Cyano-bridged {Ln₂^IIIFe₂^III} molecular squares (Ln = Gd, Tb, Dy, Ho, and Er): tuning the slow magnetic relaxation and magnetocaloric effects in zero-dimensional lanthanide Prussian blue analogues

Abstract

An isostructural series of neutral cyano-bridged tetranuclear iron(III)–lanthanide(III) complexes of general formula {[Fe(htpzb)(CN)(μ-CN)₂]₂[Ln(dmbpy)(NO₃)₂(H₂O)]₂}·2CH₃CN·2H₂O [Ln = Gd (1), Tb (2), Dy (3), Ho (4), and Er (5); htpzb = hydrotris(pyrazolyl)borate and dmbpy = 4,4′-dimethyl-2,2′-bipyridine] was synthesized and structurally and magnetically characterized. Single-crystal X-ray analysis of 1–5 revealed the formation of neutral cyano-bridged {Fe^III₂Ln^III₂} complexes (Ln = Gd, Tb, Dy, Ho, and Er) of square-like topology that crystallize in the triclinic P1̄ space group. Solid-state direct-current magnetic susceptibility analysis evidenced weak intramolecular antiferromagnetic Fe^III–Ln^III interactions in 1 (Ln = Gd) together with large local magnetic anisotropies from the Ln^III ion in 2–5 (Ln = Tb, Dy, Ho, and Er). Frequency-dependent alternating current magnetic susceptibility signals occurred for 1–5 under an applied dc magnetic field of H = 1.0 (1) or 0.5 T (2–5), indicating field-induced slow magnetic relaxation effects typical of single-molecule magnets. Depending on the non-Kramer (Tb, Ho) or Kramer (Gd, Dy, Er) nature of the Ln^III ion, a single magnetic relaxation process via Orbach or Raman mechanism (2 and 4) or a multiple magnetic relaxation process that combines Orbach or Raman plus quantum tunneling of magnetization and/or direct (1, 3, and 5) mechanisms occurred along this series. 1–5 showed large magnetocaloric effects with a high to moderate maximum value of the magnetic entropy change at optimum working temperatures just above He liquefaction [−ΔS_max = 16.51 (1), 5.42 (2), 6.02 (3), 4.56 (4), and 5.86 J kg⁻¹ K⁻¹ (5) for H = 5 T at T_opt = T_max = 2 (1), 4 (2, 3 and 5), and 6 K (4)], as well as a high to moderate magnetocaloric index at rather low optimum working fields [MCI = 6.4 (1), 3.3 (2), 4.7 (3), 0.9 (4), and 3.6 J kg⁻¹ K⁻¹ T⁻¹ (5) for H_opt = H_max = 1.0 (1), 0.6 (2), 0.4 (3), 0.8 (4), and 0.6 T (5) at T = 2 K].

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Introduction

Cyano-bridged metal complexes represent a dynamic and resourceful class of multifunctional molecular materials unveiling new facets that have continuously expanded their area of application in thermo-,^1–3 photo-,^4,5 and electrocatalysis,⁶ host–guest chemistry,⁷ energy storage,^8–10 optical sensing,¹¹ and thermometry¹² among others. More specifically, magnetic molecules containing transition metal ions linked by the light, asymmetric CN⁻ ligand, with a strong σ-donor and π-acceptor character, have been particularly attractive in magnetochemistry, as unique examples of cyano-bridged mixed-3d/nd molecule-based magnetic materials, so-called low-dimensional Prussian blue analogues (PBA).^13,14 In the past decade, however, the interest in this field is moving toward the related rare-earth hexacyanometallate derivatives, referred to as lanthanide Prussian blue analogues (Ln PBA).^15–23 This family of neutral or anionic cyano-bridged mixed-3d/4f molecule-based magnetic materials combine the intrinsic chemical versatility and structural stability of PBAs with the magnetic and magnetocaloric or optical (luminescent) properties of the lanthanide ions along with the redox and/or catalytic activities of the diamagnetic or paramagnetic first-row transition metal ions (and, occasionally, the organic ligands).

The high-spin ground state together with the large magnetic anisotropy exhibited by the majority of the lanthanide(III) ions, other than gadolinium(III), are crucial factors for the occurrence of the slow magnetic relaxation (SMR) effects in single-ion/molecule/chain magnets (SIM/SMM/SCM).^21–23 Otherwise, the isotropic gadolinium(III) ion, with a large spin ground state (S_Gd = 7/2), has been intensively exploited in molecular magnetic coolants because of its large magnetocaloric effects (MCE). Lanthanide metal complexes have therefore become promising components in the development of emerging technologies like quantum information processing (QIP) or molecular spintronics,^24,25 and adiabatic demagnetization refrigeration (ADR).^26–29 The assembly of high-nuclearity isotropic Gd^III complexes or mixed M^III–Gd^III derivatives, with a large change of magnetic entropy (−ΔS_m) with the magnetic field sweeps (ΔH) at ultra-low temperature (below liquid He) is an important topic in ADR.^26–29 Conversely, the anisotropic Ln³⁺ complexes were rarely investigated in conventional ADR.^30–39 Likewise, the nd/4f heterometallics were appealing for the investigation of MCE,^40–42 and the cyano-bridged complexes of transition and lanthanide(III) cations provide a largely unexplored area of study.⁴³

The rich library of heteroleptic polycyanometallate mononuclear complexes, with two-/three-/four- and five CN⁻ groups substituted with several blocking ligands, was the subject of several review papers^44–51 that highlighted their efficiency in acting as metalloligands to obtain low-dimensional heterobi-^44–49 and trimetallic cyano-bridged nd/nd′ coordination compounds.^50,51 In contrast, cyano-bridged 3d/4f coordination compounds were much less studied. For example, the reaction of tri- or tetracyanometallates with Ln³⁺ ions, capped with solvent molecules or chelating ligands, afforded a large variety of low-dimensional Ln PBAs, from: 0D oligonuclear complexes,^52,53 1D^54–56 and 2D⁵⁶ coordination polymers. Focusing on cyano-bridged 3d/4f tetranuclear complexes, only the low-spin (LS) [Fe^III(bpy)(CN)₄]⁻ (bpy = 2,2′-bipyridine)⁵³ as well as [Fe^III(htpzb)(CN)₃]⁻ complex anions [htpzb = hydrotris(pyrazolyl)borate]^57–60 led to square-like {Fe^III(LS)₂Ln^III₂} motifs. Our work on cyano-bridged molecular squares brought magnetic insights for the related series of general formula {[Fe^III(htpzb)]₂[Ln^III(NO₃)_x(pyim)_y(Ph₃PO)_z]₂} [Ln = La (x = 1, y = 2, z = 0); Ln = Gd, Tb, and Dy (x = 1, y = 1, z = 0); Ln^III = Ce, Eu, Sm, Pr, Nd, Gd, Tb, Dy, and Er (x = 1, y = 1, z = 1); pyim = 2-(1H-imidazol-2-yl)pyridine; Ph₃PO = triphenylphosphine oxide] showing a weak antiferromagnetic exchange interaction between Fe^III(LS) and Ln^III ions through the cyanide bridge (Ln = Eu, Sm, Nd, Gd, Tb, Dy, and Er).^57–59 SMR occurred for the Tb³⁺, Dy³⁺ and Er³⁺ derivatives including pyim and PPh₃O as capping ligands, showing how small changes in the Ln^III coordination sphere can suppress quantum tunneling effects to generate 3d/4f SMMs.⁵⁹

Cyano-bridged 3d/4f square-like motifs were also assembled from ion(III) hexacyanometallates and Ln(III) ions capped with bidentate o-phenatroline or tridentate 2,2′:6′,2″-terpyridine ligands.^61–63 However, the simultaneous employment of two structure control elements, tricyanometallates as bis-monodentate angular connector and auxiliary bidentate blocking ligands (e.g., pyim) on coordination sites of Ln^III ions to prevent polymerization, proved to be a robust approach to achieve cyano-bridged mixed-3d/4f squares as unique examples of 0D Ln PBAs. Besides, the inclusion of an additional flexible coligand (e.g., Ph₃PO) allowed the fine tuning of the lanthanide(III) environment that could further influence the magnetic behavior of the tetranuclear square complex. Therefore, we envisaged to extend the cyano-bridged square-shaped family of {Fe^III(LS)₂Ln^III₂} complexes by using sterically hindered bipyridine-type chelating organic molecules as capping ligands of Ln^III coordination sites. Herein, we report on the new cyano-bridged square-shaped tetranuclear complexes of general formula {[Fe(htpzb)(CN)(μ-CN)₂]₂[Ln(dmbpy)(NO₃)₂(H₂O)]₂}·2CH₃CN·2H₂O [Ln = Gd (1), Tb (2), Dy (3), Ho (4), and Er (5); htpzb = hydrotris(pyrazolyl)borate and dmbpy = 4,4′-dimetyl-2,2′-bipyridine]. Besides the static and dynamic magnetic properties, we also examined the magnetocaloric properties of 1–5 to determine the influence of the nature of the Ln^III ion (Ln = Gd, Tb, Dy, Ho, and Er) on the spin dynamics and thermodynamics of the resulted {Fe^III(LS)₂Ln^III₂} complexes.

