Synthesis, Structural Features and Physical Properties of a Family of Triply Bridged Dinuclear 3d-4f Complexes

Abstract

New dinuclear M^II-Ln^III complexes of general formulas [Cu(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN·H₂O (Ln^III = Gd (1), Tb (2), Dy (3) and Er (4)), [Ni(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Nd (5), Gd (6), Tb (7), Dy (8), Er (9) and Y (10)) and [Co(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Gd (11), Tb (12), Dy (13), Er (14) and Y (15)) were prepared from the compartmental ligand N,N′-dimethyl-N,N′-bis(2-hydroxy-3-formyl-5-bromo-benzyl)ethylenediamine (H₂L). In all these complexes, the transition metal ions occupy the internal N₂O₂ coordination site of the ligand, whereas the Ln^III ions lie in the O₄ external site. Both metallic ions are connected by an acetate bridge, giving rise to triple mixed diphenoxido/acetate bridged M^IILn^III compounds. Direct current (dc) magnetic measurements allow the study of the magnetic exchange interactions between the 3d and 4f metal ions, which is supported by density functional theory (DFT) theoretical calculations for the Gd^III-based counterparts. Due to the weak ferromagnetic exchange coupling constants obtained both experimentally and theoretically, the magneto-thermal properties of the less anisotropic systems (compounds 1 and 6) are also studied. Alternating current (ac)magnetic measurements reveal the occurrence of slight frequency dependency of the out-of-phase signal for complexes 8, 9 and 13, while complex 15 displays well-defined maximums below ~6 K.

1. Introduction

The design and synthesis of molecular complexes that display slow relaxation of the magnetization, i.e., single-molecule magnet behaviour (SMMs), has gained increasing attention in the past few decades [1,2,3,4,5,6]. This interest is mainly due to their potential applications, as these compounds could be used in emerging fields such as molecular spintronics, ultra-high density magnetic information storage and quantum computing [7,8]. The fundamental characteristic of SMM behaviour is the presence of an energy barrier for the reorientation of the spin of the ground state, which can be defined in terms of a large (or at least non-zero) ground spin state (S) and a large magnetic anisotropy (D).

Research efforts in the field of SMMs have shown that the use of heavy lanthanide ions (e.g., Dy^III and Tb^III) is a good strategy to obtain compounds with these unique properties, as lanthanides have large angular momentum in the ground multiplet state and, therefore, large anisotropy [9,10]. However, such complexes often display additional relaxation pathways, such as quantum tunnelling of the magnetization (QTM) or spin-phonon couplings, which lead to narrow hysteresis loops and/or the absence of slow relaxation of the magnetization without the application of an external field. Since these effects are less pronounced in 3d metal-based SMMs, hybrid 3d-4f systems appear to be a suitable solution to the aforementioned problem [11,12,13,14]. Additionally, ferromagnetic interactions between the d and f ions can lead to an increased ground spin state, a pre-requisite for the observation of SMM behaviour.

In the systems in which the magnetic interactions are not strong enough and/or the magnetic anisotropy is not large enough for the appearance of slow relaxation of the magnetization, other exciting physical phenomena such as the magneto-caloric effect (MCE) can still be studied [15]. The multiple low-lying excited and field-accessible states generated in such compounds contribute to the overall magnetic entropy, which can be modulated upon the application of an external magnetic field. Thus, hybrid 3d-4f complexes containing isotropic Gd^III ions (with a calculated maximum entropy value of Rln(2S_Gd + 1)/M_Gd = 110 J·kg⁻¹·K⁻¹) and 3d transition metal ions (e.g., Cu^II and Ni^II) are good candidates for solid state refrigeration.

With this in mind, in this work we prepare a novel family of triply bridged dinuclear 3d-4f complexes and study their magnetic properties. The flexible Mannich base N,N′-dimethyl-N,N′-bis(2-hydroxy-3-formyl-5-bromobenzyl) ethylenediamine (H₂L) ligand allows the coordination of metallic ions with different sizes, leading to a series of triply bridged M^II-Ln^III dinuclear species: [Cu(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN·H₂O (Ln^III = Gd, Tb, Dy and Er), [Ni(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Nd, Gd, Tb, Dy, Er and Y) and [Co(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Gd, Tb, Dy, Er and Y).

2. Results

The reaction of H₂L with Cu(OAc)₂·H₂O and Ln(NO₃)₃·nH₂O in a CH₃CN/MeOH mixture and in 1:1:1 molar ratio led to dark green crystals of the compounds [Cu(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN·H₂O (Ln^III = Gd (1), Tb (2), Dy (3), Er (4)). The same reaction but using Ni(OAc)₂·4H₂O instead of Cu(OAc)₂·H₂O, led to green crystals of the similar dinuclear complexes [Ni(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Nd (5), Gd (6), Tb (7), Dy (8), Er (9), Y (10)), where the major differences between the Cu^II and Ni^II-based dimers reside in the coordination environment of the 3d metal ions and the disposition of the ligands around them. The use of Co(OAc)₂·4H₂O as source of metal led to the formation of dinuclear complexes with the general formula [Co(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Gd (11), Tb (12), Dy (13), Er (14), Y (15)), which are isostructural to the Ni^II analogues (Information about the purity of the samples and the crystallographic data can be found in Tables S1–S6).

Crystal Structures

Complexes 1–4 are isostructural between them and are very similar to the Zn^II-Ln^III complexes previously reported by us [16], but contain Cu^II instead of Zn^II (Figure 1). In these complexes, the Cu^II and Ln^III ions are bridged by two phenoxido groups of the ligand and one syn-syn acetate, forming bis(phenoxido)acetate triply bridged dinuclear entities. The Cu^II ions are also coordinated to two nitrogen atoms from the amine groups (N1A and N2A), leading to CuN₂O₃ coordination spheres with geometries that can be considered as intermediate between square pyramid and vacant octahedron according to the SHAPE software (Table S7) [17]. The Cu–O and Cu–N distances are found in the 1.999(2)–2.146(2) and 2.017(2)–2.024(3) Å ranges, respectively, being the largest distances those corresponding to the Cu–O_acetate bonds (Table S5).

