Slow Relaxation of Magnetization and Magnetocaloric Effects in One-Dimensional Oxamato-Based Lanthanide(III) Coordination Polymers ^†

Abstract

Herein, we present the synthesis and characterization of a series of isostructural lanthanide(III) compounds with the N-(4-carboxyphenyl)oxamic acid (H₃pcpa) ligand of the general formula as {[Ln₂(Hpcpa)₃(H₂O)₅]}_n [Ln = Dy(III) 1, Ho(III) 2, Er(III) 3]. The structure of 3 consists of neutral zig–zag chains of Er(III) ions, with Hpcpa^2– ligands acting as bridges in a bidentate/monodentate coordination mode with five water molecules achieving the eight-coordination around the two Er(III) ions within the repeating bis(carboxylate)-bridged dinuclear units along the chain. The magnetic and magnetocaloric properties were studied for 1–3. Compound 1 presents a field-induced slow relaxation of the magnetization with a “reciprocating thermal behavior” below 5 K for H = 0.25 T, while 2 shows maxima of the magnetic entropy from 3 up to 6 K for ΔH > 2 T.

1. Introduction

The development of new multifunctional molecular materials (MMMs) is an important field of research due to the ability of these materials to combine different structures and chemical or physical properties for technological innovation. Coordination chemistry offers suitable alternatives for building MMMs for this purpose, such as coordination polymers (CPs). There are already many studies of porosity, good absorption capacity [1,2], and optical [3] and magnetic or magnetocaloric properties [4,5,6] where the CPs are used. The studies of CPs with 4f metal ions have been widely explored due to the enormous potential of working with MMMs that combine, for example, structural diversity with optical and magnetic/magnetocaloric properties [3,7]. The lanthanide(III) ions can show high coordination numbers, which allows different structures topologies for coordination polymers resulting from interaction with different organic ligands. The lanthanide(III) CPs can show good optical and magnetic/magnetocaloric properties depending on the choice of metal ion and organic ligand. These materials are interesting for applications like optoelectronics, spintronics, and cryogenic magnetic refrigeration [8].

Aromatic polyoxamato ligands have been amply used to obtain CPs with 3d metals. The great advantage of this type of ligand is the ability to build CPs with predictable structures and tunable magnetic properties; the ligand can efficiently transmit the magnetic coupling between neighboring metal atoms [9,10,11,12]. Many compounds with 4f metal ions and aromatic-substituted monooxamato ligands have been reported in the literature, most of which use ligands with monoprotonated oxamato groups. A mononuclear lanthanide(III) oxamato compound exhibiting a single-ion magnet (SIM) behavior is Me₄N[Dy^III(H-2,6-dmpa)₄]·2CH₃CN [2,6-dmpa = N-2,6-dimethylphenyloxamate]; the hydrogen-bond-mediated self-assembly of this compound in the solid state provides a first example of 2D hydrogen-bonded polymer with a herringbone net topology [9]. Other examples employing the tetrabutylammonium salt of the N-(4-chlorophenyl)oxamate ligand (4-Clpa) yielded a series of mononuclear lanthanide(III) complexes of general formula NBu₄[Ln^III(H-4Clpa)₄(dmso)], where Ln = Y, La, Nd, Eu, Gd, Tb, Dy, and Ho. Among these, the Nd, Gd, Tb, and Dy compounds exhibited a field-induced slow relaxation of magnetization typical of SIM behavior [13,14,15]. Using the sodium salt of the N-4-hydroxyphenyloxamate ligand (4-OHpa) towards the Ln(III) ions resulted in a series of a 2D Na^ILn^III supramolecular coordination networks, where Ln = Eu, Gd, Dy, and Ho, and only the Gd(III) compound presented a rare slow relaxation of the magnetization [16]. The simpler N-phenyloxamate ligand (pa) recently afforded 1D Ln^III CPs, where Ln = Eu, Gd, and Tb. These are examples of CPs featuring an aryl-monoxamato ligand without coordinating groups attached to the aromatic ring [17].