Experimental

Materials

Ln(NO₃)₃·6H₂O, dmbpy and acetonitrile were purchased from commercial sources and used as received. Ph₄P[Fe(htpzb)(CN)₃]·H₂O was prepared as described in the literature.⁶⁴

Synthesis of the compounds

1–5 were prepared by following the same general method: an acetonitrile solution (20 cm³) of Ph₄P[Fe(htptz)(CN)₃]·H₂O (0.067 mmol) was poured into an acetonitrile solution (20 cm³) containing dmbpy (0.067 mmol), and the corresponding lanthanide salt, Ln(NO₃)₃·xH₂O (0.067 mmol) [Ln^III = Gd, 1 (x = 6); Tb, 2 (x = 6); Dy, 3 (x = 5); Ho, 4 (x = 6); Er, 5 (x = 6)]. The slow evaporation of the resulting red-orange solutions at room temperature afforded red-colored plates of 1–5 after one week. All the isolated crystalline products were air stable. Yield: 50 (1), 45 (2), 60 (3), 40 (4), 80 (5). Anal. calcd for C₅₂H₅₈N₂₈B₂O₁₆Fe₂Gd₂ (1): C, 35.07; H, 3.26; N, 22.03; found: C, 35.31; H, 3.28; N, 22.14%. C₅₂H₅₈N₂₈B₂O₁₆Fe₂Tb₂ (2): C, 35.00; H, 3.25; N, 22.67; found: C, 35.30; H, 3.19; N, 22.63%. C₅₂H₅₈N₂₈B₂O₁₆Fe₂Dy₂ (3): C, 34.86; H, 3.24; N, 21.90; found: C, 35.04; H, 3.19; N, 22.06%. C₅₂H₅₇N₂₈B₂O_15.5Fe₂Ho₂ (4): C, 34.94; H, 3.19; N, 21.95; found: C, 35.03; H, 3.15; N, 22.08%. C₅₂H₅₇B₂N₂₈O_15.5Fe₂Er₂ (5): C, 34.85; H, 3.18; N, 21.89; found: C, 34.89; H, 3.14; N, 21.95%. Selected IR peaks (cm⁻¹, KBr pellets): 2149(m) (1), 2153(s) and 2123(m) (2), 2153(s) and 2122(m) (3), 2155(s) and 2123(m) (4, 5) [ν(C≡N)].

Physical techniques

Elemental analyses (C, H, N) and energy dispersive X-ray (EDX) analyses (Fe, Ln) for 1–5 were performed using a PerkinElmer 2400 analyzer and a Philips XL-30 scanning electron microscopy (SEM), respectively. The infrared spectra of 1–5 were recorded on a FTIR Bruker Tensor V-37 spectrophotometer using KBr pellets in the range 4000–400 cm⁻¹. UV-Vis spectra (diffuse reflectance technique) were recorded on a 220–1000 nm domain with a JASCO V-770 spectrophotometer, using MgO as the standard. Powder X-ray diffraction (XRD) measurements of powdered samples of 1–5 were collected at room temperature on a D8 Advance A25 Bruker diffractometer using graphite-monochromated Cu-K_α radiation (λ = 1.54056 Å).

Magnetic measurements

Direct current (dc) magnetic susceptibility and magnetization measurements were carried out on crushed crystals of 1–5 (mixed with grease to avoid any crystallite orientation) by using a Quantum Design MPMSXL-5 SQUID magnetometer. The dc magnetic susceptibility measurements were performed in the temperature ranges 2.0–300 K and under applied dc magnetic fields of 0.5 (T > 25 K) and 0.01 T (T ≤ 25 K) to prevent for saturation effects at low temperature. Magnetization measurements were performed in the temperature and field ranges of 2.0–10 K and 0–5 T, respectively, under steps of 1 K and 0.2 T. Alternating current (ac) magnetic susceptibility measurements were recorded with a Quantum Design Physical Property Measurement System (PPMS) in the temperature range 2.0–10 K under ±3.95 G oscillating field at frequencies in the range 1.0–10.0 kHz, both in zero dc field and under applied dc fields of 1.0 (1) or 0.5 T (2–5). The magnetic susceptibility data were corrected for the diamagnetism of the constituent atoms and the sample holder (a plastic bag).

Crystallographic data collection and structure determination

Crystallographic measurements for 1–5 were carried out with an Oxford-Diffraction XCALIBUR E CCD diffractometer equipped with graphite-monochromated Mo Kα radiation. The unit cell determination and data integration were carried out using the CrysAlisPro package from Oxford Diffraction.⁶⁵ The structures were solved with SHELXT program using the intrinsic phasing method and refined by the full-matrix least-squares method on F² with SHELXL.^66,67 Olex2 was used as an interface to the SHELX programs.⁶⁸ Non-hydrogen atoms were refined anisotropically. Hydrogen atoms attached to carbon were added in idealized positions and refined using a riding model. The hydrogen atoms of the OH groups were located from difference Fourier maps and their positions were refined in agreement with the H-bonds parameters. The main crystallographic data together with structure solution and refinement details are summarized in Table 1 and the corresponding CIF-files. The structural images were obtained with the Diamond 4 program.⁶⁹ The unit cell parameters and refinement conditions for 1–5 are given in Table 1. CCDC 2504399 (1), 2504400 (2), 2504401 (3), 2504402 (4), 2504403 (5).

Table 1 Crystallographic data and structure refinement parameters for 1–5

	1	2	3	4	5
Formula	C52H58N28B2O16Fe2Gd2	C52H58N28B2O16Fe2Tb2	C52H58N28B2O16Fe2Dy2	C52H57N28B2O15.5Fe2Ho2	C52H57B2N28O15.5Fe2Er2
Fw	1779.08	1782.42	1789.58	1785.43	1790.09
T [K]	180.05(10)	159.8(10)	149.9(2)	293(2)	293(2)
Space group	P1̄	P1̄	P1̄	P1̄	P1̄
a [Å]	11.6608(4)	11.6335(4)	11.6345(4)	11.6557(3)	11.6406(4)
b [Å]	11.7464(3)	11.7416(5)	11.7335(4)	11.8334(3)	11.8371(4)
c [Å]	13.5504(4)	13.4857(4)	13.4726(5)	13.6036(6)	13.5872(5)
α [°]	72.921(2)	72.912(3)	72.844(3)	72.838(3)	72.779(3)
β [°]	77.362(3)	77.393(3)	77.299(3)	77.133(3)	77.078(3)
γ [°]	74.728(3)	74.761(3)	74.785(3)	74.905(3)	74.954(3)
V [Å^3]	1691.28(9)	1678.88(12)	1675.39(11)	1709.13(11)	1704.96(11)
Z	1	1	1	1	1
ρcalc [g cm^−3]	1.747	1.763	1.774	1.735	1.743
μ [mm^−1]	2.442	2.591	2.716	2.790	2.937
Crystal size [mm]	0.25 × 0.15 × 0.05	0.15 × 0.1 × 0.03	0.3 × 0.2 × 0.1	0.25 × 0.15 × 0.1	0.3 × 0.3 × 0.25
2θ range	1.8290–28.9430	1.8310–28.7070	1.8650–29.1090	1.8300–25.5280	1.6130–28.5870
Refls collected	14 964	15 418	11 654	12 538	12 593
Indep. refls, Rint	5416, 0.0386	5240, 0.0443	5448, 0.0353	5028, 0.0441	5394, 0.0327
Data/rests/params	5892/0/464	5893/7/475	5882/0/467	6000/0/464	5952/0/464
GOF	1.059	1.029	1.074	1.016	1.039
R1, wR2 (all data)	R1 = 0.0312	R1 = 0.0383	R1 = 0.0353	R1 = 0.0535	R1 = 0.0334
	wR2 = 0.0573	wR2 = 0.0666	wR2 = 0.0627	wR2 = 0.0672	wR2 = 0.0570
CCDC no.	2504399	2504400	2504401	2504402	2504403

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Results and discussion

Synthesis and general physicochemical characterization

The stoichiometric reaction of the anionic [Fe^III(htpzb)(CN)₃]⁻ metalloligand and the preformed [Ln^III(dmbpy)(NO₃)₂(H₂O)]⁺ (Ln = Gd, Tb, Dy, Ho, and Er) complex cation (1 : 1 : 1 Fe^III/Ln^III/dmbpy molar ratio) in acetonitrile solution, at room temperature, afforded X-ray quality crystals of the isostructural series of heterometallic complexes 1–5. They were characterized by elemental (C, H, N) and EDX analyses, as well as FT-IR spectroscopy and powder XRD (see Experimental section).

