Molecular coolers: The case for [Cu^II₅Gd^III₄]

Abstract

The use of triethanolamine (teaH₃) in 3d/4f chemistry produces the enneanuclear cluster compound [Cu^II₅Gd^III₄O₂(OMe)₄(teaH)₄(O₂CC(CH₃)₃)₂(NO₃)₄]·2MeOH·2Et₂O (1·2MeOH·2Et₂O) whose molecular structure comprises a series of vertex- and face-sharing {Gd^IIICu^II₃} tetrahedra. Magnetic studies reveal a large number of spin states populated even at the lowest temperatures investigated. Combined with the high magnetic isotropy, this enables 1 to be an excellent magnetic refrigerant for low temperature applications.

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Introduction

Magnetic refrigeration is a potential and realistic short-to-medium term application envisioned for polymetallic molecules built from paramagnetic metal ions; molecules often referred to as molecular nanomagnets (MNMs).^1–3 The magnetocaloric effect (MCE) is based on the change of magnetic entropy upon application of a magnetic field and can be used for cooling applications via adiabatic demagnetisation. Recent studies have demonstrated that the MCE of isotropic MNMs can be enormous,^4–7 and larger than that of lanthanide alloys⁸ and magnetic nanoparticles.⁹ The “recipe” required for the synthesis of such molecules was recently outlined.¹⁰ The “ideal” molecule should possess: (a) a large spin ground state, S. Magnetic entropy is related to the spin by S_m = Rln(2S + 1) [where R = gas constant] and thus the larger the S the larger the magnetic entropy. (b) Molecular isotropy (D_cluster = 0) — zero-field splitting (anisotropy) orders molecular M_s levels, thus decreasing magnetic entropy changes. (c) High spin degeneracy — the presence of low-lying excited states is controlled by the exchange interaction (J) between metal ions. Weak exchange equates to multiple low-lying excited states each of which can contribute to the magnetic entropy of the system via S_m = Rln(2S + 1). (d) A small molecular mass, m_w.

In other words we need to make low molecular mass ferro- or ferrimagnets displaying zero molecular anisotropy and exhibiting weak exchange interactions. This immediately points toward the use of lanthanide ions and, in particular, the f⁷ ion Gd³⁺ in the construction of homo- and heterometallic (Gd-3d) clusters. The inherently weak exchange mediated through the core-like f-orbitals of Gd³⁺ and its isotropic electronic configuration guarantee the presence of multiple low-lying [and hence field-accesible] spin states, negating the need for ferromagnetic exchange in homometallic f-block clusters. Heterometallic complexes (e.g.Gd³⁺-Mnⁿ⁺, Gd³⁺-Cu²⁺etc) can be guaranteed to afford non-zero spin ground states on account of their differing dⁿ/fⁿ electron configurations and on the basis of literature precedents that show certain combinations, e.g.Gd³⁺-Cu²⁺, favour ferromagnetic exchange.¹¹ Molecular isotropy can be controlled in two ways: (a) through the use of isotropic metal ions (Gd³⁺, Cu²⁺, Fe³⁺) since D_cluster is governed in the main by d_single ion, or (b) through the synthesis of highly symmetric molecules since D_cluster = 0 in cubic (O_h, T_d) symmetry.

To date, the molecule with largest enhancement of the MCE is a mixed-valent [Mn^II/III₁₄] disc with values of −ΔS_m as large as 25 J kg⁻¹ K⁻¹ for liquid-helium temperatures and ΔB₀ = 7 T—almost a factor of 2 larger than that of [DyCo₂] nanoparticles.⁹ Herein we present the first Cu²⁺-Gd³⁺ candidate, by showing that [Cu^II₅Gd^III₄O₂(OMe)₄(teaH)₄(O₂CC(CH₃)₃)₂(NO₃)₄]·2MeOH·2Et₂O (1·2MeOH·2Et₂O) displays a truly enormous enhancement of the MCE with −ΔS_m reaching record values larger than 30 J kg⁻¹ K⁻¹. This cluster forms part of a family of isostructural Cu^II₅Ln^III₄ clusters in which the anisotropic members, Ln = Tb, Dy and Ho, in contrast to Gd, display single molecule magnetism features (SMM).¹¹