Our group’s extensive work with the coordination chemistry of the proligand N-(4-carboxyphenyl)oxamic acid (H₃pcpa) towards p-, d-, and f-block metal ions has led to the synthesis of a discrete Fe^III complex in addition to Pb^II, Mn^II, Co^II, Zn^II, Cd^II, Eu^III, Tb^III, and Gd^III CPs [18,19,20]. Their crystal structures revealed diverse coordination and bridging modes of the anionic Hpcpa^2– ligand (Scheme 1), highlighting its remarkable versatility in self-assembling CPs with various metal ions.

The 1D Eu and Tb CPs of the Hpcpa^2– ligand exhibited red and green emission, respectively, with the Tb compound showing a higher quantum yield due to the oxamate ligand’s superior sensitization of Tb^III ions. In contrast, the Gd analog displays slow magnetic relaxation under an applied field, classifying it as a field-induced single-molecule magnet (SMM) [19]. Focusing on the magnetic and magnetocaloric properties, we present a related series of Ln(III) CPs (Ln = Dy, Ho, and Er) with the Hpcpa^2– ligand. Their synthesis, chemical and structural characterization, and the analysis of their magnetic and magnetocaloric properties are reported herein. In this regard, highly anisotropic holmium(III), dysprosium(III), and erbium(III) ions with ⁵I₈, ⁶H_15/2, and ⁴I_15/2 ground states, respectively, are particularly well suited to test their magnetocaloric efficiency, when compared with the isotropic gadolinium(III) ion with an orbital-free ⁸S_7/2 ground state (J = 7/2 with S = 7/2 and L = 0). They possess the highest value of total angular momentum along the lanthanide(III) series because of the first-order spin-orbit coupling (SOC) effects of the 4f⁹ Dy^III (J = 15/2 with S = 5/2 and L = 5), 4f¹⁰ Ho^III (J = 8 with S = 2 and L = 6), and 4f¹¹ Er^III ions (J = 15/2 with S = 3/2 and L = 6).

2. Experimental Section

2.1. General Information

All manipulations were carried out under aerobic conditions. Chemicals were purchased from Sigma-Aldrich and used without further purification. The synthesis of the N-(4-carboxyphenyl)oxamic acid ethyl ester (EtH₂pcpa) and Na₂Hpcpa were performed following the previous report [18,19,20,21]. Elemental analysis (C, H, and N) was performed by Fisons EA1108. Solid-state infrared spectra were recorded on a Perkin Elmer Spectrum 400 FT-IR/FT-FIR spectrometer using KBr in the 400–4000 cm^–1 range, and 1H NMR were conducted by the Microanalytical Service of the Central de Análises Multiusuária of Federal University of Goiás. Thermogravimetric (TG) analysis was performed using samples obtained from the polycrystalline synthesis. The analyses were carried out at the Regional Center for Technological Development and Innovation (CRTI) on a Netzsch STA 449 F3 Nevio instrument over a temperature range of 30 to 650 °C, with a heating rate of 10 °C per minute under a synthetic air atmosphere. Powder X-ray diffraction (PXRD) data were collected for polycrystalline powders at CRTI using a Bruker D8 Discover powder diffractometer, using Cu-Kα radiation at a voltage of 40 kV and a current of 40 mA in the 2θ range 3.00–50.00° with a step-size of 0.0151°. The samples were kept at 15 rpm rotations during a measurement.