On the other hand, the LnO₉ coordination spheres are composed of two aldehyde oxygen atoms (O1A and O4A) of the ligand and four oxygen atoms belonging to two bidentate nitrate anions (O1C, O2C, O1D and O2D), as well as of the three bridging oxygen atoms mentioned previously. The LnO₉ spheres encompass assorted Ln–O bond distances, including short Ln–O distances in the 2.254(2)–2.290(2) Å range that correspond to the Ln–O_acetate bonds, intermediate Ln–O_ligand bond distances in the 2.326(2)–2.404(2) Å range and large Ln–O_nitrate distances in the 2.426(2)–2.534(2) Å range. Due to these variety on bond distances, the LnO₉ coordination spheres can be considered as intermediate between several nine-vertex polyhedral, as supported by the SHAPE software (Table S10) [17]. The intradinuclear Cu-Ln distances are in the 3.353(3)–3.380(1) Å range and are greatly influenced by the lanthanide contraction as they decrease from Gd^III to Er^III, being this effect also observable in Ln–O_ligand and Ln–O_acetate bonds (Table S5).

The average Ln–O–Cu angles are between 99.51(6) and 100.29(7)° in complexes 1–4 and, due to the acetate bridging group, the CuLn dimers show folded structures with average hinge angles in the 24.29–25.07° range (the hinge angle, β, is the dihedral angle between the O2A–Cu–O3A and O2A–Ln–O3A planes in the bridging fragment). Both aromatic rings of the ligand are almost in the same plane, forming dihedral angles ranging from 15.73 to 16.04°.

Finally, it should be mentioned that complexes 1–4 exhibit hydrogen bond interactions between the crystallization water molecules and one of the oxygen atoms of the bidentate nitrate group, one of the oxygen atoms of the acetate bridging group (O2P) and the nitrogen atom of the crystallization acetonitrile molecule (Figure S1).

Complexes 5–10 possess very similar molecular structures to that of 1–4, but consist of Ni^II–Ln^III dinuclear units and the coordination environment of Ni^II ions is different to that of the Cu^II ions (Figure 2). In these complexes, the Ni^II ions are coordinated to an additional nitrogen atom (N1F) that belongs to an acetonitrile molecule and therefore, exhibit NiN₃O₃ coordination spheres. The three oxygen atoms (O2A, O3A, O1P) and consequently, the three nitrogen atoms (N1A, N2A, N1F) occupy facial (fac) positions in these slightly distorted coordination polyhedra. In fact, computed shape measurements indicate that NiN₃O₃ coordination spheres are found in the OC-6 ↔ TPR-6 deformation pathway and are close to the octahedral geometry (75.8–77.1%) somewhat distorted to trigonal prismatic (Table S8). The Ni–O and Ni–N bond distances are similar to each other and vary between 2.051(6)–2.136(4) Å and 2.060(5)–2.108(4) Å, respectively. The lanthanide ions show similar coordination environments as in complexes 1–4, exhibiting rather asymmetric coordination spheres where the average Ln–O distances are in the range 2.275(2)–2.537(7) Å. As a matter of fact, the computed shape measurements relative to the ideal nine-vertex polyhedra for the LnO₉ coordination sphere are very close to those obtained for compounds 1–4 (Table S10). The average Ni^II–Ln^III distances are in the range 3.385(1)–3.437(2) Å and as expected, the average Ln-O_ligand bond distances steadily decrease from Nd^III to Er^III following the lanthanide contraction, with a concomitant decrease of the average Ni^II–Ln^III and Ln-O_acetate bond distances.

The M–O–Ln angles of complexes 5–10 are similar to those found in complexes 1–4 and are in the 97.6(2)–101.99(7)° range. Compared to the Cu^II-based analogues, the ligand shows more twisted disposition around the metal ions, in which the dihedral angles between the two aromatic rings are in the 69.92–71.39° range. The torsion of the ligand leads to an increase in the hinge angle compared to complexes 1–4, being in the 27.88–28.39° range.

To end up, complexes 11–15 are isostructural to complexes 5–10 but contain Co^II ions and crystallize in the triclinic P-1 space group. The CoN₃O₃ and LnO₉ coordination spheres show similar coordination environments to those found in complexes 5–10, with 71.9–72.7% octahedral geometry for Co^II ions (Table S9). Bond distances and angles are also close to those found for complexes 5–10 and further discussion on the structure of these complexes will be omitted.

3. Discussion

3.1. Magnetic Properties

The temperature dependence of the magnetic susceptibility for the dinuclear Cu^IILn^III complexes were measured on polycrystalline samples in the 5–300 K (1) and 2–300 K (2–4) temperature ranges under an applied field of 0.1 T and is given in the form χ_MT in Figure 3.

At room temperature, the χ_MT value for 1 of 8.27 cm³·K·mol⁻¹ matches very well with the expected value for non-interacting Cu^II (S = 1/2) and Gd^III (S = 7/2) ions (8.25 cm³·K·mol⁻¹ with g = 2). On cooling, the χ_MT product remains constant until 70 K and then increases at lower temperatures, reaching a maximum value of 9.31 cm³·K·mol⁻¹ at 5 K, pointing to the presence of ferromagnetic exchange interactions within the Cu^IIGd^III dinuclear unit. The field dependence of the molar magnetization at 2 K for compound 1 (Figure 3) shows a relatively rapid increase in the magnetization at low fields, in agreement with a high-spin state, and a rapid saturation of the magnetization that is almost complete above 3 T, reaching a value of 7.91 Nμ_B at 5 T. The obtained value is in good agreement with the theoretical value for a S_T = 4 spin ground state (8 Nμ_B for g = 2).

