A perfect triangular dysprosium single-molecule magnet with virtually antiparallel Ising-like anisotropy

Abstract

We report a trinuclear dysprosium single-molecule magnet, [Dy₃(μ₃-CO₃)(^Clbbpen)₃](CF₃SO₃)·6MeCN, which has a perfectly equilateral triangular structure. The Ising-like anisotropy of each Dy(III) site is oriented almost normal to the triangular plane, and magnetic dipole interactions between the spins cause an antiparallel Ising ground state. Crossing of the antiferromagnetic states by the ferromagnetic state occurs at ca. 0.2 T and gives rise to a characteristic step in magnetic hysteresis loops. This molecule thus serves as a perfectly triangular model system to explore frustrated Ising anisotropy.

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Introduction

Trinuclear complexes with a triangular arrangement of spins are of great interest in molecular magnetism, since their geometry is prototypical to realize toroidal magnetism^1–6 and spin frustration,^7–10 but they can also function as single-molecule magnets (SMMs).^11–16 Competing antiferromagnetic interactions can cause spin frustration, which in extended lattices gives rise to exotic quantum states, where the trigonal Kagomé lattice is one of the most famous examples.^17–26 In zero-dimensional systems, such as molecular magnets, frustration leads to degenerate spin ground states.⁷ Indeed, triangular trimetallic complexes are the simplest model of this phenomenon, and are small enough to obtain precise information on the quantum states,^27–34 and thus explain the observed magnetic phenomena.

Antisymmetric and anisotropic exchange interactions can remove the degeneracy of the frustrated ground state,¹⁰ and thus magnetically isotropic ions are most common for the observation of frustration in C₃-symmetric molecules.^35–40 While not impossible, designing spin frustration on the basis of strongly anisotropic ions (e.g. Ising spins) is non-trivial, since it is difficult to control the orientations of each principal magnetic axis in a molecule. The ideal frustrated Ising triangle would consist of a perfect equilateral triangle of spins whose principal magnetic axes are all perpendicular to the plane of the triangle, so that the dipolar magnetic coupling leads to a frustrated ground state.

While there have been some examples of trigonal Dy₃ complexes previously, these compounds either are not C₃ symmetric,¹³ have in-plane principal magnetic axes,^14,15 or show large tilt angles away from the normal direction.¹¹ Inspired by our recent work on highly-anisotropic Dy(III) ions in pentagonal bipyramidal geometries, e.g. the high-performance [Dy(bbpen)Br]^41a and the para-/diamagnetic cyanometallate-bridged [Dy₂(bbpen)₂{M(CN)₆}]⁻ (M = Fe, Co) via building block approaches,^41b herein we have replaced the terminal anion with a C₃-symmetric μ₃-η²:η²:η² bridging CO₃²⁻ ligand, yielding [Dy₃(μ₃-CO₃)(^Clbbpen)₃](CF₃SO₃)·6MeCN (1, H₂^Clbbpen = N,N‘-bis(5-chloro-2-hydroxybenzyl)-N,N‘-bis(2-picolyl)ethylenediamine). This new trinuclear molecular magnet has a crystallographically-enforced equilateral triangular geometry, and herein we investigate its magnetic properties such as the multi-step hysteresis loops related to the Ising-like ground states, combining experimental measurements and electronic structure calculations.

Results and discussion

The crystal structure of 1 was determined by single-crystal X-ray diffraction (Fig. 1a and Table S1†). Compound 1 crystallizes in trigonal space group R32, and the asymmetric unit contains only one half of Dy(III) ion, one half of ^Clbbpen²⁻ ligand, one third of CO₃²⁻ and one sixth of CF₃SO₃⁻. As illustrated in Fig. 1a, each Dy(III) is supported by the hexadentate ^Clbbpen²⁻ ligand, connecting with four N atoms from amines/pyridines and two O atoms from phenols. The three Dy(III) are bridged by a central CO₃²⁻ in the μ₃-η²:η²:η² coordination mode (Fig. 1a), forming an equilateral triangle. Due to the trigonal symmetry, all the intramolecular Dy⋯Dy distances are perfectly identical (4.828 Å). For compound 1, the axial and the equatorial Dy–O distances are 2.211 and 2.417 Å, respectively, and the equatorial Dy–N distances are 2.504 and 2.655 Å. The axial O–Dy–O angle is nearly linear at 161.1°. The short axial Dy–O bonds, near linear axial O–Dy–O angle, and longer equatorial bonds should generate large magnetic anisotropy at each Dy site, as observed for [Dy(bbpen)Br] and its anologues.⁴¹

