Lanthanoid Coordination Polymers Based on Homoditopic Picolinate Ligands: Synthesis, Structure and Magnetic Properties ^†

Abstract

A ditopic ligand (H₂L₁), containing picolinate subunits segmented by ethynylene bridges, has been used in the synthesis of a series of isostructural coordination polymers, formulated as [(CH₃)₂NH₂][Ln(L₁)₂]·H₂O·CH₃COOH, where Ln = Eu (1), Gd (2), Tb (3), Dy (4) and Ho (5). The single-crystal structures show that these compounds crystallise in the orthorhombic Pna2₁ space group and form 3D anionic lattices with triangular cavities. AC magnetic susceptibility measurements show that the Gd, Tb and Dy derivatives (2–4) present a slow relaxation in their magnetisation under an applied DC magnetic field. The detailed study of the AC susceptibility in compounds 2 and 4 shows that they relax following direct and Orbach mechanisms under these conditions. The Dy derivative (4) retains this behaviour in the absence of an external field, relaxing via quantum tunnelling and Orbach mechanisms. Compound 2 is one of the very few reported Gd(III) compounds showing slow relaxation in its magnetisation.

1. Introduction

There is, nowadays, a strong interest in the synthesis and physical properties of lanthanoid coordination polymers (Ln-CPs) [1,2,3]. The reasons for this are manifold: (i) their structural versatility in comparison with transition metals, with higher coordination numbers leading easily to extended frameworks of different dimensionalities, including 3D porous structures [4,5,6,7,8]. (ii) Their fascinating photophysical and magnetic properties, with potential applications in different fields, such as luminescent (bio)sensors and magnetic materials for molecular spintronics and quantum computing [9,10].

Due to the internal character of the 4f electron shell, the magnetism of lanthanoid coordination complexes has traditionally drawn less attention with respect to 3d metal ions. This situation was reversed after the report of single-molecule magnetism (SMM) in the lanthanoid bis-phthalocyaninato anions, [LnPc₂]⁻ (Ln = Dy, Tb; Pc = phthalocyanine), reported by Ishikawa and coworkers [11,12]. In these compounds, the key to SMM behaviour is the large local magnetic anisotropy that arises from the splitting of the m_J sublevels by the crystal field, giving rise to a high energy barrier for magnetisation and slow spin dynamics [13,14,15]. Most studies concern mononuclear Dy(III) compounds [16,17], but examples of other nuclearities and cations also exist [18,19,20,21,22,23], including Ln-CPs of varying dimensionality [24,25]. In this latter case, the exchange interactions between neighbouring lanthanoid cations can lead to SCM (single-chain magnet) behaviour, especially when dealing with heterometallic 3d–4f systems [26,27,28,29,30]. In most other systems, however, the exchange interactions between lanthanoid ions are rather weak and the slow magnetic relaxation observed is mainly due to single-ion anisotropy effects [31].

Lanthanoid single-ion magnetic anisotropy arises from the interaction of the ground spin-orbit coupled J level with the electrostatic crystal field. This results in a splitting of the m_J states in such a way that the energy gaps between the different ±m_J doublets (resulting in different orientations of the spins) are very sensitive to the coordination environment. Large energy gaps can be obtained by optimizing the strength and symmetry of the ligand field with respect to the shape of the electronic density of the free metal ions. This results in high energy barriers for magnetisation reversal, giving rise to slow relaxation effects and magnetic hysteresis. As described by Long and coworkers, when the shape of the free-ion electron density is oblate, as for Tb³⁺, Dy³⁺ and Ho³⁺ cations, an axial crystal field is needed to maximise the magnetic anisotropy [32]. The family of dysprosium metallocenes, with its ligand electron density concentrated above and below the xy plane, are excellent examples of SMM behaviour [33,34]. Instead, ions such as Er³⁺, having a prolate electron density, would perform better in an equatorial crystal field. It has been suggested that SMMs based on lanthanoid coordination polymers may be of interest since the lanthanoid coordination sphere can be constrained by the bridging linkers and the crystal symmetry, yielding new materials with improved magnetic properties [24,35]. Further, by using different bridging ligands, different compounds can be obtained that are essentially identical in their first coordination spheres but differ markedly in the way the lanthanoid ions assemble in the crystal lattice, giving some hints about the importance of dipolar interactions in fine-tuning magnetic behaviour [36].