The estimated value of the Fe : Ln molar ratio for 1–5 from EDX analyses is 1 : 1, in agreement with the proposed chemical formula determined from elemental analyses. The FT-IR spectra of 1–5 are very similar and support the formation of cyano-bridged {Fe^III(LS)₂Ln^III₂} complexes (Fig. S1–S5 in SI), through two distinct broad absorptions peaks at energies ranging from 2149–2155 and 2122–2123 cm⁻¹ corresponding to the stretching vibrations of the bridging and terminal cyanide ligands, respectively, of the [Fe^III(htpzb)(CN)(μ-CN)₂]⁻ units. The C–H stretching and ring stretching modes of htpzb and dmbpy ligands cover the range 2950–2750 cm⁻¹ and 1650–1410 cm⁻¹, respectively. The broad and medium intensity band in the range 2514–2553 cm⁻¹ is characteristic for the B–H stretching vibration from the htpzb ligand. For 1–5, the coordinated nitrato ligands were also identified as a strong and broad absorption at ca. 1384–1387 cm⁻¹, as well as a medium intensity band at ca. 812–816 cm⁻¹.⁷⁰ The solid-state UV-Vis spectra for 1–5 are shown in Fig. S6 in SI and exhibit similar profiles, with a UV band centered at approximately 300 nm, as well as a broad absorption covering the visible region. The intense UV absorption band likely envelops n/π–π* transitions of the dmbpy ligand, as well as ligand-to-metal charge transfer (LMCT) from the cyanide ligands to LSFe^III center.⁷¹ The broad and intense absorption at ca. 600 nm could be generated by LMCT transitions (htpz → LSFe^III, with a shoulder at ca. 430 nm) and metal to ligand charge transfer (MLCT) transitions within the {Fe^III(htpzb)(CN)₃} unit, which likely mask the characteristic, very weak, sharp absorptions of Ln^III ions.

The purity of bulk samples of 1–5 was confirmed by the agreement between their experimental and simulated powder XRD patterns (see Fig. S7–S11 in the SI).

Description of the structures

1–5 are isostructural crystallizing in the triclinic P1̄ space group (Table 1). Selected crystallographic and structural data for 1–5 are given in Tables 1 and 2.

Table 2 Selected intra- and intermolecular distances and angles for 1–5

	1	2	3	4	5
a Symmetry codes: (a) = 1 − x, 1 − y, 1 − z (1, 3–5), 1 − x, 1 − y, 2 − z (2); (b) = 1 + x, y, z (1, 3–5), −1 + x, y, z (2); (c) = 1 − x, 1 − y, 2 − z (1, 3–5), 1 − x, 1 − y, 1 − z (2).b br – bridging.c t – terminal.
Ln1–Fe1–Ln1a ^a (°)	96.34	96.18	96.22	97.16	97.16
Fe1–Ln1–Fe1a ^a (°)	83.66	83.82	83.78	82.84	82.84
Fe–Ccyanide (Å)	1.914(3)–1.936(4)	1.921(4)–1.935(5)	1.922(4)–1.941(4)	1.927(6)–1.933(5)	1.929(4)–1.934(4)
Fe–Npyrazolyl (Å)	1.970(2)–1.998(3)	1.968(3)–1.994(3)	1.971(3)–1.997(3)	1.972(4)–1.996(4)	1.974(3)–1.998(3)
(Fe1–C–N)br ^b (°)	176.1(3)/178.3(3)	177.9(4)/175.8(4)	178.5(3)/175.6(4)	175.3(5)/177.0(5)	175.9(3)/178.6(3)
(Fe1–C–N)t ^c (°)	177.1(3)	177.1(3)	176.5(4)	178.5(5)	177.4(4)
Ln1–Ndmbpy (Å)	2.486(3)/2.549(2)	2.467(3)/2.528(3)	2.454(3)/2.515(3)	2.448(4)/2.514(4)	2.427(3)/2.503(3)
Ln1–Onitrate (Å)	2.483(2)–2.522(2)	2.479(3)–2.512(3)	2.433(3)–2.508(3)	2.416(3)–2.516(3)	2.406(2)–2.512(2)
Ln1–O1 W (Å)	2.412(2)	2.386(3)	2.380(2)	2.384(3)	2.368(2)
(Ln1–Ncyanide)br ^b (Å)	2.454(3)/2.466(3)	2.449(3)/2.439(3)	2.440(3)/2.422(3)	2.409(5)/2.437(4)	2.403(3)/2.435(3)
(Ln1–N–C)br ^b (°)	168.7(3)/173.0(3)	168.8(3)/173.6(3)	169.3(3)/174.3(3)	171.3(4)/175.1(4)	171.0(3)/174.2(3)
Fe1⋯Ln1/Fe1a⋯Ln1 ^a (Å)	5.50	5.48/5.49	5.47/5.48	5.47/5.50	5.46/5.49
(π⋯π)pyrazolyl (Å/°)	3.60 Å/13.59	3.39 Å/17.37 and 17.38	3.39 Å/17.46	3.44/19.12	3.44/19.08
(π⋯π)dmbpy (Å/°)	3.80/23.57, 22.19	3.80/22.31, 23.98	3.80/22.64, 24.35	3.90/23.75, 24.76	3.91/24.09, 24.93
(C–H⋯π)pyrazolyl (Å)	2.72 Å	2.78	2.79	2.87	2.88
Fe1⋯Fe1b via (π⋯π)pyrazolyl contacts^a (Å)	7.73	8.01	8.02	8.13	8.14
Ln1⋯Ln1c (H-bonds)^a (Å)	6.53	6.51	6.50	6.56	6.56

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The crystal structure of 1–5 consists of a neutral, centrosymmetric cyano-bridged heterotetranuclear unit of square topology, {[Fe(htpzb)(CN)(μ-CN)₂]₂[Ln(dmbpy)(NO₃)₂(H₂O)]₂} [Ln = Gd (1), Tb (2), Dy (3), Ho (4), and Er (5)] (see Fig. 1 and Fig. S12a–S15a in SI), together with two acetonitrile and two water molecules of crystallization. Bond lengths and angles for 1–5 are gathered in Tables S1 and S2 in SI. Water and acetonitrile crystallization molecules are connected through O–H⋯O and O–H⋯N hydrogen bonds to the terminal CN⁻ and NO₃⁻ ligands (Fig. S12a–S15a in SI).

Fig. 1 (a) View of the square-shaped cyano-bridged heterotetranuclear unit in 1 together with the atom labelling scheme [symmetry code: (a) = 1 − x, 1 − y, 1 − z]. The water and acetonitrile crystallization molecules were omitted for the sake of clarity. (b) The octahedral surrounding of Fe^III ion. (c) Distorted tricapped trigonal prism geometry of Gd^III ion.