Fig. 1 (a) Molecular structure of 1. Dy, pink; O, red; N, blue; Cl, green; C, grey. For clarity, the hydrogen atoms are omitted; (b) the magnetic axes of the Kramers ground doublet of Dy(III) sites (blue arrows) related to C₃ symmetry in top view (left) and side view (right).

The variable temperature magnetic susceptibility of a polycrystalline sample of 1 was measured under a 1 kOe direct current (dc) field (Fig. 2). The χ_MT value at room temperature is 42.19 cm³ K mol⁻¹, in good agreement with three non-interacting Dy(III) ions (⁶H_15/2, 42.51 cm³ K mol⁻¹), and that calculated ab initio (41.14 cm³ K mol⁻¹). We note that the 2.5% discrepancy between experimental and calculated data at high temperatures is likely due a combination of uncertainties in sample mass and diamagnetic corrections, as well as the approximations introduced in the ab initio calculations. Upon cooling, the value gradually decreases to 23.31 cm³ K mol⁻¹ at 2 K, which is generally due to the depopulation of crystal field states of the J = 15/2 manifold, though might also indicate magnetic interactions or slow magnetic dynamics at low temperatures. The magnetization saturates at 15 Nμ_B at 5 K and 7 T (Fig. S4†), indicating that each Dy(III) ion has a m_J = ±15/2 ground state.⁴² Zero-field-cooled and field-cooled (ZFC-FC) magnetizations (Fig. S6†) diverge below 4.2 K, suggesting slow magnetic dynamics at low temperatures.

Fig. 2 Variable-temperature of the molar magnetic susceptibility χ_MT products under a 1 kOe dc field for 1. The dashed line corresponds to the CASSCF-SO calculations. Insert: the molar magnetic susceptibility χ_MT products between 2 K and 25 K under 1 kOe dc field. The solid line corresponds to the Dy₃ with dipolar interaction between the Dy(III); note that there is poor agreement at high temperatures because the dipolar model only accounts for the lowest Kramers doublet on each Dy(III) centre.

Investigating the magnetic dynamics of 1 with temperature- and frequency-dependent alternating current (ac) magnetic susceptibility, reveals the typical patterns of SMM behaviour (Fig. 3 and S7–S9†). Two peaks are observed in the out-of-phase (χ_M′′) signal below 21 K (Fig. S9a†), while only one peak is observed above 21 K (Fig. S9b†). The presence of two peaks indicates the existence of two relaxation times (a fast relaxation, FR, and a slow relaxation, SR, component); such behaviour has been reported previously that could involve the high-density exchange spectrum.^{11,15,16,43–49} Fitting the low temperature data with the sum of two generalized Debye functions gives α_FR = 0.34–0.49 and α_SR = 0.003–0.023 (Fig. S9a and Table S4†), while the high-temperature data are well modelled with a single generalized Debye function, giving α = 0.027–0.076 (Fig. S9b and Table S5†). The α_FR values are very large, indicating a large distribution of relaxation times, while those for α_SR and those at high temperatures are very small, indicating a narrow distribution for relaxation times.⁵⁰ Application of a magnetic field has a very small effect on the relaxation times (Fig. 4, S11, S12 and Table S8†), where the most obvious change is suppression of the FR process (Fig. S8b†); a generalized Debye fit of ac data in an optimum field of 1.2 kOe also show a reasonably narrow distribution of relaxation times with α = 0.006–0.10 (7–53 K, Fig. S10 and Table S6†). We also examine the relaxation time at lower temperatures (3–6 K) using dc magnetization decay experiments (Fig. S13 and Table S7†), both in zero and 1.2 kOe fields; the β values are 0.89–0.99 (0 kOe) and 0.80–0.85 (1.2 kOe) and thus suggest a narrow-to-moderate distribution of relaxation times, consistent with the ac data.⁵¹

Fig. 3 Variable-frequency temperature-dependent ac magnetic susceptibilities for 1 under 1.2 kOe dc field. The solid lines are guided for the eyes.