In the quest for interesting bridging ligands, our attention has been focused on chelating and anionic units, which provide thermodynamical stability and charge compensation. Previous examples of coordination polymers containing units of this type involve tetraanionic bis-bidentate dioxidobenzenedicarboxylate ligands [37,38,39] and catecholates [40]. Surprisingly, despite the fact that the picolinate ligand is a universal chelating anionic entity, only a few polytopic picolinate ligands have been reported [41,42,43,44], and their use in metal–organic frameworks are underexplored. We have reported on a family of polytopic picolinate ligands bridged by ethynylene links, which provide rigidity, linear connectivity and electron delocalisation [45,46]. Coordination polymers containing these ligands, in combination with transition metal ions, have also been described. More recently, knowing the ability of picolinate ligands to act as photosensitisers for lanthanoid luminescence [47,48], we reported on Eu(III) CPs based on the ethynylene-bridged bis-picolinate ligand 5,5′-(ethyne-1,2-diyl)dipicolinate (L₁²⁻, Figure 1), a strongly luminescent material that can be useful in the detection of several species [49]. We herein describe the whole family of isostructural compounds of formulae [(CH₃)₂NH₂][Ln(L₁)₂]·H₂O·CH₃COOH (Ln = Eu (1), Gd (2), Tb (3), Dy (4), Ho (5)), including their synthesis, structural and magnetic characterisation.

2. Materials and Methods

All chemicals and solvents were used as received. Ligand L₁²⁻ was synthesised as previously described [45].

Synthesis of [(CH₃)₂NH₂][Ln(L₁)₂]·H₂O·CH₃COOH (1–5). A solution of 5,5′-(ethyne-1,2-diyl)dipicolinic acid (15 mg, 0.056 mmol) and Ln(NO₃)₃·6H₂O (0.056 mol) in 4.5 mL of DMF/H₂O (8:1 ratio) was placed in a glass vial and stirred for 30 min until a solution was formed. Then, acetic acid was added, and the mixture was placed in an oven at 130 °C for 3 days. After cooling to room temperature at a cooling rate of 0.2 K·min⁻¹, the liquid phase was decanted, and colourless aggregated crystals from compounds 1–5 were obtained. Details concerning the yields, elemental analyses and IR spectra are given in the Supplementary Materials.

Single crystal X-ray diffraction. The suitable crystals of 1–5 were coated with paratone N oil, fixed on a small fibre loop and mounted on an Oxford Diffraction Supernova diffractometer equipped with a graphite-monochromated Enhance Mo X-Ray Source (λ = 0.71073 Å) at 120 K. The data collection routines, unit cell refinements and data processing were carried out using the CrysAlisPro v38.46 software package [50]. The structures were solved using SHELXT 2018/2 via the WinGX v2018.3 graphical interface [51] and refined using SHELXL-2018/3 [52]. Although X-ray experiments (powder and single-crystal) unambiguously support the isostructural character of the whole lanthanoid series, satisfactory data for complete structural characterization could only be obtained for the Eu (1) (reported previously) and Tb (3) derivatives. All non-hydrogen atoms were refined anisotropically for 1 (DELU and SIMU restraints were applied to C and O atoms of the acetic acid molecules to allow their anisotropic refinement). For 3, all non-hydrogen atoms were refined anisotropically, except those concerning the acetic acid molecule and O1W. H atoms on carbon atoms were included at calculated positions and refined with a riding model with relative isotropic displacement parameters. Instead, H atoms on solvent molecules and amine H atoms on dimethylammonium cations were found using Fourier difference maps and refined with constrained isotropic thermal parameters, except for the H atoms of O1W. CCDC 2068875 and CCDC 2420909 contain the supplementary crystallographic data for 1 and 3, respectively. These data were provided free of charge by the Cambridge Crystallographic Data Centre.