The {Fe^III₂Ln^III₂} entity in 1–5 is assembled from two bis-monodentate, anionic [Fe^III(htpzb)(CN)(μ-CN)₂]⁻ and two coordinatively unsaturated, cationic [Ln^III(dmbpy)(NO₃)₂(H₂O)]⁺ units. The cis-orientation of two CN⁻ bridging ligands of the fac-[Fe^III(htpzb)(CN)₃]⁻ complex anion, together with the complementary labile/free coordination sites on [Ln^III(dmbpy)(NO₃)₂(H₂O)]⁺ complex cation, gave rise to a cyclic distorted square-shaped molecule, the two Fe^III and Ln^III ions filling alternatively the corners of the square. The Ln1–Fe1–Ln1a and Fe1–Ln1–Fe1a angles in 1–5 vary in the ranges 96.18–97.16 and 82.84–83.82°, respectively, the degree of rhombic distortion being consistent with previous reports.^53,57–59

Each crystallographically independent iron(III) ion from 1–5 is six-coordinated by three carbon atoms belonging to CN⁻ ligands, disposed in a fac-arrangement, and three nitrogen atoms from the three pyrazolyl rings of the htpzb ligand, in a slightly distorted octahedral metal surrounding [CShM = 0.153 (1), 0.156 (2), 0.148 (3), 0.129 (4), and 0.126 (5), see Fig. 1b, Fig. S12b–S15b and Table S3 in SI].^72,73 The Fe–C and Fe–N bond lengths are similar in 1–5, ranging from 1.914(3)–1.941(4) and 1.968(3)–1.998(3) Å, respectively (Table 2). As far as the Fe–C–N angles from the bridging and terminal cyanide ligands are concerned, their values are close to linearity in 1–5, ranging from 175.3(5)–178.6(3) and 176.5(4)–178.5(5)°, respectively (Table 2). All these values related to the iron(III) surrounding are close to those previously reported for the cyano-bearing [Fe^III(htpzb)(CN)₃]⁻ moiety in the related homotetranuclear iron(III) complex.⁷⁴ The two distinct Fe^III⋯Ln^III intermetallic distances through the CN⁻ bridges in 1–5 range between 5.46–5.50 Å (Table 2) which are similar to previously reported cyano-bridged {LSFe^IIILn^III}₂ squares.^53,57–59 On the other hand, each crystallographically independent lanthanide(III) ion in 1–5 is capped by two N atoms from one dmbpy and four O atoms from two nitrato chelating ligands, the coordination sphere being completed by two N atoms from the CN⁻ bridges and one O atom from the aqua ligand (see Fig. 1c, Fig. S12c–S15c and Table S3 in SI).

The donor atoms around the Ln^III ions in 1–5 describe a nine-coordinated polyhedron with a geometry close to distorted tricapped trigonal prism (TCTPR) of D_3h symmetry, estimated through SHAPE 2.1 software [CShM = 1.900 (1), 1.829 (2), 1.774 (3), 1.744 (4), and 1.738 (5), see Table S3 in SI], so that the deviations from ideal TCTPR geometry decrease with increasing the number of 4f electrons along this series (n = 7–11).^72,73

It is worth mentioning that, in the earlier examples of cyano-bridged {LSFe^IIILn^III}₂ squares, the nine-coordinated surrounding of Ln^III ions is either distorted monocapped square antiprism⁵³ or muffin-like.^57–59 The bite angles of the dmbpy and nitrato chelating ligands in 1–5 are within the ranges 64.68(8)–66.22(10) and 51.38(7)–52.66(12)°, respectively (Table 2), being the main source of the polyhedron distortion from ideal tricapped trigonal prism.

The Ln1–N_dmbpy distances in 1–5 are in the range 2.427(3)–2.528(3) Å, being higher than those corresponding to the bridging cyanide ligands in the range 2.403(3)/2.466(3) Å (Table 2). Also, the Ln1–N_dmbpy bond lengths correspond well to the previously published examples including similar fragments.^75–79 The two Ln1–N1–C1 and Ln1–N2a–C2a angles involving the bridging cyanide ligands in 1–5, slightly deviate from linearity, being in the ranges of 168.7(3)–175.1(4)°, as other reports of cyano-bridged {LSFe^IIILn^III}₂ squares.^53,57–59 Also, the Ln1–O1W distance in the range 2.368(2)–2.412(2) Å is shorter than the Ln1–O bond lengths from nitrate that vary in the range 2.406(2)–2.522(2) Å (Table 2, symmetry codes (a) = 1 − x, 1 − y, 1 − z for 1, 3–5 and (a) = 1 − x, 1 − y, 2 − z for 2). Overall, the average values of the Ln1–N_dmbpy, Ln1–N_CN, Ln1–N_nitrate, Ln1–O_nitrate, and Ln1–OW distances decrease with the number of 4f electrons along this series (n = 7–11), as expected from the well-known “lanthanide contraction” phenomenon.

In the crystal lattice of 1–5, the {Fe^III₂Ln^III₂} entities are further interconnected through non-covalent, hydrogen bonding, π⋯π, and C–H⋯π interactions to build a three-dimensional supramolecular network (see Fig. 2 and Fig. S16–S23 in SI). The adjacent {Fe^III₂Ln^III₂} entities are linked via O_aqua–H⋯N and C–H⋯O_nitrate hydrogen bonds involving the crystallization acetonitrile molecules and the peripheral aqua and nitrate ligands, respectively (Table S4 in SI), developing supramolecular double-chains running parallel to the crystallographic a axis (Fig. 2, top and Fig. S16–S19 in SI). Besides, π⋯π and C–H⋯π stacking interactions established between pyrazolyl rings of htpzb ligands belonging to neighboring {Fe^III₂Ln^III₂} entities of 1–5 consolidate the supramolecular double-chains (the centroid⋯centroid distance and the angles between the normal to the ring and the centroid–centroid vector are in the ranges 3.39–3.60 Å and 13.59–19.12°, while the C–H⋯π distances are in the range 2.72–2.88 Å, Table 2). Offset π⋯π stacking interactions are established between the pyridyl rings of the outer dmbpy ligands assembling supramolecular layers in the ac crystallographic plane. The neighboring layers interact further along c axis through H-bonds established between peripheral aqua and nitrate ligands to build a 3D supramolecular network (see Table S3, Fig. 2, bottom and Fig. S20–S23 in SI). The closest intermetallic Fe1⋯Fe1b distance in 1–5 across (π⋯π)_pyrazolyl contacts is in the range 7.73–8.14 Å, whereas the smallest Ln1⋯Ln1c distance across the H-bonds is in the range 6.50–6.56 Å (Table 2).

Fig. 2 Top: View of a fragment of the crystal packing showing the layers formed by O⋯O type H-bonds, C–H⋯π and π⋯π stacking interactions established between the pyrazolyl rings for 1 [one pyrazolyl ring and the terminal cyanide ligand were removed for the sake of clarity, symmetry codes: (a) = 1 − x, 1 − y, 1 − z, (b) = 1 + x, y, z]. Bottom: View along the crystallographic c axis showing the H-bonds (black dotted lines) established between peripheral aqua (O1W) and nitrate ligands (O2) in 1. The htpzb, dmbpy and the terminal cyanide ligands, as well as the crystallization water and acetonitrile molecules were omitted for the sake of clarity [symmetry code: (c) = 1 − x, 1 − y, 2 − z].

Magnetic properties

The magnetic properties of 1–5 have been investigated, both in the dc and ac regimes, to unveil the influence of the spin ground state and magnetic anisotropy of the Ln^III ion (Ln = Gd, Tb, Dy, Ho, and Er) on the static and dynamic magnetic behavior of this series of cyano-bridged heterometallic {Ln^III₂Fe^III₂} molecular squares as illustrative examples of 0D PBA (see Table S5 in SI).^53,57–60

Static dc magnetic behavior. The dc magnetic properties of 1–5 in the form of χ_MT vs. T (χ_M being the dc molar magnetic susceptibility per {Ln^III₂Fe^III₂} unit and T the absolute temperature) and M vs. H plots (M being the molar magnetization per {Ln^III₂Fe^III₂} unit and H the applied dc magnetic field) are depicted in Fig. 3, while the normalized M vs. H/T plots are represented in Fig. S24 in SI. The static magnetic behavior of 2–5 are qualitatively similar, being different from that of 1, as expected from the magnetically isotropic nature of the Gd^III ion compared to the other magnetically anisotropic Ln^III ions (Ln = Tb, Dy, Ho, and Er) resulting from their large spin–orbit coupling (SOC).

Fig. 3 (a) Temperature dependence of χ_MT for 1–5. (b) Field dependence of M at 2 K for 1–5 (the solid lines are only eye-guides).

At room temperature, the χ_MT value of 1 is 16.70 cm³ mol⁻¹ K, a value which is close to the one expected for the sum of two magnetically isolated LS 3d⁵ Fe^III ions (S_Fe = 1/2) with an unquenched orbital momentum (²T_2g term in O_h symmetry) plus two orbital free 4f⁷ Gd^III ions (S_Gd = 7/2) with an ⁸S_7/2 ground state [χ_MT = 2 × (Nβ²g_Fe²/3k)S_Fe(S_Fe + 1) + 2 × (Nβ²g_Gd²/3k)S_Gd(S_Gd + 1) = 2 × 0.46 + 2 × 7.88 = 16.67 cm³ mol⁻¹ K with g_Fe = 2.215 and g_Gd = 2.0] (Fig. 3a). In fact, the ²T_2g term of the LS Fe^III ion in O_h symmetry is split under a rhombic distortion into a ground doublet state (²A_1g) and two excited doublet states (²B_1g and ²B_2g).