The magnetic susceptibility and magnetization data for complex 1 have been simultaneously modelled using the following Hamiltonian formula:

H = −JS_CuS_Gd − zJ′ < S_z > S_z + g_eμ_BSH

(1)

where J is the magnetic exchange pathway through the di-μ-phenoxo/syn-syn acetate triple bridge, −zJ′ < S_z > S_z accounts for the intermolecular interactions by means of the molecular field approximation, g_e is the average g factor, μ_B is the Bohr magneton and H is the magnetic field. The fit of the experimental susceptibility data using the full-matrix diagonalization PHI program [18] afforded the following set of parameters when fixing g to 2.0 for both ions: J = +2.30 cm⁻¹ and zJ′ = −0.006 cm⁻¹ with R = 2.08 × 10⁻⁵.

To support the experimental value of J_CuGd, DFT calculations were carried out on the X-ray structure as found in the solid state. The calculated J_CuGd parameter of +2.51 cm⁻¹ matches very well in sign and magnitude with the experimental one. Previous theoretical studies carried out on dinuclear Cu–(μ-O)₂–Gd complexes indicate that ferromagnetic interactions between Cu^II and Gd^III ions increase with the planarity of the Cu–(μ-O)₂–Gd bridging fragment and with the increase of the Cu–O–Gd angle [19,20,21]. Therefore, the weak ferromagnetic interactions found in this complex are not unexpected if we consider the mean Cu–O–Gd angle of 99.60° and the dihedral β angle of 25.07°.

The χ_MT values of 12.14, 14.87 and 12.06 cm³·K·mol⁻¹ respectively for complexes 2–4 at 300 K are compatible with the expected values or pairs of magnetically isolated Cu^II and Ln^III ions (Table S11). On lowering the temperature, the χ_MT product of the Cu^IIDy^III dimer (3) decreases gradually to reach a minimum value of 14.28 cm³·K·mol⁻¹ at 14 K and then increases until 14.53 cm³·K·mol⁻¹ at 4.0 K. Below this temperature, there is a small decrease to reach a value of 13.99 cm³·K·mol⁻¹ at 2.0 K. The magnetic behaviour at low temperatures of this complex is the result of two competing interactions: (1) ferromagnetic exchange interactions between the Cu^II and Dy^III ions, which lead to an increase in χ_MT and (2) crystal field splitting of the Dy^III ions, responsible for the decrease in χ_MT. The fact that χ_MT increases at low temperatures suggests that ferromagnetic interactions prevail over the effect of the crystal field splitting in this complex. On the other hand, the χ_MT products of complexes 2 and 4 remain constant on cooling until 25 and 130 K, respectively, and then drop abruptly to reach respectively values of 10.70 and 7.93 cm³·K·mol⁻¹ at 2 K. The decrease of χ_MT in the low temperature regime for 2 and 4 seems to indicate that in these compounds the effect of ferromagnetic exchange interactions is not as pronounced as in 3. The nature of the exchange interaction between Cu^II and lanthanide ions displaying spin-orbit coupling (SOC) can be known by the empirical approach developed by Costes et al. [22], which consists on representing the temperature dependence of the difference Δχ_MT = χ_MT_(CuLn) − χ_MT_(ZnLn) = χ_MT_(Cu) + J_(CuGd), where the contribution of the crystal-field effects of the Ln^III ions is removed from the χ_MT_(CuLn) data. The results obtained by this procedure using the magnetic data of the Zn^II-based analogues [16] reveal that the Δχ_MT differences show an increase at low temperatures (Figure S2), thus suggesting the occurrence of ferromagnetic interaction between Cu^II and Ln^III ions in complexes 2–4.

Upon increasing the applied external magnetic field, the magnetization of complexes 2–4 shows a relatively rapid increase at low magnetic fields and a rapid saturation that is almost complete above 4 T, reaching values of 5.92, 6.04 and 6.89 Nμ_B at 5 T respectively. These values are quite far from the expected saturation values (10 Nμ_B for complexes 2 and 4 and 11 Nμ_B for complex 3), which suggests the presence of a significant magnetic anisotropy due to the crystal field effects and/or most likely the presence of low-lying excited states that are partially (thermally and field-induced) populated.

Continuing with the Ni(II)-based complexes, the temperature dependence of χ_MT for complexes 5–10 (χ_M is the molar magnetic susceptibility per Ni^IILn^III unit) were measured in an applied field of 0.1 T and are displayed in Figure 4. Let us start with the simplest cases, the Ni–Gd (6) and Ni–Y (10) dimers. At room temperature the χ_MT value of complex 6 is 9.38 cm³·K·mol⁻¹, which is slightly high but still in good agreement with the expected value for a couple of non-interacting Ni^II (S = 1) and Gd^III (S = 7/2) ions (8.875 cm³·K·mol⁻¹). The χ_MT value increases very slowly with decreasing temperature until 70 K and then in a more abrupt way to reach a maximum value of 10.82 cm³·K·mol⁻¹ at 3.3 K. Below the temperature of the maximum, there is a small decrease to reach a value of 10.67 cm³·K·mol⁻¹ at 2.0 K (Figure S3). The increase in χ_MT indicates the existence of intramolecular ferromagnetic interactions between Ni^II and Gd^III ions, whereas the decrease at low temperatures is more likely due to the zero field splitting effects (ZFS) of the ground state and/or intermolecular antiferromagnetic (AF) interactions. The field dependence of the magnetization at 2 K for 6 (Figure 4) reveals a relatively rapid increase at low fields to reach a clear saturation that is almost complete at 3 T, reaching a value of 9.01 Nμ_B at 5 T. This value is in good agreement with the expected value for the fundamental state S_T = 9/2 with g = 2 (9 Nμ_B).