Powder X-ray Diffraction (PXRD). PXRD measurements for compounds 1–5 were collected using Cu Kα radiation (λ = 1.54056 Å) at room temperature and in a 2θ range from 2 to 40°. Polycrystalline samples were lightly ground in an agate mortar and filled into a 0.5 mm borosilicate capillary prior to being mounted and aligned on an Empyrean PANalytical powder diffractometer. Simulated diffractograms were obtained from single-crystal X-ray data using the CrystalDiffract software.

Magnetic susceptibility measurements. Variable temperature susceptibility measurements were carried out for compounds 1–5 in the temperature range of 2–300 K with an applied magnetic field of 100 mT on ground polycrystalline samples, using a Quantum Design (San Diego, CA, USA) MPMS XL-5 SQUID magnetometer. The susceptibility data were corrected for the sample holder and the diamagnetic contributions of the sample using Pascal’s constants [53]. AC susceptibility measurements were performed on the same samples for compounds 2–5 at low temperatures with different applied DC fields in a frequency range of 10 Hz–10 kHz, using Quantum Design (San Diego, CA, USA) PPMS-9 equipment.

Other characterization techniques. Thermogravimetric analyses were performed on a Mettler-Toledo TGA/SDTA/851e apparatus under an N₂ atmosphere at a scan rate of 10 K·min⁻¹. IR transmission measurements were performed from the powdered samples at room temperature in an FT-IR spectrometer (Bruker, alpha II) equipped with an attenuated total reflection (ATR) accessory in the range of 400–4000 cm⁻¹. C, H and N elemental analyses were measured in a CE INSTRUMENTS 1110 EA elemental analyser (SCSIE, Universitat de València).

3. Results and Discussion

3.1. Synthesis and Characterization

Coordination polymers 1–5 were prepared by direct reaction between the corresponding lanthanoid nitrate and ligand H₂L₁ under solvothermal conditions. Although important efforts have been devoted to obtaining single crystals of the erbium derivative, its isolation was not possible. The addition of acetic acid as a modulator was necessary in order to obtain single crystals for X-ray structural analysis. These could also be obtained from the corresponding methyl diesters, Me₂L₁. In this case, the modulator of choice was formic acid.

In order to confirm the phase purity of the bulk materials, powder X-ray diffraction measurements were performed (Figure S1). The experimental patterns recorded at room temperature for compounds 1–5 were compared with the simulated diffractogram for the Tb derivative 3 obtained from single-crystal data at 120 K. There is a perfect agreement between both subsets of patterns, discarding the presence of crystalline impurities in the materials.

The thermogravimetric analysis (Figure S2) of the different compounds is very similar, exhibiting a first weight loss between room temperature and 390 K that is associated with the release of water. A second step ascribed to the loss of acetic acid is detected between 425 and 590 K. Above this temperature, the samples start to decompose.

3.2. Structural Properties

Compounds 1–5 are isostructural and crystallise in the orthorhombic Pna2₁ space group. Their asymmetric unit contains an Ln³⁺ cation, two crystallographically independent L₁²⁻ dianions, one dimethylammonium cation and crystallization solvent molecules (one water molecule and one acetic acid). The Flack parameter is close to zero (

Table 1. X-ray crystal data for 1 and 3.

	1	3
chemical formula	C32H26EuN5O11	C32H26N5O11Tb
a (Å)	19.6440(2)	19.70340(10)
b (Å)	12.35500(10)	12.32080(10)
c (Å)	13.21490(10)	13.14510(10)
α (deg)	90.00	90.00
β (deg)	90.00	90.00
γ (deg)	90.00	90.00
V (Å3)	3207.28(5)	3191.13(4)
T (K)	119.7(8)	120.00(10)
Z	4	4
Mr (g/mol)	808.54	815.50
crystal system	orthorhombic	orthorhombic
space group	Pna21 (No. 33)	Pna21 (No. 33)
crystal dimensions (mm)	0.124    0.105    0.073	0.180    0.136    0.122
µ (Mo Kα) (mm−1)	2.025	2.286
λ (Å)	0.71073	0.71073
density (Mg/m3)	1.674	1.697
index ranges for h, k, l	−25/24, −16/16, −16/17	−25/25, −16/15, −17/17
θ range (deg)	3.298 to 28.107	3.307 to 27.710
goodness-of-fit on F2	1.082	1.115
reflns collected	118251	116487
independent reflns (Rint)	7383 (0.0975)	7172 (0.0435)
data/restraints/parameters	7383/33/453	7172/6/422
R1, wR2 [I > 2σ(I)] 1	0.0389, 0.0765	0.0308, 0.0714
R1, wR2 (all data) 1	0.0627, 0.0883	0.0356, 0.0747
absolute structure parameter	−0.039(6)	−0.026(4)