2.2. Synthesis

{[Ln₂(Hpcpa)₃(H₂O)₅]}_n [Ln = Dy^III (1), Ho^III (2) and Er^III (3)] were prepared by two different methods. The first method involved slow diffusion techniques in H-shaped tubes as follows: aqueous solutions of Dy(NO₃)₃ (0.1 mmol, 0.0348 g), HoCl₃·6H₂O (0.1 mmol, 0.0379 g), and Er(NO₃)₃·5H₂O (0.1 mmol, 0.0443 g) were placed in one arm of the corresponding H-tube, whereas an aqueous solution of Na₂Hpcpa (0.1 mmol, 0.037 g) was placed in the other arm. Water was added dropwise to fill the H-tube, which was covered with parafilm and allowed to stand at room temperature. All tubes yielded crystals; however, not all were suitable for single-crystal X-ray diffraction analysis. The second method involved mixing a solution of the rare-earth metal salt with a solution of the ligand salt in a 2:3 metal-to-ligand molar ratio. This process resulted in a polycrystalline solid, which was filtered and dried under vacuum. The yields were 78%, 81%, and 83% for 1–3, respectively. Elemental analysis (C,H,N) Calcd for C₂₇H₂₅Dy₂N₃O₂₀ (1): C 31.29; H, 2.43; N, 4.05. Found: C 30.74; H, 2.72; N, 4.04%. Anal. Calcd for C₂₇H₂₅Ho₂N₃O₂₀ (2): C, 31.14; H, 2.42; N, 4.04. Found: C 30.62; H, 2.61; N, 3.94%. Anal. Calcd for C₂₇H₂₅Er₂N₃O₂₀ (3): C 31.00; H, 2.41; N, 4.02. Found: C 30.47; H, 2.59; N, 4.05%. Selected IR data (KBr disk, cm⁻¹): 3425(br), 1651(s), 1604(s), 1537(s), 1412(s), 1311(w), 1182(w), 862(w), and 786(m) for 1; 3419(br), 1651(s), 1604(s), 1538(s), 1415(s), 1311(w), 1182(w), 862(w), and 786(m) for 2. 3434(br), 1650(s), 1604(s), 1539(s), 1415(s), 1311(w), 1182(w), 862(w), and 786(m) for 3.

2.3. Crystallographic Data Collection and Refinement

All reflections for single crystals of 3 were collected on a Bruker-AXS Kappa Duo diffractometer (Billerica, MA, USA) equipped with an APEX II CCD detector with either Mo Kα (λ = 0.71073 Å). The structure was solved by direct methods through SHELXS-2014 [22] of phase retrieval and then refined by full-matrix least-squares on F² with anisotropic thermal parameters for all non-hydrogen atoms, while the hydrogen atoms were stereochemically positioned and their displacement parameters fixed and set to isotropic [U_iso (H) = 1.2Ueq (CH or NH) or 1.5Ueq (water)]. In addition, some scattered peaks with residual electron density were still observed in the difference Fourier map located in a void for 3. Attempts were made to assign these peaks as nonstoichiometric water molecules; however, checkcif alerts arise, such as short distances with other atoms, like coordination water molecules. Therefore, PLATON/SQUEEZE [23] was used to remove their contribution to the diffraction data. The Mercury [24] and ORTEP-3 [25] programs were used within the WinGX [26] software version 4.0 package to prepare artwork representations. Crystallographic data and refinement parameters of 3 are summarized in

Table 1. X-ray diffraction data collection and refinement parameters for 3.

	3
Empirical formula	C27H25N3O20Er2
Formula weight	1046.02
Crystal system	Monoclinic
Space group	Cc
a/Å	24.290(4)
b/Å	19.873(4)
c/Å	7.4327(13)
β/°	104.998(5)
V/Å3	3465.7(11)
Z	4
T/K	296
Radiation	Mo Kα
Wavelength/Å	0.71073
ρ/g cm−3	2.005
μ//mm−1	4.897
Symmetry factor (Rint)	0.1171
Completeness to θmax/%	98.70
F(000)	2016.0
Refined parameters	272
Reflections collected	6351
R a, wR b [I > 2s(I)]	0.1087, 0.3155
R a, wR b (tall data)	0.1502
S c	1.127
ρmax and ρmin/eÅ−1	2.3400/–4.2300
CCDC	2417034

^a R = S ||F_o| − |F_c||/S |F_o|. ^b wR = [S w(|F_o|² − |F_c|²)²/S w|F_o|²]^1/2. ^c S = [S w(|F_o|² − |F_c|²)²/(n_o − np)]^1/2, where w ∝ 1/s, n_o = observed, and n_p = fitted parameters.