On the other hand, the χ_MT value of the NiY complex (10) at room temperature is 1.23 cm³·K·mol⁻¹, which is compatible with the calculated value of 1 cm³·K·mol⁻¹ for independent Ni^II ions. On cooling, the χ_MT value remains almost constant until 18 K and then drops abruptly to reach a value of 0.957 cm³·K·mol⁻¹ at 5 K, which is due to the zero field splitting (ZFS) of Ni^II ion. The magnetization of complex 10 shows a gradual increase with the applied external field reaching a value of 1.57 Nμ_B at 5 T, which is lower than the expected from the Brillouin function for an S = 1 ground state (2 Nμ_B). This behaviour is due to the strong zero field splitting of the Ni^II ion, which leads to the split of the S = 1 ground state into two M_s = 0, ±1 components, preventing the magnetization from reaching the expected value.

The magnetic behaviour of complex 6 has been modelled using the following Hamiltonian formula:

H = −JS_NiS_Gd + D_NiS_Ni² + g_eμ_BSH

(2)

where J is the coupling constant between the Ni^II and Gd^III ions, D_Ni is the ZFS parameter for Ni^II ion, g_e is the average g factor, μ_B is the Bohr magneton and H is the magnetic field. The best-fit parameters to the experimental susceptibility and magnetization data using the PHI program [18] afforded the following set of parameters: J = +0.71 cm⁻¹, g = 2.06 and D = 6.73 cm⁻¹ with R = 9.76 × 10⁻⁶. The value of the D_Ni parameter for the NiY complex extracted from the simultaneous fit of the susceptibility and magnetization data (D_Ni = 6.61 cm⁻¹, g = 2.23 and R = 1.24 × 10⁻⁴, Figure 4) supports the magnitude of the D_Ni obtained for the Gd^III-based analogue. Regarding J, it should be noted that when D_Ni was fixed to zero and a term accounting for the intermolecular interactions was introduced in the Hamiltonian by means of the molecular field approximation, −zJ′ < S_z > S_z, the fitting parameters did not significantly change: J = +0.81 cm⁻¹, g = 2.06 and zJ′ = −0.008 cm⁻¹ with R = 3.82 × 10⁻⁵.

In order to support the experimental J value found for complex 6, DFT calculations were carried out on the X-ray structure using the broken-symmetry approach. The calculated J_NiGd parameter of +0.87 cm⁻¹ agrees very well in sign and magnitude with the experimental parameters. The obtained experimental value is at the lower end of the experimental range found for alkoxo and phenoxo bridged Ni_xGd (x = 1, 2, 3) complexes with ferromagnetic interactions [23,24], which is due to the relatively small Ni–O–Gd angle (100.05°) and large Ni–(μ-O)₂–Gd dihedral angle (28.29°) found in this complex. In fact, it has been seen from experimental results and DFT calculations that in diphenoxido bridged dinuclear NiGd complexes the ferromagnetic coupling increases when increasing the planarity of the Ni–(μ-O)₂–Gd bridging fragment and the Ni–O–Gd bridging angle [23,24]. In addition, the effect of a third non-phenoxido bridge in the magnetic exchange coupling was also studied in the structurally similar complex [Ni(μ-L¹)(μ-OAc)Gd(NO₃)₂] (H₂L¹ = N,N′,N″-trimethyl-N,N″-bis(2-hydroxy-3-methoxy-5-methylbenzyl)diethylenetriamine), which was done by substituting the syn-syn acetate bridging group by two non-bridging water molecules [23]. The results of the calculations showed an increase of 0.45 cm⁻¹ in J_NiGd, indicating that the third bridge has a significant role in decreasing the magnetic exchange coupling in this type of compounds. Therefore, in view of the above considerations the weak ferromagnetic interaction between the Ni^II and Gd^III ions is not unexpected.

With respect to complexes 5 and 7–9, at room temperature the χ_MT values are in general close but slightly higher than the expected values for pairs of magnetically isolated Ni^II and Ln^III ions (Table S11). On lowering the temperature, the χ_MT values decrease gradually until ~50 K and then drop abruptly to reach a minimum value of 1.23 cm³·K·mol⁻¹ for complex 5 and values that at 5 K are in the 6.04–11.6 cm³·K·mol⁻¹ range for complexes 7–9. As in the case of complexes 1–4, this behaviour is due to the depopulation of M_J sublevels of the Ln^III ions. The empirical approach developed by Costes et al. to know the nature of the interactions between the Ni^II and Ln^III ions cannot be used for these complexes, because they are not isostructural to the Zn^IILn^III complexes reported previously.

The magnetization of complexes 7–9 (Figure 4) show relatively rapid increase at low fields, in accordance with the ferromagnetic interaction between Ni^II and Ln^III ions and a lineal increase from 1 T without reaching a clear saturation at 5 T. The magnetization values at 5 T for complexes 7 and 8 (Table S11) are close to the expected saturation magnetization values for Ln^III ions with strong easy-axis anisotropy that behave as Ising type ions and that are ferromagnetically coupled to Ni^II ions. The M value for 9 at 5 T, however, is considerably lower than the expected saturation value, which could indicate that the latter compound shows weaker axial anisotropy than complexes 7 and 8. Moreover, the magnetization of complex 5 shows a gradual increase with the applied magnetic field, reaching a value of 2.4 Nμ_B at 5 T.