¹ R1 = ∑(|F_o| − |F_c|)/∑|F_o|; wR2 = [∑[w(F_o² − F_c²)²]/ ∑[wF_o⁴]]^1/2.

), implying that the model has the correct absolute structure [54].

The presence of dimethylammonium cations is required in order to balance the negative charges of the host framework. They arise from the hydrolysis of dimethylformamide, used as a solvent during the synthesis. In the following, the structure of the Tb compound (3) is described. A comparison with the structure of the Eu derivative (1) is given in Tables S1 and S2.

The terbium cation is located in a general position and exhibits a non-coordinated tricapped trigonal prismatic (TTP) geometry (Figure 2). It is coordinated by four picolinate subunits in a chelating mode. One of these picolinate moieties acts also as a µ-carboxylato bridging ligand and occupies the ninth position in the lanthanoid coordination sphere. The Tb–O distances lie in the 2.33–2.39 Å range, much shorter than the Tb–N1 distances, which comprise between 2.58 and 2.68 Å (Table S1). This is in agreement with the reported values for Ln(III) complexes based on picolinate ligands and is due to the strong oxophilicity of the Ln³⁺ cations [55]. The triangular faces of the tricapped trigonal prism are defined by O3O6N2 and O1O5O7 atoms, whereas the capping positions over each rectangular face are occupied by N1, N3 and N4 nitrogen atoms. The angle between the trigonal faces is 175.3°, indicating a small deviation from the ideal parallel arrangement.

Continuous shape measure (CShM) calculations using SHAPE 2.1 confirm that the coordination geometries of 1 and 3 are slightly distorted tricapped trigonal prisms (with minimum CShM calculated values corresponding to D_3h symmetry, Table S2) [56,57,58]. A CShM calculation of a coordination sphere indicates its deviation from an ideal structure, regardless of its size and orientation, and is given by the following expression:

$$S\left(G\right)=min{\displaystyle \frac{{\sum }_{k=1}^N\left|Q_k–P_k\right|}{{\sum }_{k=1}^N\left|Q_k–Q_0\right|}}$$

(1)

The vectors Q_k (k = 1, 2…N) indicate the positions of the N donor atoms defining the coordination sphere, and G is a specific and perfect symmetry group with coordinates P_k (k = 1, 2…N). The distances between the vertices of the two objects are calculated until a set of P_k coordinates is found that minimises S(G) (the denominator is a size normalisation factor, Q₀ being the coordinate vector of the centre of mass in the investigated structure). The lower the CShM parameter, the better the agreement between the investigated and reference coordination geometries [59]. According to Equation (1), CShM measures must lie within the range of 100 ≥ S ≥ 0. In compounds 1 and 3, values of 3.882 and 3.891, respectively, indicate a close agreement with the ideal TTP geometry (D_3h symmetry).

The two independent L₁²⁻ bis-picolinate ligands adopt different coordination modes. Ligand A acts as a terminal (N1,O1);(N2,O3) bis-chelating ligand, adopting a transoid arrangement of the two picolinate moieties and connecting two Tb³⁺ complexes separated by the ethynylene spacer. Ligand B behaves also as a ditopic ligand, coordinating to two distant Tb³⁺ cations related by a translation along the y direction, but one of the picolinate subunits (N3O6) acts as a tridentate ligand in an (N,O);O mode, connecting two lanthanoid metal ions by anti, anti-carboxylate (O5O6) bridges that organise zigzag chains propagating along the c axis. The intrachain terbium–terbium distance is 6.6564(7) Å (Figure 3a). This connectivity results in layers of Tb(III) complexes that run parallel to the bc plane.