Fig. 4 (a) Temperature dependence of the magnetic relaxation time under 0 Oe (red) and 1.2 kOe (blue) is shown as τ versus T⁻¹ in log-linear scale and (b) τ⁻¹vs. T in log–log scale for 1. The dashed lines correspond to the equation τ⁻¹ = τ₀⁻¹exp(−U_eff/k_BT) + CTⁿ.

Examination of the temperature dependence of the relaxation times (we only discuss the SR process in zero field, due to the large distribution in the FR relaxation times and limited data) shows a strongly-temperature-dependent regime at high temperatures, and a power-law temperature dependence at lower temperatures, suggesting exponential (Orbach-like) and Raman relaxation mechanisms, respectively (Fig. 4). These data can be modelled with τ⁻¹ = τ₀⁻¹exp(−U_eff/k_BT) + CTⁿ, with best-fit parameters U_eff/k_B = 504(25) K, τ₀ = 1.3(7)×10⁻⁹ s, C = 4.5(3)×10⁻⁴ s⁻¹ K⁻ⁿ and n = 4.39(2) for the zero-field data, and U_eff/k_B = 577(26) K, τ₀ = 4.5(24)×10⁻¹⁰ s, C = 2.6(2)×10⁻⁴ s⁻¹ K⁻ⁿ and n = 4.42(2) for the 1.2 kOe data.

Magnetic hysteresis loops can be observed for 1 up to 6 K (0.02 T s⁻¹, Fig. 5a), where loops at the lowest temperatures show clear steps at ca. 0.2 and 0 T. Indeed, we also observe a slight drop in the relaxation time in field-dependent ac susceptibility measurements at 0.2 T at a higher temperature of 12 K (Fig. S12†), supporting the field position of this fast-relaxation event. Both experimental results suggest the existence of level (anti-)crossings between ground and excited states that are polarized by the applied magnetic fields, which may be related to the frustrated Ising ground states (see theoretical analysis and discussions below).

Fig. 5 (a) Variable-field magnetic hysteresis loops the powder sample 1, with a sweep rate of 0.02 T s⁻¹ from 2 to 7 K. (b) Zeeman splitting of a perfect Dy₃ Ising frustrated triangle along the z direction.

To examine the electronic structure of the Dy(III) ions, we have performed complete active space self-consistent field spin–orbit (CASSCF-SO) calculations on the single unique Dy site in 1 (see ESI† for details). We find that the ground state is m_J = ±15/2, with a first excited m_J = ±13/2 state at 439 K. The second excited state is reasonably well-described as 86% m_J = ±11/2 (825 K), but the third excited state (992 K) is strongly mixed (Table S9†). Most importantly, however, we find that the principal magnetic axis for each Ising-like Dy(III) site in 1 is almost perpendicular to the plane of the triangle (Fig. 1b); suggesting that 1 may possess near-ideal geometry to exhibit frustrated Ising behaviour. This is in contrast to most other Dy₃ triangles that have been studied with a focus on their toroidal magnetic ground states.^1,2,4–6 In those cases, the Ising-like magnetic anisotropy of the Dy(III) sites is oriented in the plane of the triangle at tangents to the vertices, and because the local magnetic anisotropy is far stronger than the magnetic interactions between the ions, the ground state is a pair of chiral non-magnetic states (Scheme 1).^1c

Scheme 1 Representations of toroidal magnetism and Ising spin frustration as in-plane type and out-of-plane type (this work).

