Relaxation Dynamics and Magnetic Anisotropy in a Low-Symmetry Dy(III) Complex

Osmium(III) Acetylacetonate and Its Missing Polymorph: A Magnetic and Structural Investigation

Despite the potential for their application, the magnetic behavior of complexes containing 4d and 5d metal ions is underexplored, evidencing the need for benchmark multi-technique studies on simple molecules. We report here a structural and magnetic study on osmium(III) acetylacetonate [Os(acac)3]. X-ray single crystal diffraction did not allow us to determine the structure of the β-polymorph of [Os(acac)3]. The combined magnetic (dc magnetic measurements on powder and cantilever torque magnetometry on single crystal) and spectroscopic (electron paramagnetic resonance, EPR) characterization is here used to provide further evidence that its structure is indeed the one of the orthorhombic "missing polymorph", analogous to the ruthenium(III) derivative. Our study shows that all acetylacetonate complexes of the eighth group of the periodic table show dimorphism and are isomorphic. The EPR characterization allowed the experimental assessment of the easy axis nature of the ground doublet and the determination of the first hyperfine coupling in an osmium complex. Torque magnetometry, applied here for the first time on an osmium-based molecule, determined the orientation of the easy axis along the pseudo C3 axis of the complex. Ac magnetometric measurements revealed in-field slow relaxation of the magnetization further slowed by the suppression of dipolar fields via magnetic dilution in the isostructural gallium(III) analogue.

Discovery of a Dysprosium Metallocene Single-Molecule Magnet with Two High-Temperature Orbach Processes

Magnetic bistability in single-molecule magnets (SMMs) is a potential basis for new types of nanoscale information storage material. The standard model for thermally activated relaxation of the magnetization in SMMs is based on the occurrence of a single Orbach process. Here, we show that incorporating a phosphorus atom into the framework of the dysprosium metallocene [(Cp^iPr5)Dy(Cp^PEt4)]⁺[B(C₆F₅)₄]⁻ (Cp^iPr5 is penta-isopropylcyclopentadienyl, Cp^PEt4 is tetraethylphospholyl) leads to the occurrence of two distinct high-temperature Orbach processes, with energy barriers of 1410(10) and 747(7) cm^–1, respectively. These barriers provide experimental evidence for two different spin–phonon coupling regimes, which we explain with the aid of ab initio calculations. The strong and highly axial crystal field in this SMM also allows magnetic hysteresis to be observed up to 70 K, using a scan rate of 25 Oe s^–1. In characterizing this SMM, we show that a conventional Debye model and consideration of rotational contributions to the spin–phonon interaction are insufficient to explain the observed phenomena.

A phospholyl-ligated dysprosium metallocene single-molecule magnet shows two high-temperature Orbach relaxation processes with effective energy barriers of 1410(10) and 747(7) cm⁻¹, and magnetic hysteresis up to 70 K when using a scan rate of 25 Oe s⁻¹.

A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion's first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

Cadmium-Inspired Self-Polymerization of {LnIIICd2} Units: Structure, Magnetic and Photoluminescent Properties of Novel Trimethylacetate 1D-Polymers (Ln = Sm, Eu, Tb, Dy, Ho, Er, Yb)

A series of heterometallic carboxylate 1D polymers of the general formula [Ln^IIICd₂(piv)₇(H₂O)₂]_n·nMeCN (Ln^III = Sm (1), Eu (2), Tb (3), Dy (4), Ho (5), Er (6), Yb (7); piv = anion of trimethylacetic acid) was synthesized and structurally characterized. The use of Cd^II instead of Zn^II under similar synthetic conditions resulted in the formation of 1D polymers, in contrast to molecular trinuclear complexes with Ln^IIIZn₂ cores. All complexes 1–7 are isostructural. The luminescent emission and excitation spectra for 2–4 have been studied, the luminescence decay kinetics for 2 and 3 was measured. Magnetic properties of the complexes 3–5 and 7 have been studied; 4 and 7 exhibited the properties of field-induced single-molecule magnets in an applied external magnetic field. Magnetic properties of 4 and 7 were modelled using results of SA-CASSCF/SO-RASSI calculations and SINGLE_ANISO procedure. Based on the analysis of the magnetization relaxation and the results of ab initio calculations, it was found that relaxation in 4 predominantly occurred by the sum of the Raman and QTM mechanisms, and by the sum of the direct and Raman mechanisms in the case of 7.