The temperature dependence of χ_MT for complexes 11–15 (χ_M is the molar susceptibility per Co^IILn^III unit) were measured in an applied field of 0.1 T and are displayed in Figure 5. The χ_MT value for the CoY complex 15 at room temperature (2.72 cm³·K·mol⁻¹) is significantly larger than the spin-only value for a high-spin Co^II ion (S = 3/2, 1.875 cm³·K·mol⁻¹ with g = 2), which is indicative of the unquenched orbital contribution of the Co^II ion in distorted octahedral geometry. Upon cooling, χ_MT remains practically constant in the high temperature range and it decreases sharply below 120 K, reaching a value of 1.82 cm³·K·mol⁻¹ at 4.5 K (Figure S4). As the molecules are well isolated in the crystal field, this decrease is most likely due to SOC effects rather than intermolecular AF interactions. The susceptibility data was fitted to Equation 3 with the PHI program [18], obtaining the following set of parameters: λ = −104.0 cm⁻¹, α = 1.216, Δ = |355.3| cm⁻¹ and δ = |89.35| cm⁻¹ with R = 3.51 × 10⁻⁶. The fit of the experimental data to the theoretical equation shows that the sign of Δ cannot be unambiguously determined from the susceptibility data, as the agreement factor (R) for positive and negative values are, in general, close. The fitting parameters are in good accordance with previously reported values for distorted octahedral Co^II complexes [25,26,27].

$$H=-\alpha \lambda LS+\Delta \left[L_z^2-L\left(L+1\right)/3\right]+\delta \left(L_x^2-L_y^2\right)+\beta H\left(-\alpha L+g_{e}S\right)$$

(3)

Regarding the magnetization plot of complex 15, at an applied field of 5 T the magnetization is not fully saturated, reaching a value of 2.6 Nμ_B (Figure 5 and Figure S4). This value is lower than the expected saturation value of 3 Nμ_B, which is due to anisotropy. The M vs. H/T plots obtained between 2 and 7 K at applied magnetic fields ranging from 0.1 to 9 T (Figure S5) are not superimposed on a single master curve, indicating that complex 15 shows a significant magnetic anisotropy. In order to quantify this anisotropy, the magnetic susceptibility data were fitted to Equation 4 using the PHI program [18], obtaining the following set of parameters: D = |35.5| cm⁻¹ and g = 2.43 with R = 1.2 × 10⁻⁴.

$$H=D\left[S_z^2-S\left(S+1\right)/3\right]+g_e{\mu }_{\mathrm{B}}SH)$$

(4)

where S is the spin ground state, D is the axial magnetic anisotropy, g_e is the average g factor, μ_B is the Bohr magneton and H is the magnetic field. The sign of D cannot be unambiguously determined from the susceptibility data either in this case.

Continuing with the CoGd complex 11, at room temperature the χ_MT value of 11.09 cm³·K·mol⁻¹ is slightly larger than the expected value for two non-interacting Co^II (S = 3/2) and Gd^III (S = 7/2) ions (9.750 cm³·K·mol⁻¹ with g = 2.0), which may be due to the orbital contribution of Co^II ions. On cooling, the χ_MT product stays constant until 140 K, then starts decreasing to reach a minimum value of 10.58 cm³·K·mol⁻¹ at 15 K and ends up increasing until 10.90 cm³·K·mol⁻¹ at 4.5 K (Figure 5 and Figure S6). The observed decrease of χ_MT is due to the thermal depopulation of the spin-orbit coupling levels arising from the ⁴T_1g ground term of Co^II ions, whereas the increase at low temperature indicates a ferromagnetic interaction between Co^II and Gd^III ions.

The magnetic behaviour of complex 11 was analysed by considering both effects and a purely octahedral Co^II coordination environment, as included in the following Hamiltonian formula:

$$H=\alpha \lambda LS-J{S}_{Co}{S}_{Gd}$$

(5)

The fit of the experimental susceptibility data using the above equation led to the following parameters: λ = −111.2 cm⁻¹, α = 0.88, J = +0.26 cm⁻¹ and g = 2.06 (considered to be the same for both ions) with R = 2.52 × 10⁻⁵. The observed coupling constant is lower than that found for the similar di-μ-phenoxo/syn-syn acetate triply bridged compound [Co(μ-L¹)(μ-OAc)Gd(NO₃)₂] (J = +0.7 cm⁻¹) [28,29], and to those found for planar di-μ-phenoxo-bridged Co^IIGd^III complexes containing a compartmental ligand (J ~ 1 cm⁻¹) [30,31]. Following the considerations made for Cu^IIGd^III and Ni^IIGd^III complexes, the observed low value of J is not unexpected if we take into account that 11 has the highest hinge angle.

The magnetization isotherm of 11 at 2 K (Figure 5 and Figure S6) shows a relatively rapid increase at low field, in agreement with a high spin ground state and a rapid saturation of the magnetization at higher fields to reach a value of 9.79 Nμ_B at 5 T, which is close to the expected saturation value for a couple of Co^II and Gd^III ions with g = 2.0 (10 Nμ_B). The experimental magnetization data falls slightly above the Brillouin curve for a pair of non-interacting Co^II (S = 3/2) and Gd^III (S = 7/2) ions with g = 2.06, thus confirming the existence of very moderate ferromagnetic interaction between the metal ions.

Regarding 12–14, the χ_MT values at room temperature are higher than those calculated for independent Co^II (S = 3/2, g = 2) and Ln^III ions in the free-ion approximation (Figure 5, Table S11), which is mainly due to the orbital contribution of the Co^II ion. The χ_MT products remain constant with decreasing temperature until 100 K and then decrease abruptly reaching the values listed in Table S11 at 2 K. This behaviour is due to both thermal depopulation of the levels that arise from spin-orbit coupling in the Co^II ion and the thermal depopulation of the M_J sublevels of the Ln^III ion.

Finally, as shown in Figure 5, upon increasing the applied external magnetic field, the magnetization of complexes 12–14 are increased to 7.87, 8.49 and 8.05 Nμ_B at 5 T, respectively, but do not reach the expected saturation values (Table S11) for a couple of Co^II and Ln^III ions. The observed behaviour is due to the anisotropy of the Co^II and Ln^III ions.