To start understanding the magnetic properties of 1, we first consider a perfect equilateral Ising triangle (principal magnetic axes perpendicular to the triangular plane). The Dy(III) ions are described as perfect m_J = ±15/2 states by S_eff = 1/2 with axial g_z = 20 (g_xy = 0), where z is the normal of the triangle. Assuming negligible superexchange and dominant dipolar interactions (eqn (1)), the coupling between these spins yields only J_zz non-zero, corresponding to a perfect frustrated Ising system.⁷

For this example, we use Dy–Dy distance from 1 (4.828 Å) to obtain J_zz = −0.770 cm⁻¹ (as the only non-zero entry of ), where the z axis is defined by the C₃ axis of the ideal triangular system. The negative value for J_zz is due to the dipolar magnetic field of each spin and leads to a frustrated ground state. The magnetic properties of such a triangle can be modelled by diagonalization of Hamiltonian eqn (2) using PHI.⁵²

The frustrated ground state is six-fold degenerate and arises from two aligned spins and one inverted spin (↑↑↓, ↑↓↑, ↓↑↑, ↓↓↑, ↓↑↓ and ↑↓↓), while the first excited state at 1.54 cm⁻¹ is doubly degenerate from the ferromagnetic alignment of the spins (↑↑↑ and ↓↓↓). Due to the pure Ising doublets of each site, all states are non-magnetic in the plane of the triangle, however both states are magnetic with a field perpendicular to the plane of the triangle (Fig. 5b); n.b. this is the opposite to toroidal magnetic states. The excited ferromagnetic state shows a crossing with the ground frustrated states in a field of ca. 0.17 T (Fig. 5b), which would be directly observable in mK single-crystal/powder magnetization experiments (Fig. S14†), and indirectly in powder magnetic susceptibility measurements (Fig. S15†). Again, this idealised model can already explain the experimentally observed steps at ca. 0.2 and 0 T in the hysteresis loop of 1 (Fig. 5a): these steps are characteristic of quantum tunnelling of magnetization (QTM), which arises from enhanced relaxation where there is a (anti-)crossing between states.

Moving to the specific case of 1, we now implement a model based on the CASSCF-SO-calculated properties of the ground Kramers doublets for the Dy sites (they are all the same due to three-fold crystallographic symmetry, Tables S9 and S10†): the g-values are not perfectly Ising (g_x = 0, g_y = 0.0005, g_z = 19.82) and the orientation of g_z is not perpendicular to the triangular plane but slightly tilted away by ca. 10° (Fig. 1b and Table S10†). Using this model (Table S10,† where z remains defined by the C₃ axis, y is parallel to the Dy1–Dy3 vector, and x is their cross product), the dipolar interaction matrices between the ions (in cm⁻¹) are given in eqn (3)–(5), which can be incorporated in the full Hamiltonian eqn (7) and solved with PHI.⁵² Note that eqn (3)–(5) are related by a 2π/3 rotation around z, such that and , where is given in eqn (6).

This purely dipolar interaction agrees well with the experimental magnetic data for this compound at low temperatures (Fig. 2 and S4†), and predicts an anti-crossing between the ferro- and antiferromagnetic states at ca. 0.15 T (Fig. S16†) in good agreement with the hysteresis data, suggesting that the superexchange contribution is minimal here, similarly as found directly for a Dy₂ species.⁵³ Compared to our model of the perfect frustrated Ising triangle, the six-fold degenerate frustrated ground state in 1 is split into three doublets at 0, 0.10 and 0.18 cm⁻¹ respectively (which represent mixed wavefunction composed of the various antiferromagnetic combinations), while the excited ferromagnetic state lies at 1.47 cm⁻¹. The lower symmetry at the Dy(III) sites and the misalignment of the magnetic axes means that some states are now weakly magnetic in the plane of the triangle (Fig. S17†) and the crossing of the ground state by the excited ferromagnetic states is smeared out over a wider field range (Fig. S16†). However, the degeneracy breaking is small (0.18 vs. 1.47 cm⁻¹), and thus, much as [Dy₃(μ₃-OH)₂(o-vanillin)₃Cl(H₂O)₅]Cl₃·4H₂O is regarded as the archetypal molecular toroic,^1,21 can be regarded as the archetypal molecular frustrated Ising magnet.

Conclusions

By utilizing a strongly anisotropic Dy(III) building unit and a C₃-symmetric CO₃²⁻ ligand, we have prepared a trinuclear dysprosium triangle with a crystallographically-enforced equilateral form. The molecule shows SMM properties with hysteresis loops visible up to 6 K, but most interestingly exhibits a clear step at ca. 0.2 T in low-temperature hysteresis data. A simple dipolar model suggests that this step arises from crossings between the ferromagnetic and near-degenerate frustrated Ising ground states. We anticipate that this molecule will be a useful model to probe Ising frustration in further detailed experimental efforts.

