronger than that of 1 as its hinge angle is smaller and the Co-O-Gd bridging angles are bigger than those for 1. However, the magnetic exchange coupling is similar for both compounds. This might be due to the fact that the J values for 6 are underestimated because the effect of the orbital contribution was not taken into account. Other structural factors, such as the deviation of the phenyl carbon atom bonded to the hydroxyl group with respect the Co(O)₂Gd bridging plane, or the dihedral angle between the phenyl ring and the bridging Co(O)₂Gd bridging plane, may also be responsible. To analyze the magnetic data of 8 the following isotropic Hamiltonian was used:

The field dependences of the magnetization at 2 K for complexes 6 and 8 are given in Figs. S3 and S4, respectively. These plots show a relatively rapid increase in the magnetization at low field, in agreement with a high spin state for these complexes, and a rapid saturation of the magnetization that is almost complete at the maximum applied field of 5 T, reaching values of 9.12 μ_B and 18.58 μ_B, close to those expected for the corresponding saturation values of 9.15 μ_B and 18.30 μ_B, respectively. In keeping with the ferromagnetic interaction observed for these compounds, the experimental data are well above the Brillouin curve for a pair of non-interacting Co^II (S_eff = 1/2; g = 4.2 for 6 and 4.3 for 8) and Gd^III ions (g = 2.0).

We now discuss the magnetic properties of the Co-Tb compounds 2 and 7. At room temperature, the χ_MT values for 2 and 7 (14.88 cm³ K mol⁻¹ and 15.08 cm³ K mol⁻¹, respectively) are higher than those calculated [13.69 cm³ K mol⁻¹] for independent Co^II (S = 3/2 with g_Co = 2.0) and Tb^III (4f⁸, J = 6, S = 3, L = 3, ⁶F₇, g_J = 3/2) ions in the free-ion approximation. This difference is mainly due to the orbital contribution of the Co^II ion with an octahedral geometry and a ⁴T_1g ground term. The χ_MT products for 2 and 7 decrease slowly with decreasing temperature down to minimum values of 12.52 cm³ K mol⁻¹ and 13.25 cm³ K mol⁻¹, respectively, at 12 K. This behaviour is due to both the thermal depopulation the spin-orbit coupling levels arising from the ⁴T_1g ground term of the octahedral Co^II ion and the thermal depopulation of the Stark sublevels of the Tb^III ion, which arise from the splitting of the ⁷F₆ ground term by the ligand field and whose width is of the order of 100 cm⁻¹ [23]. Below 30 K, the χ_MT product increases to reach a maximum value of 13.20 cm³ K mol⁻¹ at 2 K for 2 and 13.58 cm³ K mol⁻¹ at 4 K for 7. Below this temperature, compound 7 shows a sharp decrease down to 2 K to a value of 13.14 cm³ K mol⁻¹. The increase in χ_MT below 30 K is due to a ferromagnetic interaction between Co^II and Tb^III, whereas the decrease of χ_MT below 4 K in the case of 7 is likely associated with the presence of antiferromagnetic intermolecular interactions between the dinuclear complexes through the hydrogen bonds.

At room temperature, the χ_MT products for 4 and 5 are 16.66 cm³ K mol⁻¹ and 13.95 cm³ K mol⁻¹, respectively, which are higher than the calculated values by using the free-ion approximation of 15.94 cm³ K mol⁻¹ and 13.35 cm³ K mol⁻¹, respectively, for independent Co^II and Ln^III (Ho^III, L = 6, S = 2, J = 8, g_J = 5/4, ⁵I₈; Er^III, L = 6, S = 3/2, J = 15/2, g_J = 6/5, ⁴I_15/2) due to the orbital contribution of the Co^II ions.