3.2. Dynamic Magnetic Properties

Dynamic alternating current (ac) magnetic susceptibility measurements as a function of the temperature at different frequencies were performed on the most promising complexes. However, under zero-external field none of them showed frequency dependency of the in-phase (χ_M′) and out-of-phase signals (χ_M″), which could be due to fast resonant zero-field quantum tunnelling of the magnetization (QTM) through degenerate energy levels. When the ac measurements were performed in the presence of a small external direct current (dc) field of 1000 Oe, complexes 8 (Ni^IIDy^III), 9 (Ni^IIEr^III) and 13 (Co^IIDy^III) showed a weak frequency dependency, but with the maxima of χ_M″ appearing below the instrument detection limit (Figures S7 and S8). Thus, the energy barrier (U_eff) and relaxation time (τ₀) cannot be obtained via the convectional Arrhenius method. However, if we assume that there is only one relaxation process, the Debye model (Equation (6)) could provide a rough estimate of U_eff and τ₀ values [32],

$$\ln \raisebox{1ex}{${\chi }_{\mathrm{M}}″$}\!\left/ \!\raisebox{-1ex}{${\chi }_{\mathrm{M}}\prime $}\right.=\ln \left(2\mathsf{\pi }\nu {\tau }_0\right)+\raisebox{1ex}{$E_a$}\!\left/ \!\raisebox{-1ex}{$k_{B}T$}\right.$$

(6)

yielding U_eff values of 7.76, 11.91 and 12.30 K and relaxation times (τ₀) of 5.78 × 10⁻⁷, 5.12 × 10⁻⁸ and 7.76 × 10⁻⁹ s for complexes 8, 9 and 13, respectively (Figure S8). Thus, all these results highlight that the simple mixing of 3d and 4f ions does not always lead to the desired behaviour. The worsening of the properties compared to the Zn^IILn^III analogues [16] has been ascribed to the weak exchange interactions between the 3d and 4f ions, which generate multiple low-lying excited states separated by small energies. In addition, due to the weak exchange interactions, the 3d metal ions can create random transversal fields for the lanthanide ions, thus favouring the quantum tunnelling of the magnetization [33,34,35,36,37,38,39].

Finally, Co^IIY^III complex 15 displays slow relaxation of the magnetization with maxima below ~6 K after the application of an external field of 1000 Oe (Figure 6). Note that this field was chosen because it induces the slowest relaxation rate, which does not significantly vary until fields as high as 3500 Oe (Figure S9). The Cole–Cole diagrams obtained under this field in the temperature range 2.0–6.4 K exhibit semicircular shapes, with α values in the 0.27–0.05 range, suggesting multiple relaxation processes (Figure S10). The temperature dependence of the magnetic relaxation times were used to construct an Arrhenius plot, which led to an effective energy barrier for the reversal of the magnetization of 15.68 K with τ₀ = 1.73 × 10⁻⁶ s. The obtained U_eff is much lower than the expected value from the energy gap between the M_s = ±1/2 and M_s = ±3/2 levels from dc measurements (energy gap = 2D = 71 cm⁻¹ = 102 K assuming E = 0), but in good agreement with those found for other monometallic Co^II SMMs exhibiting D > 0 and field induced slow relaxation of the magnetization through a Raman mechanism, which show apparent U_eff values of ~20 cm⁻¹ [25].

3.3. Magneto-Thermal Properties

Magnetic isotropy and high ground spin-state are two factors that favour the observation of a large magneto-caloric effect (MCE) [15,40,41,42,43,44]. Moreover, if the magnetic exchange interaction between the metal ions is weak, a large MCE could be attained [15,40,41,42,43,44]. Thus, the isotropic nature of the Cu^II and Gd^III ions and the weak ferromagnetic exchange interactions, as well as the relatively large metal/ligand mass ratio (which limits the amount of passive, non-magnetic elements) makes compound 1 a good candidate to display large MCE. For comparative purposes, the magnetic entropy changes (−ΔS_m) that characterize the MCE have also been calculated for the Ni^IIGd^III complex (6), as Ni^II ions generally exhibit weak second-order spin-orbit anisotropy (ZFS zero-field splitting). However, MCE has not been measured for the Co^IIGd^III compound (11), because, as is well known, octahedral Co^II ions exhibit a large first-order magnetic anisotropy that significantly reduces the MCE effect.

The fitting of the experimental isothermal magnetization data (Figure 7 and Figure S12) to the Maxwell relation (Equation (7), B_i and B_f are the initial and final applied magnetic fields, respectively) leads to maximum −ΔS_m values that appear in

Table 1. Maximum magnetic entropy change values (−ΔS_m) for complexes 1 and 6 and for [Mn(CH₃OH)(μ-L¹)Gd(NO₃)₃] at 7 T.

Complex	ST	J (cm−1)	−ΔSm Max (J·kg−1·K−1)	T/K
1	4	+2.3	17.1	3
6	9/2	+0.7	17.4	3
[Mn(CH3OH)(μ-L1)Gd(NO3)3] a	6	+0.99	23.5	2.7

^a H₂L¹ = N,N′,N″-trimethyl-N,N″-bis(2-hydroxy-3-methoxy-5-methylbenzyl)-diethylenetriamine [45].