The layers are further connected by ligand A, binding two Tb³⁺ cations separated by a distance of 12.8146(6) Å. This yields a 3D anionic lattice showing triangular cavities (Figure 3b). Dimethylammonium countercations sit within these cavities and are hydrogen-bonded to a coordinating picolinate oxygen atom (H-bond distance N5···O7: 2.741(9) Å) and a water molecule (H-bond distance N5···O1W: 2.704(14) Å). On the other hand, the acetic acid molecule forms a short–strong H-bond with a non-coordinated oxygen atom (H-bond distance O9···O4: 2.486(19) Å).

Both anions deviate considerably from a planar structure. Ligand A adopts a transoid conformation, with a dihedral angle between the two pyridine rings close to 27°. In ligand B, however, the two pyridine rings are almost perpendicular to each other, with a dihedral angle of about 80°. This may be attributed to the fact that this ligand binds to a third Ln³⁺ cation via the anti, anti-carboxylate (O5O6) bridge. For the same reason, the torsion angle involving the O5 carboxylate oxygen atom (12.59°) is higher than those obtained for the other carboxylate moieties (0.82–8.82°). With respect to the bending of the triple bond, it is similar in both ligands, with a maximum deviation of 8.23° to the ideal –C–C≡C– and –C≡C–C– angles of 180°. Table S3 lists the relevant angles for comparing the crystal structures of 1 and 3.

Although compounds 1–5 are isostructural, it can be observed that, as the atomic number increases, cell volume decreases. This is a clear signature of the lanthanoid contraction effect (Figure S3).

3.3. Magnetic Properties

Magnetic susceptibility measurements were performed on the bulk samples 1–5, in a static dc magnetic field of 100 mT. The thermal variation in the χ_mT product (χ_m = molar magnetic susceptibility) in the 2–300 K temperature range (Figure 4) shows constant values at high temperatures, in agreement with those expected for the Ln³⁺ ions in their ground states (

Table 2. Experimental and expected χ_mT values (emu·K·mol⁻¹) at 300 K and magnetic parameters extracted from the fit of the DC magnetic data for 1–5.

	1	2	3	4	5
Experimental χmT	1.55	7.86	12.05	13.65	14.04
Expected χmT	0 (1.50)	7.87	11.82	14.05	14.04
λ (cm−1)	389(2)
Experimental g		2.023(4)	1.528(2)	1.301(2)	1.195(2)
Expected g		2.0	1.5	1.33	1.20
|D| (cm−1)		0.27(3)	0.15(1)	1.35(6)	1.14(2)
zj (cm−1)		−0.018(2)	−0.091(2)	−0.032(1)	−0.079(1)

) [60]. The exception of this is the europium derivative (1), with a value of χ_mT at room temperature equal to 1.55 emu·K·mol⁻¹, showing a steady decrease in the χ_mT signal upon cooling until the signal practically vanishes at 2 K, as expected for the diamagnetic ⁷F₀ ground state of Eu³⁺ ions. The non-zero value observed at room temperature indicates the thermal population of excited ⁷F_J (J = 1–6) multiplet levels resulting from the splitting of the ⁷F ground term by first-order spin-orbit coupling (λ). In fact, the two first excited states (⁷F₁ and ⁷F₂) are quite close to the ground state, and they can be populated at room temperature. Accordingly, we can fit the magnetic susceptibility data for compound 1 to a simple expression that is only dependent on the first-order spin-orbit coupling parameter (λ), as follows:

$${\chi }_{m}T={\displaystyle \frac{N{\beta }^2}{3kTx}}{\displaystyle \frac{24+{\left(\frac{27x}{2}-\frac{3}{2}\right)e}^{-x}+{\left(\frac{135x}{2}-\frac{5}{2}\right)e}^{-3x}+{\left(189x-\frac{7}{2}\right)e}^{-6x}+{\left(405x-\frac{9}{2}\right)e}^{-10x}+{\left(\frac{1485x}{2}-\frac{11}{2}\right)e}^{-15x}+{\left(\frac{2457x}{2}-\frac{13}{2}\right)e}^{-21x}}{1+{3e}^{-x}+{5e}^{-3x}+{7e}^{-6x}+{9e}^{-10x}+{11e}^{-15x}+{13e}^{-21x}}}$$

(2)

with x = λ/kT. Equation (2) very satisfactorily reproduces the magnetic data for compound 1 with λ = 389(2) cm⁻¹ (solid line in Figure 4). This value is similar to those reported in other Eu^III compounds [61,62,63].