Upon cooling, χ_MT decreases slightly and quasi-linearly down to 20 K due to the SOC effects of the LS Fe^III ions, below this temperature χ_MT abruptly falling down to reach a minimum value of 13.67 cm³ mol⁻¹ K at 2.0 K. This value is well below that expected for the sum of two magnetically isolated LS Fe^III ions at this low temperature plus two isotropic Gd^III ions (χ_MT = 2 × 0.15 + 2 × 7.875 = 16.05 cm³ mol⁻¹ K) which unambiguously supports the occurrence of an antiferromagnetic interaction between the LS Fe^III and Gd^III ions through the cyanide bridge in 1.

Hence, the maximum M value at 2 K for H = 5 T is 14.8Nβ (Fig. 3b), which is below that expected for the sum of two Gd^III and two low-spin Fe^III ions, magnetically non-interacting [M = 2 × (g_FeS_Fe + g_GdS_Gd)Nβ = 16.2Nβ (with g_Gd = 2.0 and g_Fe = 2.2)], being close to that of a tercet ground state [S = 2(S_Gd − S_Fe) = 6] resulting from the antiparallel alignment of the spin momenta of the LS Fe^III and Gd^III ions [M = gSNβ = 12.4Nβ with g = (19/28)g_Gd + (9/28)g_Fe = 2.06]. Moreover, the reduced isothermal magnetization curves from 2 up to 10 K are almost overlapped (Fig. S24a in SI), in agreement with the small, if not negligible, local magnetic anisotropy of the Gd^III ions.

On the other hand, the χ_MT values at room temperature for 2–5 are equal to 25.17 (2), 29.10 (3), 28.70 (4), and 23.79 cm³ mol⁻¹ K (5) (Fig. 3a). These values well correspond to the theoretical ones for the sum of two magnetically non-interacting LS 3d⁵ Fe^III ions with a significant orbital contribution [χ_MT = 2 × (Nβ²g_Fe²/3k)S_Fe(S_Fe + 1) = 2 × 0.46 = 0.92 cm³ mol⁻¹ K with g_Fe = 2.215] plus two magnetically isolated 4f⁸ Tb^III (2), 4f⁹ Dy^III (3), 4f¹⁰ Ho^III (4), and 4f¹¹ Er^III ions (5) with ⁷F₆ (J_Tb = 6, L_Tb = 3, and S_Tb = 3), ⁶H_15/2 (J_Dy = 15/2, L_Dy = 5/2, and S_Dy = 5/2), ⁵I₈ (J_Ho = 8, L_Ho = 3/2, and S_Ho = 2), and ⁴I_15/2 ground states (J_Er = 15/2, L_Er = 3/2, and S_Er = 3/2) [χ_MT = 2 × (Nβ²g_J²/3k)J(J + 1) = 23.64 (2), 28.34 (3), 28.14 (4), and 22.96 cm³ mol⁻¹ K (5) with g_J = 3/2, 4/3, 5/4, and 6/5, respectively], being well-separated from the first excited states that are then unpopulated in all the temperature range investigated. Upon cooling, χ_MT for 2–5 (Fig. 3a) continuously decreases down to ca. 150 K, below this temperature χ_MT sharply dropping to attain a minimum value of 13.36 (2), 18.04 (3), 6.10 (4), and 12.75 cm³ mol⁻¹ K (5) at 1.9 K. Overall, this magnetic behavior obeys to the occurrence of a large SOC of the magnetically anisotropic Ln^III ions (Ln = Tb, Dy, Ho, and Er) in 2–5, together with an antiferromagnetic interaction between the LS Fe^III and Ln^III ions through the cyanide bridge, as observed in 1. In fact, the isothermal magnetization curves for 2–5 at 2.0 K are far from reaching saturation, and M attains maximum values of 10.46 (2), 10.92 (3), 11.92 (4), and 9.32Nβ (5) for H = 5 T (Fig. 3b). These values are far below those expected for the corresponding ground states [J = 2(J_Ln − S_Fe) = 11 (2), 14 (3), 15 (4), and 14 (5)] resulting from the antiparallel alignment of the total momenta of the LS Fe^III and Ln^III ions [M = g_JJNβ = 19.15 (2), 22.88 (3), 23.76 (4), and 21.70 Nβ (5) with g_J = 1.74, 1.63, 1.58, and 1.55, respectively]. Also, the reduced isothermal magnetization curves for 2–5 from 2 to 10 K did not collapse, indicating a significant local magnetic anisotropy of the Ln^III ions (Ln = Tb, Dy, Ho, and Er, see Fig. S24b–e in SI).

Dynamic magnetic behavior. The dynamic magnetic properties of 1–5 have been investigated by variable-temperature (T = 2.0–10 K) and variable-frequency (ν = 1–10 kHz) alternating current (ac) magnetic susceptibility measurements under an oscillating ac field of 5 Oe, both in the absence and the presence of an applied direct current (dc) field (see Experimental section).

The and vs. T plots of 1–5 (where and represent the in-phase and out-of-phase components of the molar ac magnetic susceptibility per {Ln^III₂Fe^III₂} unit) under an applied dc field (H) of 1.0 (1) or 0.5 T (2–5) are depicted in Fig. 4. No signal occurred at zero dc field for any member of this series (data not shown), as expected for a fast magnetic relaxation due to the quantum tunneling of magnetization (QTM). Under a small dc field [H = 1.0 (1) and 0.5 T (2–5)], however, very weak but not negligible frequency-dependent maxima appeared, which are indicative of a slow magnetic relaxation typical of field-induced SMMs. This situation contrasts with that found for the other reported examples of cyano-bridged {Fe^III₂Ln^III₂} squares, which only in a few cases show incipient frequency-dependent signals, but with no maxima, in the presence of a small dc field (Table S5).^57–59 In particular, the isostructural series of complexes of general formula [Fe{hbpzb}(CN)(μ-CN)₂Ln(NO₃)₂(pyim)(Ph₃PO)]₂·2CH₃CN [Ln = Tb, Dy, and Er; hbpzb = hydrotris(pyrazolyl)borate, pyim = 2-(1H-imidazol-2-yl)pyridine, and Ph₃PO = triphenylphosphine oxide] showed very incipient signals at H = 0.1 or 0.25 T.⁵⁹

Fig. 4 Temperature dependence of and (a–e) for 1–5 at ±5 Oe oscillating field in the frequency range of 1.0–10.0 kHz (green to violet) and under applied static magnetic field of 1.0 (1) or 0.5 T (2–5). The solid lines are only eye-guides.

The magnetic relaxation times (τ) at H = 1.0 (1) or 0.5 T (2–5) can be alternatively calculated from the least-squares fitting of the respective or vs. ν plots through the generalized Debye model [eqn (1) and (2)] (Fig. S25 in SI).⁸⁰ The τ values calculated from the vs. ν plots are fairly more accurate than those from the vs. ν plots, as far as the magnetic relaxation rate is equal to the angular frequency of the oscillating ac field at the maxima (τ⁻¹ = ω_max = 2πν_max). They are represented in Fig. 5 in the form of the ln τ vs. 1/T (so-called Arrhenius) and ln τ vs. ln T plots. On the other hand, the vs. (so-called Cole–Cole or Argand) plots for 2–5 in the temperature range 2.0–6.0 K give almost perfect semicircles, while those for 1 in the temperature range 2.0–9.0 K yield minor arcs in the low-temperature range and semicircles above 6 K (Fig. S26 in SI). The adiabatic (χ_S) and isothermal (χ_T) magnetic susceptibilities as well as the exponential factor (α) for 1–5 were accurately obtained from the least-squares fitting of the respective Argand plots (Fig. S27 in SI).

Fig. 5 Ln τ vs. 1/T (Arrhenius) (a) and ln τ vs. ln T (b) plots of τ for 1–5 under an applied dc field of 1.0 (1) or 0.5 T (2–5). The solid lines represent the best-fit curves for ORB (2 and 4) and ORB plus QTM (1, 3, and 5) mechanisms (a) or, alternatively, RAM (2 and 4) and RAM plus QTM and DIR (1, 3, and 5) mechanisms (b) (see text).