Single-Ion Anisotropy and Intramolecular Interactions in CeIII and NdIII Dimers

This article reports the syntheses, characterization, structural description, together with magnetic and spectroscopic properties of two isostructural molecular magnets based on the chiral ligand N,N'-bis((1,2-diphenyl-(pyridine-2-yl)methylene)-(R,R/S,S)-ethane-1,2-diamine), L1, of general formula [Ln2(RR-L1)2(Cl6)]·MeOH·1.5H2O, (Ln = Ce (1) or Nd (2)). Multifrequency electron paramagnetic resonance (EPR), cantilever torque magnetometry (CTM) measurements, and ab initio calculations allowed us to determine single-ion magnetic anisotropy and intramolecular magnetic interactions in both compounds, evidencing a more important role of the anisotropic exchange for the NdIII derivative. The comparison of experimental and theoretical data indicates that, in the case of largely rhombic lanthanide ions, ab initio calculations can fail in determining the orientation of the weakest components, while being reliable in determining their principal values. However, they remain of paramount importance to set the analysis of EPR and CTM on sound basis, thus obtaining a very precise picture of the magnetic interactions in these systems. Finally, the electronic structure of the two complexes, as obtained by this approach, is consistent with the absence of zero-field slow relaxation observed in ac susceptibility.

Magnetic Anisotropy Trends along a Full 4f-Series: The fn+7 Effect

The combined experimental and computational study of the 13 magnetic complexes belonging to the Na[LnDOTA(H2O)] (H4DOTA = tetraazacyclododecane-N,N',N″,N‴-tetraacetic acid and Ln = Ce-Yb) family allowed us to identify a new trend: the orientation of the magnetic anisotropy tensors of derivatives differing by seven f electrons practically coincide. We name this trend the fn+7 effect. Experiments and theory fully agree on the match between the magnetic reference frames (e.g., the easy, intermediate, and hard direction). The shape of the magnetic anisotropy of some couples of ions differing by seven f electrons might seem instead different at first look, but our analysis explains a hidden similarity. We thus pave the way toward a reliable predictivity of the magnetic anisotropy of lanthanide complexes with a consequent reduced need of computational and synthetical efforts. We also offer a way to gain information on ions with a relatively small total angular momentum (i.e., Sm3+ and Eu3+) and on the radioactive Pm3+, which are difficult to investigate experimentally.

Slow Magnetic Relaxation in a Co2 Dy Trimer and a Co2 Dy2 Tetramer

The combination of Co(III) and Dy(III) with a compartmental Schiff base ligand (H₃ L=3-[(2-Hydroxy-3-methoxy-benzylidene)-amino]-propane-1,2-diol), presenting three different coordinating pockets, has allowed the synthesis of two novel Co(III)-Dy(III) complexes: [Co₂ Dy(HL)₄ ]NO₃  ⋅ 2CH₃ CN (1), a rare example of trinuclear linear Co^III ₂ Dy^III complex (and the first with slow relaxation of magnetization in absence of a DC field) and [Co₂ Dy₂ (μ₃ -OH)₂ (HL)₂ (OAc)₆ ] ⋅ 4.6H₂ O (2), the first tetranuclear Co^III ₂ Dy^III ₂ cluster with a rhomb-like structure where the Co(III) ions are connected along the short diagonal of the rhomb. 1 presents two different relaxation processes: a fast relaxation dominated by Quantum tunnelling (QT) and a slow relaxation with an energy barrier of 40 K. 2 shows two close relaxation processes without applied DC fields that follow QT and Orbach mechanisms whereas for H_DC =500 Oe, the QT is cancelled and a direct term appears. Here we present the synthesis, X-ray structure and magnetic characterization of these two Co(III)-Dy(III) single-ion/molecule magnets.

A stable dysprosium(iii) complex with a terminal fluoride ligand showing high resolution luminescence and slow magnetic relaxation

An air-stable dysprosium(iii) complex, [C(NH₂)₃]₄[DyF(piv)₄](piv)₂ (piv = pivalate), with a terminal fluoride ligand protected by forming extensive hydrogen bonds with peripheral guanidiniums has been isolated. Though the magnetic data failed to determine the energy barrier for the magnetic reversal (U_eff) accurately, the fine emission spectrum of the ⁴F_9/2→⁶H_15/2 transition at 4.2 K and ab initio calculations reveal that the U_eff is about 376(20) K, which is among the highest for high-coordinate (coordination numbers ≥ 9) lanthanide mononuclear magnets.