Experimental section

Materials and methods

All reactions and manipulations were carried out under aerobic conditions. The ligand N,N′-bis(5-chloro-2-hydroxybenzyl)-N,N′-bis(2-picolyl)ethylenediamine (H₂^Clbbpen) was prepared in good yield according to the reported methods.⁵⁴ All other starting reagents were commercially available and used without further purification. The C, H, and N microanalyses were performed with an Elementar Vario-EL CHNS elemental analyzer. The FT-IR spectra were recorded from KBr pellets in the range 4000–400 cm⁻¹ on an EQUINOX 55 spectrometer. Thermogravimetric analysis was carried out on a NETZSCH TG209F3 thermogravimetric analyzer. Ac magnetic measurements were performed with a 5 Oe oscillating field. Magnetic susceptibility measurements were performed with a Quantum Design PPMS VSM and MPMS XL-7 SQUID. Data were corrected for the diamagnetic contribution calculated from Pascal constants. X-ray powder diffraction intensities for polycrystalline samples were measured on Bruker D8 Advance Diffractometer (Cu-K_α, λ = 1.54056 Å). Single-crystal diffraction data were collected on a Bruker D8 QUEST diffractometer with Mo-K_α radiation (λ = 0.71073 Å) for complex 1. The structures were solved based on SHELXS methods by using OLEX2 program,^55,56 and all non-hydrogen atoms were refined anisotropically by least-squares on F² using the SHELXL.⁵⁷

[Dy₃(μ₃-CO₃)(^Clbppen)₃](CF₃SO₃)·6CH₃CN (1). A solution of Dy(CF₃SO₃)₃ (61 mg, 0.1 mmol), H₂^Clbbpen (53 mg, 0.1 mmol), tetramethylammonium bicarbonate (16 mg), pyrazine (16 mg) and triethylamine (0.05 mL) in acetonitrile (9 mL) was sealed in a 23 mL Teflon-lined stainless container and heated at 70 °C for 3 days and then cooled to ambient temperature at a rate of 10 °C h⁻¹. The resulting mixture was filtered, and then the filtrate was left to stand at room temperature. After several days, colorless block crystals were obtained (yield ca. 13 mg, 32%). Elem anal. calcd: C, 46.95%; H, 3.86%; N, 10.06%. Found: C, 46.92%; H, 3.93%; N, 9.90%.

Computational details

We have performed complete active space self-consistent field spin–orbit (CASSCF-SO) calculations on the X-ray structure of 1 with no optimisation using MOLCAS 8.0.⁵⁸ The Dy^III ion was described using the ANO-RCC-VTZP basis, the first coordination sphere atoms with the ANO-RCC-VDZP basis and all other atoms described with the ANO-RCC-VDZ basis.^59,60 The metal centres not in focus of the calculation were substituted for diamagnetic Lu^III ions with the ANO-RCC-VDZ basis. We employed Cholesky decomposition of the two electron integrals with a threshold of 10⁻⁸. The active space incorporated the 9 4f electrons of Dy(III) in seven 4f orbitals. State-averaged CASSCF calculations were performed for 21 sextet, 224 quartet and 490 doublet spin states, and then 21 sextets, 128 quartets and 130 doublets were mixed by SO coupling in the RASSI routine. The wavefunctions were extracted using SINGLE_ANISO where the quantisation axis was the principal g_z-value of the ground Kramers doublet.⁶¹ As 1 is symmetric, only one calculation was performed owing to the crystallographic symmetry.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (2018YFA0306001), the NSFC (Grant No., 21620102002, 21771200, 21822508, 21821003), and the Pearl River Talent Plan of Guangdong (2017BT01C161). NFC thanks The Royal Society for a University Research Fellowship and MJG thanks The University of Manchester for a President's Doctoral Scholarship award.

Notes and references

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Footnotes

† Electronic supplementary information (ESI) available: Synthesis, additional characterization, crystal structure data, ab initio calculations of 1. CCDC 1983277. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/d0qi00655f

‡ These authors contributed equally to this work.

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