, whereas selected bond distances and angles are listed in Table S2 and Table S3, respectively. All crystallographic data are available from the CCDC. The CCDC number is 2417034 (3).

2.4. Magnetic Measurements

Variable-temperature (2–300 K) direct-current (dc) magnetic susceptibility measurements under an applied magnetic field of 0.5 T and variable-temperature (2–10 K) and variable-field (0–5 T) magnetization measurements were carried out using a Quantum Design Superconducting Quantum Interference Device (SQUID) magnetometer.

Variable-temperature (2–16 K) and variable-field (0–0.25 T) alternating-current (ac) magnetic susceptibility measurements under a ±5.0 Oe oscillating field at frequencies in the range 0.1–10 kHz were performed with a Quantum Design Physical Property Measurement System (PPMS). The magnetic measurements, performed on powdered samples embedded in eicosane to prevent any crystal reorientation, were corrected for the diamagnetism of the constituent atoms and the sample holder.

3. Results

3.1. Syntheses and General Physicochemical Characterization of 1–3

The preparation of 1–3 was performed by slow diffusion in the H tube that yielded X-ray quality single crystals for 3 and polycrystalline samples for 1 and 2. All of them were also prepared using the precipitation method with good yields. The infrared spectra of the complexes can be seen in Figure S1. All compounds present characteristic bands of the ligand such as stretching of the C=O amide bond and C–H and C=C phenyl bonds. They also show strong absorptions in the high-frequency region above 3400 cm⁻¹ due to stretching vibrations of the O–H bond of crystallization and coordination water molecules involved in hydrogen bonding. At the same region, superimposed on the broad O–H stretching band, it is possible to observe a narrow band of N–H stretching, thus being an indication that the nitrogen of the oxamate group is not involved in metal coordination. The PXRD patterns for the polycrystalline samples of 1–3 (Figure 1) indicated that all compounds were isostructural, possessing the same structure of 3 described below, and confirmed the phase purity of the compounds.

The TG curves (Figure S2) of 1–3 are similar. They lose about 10% of their weight up to 170 °C, which can be attributed to the loss of six water molecules [calculated/found = 10.2/10.9 (1), 10.2/10.5, (2) and 10.1/9.7 (3)]. This first mass loss is followed by an almost plateau up to 350 °C. Two major mass losses occur between 350 and 450 °C due to the decomposition of the anhydrous phases. The final waste from thermal decomposition can be attributed to the respective lanthanide oxides (Ln₂O₃).

The electronic spectra in the UV-vis-NIR region of 1–3 were collected at room temperature (Figure S3). The diffuse reflectance spectra display characteristic absorption lines of 4f transitions [27,28,29] of the Dy^III, Ho^III and Er^III ions [1: ⁶H_15/6 → ⁶H_7/6 + ⁶F_9/2 (1106 nm), ⁶H_15/6 → ⁶F_7/2 (910 nm), ⁶H_15/6 → ⁶F_5/2 (807 nm), ⁶H_15/6 → ⁶F_3/2 (756nm), ⁶H_15/6 → ⁴F_9/2 (474 nm), ⁶H_15/6 → ⁴I_15/2 (463 nm), and ⁶H_15/6 → ⁴G_11/2 (427 nm); 2: ⁵I₈ → ⁵I₆ (1159 nm), ⁵I₈ → ⁵I₅ (897 nm), ⁵I₈ → ⁵I₄ (753 nm), ⁵I₈ → ⁵F₅ (643 nm), ⁵I₈ → ⁵S₂ (538 nm), ⁵I₈ → ⁵F₄ (486 nm), ⁵I₈ → ⁵F₃ (474 nm), ⁵I₈ → ⁵F₂ (468 nm), ⁵I₈ → ⁵G₆ (450 nm), ⁵I₈ → ⁵G₅ (418 nm), ⁵I₈ → ⁵G₄ (386 nm), and ⁵I₈ → ³K₇ (382 nm); 3: ⁴I_15/2 → ⁴I_11/2 (980 nm), ⁴I_15/2 → ⁴I_9/2 (802 nm), ⁴I_15/2 → ⁴F_9/2 (652 nm), ⁴I_15/2 → ⁴S_3/2 (544 nm), ⁴I_15/2 → ⁴H_11/2 (520 nm), ⁴I_15/2 → ⁴F_7/2 (488 nm), ⁴I_15/2 → ⁴F_5/2 (451 nm), ⁴I_15/2 → ⁴F_3/2 (444 nm), ⁴I_15/2 → ⁴H_9/2 (407 nm), and ⁴I_15/2 → ⁴G_11/2 (378 nm)].

