Intramolecular bridging strategies to suppress two-phonon Raman spin relaxation in dysprosocenium single-molecule magnets

Dy(III) bis-cyclopentadienyl (Cp) sandwich compounds exhibit extremely strong single-ion magnetic anisotropy which imbues them with magnetic memory effects such as magnetic hysteresis, and has put them at the forefront of high-performance single-molecule magnets (SMMs). Owing to the great success of design principles focused on maximising the anisotropy barrier, ever higher Ueff values have been reported leading to significant slow down of single-phonon Orbach spin relaxation. However, anisotropy-based SMM design has largely ignored two-phonon Raman spin relaxation, which is still limiting the temperatures at which a memory effect can be observed. In this work, we study the suppression of Raman relaxation through covalent bridging of the Cp ligands by alkyl chains, testing the hypothesis that increasing the rigidity of the ligand framework results in a blue shift of low frequency vibrations in the first coordination sphere of the Dy(III) ion. This reshaping of the vibrational low-energy density of states (DOS) results in lower occupation of pseudo-acoustic phonons available to drive Raman relaxation at low temperatures. We simulate Orbach and Raman spin relaxation in a series of zero-, mono-, di- and tri-bridged [Dy(Cpttt)2]+ analogues fully ab initio, using a quantum mechanics (QM)/molecular mechanics (MM) condensed phase embedding protocol in a periodic solvent matrix as a generic and experimentally testable environment model that can include (pseudo-)acoustic phononic degrees of freedom. We show that this approach can simulate magnetic relaxation dynamics in the condensed phase for the existing non-bridged [Dy(Cpttt)2]+ compound with quantitative experimental accuracy. Subsequently, we find a significant slowing down of Raman relaxation can be achieved for the singly-bridged SMM, while the introduction of further bridges leads to faster relaxation. A key result being that we find the two-phonon Raman rates correlate with the purity of the first-excited Kramers doublet in terms of its mJ = ±13/2 content. Even though the bridging design principle is successful at progressively reshaping the low-energy DOS, the introduction of linker atoms in the equatorial plane successively degrades magnetic anisotropy, suggesting the importance of refined design of the linker chemistry. The accuracy of our results emphasises the value of a generic periodic solvent embedding model, such that it permits the modelling of molecular spin dynamics in the condensed phase without knowledge of a crystal structure. This allows the study of hypothetical molecules or aggregates under real-world conditions, which we expect to have utility beyond the field of molecular magnetism.

Unravelling the Highest Magnetic Anisotropy Among all the n-Shells in 20 Metallocene

Single-molecule magnets (SMMs) with a large magnetization reversal barrier are predominated by the lanthanide systems due to their strong spin-orbit coupling (SOC). However, the transition metals have also emerged as potential contenders and the largest magnetic anisotropy has been identified for a cobalt system among any d-series-based SMMs (Bunting et al. Science 2018, 362, eaat7319). In this work, we have explored the magnetic anisotropy in highly axial ligand field systems of metallocene, having different d-subshell (3d4, 4d4, and 5d4). The wave function-based multireference methods including static and dynamic electron correlations have been employed to investigate the zero-field splitting (ZFS) parameters. Here, we report exceptionally large magnetic anisotropy for a 5d complex of [WCp2]0 with the highest energy barrier that is nearly twice as high as the previous record value for the Co complex. We have also observed that the axial ZFS parameter (D) is increasing down the group in the order of 3d < 4d < 5d, pertaining to a large SOC.

It's not just the size that matters: crystal engineering of lanthanide-based coordination polymers

Synthesis and characterization of Lewis base free coordination polymers of selected lanthanides are presented. For this purpose, the substituted CotTIPS ligand (CotTIPS = 1,4-bis-triisopropylsilyl-cyclo-octatetraendiide) was used to synthesize homoleptic, anionic multidecker compounds of the type [K{LnIII(ɳ8-CotTIPS)2}]n. Depending on the solvent used for crystallization and the ionic radii of the lanthanide cations, three different categories of one-dimensional heterobimetallic coordination polymers were obtained in the solid state. For the early lanthanides La and Ce a unique helical conformation was obtained by crystallization from toluene, while the ionic radius of Pr seems to be a turning point towards the crystallization of zigzag polymers. For Er a third structural motif, a trapezoidal wave polymer was observed. Additionally, the zigzag polymer for all compounds could be obtained by changing the solvent from toluene to Et2O, reavealing a correlation between solid-state structure and ionic radii as well as solvent. While photoluminescence (PL) properties of Cot-lanthanide compounds are scarce, the La complexes show ligand centered green luminescence, whereas the Ce complexes reveal deep red emission origin from d-f transitions. The Er-compounds are single-molecule magnets, in which the magnetic relaxation of each Er ion occurs isolated from its neighbors at temperatures above 10 K, while below 9 K a strong antiferromagnetic coupling between the Er ions was seen.