.

$$\Delta S_m=\left(T,\Delta B\right)=\underset{B_i}{\overset{B_f}{{\displaystyle \int }}}{\left[\frac{\partial M\left(T,B\right)}{dT}\right]}_{B}dB$$

(7)

The integration results for 1 and 6 display a gradual increase of −ΔS_m with decreasing temperature from 6 K to 2 K (Figure 7 and Figure S12) and increasing applied magnetic field. The simulation of the temperature and field dependence of −ΔS_m for 1 (solid lines in Figure 7), using the magnetic parameters (g, J and zJ) extracted from the fitting of the magnetization and susceptibility data, show that the −ΔS_m values are almost coincident with those extracted from the integration of the field dependence of the magnetization (Figure 7) at different temperatures, thus supporting the −ΔS_m values extracted from experimental magnetization data. The −ΔS_m reaches a maximum value of 17.09 J·kg⁻¹·K⁻¹ for ΔH = 7 T at 3.0 K, which is smaller than the full magnetic entropy content per mole of the Cu^IIGd^III complex (23.67 J·kg⁻¹·K⁻¹, calculated by means of the expression Rln(2S_Gd + 1) + Rln(2S_Cu + 1) = 2.77 R). Even though the simulated MCE value at 2 K and 7 T (18.26 J·kg⁻¹·K⁻¹) is lower than that calculated for the full magnetic entropy content for 1, it is close to the value expected for a ferromagnetically coupled Cu^IIGd^III dimer (2.19 R = 18.82 J·kg⁻¹·K⁻¹). Compared to other {CuGd}_n complexes, the −ΔS_m (simulated at 2K)/−ΔS_m (full entropy content) ratio of 0.77 obtained for 1 is slightly lower than the 0.83 ratio observed for the Cu₆Gd₆ complex [{(HL²)(L²)(DMF)Cu^IIGd^III(DMF)(H₂O)}₆]·6DMF (DMF = N,N-dimethylformamide; H₃L²= Schiff base obtained from the condensation of 3-formylsalicylic acid with hydroxylamine) [46]. This fact can be because [{(HL²)(L²)(DMF)Cu^IIGd^III(DMF)(H₂O)}₆]·6DMF exhibits weaker ferromagnetic interactions (J = +1.01 cm⁻¹) than 1, which favours the spin polarization at relatively low magnetic fields (the stronger the ferromagnetic interaction, the smaller the MCE). However, [Gd^III₂Cu^II₂(OH)₂(NO₃)_2.5(OAc)_3.5(L³)₂]_n (L³ = 2-pyridinylmethanol) [47] displays a ratio of 0.56 due to strong CuGd magnetic interactions, with calculated absolute values in the 3.2–4.2 cm⁻¹ range. It is worth noting that, as expected, the maximum −ΔS_m value observed for 1 with a Gd/Cu = 1 is generally larger than those found for other less magnetic dense complexes with Gd/Cu ratios lower than 1.

For the Ni^IIGd^III complex (6) the maximum value of −ΔS_m is of 17.38 J·kg⁻¹·K⁻¹ at T = 3 K and an applied field change ΔH = 7 T (Figure S12, inset). This value is also smaller than the full magnetic entropy content per mole, which is of 3.18 R = 28.41 J·kg⁻¹·K⁻¹. However, this value is close to the expected value for a ferromagnetically coupled Ni^IIGd^III complex (2.30 R = 18.55 J·kg⁻¹·K⁻¹). The temperature dependence of the –ΔS_m values at different applied magnetic fields (Figure S12, inset) can be reproduced reasonably well using the magnetic parameters (J, g and D) extracted from the simultaneous fitting of the magnetic and susceptibility data, thus underpinning the –ΔS_m values extracted from the field and temperature dependence of the magnetization. Compared to other (NiGd)_n systems, such as Ni₆Gd₆ [48] and Ni₂Gd₂ [49] with –ΔS_m values of 26.5 and 34.4 J·kg⁻¹·K⁻¹, respectively, compound 6 exhibits a lower –ΔS_m value and a smaller −ΔS_m (simulated at 2K)/−ΔS_m (full entropy content) ratio (0.70 and 0.91 for the two former compounds and 0.61 for compound 6). This latter fact could be due to both a larger J value and a larger magnetic anisotropy for 6 compared to the other (NiGd)_n systems. Even though complex 1 has lower S_T and higher J values than 6, both complexes exhibit similar MCE. This result shows clearly the relatively stronger impact of the anisotropy of the Ni^II ion on the MCE. It is worth mentioning that the closely structurally related Mn^IIGd^III dinuclear complex, previously reported by one of us [45], displays the largest −ΔS_m value in this series. This fact is not surprising taking into account that in this compound both paramagnetic ions are magnetically isotropic, the S_T is the largest in the series and the J value is rather small.

4. Materials and Methods

4.1. General Procedures

All analytical reagents were purchased from commercial sources and used without further purification. All syntheses were performed under ambient laboratory atmosphere. The H₂L ligand was prepared according to a previously described procedure [50].

4.2. Preparation of Complexes

[Cu(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN·H₂O (Ln^III = Gd (1), Tb (2), Dy (3), Er (4)). A general procedure was used for the preparation of these complexes: to a solution of 25.0 mg (0.125 mmol) of Cu(OAc)₂·H₂O in 5 mL of acetonitrile/methanol (80:20) mixture were added with continuous stirring 64.3 mg (0.125 mmol) of H₂L and 0.125 mmol of the corresponding Ln(NO₃)₃·nH₂O. The resulting solution was filtered and allowed to stand at room temperature. After several days, well-formed prismatic dark green crystals of compounds 1–4 were obtained in yields in the range 35–41% (Supporting Information, Table S1), which were filtered, washed with acetonitrile and air-dried.

[Ni(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Nd (5), Gd (6), Tb (7), Dy (8), Er (9), Y (10)). These compounds were prepared with yields in the range 45–57% (Supporting Information, Table S1) following the procedure for 1–4, but using Ni(OAc)₂·4H₂O (31.1 mg, 0.125 mmol) instead of Cu(OAc)₂·H₂O.

[Co(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Gd (11), Tb (12), Dy (13), Er (14), Y (15)). These compounds were prepared as orange crystals following the same procedure as for 1–4, except that Co(OAc)₂·4H₂O (31.1 mg, 0.125 mmol) was used as source of metal. Yields: 39–54%.

The purity of the complexes was checked by elemental analysis (Supporting Information, Table S1).