3.2. Description of the Structure of 3

The crystallographic results reveal that 3 crystallizes in the monoclinic Cc space group and forms zig–zag chains parallel to the crystallographic b axis [101] direction, as shown in Figure 2. The asymmetric dinuclear unit, shown in Figure 2a, consists of two crystallographically independent Er^III ions (Er1 and Er2), three anionic Hpcpa²⁻ ligands, and five coordinated water molecules. The Er1 and Er2 ions exhibit eight-coordination, with three (Er1) or two (Er2) water molecules, four (Er1) or three (Er2) carboxylate oxygen atoms, and one (Er1) or two (Er2) amide oxygen atoms, defining a geometry intermediate between triangular dodecahedron (D_2d), square antiprism (D_4d), and biaugmented trigonal prism (C_2v), as determined by the SHAPE program (see Table S1). The Er1−O bond lengths range from 2.24(3) to 2.63(3) Å, while the Er2−O bond lengths range from 2.27(3) to 2.58(3) Å (see Table S2). Additionally, the Er^III−O (water) and Er^III−O (oxamate) distances are consistent with previously reported structures. The O−Er^III−O bond angles range from 60.4(8)° to 147.9(10)° (see Table S2). These angles were comparable with related compounds reported in the literature.

Double syn−syn carboxylate(oxamate) groups connect Er1 and Er2 into pairs within each chain, the erbium−erbium separation being 4.961(4) Å for Er1···Er2. These dinuclear units are, in turn, interlinked by three Hpcpa²⁻ ligands, one of them through the μ-κ²O,O’:κO’’ coordination mode and the other two across the μ₃-κ²O,O′:κO″:κO‴ one, resulting in neutral 1D CPs (Figure 2b). Two root mean square deviation (rmsd) planes were fitted through the atoms that connect the erbium cations across the oxamate bridge in the double syn−syn conformation cited above. The planes were defined as A and B and fitted through the C6B,C9B,O4B,O5B and C6C,C9C,O4C,O5C sets of atoms, respectively.

Within the resulting triple-stranded moieties, the values of the metal–metal distances through these extended μ-κ²O,O′:κO″- and μ₃-κ²O,O′:κO″:κO‴-Hpcpa²⁻ bridges are 10.152(2), 12.227(5), and 12.220(6) Å for Er1···Er2ⁱ, Er1···Er1ⁱ and Er2···Er2ⁱ [symmetry operations (ⁱ): = ½ + x, ½ − y, ½ + z], respectively (Figure 2c). Additionally, the interaction between two parallel chains through hydrogen bonds and π−π interactions results in a supramolecular 2D network (Figure 3) in which the shortest interlayer contact between the erbium atoms is 6.075(3) Å [Er1 and Er2ⁱⁱ, symmetry operations (ⁱⁱ): = x, −y, ½ + z]. These π−π interactions occur along the crystallographic c axis with values of the distance between centroids of 3.717 (2) Å (see Figure 3a).