Direct observation of magnetoelastic coupling in a molecular spin qubit: new insights from crystal field neutron scattering data

Single-molecule magnets are promising candidates for data storage and quantum computing applications. A major barrier to their use is rapid magnetic relaxation and quantum decoherence due to thermal vibrations. Here we report a reanalysis of inelastic neutron scattering (INS) data of the candidate qubit Na9[Ho(W5O18)2]·35D2O, wherein we demonstrate for the first time that magnetic relaxation times and mechanisms can be directly observed as crystal field (CF) peak broadening in INS spectra of a lanthanoid molecular system. The magnetoelastic coupling between the lower energy CF states and phonons (lattice vibrations) is determined by the simultaneous measurement of CF excitations and the phonon density of states, encoded within the same INS experiment. This directly results in the determination of relaxation coupling pathways that occur in this molecule. Such information is invaluable for the further advancement of SMMs and to date has only been obtained from techniques performed in external magnetic fields. Additionally, we determine a relaxation rate of quantum-tunnelling of magnetisation that is consistent with previously measured EPR spectroscopy data.

Inelastic Neutron Scattering Measurement of the Ground State Tunneling Gap in Tb and Ho Analogues of a Dy Field-Induced Single-Molecule Magnet

Recent advances in single-molecule magnet (SMM) research have placed great value on interpretation of inelastic neutron scattering (INS) data for rare earth (RE)-containing SMMs. Here, we present the synthesis of several rare earth complexes where combined magnetic and INS studies have been performed, supported by ab initio calculations. The reaction of rare earth nitrate salts with 2,2'-bipyridine (2,2'-bpy) and tetrahalocatecholate (X₄Cat^2-, X = Br, Cl) ligands in methanol (MeOH) afforded two new families of compounds [RE(2,2'-bpy)₂(X₄Cat)(X₄CatH)(MeOH)] (X = Br and RE = Y, Eu, Gd, Tb, Dy, Ho, Yb for 1-RE; X = Cl and RE = Y, Tb, Dy, Ho, and Yb for 2-RE). Addition of triethylamine (Et₃N) to the reaction mixture delivered Et₃NH[RE(2,2'-bpy)₂(Br₄Cat)₂] (3-RE, RE = Er and Yb). Interestingly, cerium behaves differently to the rest of the series, generating (2,2'-bpyH)₂[Ce(Br₄Cat)₃(2,2'-bpy)] (4-Ce) with tetravalent Ce(IV) in contrast to the trivalent metal ions in 1-3. The static magnetic properties of 1-RE (RE = Gd, Tb, Dy and Ho) were investigated in conjunction with INS measurements on 1-Y, 1-Tb, and 1-Ho to probe their ground state properties and any crystal field excitations. To facilitate interpretation of the INS spectra and provide insight into the magnetic behavior, ab initio calculations were performed using the single-crystal X-ray diffraction structural data of 1-RE (RE = Tb, Dy and Ho). The ab initio calculations indicate ground doublets dominated by the maximal angular momentum projection states of Kramers type for 1-Dy and Ising type for 1-Tb and 1-Ho. Dynamic magnetic susceptibility measurements indicate that 1-Dy exhibits slow magnetic relaxation in the presence of a small applied magnetic field mainly through Raman pathways. Inelastic neutron scattering spectra exhibit distinct transitions corresponding to crystal field-induced tunneling gaps between the pseudo-doublet ground state components for 1-Tb and 1-Ho, which is one of the first direct experimental measurements with INS of such tunneling transitions in a molecular nanomagnet. The power of high-resolution INS is demonstrated with evidence of two distinct tunneling gaps measurable for the two crystallographically unique Tb coordination environments observed in the single crystal X-ray structure.

Data-driven design of molecular nanomagnets

Three decades of research in molecular nanomagnets have raised their magnetic memories from liquid helium to liquid nitrogen temperature thanks to a wise choice of the magnetic ion and coordination environment. Still, serendipity and chemical intuition played a main role. In order to establish a powerful framework for statistically driven chemical design, here we collected chemical and physical data for lanthanide-based nanomagnets, catalogued over 1400 published experiments, developed an interactive dashboard (SIMDAVIS) to visualise the dataset, and applied inferential statistical analysis. Our analysis shows that the Arrhenius energy barrier correlates unexpectedly well with the magnetic memory. Furthermore, as both Orbach and Raman processes can be affected by vibronic coupling, chemical design of the coordination scheme may be used to reduce the relaxation rates. Indeed, only bis-phthalocyaninato sandwiches and metallocenes, with rigid ligands, consistently present magnetic memory up to high temperature. Analysing magnetostructural correlations, we offer promising strategies for improvement, in particular for the preparation of pentagonal bipyramids, where even softer complexes are protected against molecular vibrations.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Understanding the effect of structural changes on slow magnetic relaxation in mononuclear octahedral copper(II) complexes