The relatively low values of the α parameter [α = 0.18–0.65 (1)/0.15–0.41 (2)/0.32–0.41 (3)/0.23–0.47 (4)/0.20–0.31 (5); Fig. S27 in SI] supports a narrow distribution of τ values in the magnetic relaxation process for 1–5 typical of SMMs (α = 0 and 1 for single and infinite relaxation processes, respectively).

The Arrhenius plots for 2 and 4 give straight lines indicating an Orbach (ORB) spin–lattice relaxation mechanism [eqn (4)]. However, experimental data for 1, 3, and 5 deviate from linearity at low temperatures and they tend to saturate (3 and 5) or really saturate (1) because of the aforementioned temperature-independent QTM [eqn (5)]. Hence, the QTM process is completely or partly suppressed after applying the dc field along this series of {Fe^III₂Ln^III₂} squares, depending on the non-Kramer (Tb, Ho) or Kramer (Gd, Dy, Er) nature of the Ln^III ion, respectively. Satisfactory least-squares fits were obtained through the appropriate expressions derived from a single magnetic relaxation process via ORB mechanism (2 and 4) or a double magnetic relaxation process that combines ORB plus QTM (1, 3, and 5) mechanisms (solid lines in Fig. 5a).

τ⁻¹ = τ_ORB⁻¹ = τ₀⁻¹ exp(−U_eff/k_BT) (4)

τ⁻¹ = τ_QTM⁻¹ (5)

τ⁻¹ = τ_DIR⁻¹ = AT (6)

τ⁻¹ = τ_RAM⁻¹ = CTⁿ (7)

The resulting magnetic relaxation parameters of 1–5 are given in Table 3 and they are depicted in Fig. S28 in SI. The preexponential factor of the ORB process for 1–5 is within the range observed for other SMMs [τ₀ = 3 (1)/41 (2)/9.9 (3)/58 (4)/81 µs (5); Table 3] (Fig. S28b in SI). Notably, the effective energy barrier of the ORB process for the non-Kramer Tb(III) and Ho(III) derivatives 2 and 4 is one order of magnitude smaller than for the Kramer Dy(III) and Er(III) derivatives, 3 and 5 [U_eff = 0.92 (2)/8.8 (3)/0.78 (4)/3.81 cm⁻¹ (5); Table 3] (Fig. S28c). Hence, an overall increase of the U_eff values occurs along this series in the order {Fe^III₂Ho^III₂} < {Fe^III₂Tb^III₂} < {Fe^III₂Er^III₂} < {Fe^III₂Dy^III₂}, while for the previously reported cyano-bridged {Fe^III₂Ln^III₂} squares analogues the Er(III) derivative had the largest value of U_eff [U_eff = 13–17 (Tb)/25–28 (Dy)/38–40 cm⁻¹ (Er); Table S5].⁵⁹ The observed trend would be related to the different magnetic anisotropies of the {Fe^III₂Ln^III₂} ground state resulting from the antiparallel alignment of the spin and total momenta of the LS Fe^III and Ln^III ions [J = 2(J_Ln − S_Fe) = 11 (Tb), 14 (Dy), 15 (Ho), and 14 (Er)]. Otherwise, the U_eff value of 18 cm⁻¹ for 1 is extremely large to be associated with a magnetic anisotropy energy barrier given the almost isotropic nature of the Gd^III ions (see discussion above). Slow-rate spin-phonon transitions between the vibronic energy levels of the {Fe^III₂Gd^III₂} square could be the source of the slower magnetic relaxation in 1. Alternatively, the ln τ vs. ln T plots, which also give straight lines for 2 and 4 supporting a Raman (RAM) spin–lattice relaxation mechanism [eqn (7)]. Once again, the experimental data for 1, 3, and 5 deviate from linearity at low temperatures due to the aforementioned QTM and/or DIR mechanisms [eqn (5) and (6), respectively]. Satisfactory least-squares fits were thus obtained through the appropriate expressions derived from a single magnetic relaxation process via RAM mechanism (2 and 4) or a multiple magnetic relaxation process that combines RAM plus QTM and DIR (1, 3, and 5) mechanisms (solid lines in Fig. 5b).

Table 3 Selected least-squares fitting parameters for the magnetic relaxation processes of 1–5

	H (T)	τQTM ^a (µs)	τ0 ^b (µs)	Ueff ^b (cm^−1)	A^c (s^−1 K^−1)	C^d (s^−1 K^−n)	n^d
a Coefficient factor for the temperature-independent QTM process (τ^−1 = τQTM^−1).b Pre-exponential factor and effective energy barrier for the ORB process [τ^−1 = τ0^−1 exp(−Ueff/kBT)].c Coefficient factor for the DIR process (τ^−1 = AT).d Coefficient factor and exponent for the RAM process (τ^−1 = CT^n).
1	1.0	132	3	18	—	—	—
		152	—	—	470	3	3.9
		126	3	16	—	0.04	3.4
2	0.5	—	41	0.92	—	—	—
		—	—	—	—	10 100	0.38
3	0.5	85	9.9	8.8	—	—	—
		109	—	—	1020	50	2.8
		109	61	3.3	—	33	2.8
4	0.5	—	58	0.4	—	—	—
		—	—	—	—	8200	0.32
5	0.5	50	81	3.8	—	—	—
		51	—	—	660	10	3.6
		94	95	0.05		58	2.7

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The Raman exponent for 2 and 4 is extremely low and not physically meaningful [n = 0.38 (2)/0.32 (4); Table 3], so that a Raman (n ≥ 2) or even a direct (n = 1) process can be definitely discarded. Yet, the low n value for 1, 3, and 5 agree with a Raman process assisted by optical phonons [n = 3.9 (1)/2.8 (3)/3.6 (5); Table 3] (Fig. S28f in SI), as an alternative to the Orbach process discussed above. Indeed, satisfactory fits were also obtained by consider the simultaneous contributions of Raman, Orbach and QTM mechanisms for 1, 3, and 5, with values of the respective magnetic relaxation parameters within the normal range for SMMs (see Table 3). However, their reliability is clearly limited by the large number of fitting parameters, which could lead to overparameterization. Otherwise, the coefficient factors of the DIR and RAM processes are within the range observed for other SMMs [A = 470 (1)/1020 (3)/660 s⁻¹ K⁻¹ (5) and C = 3 (1)/50 (3)/10 s⁻¹ K⁻ⁿ (5); Table 3], increasing in the order {Fe^III₂Gd^III₂} < {Fe^III₂Er^III₂} < {Fe^III₂Dy^III₂} along this series (Fig. S28d and S28e in SI). On the other hand, the relaxation times of the QTM process are similar regardless of the magnetic relaxation model employed, either ORB plus QTM [τ_QTM = 132 (1)/85 (3)/50 µs (5); Table 3] or RAM plus QTM and DIR [τ_QTM = 152 (1)/109 (3)/51 µs (5); Table 3], increasing in the order {Fe^III₂Er^III₂} < {Fe^III₂Dy^III₂} < {Fe^III₂Gd^III₂} along this series (Fig. S28a in SI).

Magnetocaloric properties

The magnetocaloric properties of 1–5 have been studied by variable-temperature (T = 2.0–10 K, with ΔT = 1 K) and variable-field (H = 0–5 T, with ΔH = 0.2 T) magnetization measurements to reveal the influence of the spin ground state and magnetic anisotropy of the Ln^III ion (Ln = Gd, Tb, Dy, Ho, and Er) on the magnetothermal behavior for this series of cyano-bridged heterometallic {Ln^III₂Fe^III₂} molecular squares as illustrative examples of 0D PBA (Table S6 in SI). Selected magnetocaloric data for 1–5 are summarized in Table 4 and they are depicted in Fig. 6.

Fig. 6 Histogram plots showing the variation of the maximum values (in gravimetric units) of −ΔS_m (a) and MCI (b) for 1–5 (data from Table 4). The solid lines are the corresponding optimum values of the temperature and the magnetic field. The inset shows the maximum values (in molar units) of −ΔS_m (a) for 1–5. The dotted and dashed lines correspond to the calculated values for two low-spin iron(III) and two lanthanide(III) ions, magnetically isolated or antiferromagnetically coupled, respectively, considering a negligible zero-field splitting (see text).