The interaction between two chains is established by hydrogen bonds interactions, which occur along the b and c axes. The connection between two chains through O−H···O hydrogen bonds along the b axis can be observed in Figure 3. These intermolecular interactions involve oxygen atoms belonging to coordinated water molecules (O1W, O2W, O3W, O4W, and O5W) and oxamate oxygen atoms (O1B and O2B). The connection between the chains is also observed along the c axis (Figure 3b). These interactions involve coordinated water molecules (O1W, O2W, O4W, and O5W) and oxamate oxygen atoms (O1A, O2A, O5A, and O2C). The molecular contacts include O−H···O interactions that are mainly established by water molecules and oxamate oxygen atoms. The geometric parameters of the hydrogen bond interactions for 3 are summarized in Table S3.

3.3. Magnetic Properties of 1–3

The dc magnetic properties of 1–3 in the form of the χ_MT vs. T plots [where χ_M represents the dc magnetic susceptibility per two lanthanide(III) ions] are presented in Figure S4. At 300 K, the χ_MT values are 27.0 (1), 27.3 (2), and 21.5 cm³ mol⁻¹ K (3). Such values are close to the calculated value for two magnetically isolated Ln^III ions with ⁵I₈ (Ln = Ho), ⁶H_15/2 (Ln = Dy), and ⁴I_15/2 (Ln = Er) ground states, well separated from the low-lying excited states. Then, χ_MT decreases with decreasing temperature due to the thermal depopulation of the M_J states resulting from the ligand field (LF) splitting, reaching values of 15.1 (1), 10.0 (2) and 9.3 cm³ mol⁻¹ K (3) at 1.9 K. However, the occurrence of antiferromagnetic interactions between the Ln^III ions through the double syn−syn carboxylate bridge cannot be discarded [16]. The normalized isothermal magnetization (M vs. H/T) curves do not superimpose below 10 K in agreement with the strong magnetic anisotropy of these ions, as shown in the inset of Figure S4.

The ac magnetic properties of 1–3 were investigated under different applied dc magnetic fields (H = 0, 0.1 and 0.25 T). Their behaviors are shown in Figure 4, Figures S5 and S6 in the form of χ_M′ and χ_M″ vs. T or ν plots [χ_M′ and χ_M″ being the in-phase and out-of-phase ac molar magnetic susceptibilities per two lanthanide(III) ions, T the temperature, and ν the frequency of the oscillating ac field]. Even though the static dc magnetic properties of 1–3 are similar, that is not the case concerning their dynamic ac magnetic properties. Neither the frequency dependence of χ_M′ nor a χ_M″ signal was observed for 2. However, slow magnetic relaxation phenomena occur in 1 and 3. While in 3, only field-induced incipient signals of χ_M′ and χ_M″ are observed by applying a H, 1 exhibits frequency- and temperature dependence of the χ_M′ and χ_M″ even in the absence of H, which varies significantly by changing the T, ν, or H. Only incipient χ_M″ signals are observed for 1 under H = 0 or 0.1 T [Figure 4a,b(right)], while χ_M″ maxima arise under H of 0.25 T [Figure 4c(right)]. For instance, these maxima slightly shift toward higher temperatures with increasing ν from 0.1 to 1 kHz but revert with the further increase in ν up to 10 kHz. This uncommon behavior noted for the χ_M″ vs. T plots was described by Boča and collaborators as a phenomenological “reciprocating thermal behavior” due to a “strange” relaxation mechanism [30].