The χ_mT values of the isotropic Gd³⁺ derivative (2) remain essentially constant in the whole temperature range and decrease abruptly only at temperatures below 10 K. This behaviour indicates that, despite the presence of carboxylate bridges between neighbouring Ln³⁺ ions, the exchange interactions are very weak [64,65]. In the other compounds (3–5), the decrease is more gradual and may be ascribed to the progressively thermal depopulation in the highest ground-state Ln³⁺ sublevels that arise from the splitting of the ground term by the ligand field.

Given the lack of significant interactions, we have fitted the χ_mT product for compounds 2–5 to a simple model, including a ZFS contribution (D) and a very weak antiferromagnetic coupling (zj), modelled using the mean-field approximation with the program PHI (solid lines in Figure 4) [66]. The parameters found in the fit are displayed in Table 2.

The good magnetic isolation provided by the picolinate ligands prompted us to measure the AC magnetic susceptibility at low temperatures for 2–5 in different applied DC fields to look for slow relaxation in the magnetisation (SRM). With the exception of the Ho derivative (5), the compounds show the presence of a frequency-dependent out-of-phase signal (χ″_m) at low temperatures when a DC field is applied (Figures S4–S7). Interestingly, for the Dy derivative (4), we could observe an out-of-phase signal even in the absence of a DC field, although with a lower intensity (Figure S6). The lack of SRM in 2–3 when no DC field is applied is due to the presence of an efficient relaxation in the magnetization through a quantum tunnelling mechanism. This fast relaxation is suppressed in a DC field. As it can be seen in Figures S4–S6, the intensity of the χ″_m signal initially increases with an increase in the magnetic field and shows two different maxima, one at low frequencies (slow relaxation process with a relaxation time τ₁), and a second one at high frequencies (fast relaxation process, τ₂). In the Gd (2) and Dy (4) derivatives, we can clearly observe how the maximum of the fast relaxation process (τ₂) shifts to lower frequencies and increases in intensity, reaching a minimum frequency and a maximum intensity for DC fields of around 120 mT in 2 and 80 mT in 4 (Figures S4 and S6, respectively). In the Tb derivative (3), the two maxima appear outside the frequency range of our equipment, although we could determine that the maximum intensity is reached for DC values around 140 mT (Figure S5).

The fitting of the frequency dependence of χ″_m to a Debye model for the two relaxation processes (Equation (3), solid lines in Figures S4–S6) gives us the relaxation times (τ) for each applied DC field [67]. Note that, since the maxima of the first relaxation process lie outside the measured frequency range, τ₁ values are unreliable in all cases. This applies also to the τ₂ value for compound 3. The field dependence of τ₂ for compounds 2 and 4 show, as expected, maxima at values around 120 and 80 mT, respectively (Figures S8 and S9). Despite that there are seven adjustable parameters in Equation (3), the isothermal (χ_T1 and χ_T2) and adiabatic (χ_S) susceptibilities, as well as the relaxation times (τ₁ and τ₂), can be easily estimated from the in-phase signal (χ′_m) values at different frequencies and from the position of the low- and high-frequency maxima, respectively. Note also that, although there is only one crystallographically independent Ln³⁺ ion in compounds 2–4, the presence of two different relaxation processes has already been observed in other lanthanoid-based lattices and has been attributed to the presence of relaxation pathways via excited states [68].