When the temperature is lowered, the χ_MT product for 4 and 5 decreases, first slightly until ∼60–70 K and then sharply to reach values of 6.57 cm³ K mol⁻¹ at 2 K for 4 and 8.65 cm³ K mol⁻¹ at 4 K for 5. This behaviour is mainly due to the depopulation of the Stark sublevels of the Ho^III and Er^III ion, which arise from the splitting of the ⁵I₈ and ⁴I_15/2 ground terms, respectively, by the ligand field, as well as to the thermal depopulation of the levels that arise from spin-orbit coupling in the Co^II ion. In the case of 5, the χ_MT product increases below 5 K which is due to the ferromagnetic interaction between the Co^II and Er^III ions. In order to know the nature of the magnetic interaction between Co^II and Ho^III ions in 4 and to confirm the ferromagnetic interaction between Co^II and Er^III ions in 5, the empirical approach developed by Costes et al. was applied [24]. In this approach, the contribution of the crystal-field effects of the Ln^III ion is removed by subtracting from the experimental χ_MT data of 4 and 5 those of the isostructural Zn-Ho and Zn-Er complexes, respectively, whose magnetic behaviour depends only on the Ln^III ion. The difference Δχ_MT = (χ_MT)_CoLn − (χ_MT)_ZnLn = (χ_MT)_Co + J_CoLn is therefore related to the nature of the overall exchange interaction between the Co^II and Ln^III ions. Thus, positive values are related to ferromagnetic coupling whereas negative values are related to antiferromagnetic interactions. The Δχ_MT values first slightly decrease due to the thermal depopulation of the spin-orbit coupling levels of the Co^II ion until they reach a minimum at ∼20 K and then increase down to 2 K, thus indicating a ferromagnetic interaction between Co^II and Ln^III ions. It appears that the magnetic exchange coupling is higher for 5 than for 4 as the former shows an increase in χ_MT at low temperature and the latter does not. The fact that Δχ_MT values for 5 begin to increase at higher temperatures than for 4 is also supporting evidence of the above supposition.

The temperature dependence of compound 3 (Fig. 4) is similar to that observed for compound 2. The value at 300 K (16.08 cm³ K mol⁻¹) is close to that expected (16.04 cm³ K mol⁻¹) for independent Co^II (S = 3/2 with g_Co = 2.0) and Dy^III (4f⁹, J = 15/2, S = 5/2, L = 5, ⁶H_15/2, g_J = 4/3) ions in the free-ion approximation. The χ_MT value decreases with decreasing temperature down to a minimum value of 3.96 cm³ K mol⁻¹ at 12 K, then increases at lower temperatures, reaching a maximum value of 15.46 cm³ K mol⁻¹ at 2 K. The decrease between 300 and 12 K is due, as in compounds 2 and 7, to the thermal depopulation of the Stark sublevels of the Dy^III ion and to the depopulation of the spin-orbit coupling levels of the Co^II ion. It should be noted that, in contrast to that observed for compounds 4 and 5, the difference Δχ_MT = (χ_MT)_CoLn–(χ_MT)_ZnLn = (χ_MT)_Co + J_CoLn for complex 3 does not decrease on lowering the temperature. This can be due to the fact that the CoO₃N₃ octahedral coordination environment is rather distorted toward a trigonal prismatic geometry (it exhibits 70% of octahedral geometry), which leads to a partial quenching of the orbital angular momentum and, consequently, to a smaller spin-orbit coupling that is ultimately responsible for the decrease in the Δχ_MT vs T plot in the high temperature region. The increase of χ_MT in the low temperature region supports the existence of a ferromagnetic interaction between Co^II and Dy^III ions.

The thermal dependence of χ_MT for compounds 9-12 (Fig. 6) show a similar behaviour to those observed for the analogous acetate-diphenoxo triply-bridged dinuclear Co-Ln complexes 2-5. With the exception of 11, these complexes show an increase of χ_MT in the low temperature region, which is in agreement with the ferromagnetic interaction expected for these compounds. Conversely, in the case of 11, the χ_MT product steadily decreases down to 2 K, as for compound 4. To know whether or not the interaction between the Ho^III and Co^II is ferromagnetic in nature, we have followed the same strategy as for compounds 3-5. We have used the thermal dependence of χ_MT for the acetate-diphenoxo Zn^IIHo^III compound [19] to be subtracted from compound 11, because we have not succeeded in obtaining the analogous dicyanamide-bridged Zn₂Ho₂ tetranuclear compound. Nevertheless, in view of the results for compounds 8-12, the magnetic behaviour of the ZnHo and Zn₂Ho₂ compounds must be very similar. As can be observed from Fig. 6, the temperature dependence of the Δχ_MT = (χ_MT)_Co2Ho2 − 2(χ_MT)_ZnHo ≈ 2(χ_MT)_Co + J_CoHo (where J_CoHo is the magnetic interaction through the diphenoxo pathway) clearly shows that the J_CoHo is also ferromagnetic. Conversely to that observed for compound 4, the Δχ_MT in the high temperature region for compound 11 does not decrease, thus indicating a smaller spin-orbit coupling effect in this compound than in 4, which is in agreement with the larger distortion of the coordination environment observed for 11.