Results and discussion

The reaction of Cu(NO₃)₂·3H₂O and Gd(NO₃)₃·6H₂O with triethanolamine (teaH₃) and trimethylacetic acid in a basic alcoholic solution leads to the formation of blue crystals of [Cu^II₅Gd^III₄O₂(OMe)₄(teaH)₄(O₂CC(CH₃)₃)₂(NO₃)₄]·2MeOH·2Et₂O (1·2MeOH·2Et₂O).‡ Compound 1 (Fig. 1A) crystallises in the triclinic space group P1̄ with the asymmetric unit containing half the cluster which lies upon an inversion centre. The complex contains five Cu^II (Cu1–Cu3 and symmetry equivalent, s.e.) and four Gd^III (Gd1, Gd2 and s.e.) ions; the Cu^II ions forming a planar ‘bow-tie’ arrangement, with the four Gd^III ions forming a rectangle perpendicular to this (Fig. 1B). The metallic skeleton thus describes four vertex and face-sharing {GdCu₃} tetrahedra (Fig. 1C). Two central trigonal bipyramidal μ₅-O²⁻ ions (O1 and s.e.) link the perpendicular Cu₅ and Gd₄ frameworks together. The central Cu^II ion (Cu1) is four coordinate and in a square planar geometry with a [CuO₄] coordination sphere. The outer four Cu^II ions (Cu2, Cu3 and symmetry equivalents) are also four coordinate and square planar but with [CuO₃N] coordination spheres and with an additional long (axial) contact to a non-bonded O-atom (O13 and s.e.) of a teaH ligand (∼2.4–2.7 Å). The Gd^III ions are eight coordinate and in distorted square antiprismatic geometries, with [GdO₈] coordination spheres. The two carboxylates and four methoxide ions each bridge in a μ-fashion across the short edge of the Gd₄ rectangle, with one exception, O2(OMe⁻) and symmetry equivalent is μ₃-bridging, the additional bond being to the central Cu^II ion. The NO₃⁻ ions each chelate to a Gd^III ion at the four “outer” corners of the Gd₄ rectangle. The doubly deprotonated μ₃ : η² : η² : η¹ : η⁰ teaH ligands each encapsulate one Cu^II ion using two O-atoms and one N-atom and then attach it to the long rectangular edge of the Gd₄ rectangle via their two μ-O-atoms. The non-bonding alcohol arms are protonated, two of which form H-bonds to solvent MeOH molecules and two of which form inter-molecular H-bonds to the NO₃⁻ ions of adjacent clusters. The latter interaction directs the formation 1-D H-bonded chains down the c-axis of the crystal.

Fig. 1 A) The molecular structure of complex 1. Colour code: Gd = purple, Cu = green, O = red, N = blue, C = grey. H-atoms are omitted for clarity. B) The metallic skeleton highlighting the two “interpenetrating” metal frameworks; the Cu₅ “bow-tie” and the Gd₄ rectangle. C) The metallic skeleton drawn to emphasise the four face- and vertex-sharing {Cu₃Gd} tetrahedra. The Gd⋯Gd distances across the short and long rectangular edges are 3.735 Å and 5.279 Å, respectively. The Cu1⋯Cu2,3 distances are ∼3.5 Å; the Cu2⋯Cu3 distance is ∼3.1 Å and the Cu⋯Gd distance, ∼3.3 Å. Cu1–O1–Cu2, 123.88°, Cu1–O1–Cu3, 128.95°, Cu2–O1–Cu3, 107.05°.

The DC magnetic susceptibility of 1 was collected in an applied field B₀ = 0.01 T over the 2–300 K temperature range (Fig. 2). The room-temperature χ_MT value of 33.0 cm³ K mol⁻¹ stays nearly constant with decreasing temperature down to ∼30 K, below which it increases significantly reaching a value of 48.6 cm³ K mol⁻¹ at 2 K, indicating that dominant ferromagnetic pathways are present. The χ_MT value expected for an uncoupled [Cu^II₅Gd^III₄] unit (g = 2.00) is 33.33 cm³ K mol⁻¹, in good agreement with the experimental data at high temperatures. The magnetisation measurements (inset of Fig. 2) show a saturation value of 31.3 Nμ_B at the lowest investigated temperature T = 2 K, suggesting a net spin state S = 31/2. This can be rationalised assuming the central Cu^II to be antiferromagnetically coupled to the outer Cu sites in the ‘bow-tie’. This is likely to occur as the average Cu(central)–O–Cu(outer) bond angle is ∼126° which will likely be antiferromagnetic and stronger than the outer Cu–O–Cu interactions (average angle of 107°) forcing the four Cu sites to align parallel to each other. The Cu⋯Gd interactions between the outer Cu ions and the Gd ions are likely weak and ferromagnetic, as has been noted for a number of Gd and Cu ions bridged by two O-atoms.¹² The weak exchange promoted by the lanthanide ions will most likely lead to several spin states energetically close to an ill-defined ground state, a sought after situation for observing an enhanced MCE.^5–7,10

Fig. 2 Temperature-dependence of χ_MT for 1 collected for B₀ = 0.01 T. Inset: Field-dependence of the molar magnetisation for the indicated temperatures.