A method to predict both the relaxation time of quantum tunneling of magnetization and the effective barrier of magnetic reversal for a Kramers single-ion magnet

A method to predict the relaxation time of quantum tunneling of magnetization and the magnetic reversal barrier with efficiency and reliability.

Covalency and magnetic anisotropy in lanthanide single molecule magnets: the DyDOTA archetype

Lanthanide ions when complexed by polyamino-polycarboxylate chelators form a class of compounds of paramount importance in several research and technological areas, particularly in the fields of magnetic resonance and molecular magnetism. Indeed, the gadolinium derivative is one of the most employed contrast agents for magnetic resonance imaging while the dysprosium one belongs to a new generation of contrast agents for T2-weighted MRI. In molecular magnetism, Single Molecule Magnets (SMMs) containing lanthanide ions have become readily popular in the chemistry and physics communities since record energy barriers to the reversal of magnetization were reported. The success of lanthanide complexes lies in their large anisotropy due to the contribution of the unquenched orbital angular momentum. However, only a few efforts have been made so far to understand how the f-orbitals can be influenced by the surrounding ligands. The outcomes have been rationalized using mere electrostatic perturbation models. In the archetype compound [Na{Dy(DOTA) (H2O)}]·4H2O (Na{DyDOTA}·4H2O) an unexpected easy axis of magnetization perpendicular to the pseudo-tetragonal axis of the molecule was found. Interestingly, a dependency of the orientation of the principal magnetization axis on the simple rotation of the coordinating apical water molecule (AWM) - highly relevant for MRI contrast - around the Dy-OAWM bond was predicted by ab initio calculations, too. However, such a behaviour has been contested in a subsequent paper justifying their conclusions on pure electrostatic assumptions. In this paper, we want to shed some light on the nature of the subtle effects induced by the water molecule on the magnetic properties of the DyDOTA archetype complex. Therefore, we have critically reviewed the structural models already published in the literature along with new ones, showing how the easy axis orientation can dangerously depend on the chosen model. The different computed behaviors of the orientation of the easy axis of magnetization have been rationalized as a function of the energy gap between the ground and the first excited doublet. Magneto-structural correlations together with a mapping of the electrostatic potential generated by the ligands around the Dy(iii) ion through a multipolar expansion have also been used to evidence and quantify the covalent contribution of the AWM orbitals.

Ab Initio Prediction of Tunneling Relaxation Times and Effective Demagnetization Barriers in Kramers Lanthanide Single-Molecule Magnets

Single-molecule magnets (SMMs) are promising candidates for molecule-based quantum information devices. Their main limitation is their cryogenic operative temperature. To achieve devices performing at higher temperatures, demagnetization mechanisms must be suppressed by chemical tuning. Electronic structure calculations can provide useful information to rationalize SMM behavior, but they do not provide a direct prediction for the key experimental parameters describing magnetic relaxation (i.e., tunneling relaxation time (τ_QT) and effective demagnetization barrier ( U_eff)). In this Letter, a first-principles model is proposed to predict τ_QT and U_eff for mononuclear, half-integer spin SMMs, allowing direct comparison with experiment. Model accuracy was assessed against experimental data for 18 mononuclear Ln^III complexes (15 Dy^III and 3 Er^III) and applied to 3 of the current best-performing SMMs, correctly predicting nontrivial relaxation pathways. The model shows that the combination of single-ion anisotropy and spin-spin dipolar coupling can account for the major part of tunneling demagnetization for the studied systems.

Modulation of the Coordination Environment around the Magnetic Easy Axis Leads to Significant Magnetic Relaxations in a Series of 3d-4f Schiff Complexes