Unfortunately, the incipient nature of the data prevented accurate analysis of most of the ac magnetic measurements. Thus, only the magnetic relaxation time (τ) values for 1 at H = 0.25 T were extracted by fitting the χ_M′ and χ_M″ vs. ν plots through the generalized Debye model [31]. They are shown as an Arrhenius plot in Figure 5. At higher temperatures (above 5 K), the experimental data follow an Arrhenius law of a thermally activated magnetic relaxation process referring to the climbing of the energy barrier to spin reversal. However, below 5 K, the relaxation process speeds up again upon cooling, and the “strange” mechanism becomes a more efficient path for the spin reversal. So, the experimental relaxation times can be satisfactorily simulated through a model that considers a two-phonon Orbach mechanism [τ⁻¹ = τ₀⁻¹ exp(−U_eff/k_BT)] plus a “strange” one [τ⁻¹ = FT ^−k, with k > 0]. The best-fit values of τ₀ and U_eff [1.50(3) × 10⁻⁶ s and 14.81(13) cm⁻¹] are within the range found in other Dy(III) compounds [32]. Meanwhile, the found values of F and k are 1.96(4) × 10⁶ K^k s⁻¹ and 4.2(2), respectively. Only two examples were reported in the literature: a dinuclear {Ni^IIGd^III} complex with a Schiff’s Base ligand and a Dy^III chain represented by the formulas [Ni(vanen)Gd(H₂O)Cl₃] and [Dy(DPOA)(NO₃)(H₂O)₂]_n·nH₂O. For the Dy compound, the reported parameters related to the “strange” mechanism [τ⁻¹ = FT ^−k, with k > 0] are F = 1.0 × 10⁴ K^k s⁻¹ and k = 2.8, values comparable to those found for compound 1 in our work [30]. Still, it is hard to argue on those “strange” parameters since, to date, this type of relaxation mechanism has only a phenomenological meaning.

3.4. Magnetocaloric Properties of 1–3

The magnetocaloric effect (MCE) of 1–3 has been investigated by variable-temperature (T = 2–10 K) and variable-field (H = 0–5 T) magnetization measurements (see Section 2). The field and temperature dependence of the magnetic entropy change (ΔS_m) upon connecting the magnetic field (ΔH = H − H₀ with H₀ = 0) has been estimated from the M vs. H and T plots (M being the gravimetric magnetization) according to the Maxwell equation (Figure 6), as reported elsewhere [33,34].

The –ΔS_m vs. H and T plots show a monotonic increase with decreasing the temperature or increasing the field for 1 and 3 (Figure 6a and c, respectively), whereas 2 evidences a decrease upon cooling further for T < 5 K with the progressive development of a maximum from 3 up to 6 K for ΔH > 2 T (Figure 6b). Interestingly, the –ΔS_m maxima for 2 occur for ΔH > 2 T, whereas it does not show slow magnetic relaxation effects above 2 K. In contrast, no –ΔS_m maxima are observed for 1 and 3 for ΔH < 5 T, evidencing thus that the blockage of the magnetization that occurs at low temperatures under the application of a weak dc magnetic field [T_B < 4.5 (1) and 3.5 K (3) for H = 0.025 T] does not preclude the observation of a significant MCE along this series.

The maximum –ΔS_m value in gravimetric units for ΔH = 5 T increases from 2 to 1 and 3 [9.4 (1)/6.6 (2)/9.7 J kg⁻¹ K⁻¹ (3) at T = 2 (1)/6 (2)/2 K (3)], being comparable to those of the gadolinium(III)–gallium(III) garnet used as commercial cryogenic material [–ΔS_m = 6.5 and 28.0 J kg^–1 K^–1 at T = 2 and 10 K, respectively, for ΔH = 8 T] [35]. Moreover, the corresponding –ΔS_m value for ΔH = 1 T [5.8 (1)/1.4 (2)/4.4 J kg⁻¹ K⁻¹ (3) at T = 2 (1)/6 (2)/2 K (3)] reaches up to 62 (1), 21 (2), and 45% (3) of the maximum –ΔS_m value. This relatively weak magnetic field is close enough to the stronger field to be achieved with the standard permanent magnets used commercially (ranging from 0.5 to 1 T for ceramic magnets and up to 1.4 T for neodymium ones). These two features (high magnetic entropy changes and large slope of the corresponding isothermal magnetic entropy variation curves) are mandatory for potential applications in CMR.