We next turn to the evaluation of the magnetothermal properties of 1 by presenting its temperature-dependent heat capacity (C) collected for several field values (Fig. 3).

Fig. 3 Temperature-dependence of the heat capacity C normalised to the gas constant R for 1 at several applied fields; the dotted line is the Debye fit to the lattice contribution, whereas the solid lines are the calculated Schottky contributions (see text). Inset: T-dependence of the entropy, as obtained from the C data.

At high temperatures, the heat capacity is dominated by a non-magnetic contribution arising from thermal vibrations of the lattice, which is modelled with the well-known low-T Debye function (dotted line in Fig. 3) yielding a value of Θ_D = 23 K for the Debye temperature, typical for this class of cluster compound.¹ At low temperatures, the heat capacity is dependent upon the applied field. Indeed, the splitting of the molecular spin states results in a broad (Schottky-type) feature, which shifts to higher T by increasing the applied field. This behaviour can be explained using the same model which was suggested by the M_mol(T, B₀) data, namely an antiferromagnetic core formed by the Cu^II spins (providing a net spin S_[Cu] = 3/2, g = 2 at low temperatures) that weakly couples to the peripheral Gd^III spins. As a comparison with the experimental data, Fig. 3 shows the contributions (solid lines for B₀ = 1, 3, 6 and 9 T, respectively) that result by summing together the calculated Schottky curves arising from the field-split levels of a central S_[Cu] = 3/2 net spin and four independent Gd^III (S = 7/2, g = 2) spins. It can be seen that the higher fields promote a larger decoupling between the spin centres, yielding an increasingly better agreement. The relatively poorer agreement at lower fields and temperatures can likely be ascribed to the presence of low-lying excited spin states, in accordance with the interpretation of the M_mol(T,B₀) data. From the experimental heat capacity, the temperature dependence of the entropy is obtained by integration, i.e. using Entropy(T) = ∫C(T)/TdT, and is depicted in the inset of Fig. 3 for several applied fields. One can notice the ∼9 R “plateau” for the zero-field entropy in the 2 < T < 8 K temperature range, which again can be understood within the frame of a model of four weakly coupled Gd^III spins to a central S_[Cu] = 3/2 core. Above 2–3 K, the Cu⋯Gd interactions are fully decoupled, therefore the expected entropy/R should be 4 x ln(8) + ln(4) = 9.7, in agreement with the experimental value reached at the plateau. Above approximately 8 K, the zero-field entropy content increases steadily because of the dominant lattice heat capacity (see Fig. 3).

We next evaluate the MCE of 1, i.e. both the magnetic entropy change ΔS_m and adiabatic temperature change ΔT_ad from the temperature and field dependencies of the entropy.¹⁰ The results are summarised in Fig. 4. We report a record value of −ΔS_m which reaches ∼31 J kg⁻¹ K⁻¹ at T = 3 K for ΔB₀ = 9 T. This is what we could have expected considering the large net magnetic moment of the molecule, combined with the negligible anisotropy and the weak intra-cluster interactions that promote low-lying excited spin states.¹⁰ An added “pro” is the relatively small molecular mass (m_w = 2141.8 g), which results from the relatively low ratio of ligands present. These being non-magnetic, contribute passively to the MCE. Likewise, the ΔT_ad is extraordinarily large (see bottom panel of Fig. 4). We refer particularly to the cooling rate K T⁻¹, which goes from more than 1 K T⁻¹ for ΔB₀ = 9 T to well over 2 K T⁻¹ for ΔB₀ = 1 T, setting this material among the most efficient refrigerants for the liquid-helium temperature range.¹⁰ Finally, we note an excellent agreement between the −ΔS_m obtained from the C data with that obtained by applying the Maxwell equation to the isothermal magnetisation curves (the asterisks in Fig. 4),¹⁰ suggesting that both independent procedures can be effectively used to characterise 1 with respect to its MCE.