A series of Salen-type Zn(II)-Dy(III) complexes [L¹Zn(II)ClDy(III)(acac)₂]·H₂O (1), [L¹Zn(II)BrDy(III)(acac)₂]·H₂O (2), [L¹Zn(II)(H₂O)Dy(III)(acac)₂]·CH₂Cl₂·PF₆ (3), [L²Zn(II)(H₂O)Dy(III)(acac)₂]·PF₆ (4), and Co(III)-Dy(III) complexes [L¹Co(III)Br₂Dy(III)(acac)₂]·CH₂Cl₂ (5), [L²Co(III)Cl₂Dy(III)(acac)Cl(MeO)] (6), [L²Co(III)Cl₂Dy(III)(acac)Cl(H₂O)] (7), and [L²Co(III)Cl₂Dy(III)(NO₃)₂(MeO)] (8) heterobinuclear single-molecule magnets (SMMs) were synthesized and magnetically characterized. These complexes were constructed by incorporating diamagnetic Zn(II) and Co(III) ions with acetylacetone (acac) and compartmental Schiff-base ligands (H₂L¹ = N, N'-bis(2-oxy-3-methoxybenzylidene)-1,2-phenylenediamine; H₂L² = N, N'-bis(2-oxy-3-methoxybenzylidene)-1,2-diaminocyclohexane). In the Zn(II)-Dy(III) (1-4) system, the coordination environments of the Dy(III) ions are nearly identical, but the apical coordination atom to the Zn(II) ion is different. Complexes 1, 2, and 4 displayed no magnetic relaxation in the absence of external magnetic field, but complex 3 displayed more pronounced SMM behavior with a relaxation energy barrier U_eff/ k_B 38 K and magnetic hysteresis at 1.8 K. The SMM performances of 5, 6, and 7 were enhanced significantly by incorporating an octahedral Co(III) instead of square-pyramidal Zn(II) and replacing one of acac^- group around Dy(III) ion by a neutral O atom, displaying U_eff of 167, 118, and 75 K as well as magnetic hysteresis up to 3.5 K. These studies indicated that the remote diamagnetic Zn(II) and Co(III) ions played a key role, and the SMM properties were very strongly related to the special coordination atoms configuration around Dy(III) ion. When this coordination configuration around was broken as 8 exhibited, however, it resulted in a dramatically decreased SMM performance. From this work, the key factors that significantly affect the SMM performance of these heteronuclear Zn(II)/Co(III)-Dy(III) SMMs are unambiguously presented.

Lanthanide(III) (Eu, Gd, Tb, Dy) Complexes Derived from 4-(Pyridin-2-yl)methyleneamino-1,2,4-triazole: Crystal Structure, Magnetic Properties, and Photoluminescence

The reaction of lanthanide(III) nitrates with 4-(pyridin-2-yl)methyleneamino-1,2,4-triazole (L) was studied. The compounds [Ln(NO3 )3 (H2 O)3 ]⋅2 L, in which Ln=Eu (1), Gd (2), Tb (3), or Dy (4), obtained in a mixture of MeCN/EtOH have the same structure, as shown by XRD. In the crystals of these compounds, the mononuclear complex units [Ln(NO3 )3 (H2 O)3 ] are linked to L molecules through intermolecular hydrogen-bonding interactions to form a 2D polymeric supramolecular architecture. An investigation into the optical characteristics of the Eu3+ -, Tb3+ -, and Dy3+ -containing compounds (1, 3, and 4) showed that these complexes displayed metal-centered luminescence. According to magnetic measurements, compound 4 exhibits single-ion magnet behavior, with ΔEeff /kB =86 K in a field of 1500 Oe.

Tm(iii) complexes undergoing slow relaxation of magnetization: exchange coupling and aging effects

The present study focuses on the dynamic magnetic behaviour of exchange coupled 3d-4f complexes containing the scarcely investigated non-Kramers Tm³⁺ center, the 3d metal ions being either the low-spin Fe³⁺ (1) or the diamagnetic Co³⁺ (2) ion. Both complexes display field-induced slow relaxation of magnetization. The field and temperature dependences of the relaxation rate provided indication of relevant contributions from quantum tunnelling, direct, Orbach and Raman processes, with only minor effects from exchange coupling interactions. Furthermore, the aged sample of 2 exhibited an additional relaxation process, possibly due to structural modifications accompanied by solvent loss, highlighting the importance of a careful consideration of this factor when analysing the magnetization dynamics in solvated systems.

Exploring the Influence of Diamagnetic Ions on the Mechanism of Magnetization Relaxation in {CoIII2LnIII2} (Ln = Dy, Tb, Ho) "Butterfly" Complexes