The overall enhancement of the MCE in the order 2 < 1 ≈ 3 is likely explained by the larger magnetic anisotropy of the 4f¹⁰ Ho^III ion (⁵I₈) compared to the 4f⁹ Dy^III (⁶H_15/2) and 4f¹¹ Er^III (⁴I_15/2) ions, despite the larger J value in the former case. Indeed, the maximum –ΔS_m values in molar units [9.7 (1)/6.9 (2)/10.1 J mol⁻¹ K⁻¹ (3) at T = 2 (1)/6 (2)/2 K (3) for ΔH = 5 T] are somewhat lower than the limiting values for two magnetically isolated Ln^III ions with no zero-field splitting (zfs) [–ΔS_m = 2Rln(2J + 1) = 46.1 (Dy)/47.1 (Ho)/46.1 J mol⁻¹ K⁻¹ (Er) with J = 15/2 (Dy), 8 (Ho), and 15/2 (Er)]. By comparison, the –ΔS_m values in molar units (per mol of lanthanide atom) [3.0 (1)/0.7 (2)/2.3 J mol⁻¹ K⁻¹ (3) at T = 2 (1)/6 (2)/2 K (3) for ΔH = 1 T] are similar to those reported for the gadolinium(III)–gallium(III) garnet and its dysprosium(III)-substituted derivatives of general formula (Dy_xGd_1-x)₃Ga₅O₁₂ [x = 0 (GGG), 0.5 (DGGG), and 1 (DGG)] [–ΔS_m = 3.1–3.3 J mol⁻¹ K⁻¹ at T = 5 K for ΔH = 2 T] [36].

In this respect, the MCE efficiencies for 1–3 are comparable to those of related magnetically anisotropic lanthanide(III) metal–organic frameworks (MOFs) and its mixed gadolinium(III)-substituted heterometallic derivatives of general formula [(Ln_xGd_1-x)(HCO₂)₃]_n, [(Ln_xGd_1-x)(HCO₄)]_n, [(Ln_xGd_1-x)₃(ad)_4.5(DMF)₂]_n, and [(Ln_xGd_1-x)₃(cb)₄(NO₃)(DMF)_y]_n [ad = adipate and cb = 1,7-di(4-carboxyphenyl)-1,7-dicarba-closo-dodecaborane with Ln = Eu, Tb, Dy, Ho, Er (x = 0–1)], which have been recently proposed as efficient molecular cryomagnetic refrigerants [37,38,39,40,41] in place of traditional purely inorganic intermetallic alloys and oxides, such as mixed lanthanide-transition metal antimonides and tellurides, Ln₆MSb₂ and Ln₆MTe₂ (Ln = Gd, Tb, and Dy; M = Mn, Fe, Co, and Ni), or lanthanide–gallium garnets, Ln₃Ga₅O₁₂ (Ln = Gd, Tb, Dy, and Nd) [42,43].

4. Conclusions

The magnetic properties of 1–3 are very variable. Although the dc magnetic susceptibility measurements reveal similar trends for all compounds, the ac magnetic properties diverge, with only compounds 1 and 3 displaying slow magnetic relaxation phenomena. The temperature- and frequency-dependent ac susceptibility behavior in 1 is especially remarkable due to a “strange” relaxation mechanism, which has been phenomenologically described but not fully understood to date. This isostructural series of oxamato-based Ln^III CPs also exhibits weak (Ln = Ho) to moderate (Ln = Dy and Er) MCE with magnetic entropy change maxima at relatively high temperatures (Ln = Ho), far above He liquefaction.

These findings reinforce the potential of lanthanide-based compounds as efficient molecular cryomagnetic refrigerants, comparable to traditional materials such as gadolinium–gallium garnets, as new optional materials for magnetic refrigeration technology. Further exploration of the “strange” relaxation mechanism and its impact could lead to new insights in understanding some enigmatic features of the slow magnetic relaxation phenomena.