Dynamic ac magnetic susceptibility measurements as a function of the temperature at different frequencies and under zero-external field clearly show that only complex 3 exhibits a frequency dependence of the in-phase (χ′_M) and out-of-phase (χ′′_M) signals (Fig. S5) but without reaching a maximum in temperature dependence of the χ′′_M above 2 K, even at frequencies as high as 1400 Hz. This behaviour indicates that 3 exhibits slow relaxation of the magnetization and possibly SMM behaviour. However, either the energy barrier for the flipping of the magnetization is not high enough to trap the magnetization in one of the equivalent configurations above 2 K or the energy barrier is reduced to an effective value by quantum tunneling of the excited states leading to a flipping rate that is too fast to observe the maximum in the χ′′_M above 2 K. When the ac measurements were performed in the presence of a small external dc field of 1000 G to fully or partly suppress the quantum tunneling relaxation of the magnetization, compound 3 shows typical SMM behaviour below 5 K with maxima in the 2.25 K (665 Hz)-2.5 K (1300 Hz) range (Fig. 7).

From the temperatures and frequencies of the maxima observed for the χ′′_M signals, and by using an Arrhenius plot, τ = τ₀ exp(Δ/k_BT), the thermally activated energy barrier for the flipping of the magnetization (Δ/k_B) was estimated to be 7.6 K and the flipping rate τ₀ = 1.3 × 10⁻⁵ s. The value of Δ/k_B is at the lower end of the experimental range found for similar 3d/4f SMM systems [6,19]. However, the τ₀ value is much larger than expected, which suggests that the quantum tunneling of the magnetization is only partly suppressed by the applied field of 1000 G and, therefore, the thermal energy barrier should be higher than 7.6 K.

In order to shed light on the origin of this behaviour, we have performed fragment CASSCF calculations within the MOLCAS 7.2 ab initio package [14]. We have investigated the local magnetic anisotropies of the Co^II and Dy^III on the hypothetical complexes Co-La and Zn-Dy, respectively, which have the same structural parameters as compound 3. The ground Kramers doublet arising from the ligand field splitting of the ⁶H_15/2 ground atomic term show strong axial anisotropy with g_z = 18.9 (g_x = 0.06 and g_y = 0.09) along the main anisotropy axis, which lies close to the Dy–Co direction (Fig. 8a). The cobalt atom, as expected, is much less anisotropic with g_z = 6.71 along the main anisotropy axis (g_x = 2.02 and g_y = 3.63), which is placed not too far from the normal of the Co-Dy direction (Fig. 8b).

The combination of these magnetic anisotropies could produce a highly uniaxial magnetoanisotropy whose main anisotropy axis would lie close to the Dy anisotropy axis. At low temperature (below ∼30 K), the ground doublet sub-level of Dy^III (with Jz = ±15/2) is further split into two levels because of the magnetic exchange interaction with the ground doublet with S_eff = 1/2 of the cobalt(II) ion. It has been suggested that the energy gap between these two levels is related to the observed energy barrier [25]. Because the magnetic exchange coupling between Dy^III and Co^II is expected to be very weak (the J_CoLn is ∼+1 cm⁻¹ for the Gd-Co complexes 1, 6 and 8, and it should be lower than this value for heavy Ln^III ions because of the lanthanide contraction) a small energy barrier for the reversal of the magnetization is also expected, which is in good agreement with the observed results for compound 3. For the compounds 2, 4, 5 and 7, a weaker uniaxial anisotropy and/or a smaller J_CoLn coupling constant promote smaller values of the energy barrier and consequently do not show any out-of-phase signal (χ′′′_M) under zero dc applied field. Moreover, the existence of transverse anisotropy could lead to large tunnel splittings and therefore to the observed efficient zero-field quantum tunneling of magnetization.

The fact that tetranuclear Co₂Ln₂ compounds 9-11 do not exhibit slow relaxation of the magnetization even under an external dc field may be related to the existence of very weak Co-Ln antiferromagnetic interactions between each pair of centrosymmetrically related dinuclear Co-Ln units. These interactions lead to small separations of the low lying split sublevels and consequently to a smaller energy barrier for the flipping of the magnetization.