$${\chi }^{″}\left(\omega \right)=\left({\chi }_{T1}-{\chi }_S\right){\displaystyle \frac{{\left(\omega {\tau }_1\right)}^{1-{\alpha }_1}\mathrm{c}\mathrm{o}\mathrm{s}\left(\frac{\pi {\alpha }_1}{2}\right)}{1+2{\left(\omega {\tau }_1\right)}^{1-{\alpha }_1}\mathrm{s}\mathrm{i}\mathrm{n}\left(\frac{\pi {\alpha }_1}{2}\right)+{\left(\omega {\tau }_1\right)}^{2-2{\alpha }_1}}}+\left({\chi }_{T2}-{\chi }_{T1}\right){\displaystyle \frac{{\left(\omega {\tau }_2\right)}^{1-{\alpha }_2}\mathrm{c}\mathrm{o}\mathrm{s}\left(\frac{\pi {\alpha }_2}{2}\right)}{1+2{\left(\omega {\tau }_2\right)}^{1-{\alpha }_2}\mathrm{s}\mathrm{i}\mathrm{n}\left(\frac{\pi {\alpha }_2}{2}\right)+{\left(\omega {\tau }_2\right)}^{2-2{\alpha }_2}}}$$

(3)

The relaxation times obtained from the fit to the Debye model increase as the DC field increases, reaching maxima at around 120 mT for the Gd derivative (Figure S8) and 80 mT for the Dy compound (Figure S9). This behaviour can be well reproduced with the general model (Equation (4)) [69], using the parameters displayed in Table S4 (solid lines in Figures S8 and S9).

$${\tau }^{-1}=\mathrm{A}{H}^{\mathrm{n}}T+{\displaystyle \frac{{\mathrm{B}}_1}{1+{\mathrm{B}}_2{H}^2}}+\mathrm{D}$$

(4)

In this equation, A, B₁, B₂ and D are parameters corresponding to the different relaxation mechanisms: direct (A), quantum tunnelling (B₁ and B₂), and Raman and Orbach (D, since they are field-independent). H is the applied DC magnetic field and n is equal to 4 or 2 for Kramers (Gd and Dy) and non-Kramers (Tb) ions, respectively.

A detailed study of the frequency dependence of χ″_m at different temperatures was performed under a constant DC field set at the values where relaxation time τ₂ and signal intensity are the highest. The frequency dependence of χ″_m in an applied DC field of 120 mT for the Gd derivative (2) shows at 1.9 K a maximum of around 740 Hz that shifts to higher frequencies as the temperature increases (Figure 5a). The fit of this data to the Debye model for the two relaxation processes (Equation (3)), gives us the relaxation times at each temperature. These data, displayed in an Arrhenius plot (lnτ vs. 1/T, Figure 5b), show linear dependence at high temperatures for 2, with a clear curvature at lower temperatures. This result suggests the presence of an Orbach thermally activated relaxation mechanism (second term in Equation (5)), with additional Raman and/or direct mechanisms (third and fourth terms, respectively, in Equation (5)) [70]. Attempts to fit the Arrhenius plot for compound 2 to all the possible mechanisms in Equation (5) show that the best fit is obtained including only the Orbach and direct mechanisms (second and fourth terms in Equation (5)), using the parameters displayed in Table S5 (solid line in Figure 5b).

$${\tau }^{-1}={\tau }_{QT}^{-1}+{\tau }_0^{-1}\exp \left(-{\displaystyle \frac{U_{\mathrm{e}\mathrm{f}\mathrm{f}}}{kT}}\right)+C{T}^n+A{H}^{4}T$$

(5)

The Tb derivative (3) also shows two different relaxation processes but none of them exhibit a corresponding maximum in the frequency range measured (Figure S10). Therefore, the relaxation times obtained with the Debye model, including the two relaxation processes (Equation (3)), are unreliable and preclude the extraction of relevant parameters from the Arrhenius plot.

Finally, for the Dy derivative (4), we studied the thermal dependence of the out-of-phase signal in both zero and 80 mT DC fields. In both cases, at 1.9 K, we observe maxima in the χ″_m signal at 3200 Hz, with the signal in H_DC = 80 mT being stronger (Figure 6). As the temperature is increased under the zero DC field, the maximum remains almost unchanged, in the range of 1.9–5.2 K (Figure 6a), and shifts to higher frequencies above around 5.4 K (Figure S11). For H_DC = 80 mT, when the temperature is increased, the maximum shifts very fast to higher frequencies (Figure 6b).