4.3. Physical Measurements

Elemental (C, H, and N) analyses were performed on a Leco CHNS-932 microanalyzer (Elemental Microanalysis Ltd., Devon, UK). Infrared spectra were recorded in the region 400–4000 cm⁻¹ on a Nicolet 6700 FTIR (Fourier transform infrared) spectrophotometer (Thermo Phisher Scientific, TX, USA) with samples as KBr disks. Variable temperature magnetic susceptibility measurements and magnetization measurements at 2 K on polycrystalline samples were measured in several devices: a PPMS (physical property measurement system)—Quantum Design Model 6000 magnetometer, a Quantum Design SQUID MPMS XL-5 device and a Quantum Design SQUID MPMS-7T device (Quantum Design, San Diego, CA, USA). Alternating current magnetic measurements in a 3.5 G ac field oscillating at 60–10,000 Hz were performed on a PPMS—Quantum Design Model 6000 magnetometer.

4.4. Single-Crystal Structure Determination

Single crystals of suitable dimensions were used for data collection. Intensity data for compounds 1, 6, 8, 10, 12 and 13 were collected at 100 (2) K on an Agilent Technologies SuperNova diffractometer (mirror-monochromated Mo Kα radiation, λ = 0.71073 Å) equipped with an Eos CCD detector. In the case of compounds 2–4, 9 and 14, data collection was also carried out at 100 (2) K, but the Supernova diffractometer was equipped with Cu Kα radiation (λ = 1.54184 Å) and an Atlas CCD detector. In all cases, data frames were processed (unit cell determination, intensity data integration, correction for Lorentz and polarization effects, and analytical absorption correction) using the CrysAlis software package [51].

Diffraction intensities of compounds 5 and 7 were collected on a Bruker SMART X2S benchtop diffractometer, with doubly curved silicon crystal monochromated Mo Kα (λ = 0.71073 Å) radiation and Breeze CCD detector at 200 (2) K. Finally, the collection of the diffraction intensities for 11 and 15 were carried out with a Bruker 8 Venture with a photon detector equipped with graphite monochromated Mo Kα (λ = 0.71073 Å) radiation. For data reduction, the Bruker Saint program was used [52]. The data were corrected for Lorentz and polarization effects and an empirical absorption correction (SADABS) was applied [53].

The structures were solved by direct methods and refined by full-matrix least-squares with SHELX-2014 [54]. Anisotropic temperature factors were assigned to all atoms except for the hydrogen atoms, which are riding their parent atoms with an isotropic temperature factor arbitrarily chosen as 1.2 times that of the respective parent. The crystal data for 1–15 along with some refinement details are summarized in Supporting Information Tables S2–S4. Selected bond lengths and angles are given in Supporting Information Tables S5 and S6. Cambridge Crystallographic Data Centre (CCDC) reference numbers for the structures are 2052561–2052575.

4.5. Computational Details

Theoretical coupling constants were calculated using the broken symmetry approach proposed by Noodleman et al. [55,56,57]. All theoretical calculations were carried out at the density functional theory (DFT) level using the hybrid density functional B3LYP (Becke, 3-parameter, Lee–Yang–Parr) [58,59,60,61] as implemented in the Gaussian 09 program [62]. The triple-ζ quality 6–311G* basis set was used for all electrons in non-metal atoms, while the CREMBEL pseudopotential was used for core electrons of metal atoms [63,64]. Calculations were performed on complexes 1 and 6 derived from experimental crystallographic geometries. The approach used to determine the exchange coupling constants for polynuclear complexes has been described in detail elsewhere [65,66,67,68].

The J values of the dinuclear complexes were determined by calculating the energy difference between the high spin state (E_HS) and broken symmetry state (E_BS), according to the following equation:

$$J=\frac{E_{LS}-E_{HS}}{2S_1{S}_2+S_2}$$

(8)

where S₁ and S₂ are the local spins for each metal centre and S₁ > S₂.

5. Conclusions

We have demonstrated that the Mannich-type ligand H₂L (N,N′-dimethyl-N,N′-bis(2-hydroxy-3-formyl-5-bromo-benzyl)ethylenediamine), with high backbone flexibility and inner N₂O₂ and outer O₄ coordination sites, allows the preparation of a series of dinuclear M^II–Ln^III complexes. In this complexes, the M^II ions occupy the internal coordination sites whereas the oxophilic Ln^III ions occupy the external coordination sites, leading to acetate-diphenoxo triply bridged dinuclear complexes [Cu(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN·H₂O (Ln^III = Gd, Tb, Dy and Er), [Ni(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Nd, Gd, Tb, Dy, Er and Y) and [Co(CH₃CN)(µ-L)(µ-OAc)Ln(NO₃)₂]·CH₃CN (Ln^III = Gd, Tb, Dy, Er and Y). Although the coordination environment of the Ln^III ions is similar in all complexes, the Ni^II and Co^II ions are coordinated to an additional acetonitrile molecule compared to the Cu^II-based analogues, which leads into a more twisted disposition of the ligand around the metal ions and an increase in the hinge angle for the former. dc magnetic measurements have been carried out in order to study the magnetic exchange interactions between M^II and Ln^III ions and the results obtained for the Gd^III-based complexes have been supported by DFT theoretical calculations. The MCE extracted from the isothermal magnetization curves of the Gd analogues suggests that in these dinuclear systems, the magnetic entropy changes (−ΔS_m) depend more on the magnetic anisotropy than in the total spin and magnetic exchange interactions. Dynamic ac magnetic susceptibility measurements show that the Ni^IIDy^III, Ni^IIEr^III and Co^IIDy^III analogues exhibit slight frequency dependency of the out-of-phase signal at different temperatures, while the Co^IIY^III analogue displays slow relaxation of the magnetization below ~6–7 K under an applied field of 1000 Oe.