Table 4 Selected magnetocaloric data for 1–5

	H^a (T)	Tmax ^b (K)	−ΔSmax ^c (J kg^−1 K^−1)	T^d (K)	Hmax ^e (T)	MCI^f (J kg^−1 K^−1 T^−1)
a Magnetic field value.b Temperature value of the maximum of the magnetic entropy change.c Value of the maximum of the magnetic entropy change (in gravimetric units).d Temperature value.e Magnetic field value of the maximum of the magnetocaloric index.f Value of the maximum of the magnetocaloric index (in gravimetric units).
1	5.0	<2.0	16.51	2.0	1.0	6.4
2	5.0	4.0	5.42	2.0	0.6	3.3
3	5.0	4.0	6.02	2.0	0.4	4.7
4	5.0	6.0	4.56	2.0	0.8	0.9
5	5.0	4.0	5.86	2.0	0.6	3.6

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The magnetic entropy change (−ΔS_m) after switching on the magnetic field (ΔH = H − H₀ = H with H₀ = 0) can be estimated from the M vs. H and T plots (M being the gravimetric magnetization per {Ln^III₂Fe^III₂} unit), according to the Maxwell equation.⁸¹ The corresponding −ΔS_m vs. T and H color contour maps and plots for 1–5 are represented in Fig. 7a–e and Fig. S29 in SI, respectively.

Fig. 7 Contour color map for the temperature and field dependence of the magnetic entropy change (−ΔS_m) (a–e) and of the magnetocaloric efficiency index (MCI) (e–i), defined as −∂(ΔS_m)/∂H (in gravimetric units), after switching on the magnetic field for 1–5, in the applied dc magnetic field and temperature ranges 2–10 K and 0–5 T, respectively.

Once again, the magnetothermal behavior of 2–5 are qualitatively similar, being different from that of 1, as expected from the magnetically isotropic nature of the Gd^III ion compared to the other magnetically anisotropic Ln^III ions (Ln = Tb, Dy, Ho, and Er).

For 1, the increase of magnetic field or the decrease of temperature determines a gradual increase of the magnetic entropy change for T > 2 K and H < 5 T (Fig. 7a, Fig. S29a and S29f in SI).

The maximum −ΔS_m value (in gravimetric units) is 16.51 J kg⁻¹ K⁻¹ at T = 2 K for H = 5 T (Table 4), being larger than that reported for the only other example of cyano-bridged {Fe^III(LS)₂Gd^III₂} tetranuclear complex investigated to date as cryomagnetic refrigerant of formula {[Fe(htpzb)(CN)₂(μ-CN)][Gd(H₄L)(H₂O)₂]}₂·8H₂O·2CH₃OH [H₆L = N,N′-(2,6-pyridine-dicarboxyl)disalicylhydrazide] (−ΔS_max = 12.70 J kg⁻¹ K⁻¹ at T = 4.0 K for H = 7.0 T; Table S6).⁴³ However, it is smaller than that reported for the related hydroxo/azido-bridged {Fe^III(HS)₃Gd^III₂} pentanuclear complex of formula TBA₃[Fe₃Gd₂(N₃)₁₅(OH)₃(tipaH₃)₂] (TBA = tetrabutylammonium and tipaH₃ = triisopropanolamin) (−ΔS_max = 21.1 J kg⁻¹ K⁻¹ at T = 6.0 K for H = 7.0 T).⁴²

The maximum −ΔS_m value (in molar units) of 29.35 J mol⁻¹ K⁻¹ for 1 is smaller than the theoretical value for two LS Fe^III and two Gd^III ions, magnetically uncoupled [−ΔS_m = 2R ln(2S_Fe + 1) + 2R ln(2S_Gd + 1) = 5.55R = 45.89 J mol⁻¹ K⁻¹], being somewhat above than that of a tercet ground state [S = 2(S_Gd − S_Fe) = 6] resulting from the antiparallel alignment of the spin momenta of the LS Fe^III and Gd^III ions [−ΔS_m = R ln(2S + 1) = 2.56R = 21.32 J mol⁻¹ K⁻¹]. This situation conforms to the partial thermal population of the low-lying states of higher multiplicity (S > 6) for the {Fe^III(LS)₂Gd^III₂} complex, as expected for a relatively weak antiferromagnetic interaction between the LS Fe^III and two Gd^III ions through the cyanide bridges found in 1.

Unlike 1, the isofield curves of the magnetic entropy change for 2–5 develop a maximum with increasing the magnetic field for H > 2.6 (2), 3.0 (3), 1.0 (4), and 3.6 T (5) (Fig. S29b–e in SI), concomitantly with an intercrossing of the isothermal curves with decreasing the temperature for T < 4.0 (2), 3.0 (3), 5.0 (4), and 3.0 K (5) (Fig. S29g–j in SI). Hence, the maximum −ΔS_m values (in gravimetric units) are 5.42 (2), 6.02 (3), 4.56 (4), and 5.86 J kg⁻¹ K⁻¹ (5) at the optimum working temperatures T_opt = T_max = 4.0 (2), 4.0 (3), 6.0 (4), and 4.0 K (5) for H = 5 T (Table 4 and Fig. 6a). Interestingly, the maximum −ΔS_m values (in gravimetric units) for 1–5 are within the range observed earlier for mixed-3d/4f 0D PBA derivatives proposed as cryomagnetic refrigerants (−ΔS_max = 3.8–17.7 J kg⁻¹ K⁻¹ at T = 2–8 K for H = 7 T; Table S6 in the SI).^82–84 Moreover, they are comparable to those reported for the lanthanide gallium garnets of general formula Ln₃Ga₅O₁₂ [−ΔS_max = 35.31 (Gd), 11.22 (Tb), and 14.52 J kg⁻¹ K⁻¹ (Dy) at T = 4 (Gd), 3 (Tb), and 2 K (Dy) for H = 3 (Gd), 4 (Tb), and 2 T (Dy)].^85,86

The maximum −ΔS_m values (in molar units) for 2–5 [−ΔS_max = 9.66 (2), 10.77 (3), 8.14 (4), and 10.48 J mol⁻¹ K⁻¹ (5)] are significantly smaller than for 1 (−ΔS_max = 12.70 J kg⁻¹ K⁻¹) (inset of (Fig. 6a)). Overall, they vary in the order: 1 (Gd) ≫ 3 (Dy) ≈ 5 (Er) > 2 (Tb) > 4 (Ho), despite the increase of the total momentum almost in the inverse order: 4 (J_Ho = 8) > 3 = 5 (J_Dy = J_Er = 15/2) > 2 (J_Tb = 6) > 1 (J_Gd = 7/2). This situation is likely explained because of the increase of the local magnetic anisotropy from the Gd^III ion to the other Ln^III ions (Ln = Tb, Dy, Ho, and Er) along this series of cyano-bridged {Fe^III(LS)₂Ln^III₂} complexes. Hence, the −ΔS_max values for 2–5 are almost five-fold lower than the ones calculated for two low-spin iron(III) and two lanthanide(III) ions, magnetically isolated, considering a negligible zero-field splitting [−ΔS_m = 2R ln(2J_Fe + 1) + 2R ln(2J_Ln + 1) = 54.17 (2), 57.62 (3), 58.63 (4), and 56.72 J mol⁻¹ K⁻¹ (5)] (dotted line in the inset of Fig. 6a).

Otherwise, they are yet three-fold lower than those calculated for the ground state resulting from the antiparallel alignment of the total momenta of the LS Fe^III and Ln^III ions [−ΔS_m = R ln(2J + 1) = 26.07 (Tb), 28.00 (Dy), 28.55 (Ho), and 28.00 J mol⁻¹ K⁻¹ (Er) with J = 2(J_Ln − J_Fe) = 11 (Tb), 14 (Dy), 15 (Ho), and 14 (Er)] (dashed line in the inset of (Fig. 6a)). In fact, the large energy splitting of the ground state of the magnetically anisotropic Ln^III ions into their ±mJ levels strongly minimizes the magnetic entropy at zero field, thereby reducing the maximum magnetic entropy change after switching on the magnetic field.

On the other hand, the isothermal curves for 1, 2, 3, and 5 rapidly increase monotonically, tending to saturate at lower temperatures (Fig. S29f–h and S29j in SI). In contrast, for 4, the increase of the isothermal curves (Fig. S29i in SI) is more abrupt, the magnetic entropy change diverting at higher temperatures, while a slight tendency of saturation occurred at low temperatures (2 and 3 K). At low magnetic field, H = 1 T, the maximum value of the magnetic entropy change is 5.04 (1), 2.18 (2), 3.75 (3), 1.95 (4), and 2.94 J kg⁻¹ K⁻¹ (5) at 2 (1, 2, 3, 5) and 4 K (4), representing 30 (1), 40 (2), 62 (3), 32 (4), and 50% (5) from the −ΔS_max value. This means that −ΔS_m are significant even at weak H comparable with ceramic (0.5–1 T) or Nd-based permanent magnets (1.4 T) and, also, are of interest in cryomagnetic refrigeration applications for which high −ΔS_max values and large slope of the field dependence of −ΔS_m plots are required.