This behaviour indicates that in a zero static field, the predominant mechanism for the relaxation of the magnetisation at low temperatures is quantum tunnelling, which is temperature independent, whereas, at higher temperatures, there is a thermally activated mechanism (Orbach type, see below). As expected, when H_DC = 80 mT, the quantum tunnelling is suppressed and the magnetisation relaxes through temperature-dependent mechanisms (direct and Orbach, see below).

As in compound 2, we fitted the data to a Debye model for the two relaxation processes (Equation (3)) to obtain the relaxation times of the fast relaxation process (τ₂) at each temperature. The Arrhenius plot (lnτ versus 1/T, Figure 7), in a zero static field, shows an almost temperature-independent behaviour at low temperatures and a curvature as the temperature increases, reaching linear behaviour at higher temperatures. This behaviour suggests the presence of quantum tunnelling and Orbach relaxation mechanisms (first and second terms in Equation (5)). Accordingly, we have fit the data with these two terms to obtain the parameters gathered in Table S5 (solid line in Figure 7a). When H_DC = 80 mT, the Arrhenius plot shows linear behaviour with a slight curvature at low temperatures, indicative of the presence of Orbach, direct, and/or Raman mechanisms. Attempts to fit the data with the three possible mechanisms (quantum tunnelling was discarded under the presence of an applied DC field) show that the data can be fitted to Orbach and direct mechanisms, using the parameters shown in Table S5 (solid line in Figure 7b).

The frequency dependence of the in-phase signals (χ′_m) for compounds 2–4 show an inflexion point corresponding to the maxima in the out-of-phase signals (Figures S12–S16). The Cole–Cole plots (χ″_m vs. χ′_m, Figures S17–S21) show the typical semi-circular shapes in all cases, with one or two semicircles depending on the number of relaxation processes observed in the out-of-phase plots.

It is interesting to note that 2 is one of the few reported Gd(III) lattices showing slow relaxation in its magnetisation (SRM). Thus, although there are hundreds of reports on Dy(III) compounds showing SRM [71,72,73,74], the number of compounds with Gd(III) showing SRM is, by far, much lower. This is due to the fact that the Gd³⁺ ion has a half-filled 4f⁷ configuration with a ground multiplet ⁸S_7/2 with no orbital contribution. In the first stage, slow relaxation in Gd(III) complexes has been ascribed to a phonon-bottleneck effect [75]. This picture assumes that the wavelength of the resonant phonon is larger than the separation between Gd³⁺ ions, a situation that is possible in our case. Indeed, the first reports on SRM for Gd(III) compounds invariably are related to polymeric structures showing relatively short Gd–Gd distances [31,76,77,78], although, recently, well-isolated mononuclear Gd(III) compounds exhibiting SRM have been reported [79] and it has been argued that zero-field splitting in strongly distorted environments could account for the efficiency of the resonant phonon trapping [80]. Thus, the observation of SRM for Gd(III) compounds might be more common than initially expected, as the recent literature provides more examples of this behaviour. An extensive list of materials is given in Table S6 [81,82,83,84,85,86,87,88,89,90,91,92,93,94,95].

4. Conclusions

A segmented ligand L₁²⁻, containing two picolinate anions connected by ethynylene bridges, has been used in the synthesis of five isostructural 3D anionic lattices with triangular cavities, formulated as [(CH₃)₂NH₂][Ln(L₁)₂]·H₂O·CH₃COOH, where Ln = Eu (1), Gd (2), Tb (3), Dy (4) and Ho (5). AC magnetic measurements show that 2–4 present slow relaxation when a DC magnetic field is applied, whereas the Dy derivative (4) exhibits slow relaxation in its magnetisation, even in the absence of a static field. The AC susceptibility in compounds 2 and 4 shows that, in both compounds, the dynamic properties follow direct and Orbach mechanisms in a DC field. When this field is switched off, magnetic relaxation in 4 follows quantum tunnelling and Orbach mechanisms. Compound 2 constitutes one of the very rare examples of slow relaxation in a Gd(III) compound.