Fig. 4 Top: T-dependencies of the magnetic entropy change as obtained from C (filled dots) and M_mol (asterisks) experimental data, for the indicated applied field changes. Bottom: T-dependencies of the adiabatic temperature change obtained from Cexperimental data, for the indicated applied field changes.

Conclusions

The use of teaH₃ in heterometallic 3d–4f chemistry has led to the isolation of an unusual but beautiful [Cu^II₅Gd^III₄] cluster comprising a series of vertex- and face-sharing {GdCu₃} tetrahedra. The low molecular mass, the constituent isotropic metal ions, the ferromagnetic Cu^II-Gd^III interaction and the inherent weak exchange propagated by the lanthanide ions results in the population of numerous S states even at the lowest temperatures measured. This is reflected in a truly enormous enhancement of the MCE with −ΔS_m values larger than 30 J kg⁻¹ K⁻¹; the largest value seen for any molecular compound. This clearly demonstrates that [Cu^II-Gd^III] cluster compounds — for so long studied because of the ferromagnetic exchange between the 3d and 4f metal ions — can be successfully exploited for magnetic refrigeration.

Acknowledgements

This work was supported by an ARC Discovery grant (KSM), the Spanish MICINN (contracts MAT2009-13977-C03 and CSD2007-00010); the EPSRC, Leverhulme Trust and the Royal Society of Chemistry (EKB).

Notes and references

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Footnotes

† CCDC reference number 809026. For crystallographic data in CIF or other electronic format see DOI: 10.1039/c1sc00038a

‡ [Cu^II₅Gd^III₄O₂(OMe)₄(teaH)₄(O₂CC(CH₃)₃)₂(NO₃)₄]·2MeOH·2Et₂O (1·2MeOH·2Et₂O). Cu(NO₃)₂·3H₂O (0.2 g, 1 mmol) was dissolved in 20 ml of MeOH followed by the addition of triethanolamine (0.13 ml, 1 mmol), pivalic acid (0.05 g, 0.5 mmol) and triethylamine (0.5 ml, 3.5 mmol) to give a green/blue solution. To this Gd(NO₃)₃·6H₂O (0.45 g, 1 mmol) was added to give a deep blue solution. This was then stirred for 4 h, allowed to stand and was then layered with diethyl ether. After 3–5 days blue crystals of 1 had formed. Yield: 102 mg, 39.2%. Anal. Calculated (found) for 1·2MeOH·2Et₂O: Cu₅Gd₄C₄₈H₁₁₀O₃₈N₈ : C, 24.49 (24.20); H, 4.71 (4.29); N, 4.76 (4.59). Selected ATR IR data (cm⁻¹): 2957w, 2856s, 1559s, 1483s, 1457sh, 1423s, 1377w, 1360w, 1298s, 1251w, 1227w, 1155w, 1133w, 1083s,1022s, 916m, 896m, 817w.X-Ray crystallographic measurements were performed at 100(2) K at the Australian synchrotron MX1 beam-line as described elsewhere.¹³ The data collection and integration were performed within Blu-Ice¹³ and XDS¹⁴ software programs. The data collection and integration were performed within SMART and SAINT+ software programs, and corrected for absorption using the Bruker SADABS program. 1 was solved by direct methods (SHELXS-97) and refined (SHELXL-97) by full least matrix least-squares on all F² data.¹⁵ Crystallographic details are available in the Supporting Information in CIF format.† CCDC number 809026. These data can be obtained free of charge from the Cambridge Crystallographic Data Centre viahttp://www.ccdc.cam.ac.uk/data_request/cif.Crystal data for 1: M, g mol⁻¹ = 2354.16, Crystal system = Triclinic, P1̄, a = 11.050(2), b = 13.830(3), c = 14.030(3) Å, α = 78.80(3), β = 83.81(3), γ = 69.28(3)°, V/ų = 1965.4(8), T/K = 100(2), Z = 1, ρ_c/g cm⁻³ = 1.989, λ_b/Å = 0.7182, data measured = 12139, Ind. Reflns = 7056, R_int = 0.0315, Reflns with I > 2σ(I) = 6876, parameters = 477, restraints = 0, R1c, wR2c = 0.0398, 0.099, goodness of fit = 1.132, Largest residuals/e Å⁻³ = 1.09, −1.331.

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