In this respect, it is convenient to introduce the magnetocaloric efficiency index (MCI) as a new figure of merit for cryomagnetic refrigerants, defined as MCI = −∂(ΔS_m)/∂H, which corresponds precisely to −∂M/∂T according to the Maxwell equation .⁸⁷ Hence, the isofield and isothermal curves for 1–5 develop narrow to broad maxima of MCI which shift toward higher temperatures or fields with increasing the field or the temperature, respectively (Fig. 7e–i and Fig. S30 in SI). These MCI maxima cover a broad (1) to narrow (2–5) field range [H_max = 1.0–3.8 (1)/0.6–1.8 (2)/0.4–1.6 (3)/0.8–2.8 (4)/0.6–2.2 T (5) for T = 2–10 K] (Fig. S30f–j in SI), so that the lowest optimum working field [H_opt = H_max = 1.0 (1)/0.6 (2)/0.4 (3)/0.8 (4)/0.6 T (5) at T = 2 K; Table 4] along this family of cyano-bridged {Fe^III(LS)₂Ln^III₂} molecular squares decrease in the order: 1 (Gd) > 4 (Ho) > 2 (Tb) = 5 (Er) > 3 (Dy). The intensity and the location of these MCI maxima in the low-field region are both mandatory for the practical applications of mixed-3d/4f 0D PBA derivatives as magnetic refrigerants at low temperatures, just above the He liquefaction temperature.

Hence, the MCI performance for 1 is rather high at the optimum working field (MCI = 6.4 J kg⁻¹ K⁻¹ T⁻¹ for H_opt = 1.0 T at T = 2 K; Table 4). However, high to moderate MCI performances can be obtained using smaller optimum working fields for 2–5 [MCI = 3.3 (2), 4.7 (3), 0.9 (4), and 3.6 J kg⁻¹ K⁻¹ T⁻¹ (5) for H_opt = H_max = 0.6 (2), 0.4 (3), 0.8 (4), and 0.6 T (5) at T = 2 K; Table 4 and Fig. 6b], approaching the H values of the permanent magnets used commercially (ranging from 0.15 and 2 T for Alnico, a common refrigerator magnet). In this family of cyano-bridged {Fe^III(LS)₂Ln^III₂} molecular squares, a decrease of the MCI performance at the optimal working field is found with increasing the magnetic anisotropy in the order: 1 (Gd) > 3 (Dy) > 5 (Er) ≈ 2 (Tb) > 4 (Ho), so that it decreases approximately with increasing the J value in the order: 1 (J_Gd = 7/2) < 2 (J_Tb = 6) < 3 = 5 (J_Dy = J_Er = 15/2) < 4 (J_Ho = 8). Otherwise, the corresponding lanthanide gallium garnets Ln₃Ga₅O₁₂ show similar MCE performances than 1–5, but at higher optimum working fields [MCI = 8.47 (Gd), 4.90 (Tb), and 6.84 J kg⁻¹ K⁻¹ (Dy), at T = 4 K for H_opt = 2 (Gd), 1 (Tb), and 1 T (Dy)].⁸⁷

Conclusions

A new isostructural series of cyano-bridged mixed-3d/4f square-shaped tetranuclear complexes was obtained through the “complex-as-ligand/complex-as-metal” strategy by employing heteroleptic iron(III) tricyanometallates with the scorpionate-like hydrotris(pyrazolyl)borate ligand (htpzb) that acts as angular connector toward coordinatively unsaturated lanthanide(III) complexes capped with chelating 4,4′-dimethyl-2,2′-bipyridine (dmbpy) and nitrate ligands.

These antiferromagnetically coupled {Fe^III₂Ln^III₂} squares (Ln = Gd, Tb, Dy, Ho, and Er) constitute a unique class of field-induced single-molecule magnets (SMMs). Remarkably, {Fe^III₂Gd^III₂} is a rare example of quasi-isotropic gadolinium(III)-containing SMM that exhibit slow magnetic relaxation (SMR) under a low applied field (H = 1.0 T) at relatively high blocking temperatures (T_B up to 6.0 K). The orbital contribution of the other lanthanides(III) gives rise to significant magnetic anisotropy that, together with their large magnetic moments, provide the main “ingredients” for the assembly of SMMs. The SMR properties of the resulting {Fe^III₂Ln^III₂} squares occurred, however, at lower blocking temperatures (T_B < 4.0 K) under a lower applied field (H = 0.5 T), being very sensitive to the nature of the magnetically anisotropic Ln^III ions (Ln = Tb, Dy, Ho, and Er). Besides, the octahedral low-spin (LS) iron(III) building block with first order orbital moment has a pronounced molecular easy axis of magnetization, being well-suited for the assembly of mixed-3d–4f SMMs.

The magneto-thermal properties along this series of {Fe^III₂Ln^III₂} squares also depends on the magnetic anisotropy of the Ln^III ions (Ln = Gd, Tb, Dy, Ho, and Er), the large magnetocaloric efficiency being found for the magnetically isotropic {Fe^III₂Gd^III₂} square at optimal working temperature and field of 2.0 K and 1.0 T, respectively, while the magnetically anisotropic {Fe^III₂Ln^III₂} squares (Ln = Tb, Dy, Ho, and Er) showed moderate to high magnetocaloric efficiencies at higher optimum working temperatures (T_opt = 4.0–6.0 K) and lower optimum working fields (H_opt = 0.4–1.0 T). This new family of cyano-based mixed-3d/4f SMMs belonging to the large class of zero-dimensional (0D) lanthanide Prussian blue analogues (Ln PBA) then emerges as a new route toward molecular magnetic coolers operating just above the helium liquefaction temperature. Therefore, the perspectives of exploration MCE in high-dimensional (2D and 3D) lanthanide PBA are wide and promising and could provide very interesting multifunctional molecular materials that advance the knowledge in magnetochemistry and, also, of relevance in adiabatic demagnetization refrigeration (ADR).

Conflicts of interest

There are no conflicts to declare.

Data availability

The authors declare that the data supporting this article have been included as part of the supplementary information (SI).

Supplementary information: FTIR spectra (Fig. S1–S5, 1–5); UV-Vis spectra for 1–5 (Fig. S6); PXRD patterns (Fig. S7–S11, 1–5); square-like units and Fe^III/Ln^III coordination polyhedra (Fig. S12–S15, 2–5); drawings of the crystal packing for 2–5 (Fig. S16–S23, 2–5); crystallographic data (Tables S1 and S2, 1–5), SHAPE analysis (Table S3, 1–5) and H-bond parameters (Table S4, 1–5), dc and ac magnetic parameters for cyano-bridged {Ln^III₂Fe^III₂} squares (Table S5); dc plots of M vs. HT⁻¹ for 1–5 (Fig. S24); ac plots of χ′ and χ″ vs. ν for 1–5 (Fig. S25); Cole–Cole plots for 1–5 (Fig. S26); temperature dependence of χ_T, χ_S, and α parameters plots for 1–5 (Fig. S27); plots showing the variation of the values of τ_QTM (a), τ₀ (b), and U_eff (c), A (d), C (e), and n (f) for the QTM, and ORB, DIR, and RAM relaxation mechanisms in 1–5 series (Fig. S28); selected magnetocaloric data for mixed-3d/nd 0D PBAs proposed as cryomagnetic refrigerants (Table S6); temperature and field dependence of −ΔS_m (Fig. S29) and of MCI plots, respectively (Fig. S30) for 1–5. See DOI: https://doi.org/10.1039/d5qi02520f.

CCDC 2504399–2504403 contain the supplementary crystallographic data for this paper.^88a–e

Acknowledgements

This work was supported by grants of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI – UEFISCDI, project number project number PN-III-P1-1.1-TE-2019-0352, within PNCDI III and project number PN-IV-P2-2.2-MC-2024-0533, within PNCDIV, the Spanish MINECO (Projects PID2019-109735GB-I00 and Unidad de Excelencia María de Maeztu CEX2019-000919-M), and the Generalitat Valenciana (AICO/2020/183 and AICO/2021/295). M. P. acknowledges the PEDECIBA and CSIC for a postdoctoral stage. The authors would like to thank Dr Rafael Ruíz-García (Institute of Molecular Sciences, University of Valencia) for his helpful discussions on the magnetic properties of these compounds, and for his support in finalizing this manuscript.

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Footnote

† Passed away, July 2024.

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