The synthesis and magnetic and theoretical studies of three isostructural heterometallic [Co^III₂Ln^III₂(μ₃-OH)₂(o-tol)₄(mdea)₂(NO₃)₂] (Ln = Dy (1), Tb (2), Ho (3)) "butterfly" complexes are reported (o-tol = o-toluate, (mdea)^2- = doubly deprotonated N-methyldiethanolamine). The Co^III ions are diamagnetic in these complexes. Analysis of the dc magnetic susceptibility measurements reveal antiferromagnetic exchange coupling between the two Ln^III ions for all three complexes. ac magnetic susceptibility measurements reveal single-molecule magnet (SMM) behavior for complex 1, in the absence of an external magnetic field, with an anisotropy barrier U_eff of 81.2 cm^-1, while complexes 2 and 3 exhibit field induced SMM behavior, with a U_eff value of 34.2 cm^-1 for 2. The barrier height for 3 could not be quantified. To understand the experimental observations, we performed DFT and ab initio CASSCF+RASSI-SO calculations to probe the single-ion properties and the nature and magnitude of the Ln^III-Ln^III magnetic coupling and to develop an understanding of the role the diamagnetic Co^III ion plays in the magnetization relaxation. The calculations were able to rationalize the experimental relaxation data for all complexes and strongly suggest that the Co^III ion is integral to the observation of SMM behavior in these systems. Thus, we explored further the effect that the diamagnetic Co^III ions have on the magnetization blocking of 1. We did this by modeling a dinuclear {Dy^III₂} complex (1a), with the removal of the diamagnetic ions, and three complexes of the types {K^I₂Dy^III₂} (1b), {Zn^II₂Dy^III₂} (1c), and {Ti^IV₂Dy^III₂} (1d), each containing a different diamagnetic ion. We found that the presence of the diamagnetic ions results in larger negative charges on the bridging hydroxides (1b > 1c > 1 > 1d), in comparison to 1a (no diamagnetic ion), which reduces quantum tunneling of magnetization effects, allowing for more desirable SMM characteristics. The results indicate very strong dependence of diamagnetic ions in the magnetization blocking and the magnitude of the energy barriers. Here we propose a synthetic strategy to enhance the energy barrier in lanthanide-based SMMs by incorporating s- and d-block diamagnetic ions. The presented strategy is likely to have implications beyond the single-molecule magnets studied here.

Slow magnetisation relaxation in tetraoxolene-bridged rare earth complexes

Two tetraoxolene-bridged dinuclear Dy(iii) complexes exhibit slow relaxation in ac magnetic susceptibility studies with zero-field quantum tunnelling of the magnetisation that is suppressed by the application of a dc magnetic field.

Lanthanide coordination complexes framed by sodium ions: slow relaxation of the magnetization in the Dy(III) derivative

Three tetranuclear lanthanide complexes framed by sodium ions were isolated and characterised and the Dy(iii) complex exhibited SMM behaviour.

Novel mononuclear and 1D-polymeric derivatives of lanthanides and (η6-benzoic acid)tricarbonylchromium: synthesis, structure and magnetism

Novel derivatives of lanthanides and (η⁶-benzoic acid)tricarbonylchromium were synthesized and characterized; complexes of Tb, Dy, Er and Yb exhibit SMM behavior.

Strategies toward High-Temperature Lanthanide-Based Single-Molecule Magnets

Lanthanide-based single-molecule magnets are leading materials for achieving magnetization blocking at the level of one molecule. In this paper, we examine the physical requirements for efficient magnetization blocking in single-ion complexes and identify the design principles for achieving very high magnetization blocking barriers in lanthanide-based compounds. The key condition is the preponderant covalent binding of the Ln ion to one of the ligand atoms, tremendously enhancing the axial crystal field. We also make an overview of practical schemes for the implementation of this principle. These are (1) the effective lowering of the coordination number via displacement of the Ln ion to one of the atoms in the coordination polyhedron, (2) the design of two-coordinated complexes, and (3) the stabilization of diatomic compounds in cages and on surfaces. The last proposal is appealing in connection to spintronics applications, especially via the exploration of robust and highly anisotropic [LnX] units displaying multilevel blocking barriers of thousands of Kelvin and prospects for room-temperature magnetization blocking.

A planar triangular Dy3 + Dy3 single-molecule magnet with a toroidal magnetic moment

The modification of the axial coordination ligands of the Dy₃ + Dy₃ triangles results in a unique Dy₆ complex, in which single-molecule magnet behavior and meanwhile a toroidal magnetic moment in the ground state have been observed.

Encapsulation of a [Dy(OH2)8]3+ cation: magneto-optical and theoretical studies of a caged, emissive SMM

The magnetization dynamics of an emissive [Dy(OH₂)₈]³⁺ complex with local pseudo D_4d symmetry encapsulated within a supramolecular cage have been unraveled by magneto-optical and ab initio studies.