Current advances in molecular magnetism are aimed at the construction of molecular nanomagnets and spin qubits for their utilization as high-density data storage materials and quantum computers. Mononuclear coordination compounds with low spin values of S = ½ are excellent candidates for this endeavour, but knowledge of their construction via rational design is limited. This particularly applies to the single copper(II) spin center, having been only recently demonstrated to exhibit slow relaxation of magnetisation in the appropriate octahedral environment. We have thus prepared a unique organic scaffold that would allow one to gain in-depth insight into how purposeful structural differences affect the slow magnetic relaxation in monometallic, transition metal complexes. As a proof-of-principle, we demonstrate how one can construct two, structurally very similar complexes with isolated Cu(II) ions in an octahedral ligand environment, the magnetic properties of which differ significantly. The differences in structural symmetry effects and in magnetic relaxation are corroborated with a series of experimental techniques and theoretical approaches, showing how symmetry distortions and crystal packing affect the relaxation behaviour in these isolated Cu(II) systems. Our unique organic platform can be efficiently utilized for the construction of various transition-metal ion systems in the future, effectively providing a model system for investigation of magnetic relaxation via targeted structural distortions.

Triangulo-{ErIII 3} complex showing field supported slow magnetic relaxation

The triangulo-{Er3} complex [Er3Cl(o-van)3(OH)2(H2O)5]Cl3·nH2O (n = 9.4; H(o-van) = o-vanillin) (1) was generated by an in situ method. The isolated Er(iii) complex 1 was characterized by elemental analysis and molecular spectroscopy. The results of single crystal X-ray diffraction studies have shown that 1 is built up of trinuclear [Er3Cl(o-van)3(OH)2(H2O)5]3+ complex cations, chloride anions and water solvate molecules. Within the complex cation the three Er(iii) central atoms are placed at the apexes of a triangle which are bridged by three (o-van)- ligands with additional chelating functions and two μ3-OH- ligands. Additionally five aqua and one chlorido ligands complete the octa-coordination of the three Er(iii) atoms. AC susceptibility measurements reveal that the compound exhibits slow magnetic relaxation with two relaxation modes.

Impact of Ligand Substituents on the Magnetization Dynamics of Mononuclear DyIII Single-Molecule Magnets

Two mononuclear Dy^III single-molecule magnets with different ligand substituents located far from the coordinating atoms, [Dy(L-NO₂)(NO₃)] (1) and [Dy(L-Me)(NO₃)] (2), and their diamagnetic-ion diluted analogues, 1' and 2', were structurally and magnetically characterized. 1 and 2 have nearly identical coordination environments of Dy^III ions with D_2d symmetry but different magnetization dynamics. No Orbach process was observed for 1 and 1' in the testing temperature and frequency range, but effective energy barriers of 575 and 829 K for 2 and 2' were obtained, respectively. The opened hysteresis loops were observed until 6 K for 1 and 10 K for 2. Ab initio calculations reveal that the energy gaps between ground and low-lying excited states of 2 are higher than those of 1 and the relaxation rate through quantum tunneling of magnetization of 2 is lower than that of 1 due to the electronic effect of the axial coordinating oxygen atoms influenced by ligand substitutions.

Importance of an Axial LnIII-F Bond across the Lanthanide Series and Single-Molecule Magnet Behavior in the Ce and Nd Analogues

The recently reported compound [Dy^IIILF](CF₃SO₃)₂·H₂O (L = 1,4,7,10-tetrakis(2-pyridylmethyl)-1,4,7,10-tetraaza-cyclododecane) displays a strong axial magnetic anisotropy, due to the short axial Dy–F bond, and single-molecule magnet (SMM) behavior. Following our earlier [Dy^IIILF]²⁺ work, herein we report the systematic structural and magnetic study of a family of [Ln^IIILF](CF₃SO₃)₂·H₂O compounds (Ln(III) = 1-Ce, 2-Pr, 3-Nd, 4-Eu, 5-Tb, 6-Ho, 7-Er, 8-Tm, and 9-Yb). From this series, the Ce(III) and Nd(III) analogues show slow relaxation of the magnetization under an applied direct current magnetic field, which is modeled using a Raman process. Complete active space self-consistent field theoretical calculations are employed to understand the relaxation pathways in 1-Ce and 3-Nd and also reveal a large tunnel splitting for 5-Tb. Additional computational studies on model compounds where we remove the axial F^– ligand, or replace F^– with I^–, highlight the importance of the F^– ligand in creating a strong axial crystal field for 1-Ce and 3-Nd and for promoting the SMM behavior. Importantly, this systematic study provides insight into the magnetic properties of these lighter lanthanide ions.

The structural and magnetic properties of a family of [Ln^IIILF](CF₃SO₃)₂·H₂O (L = 1,4,7,10-tetrakis(2-pyridylmethyl)-1,4,7,10-tetraaza-cyclododecane) compounds are reported. In addition to the previously reported Dy(III) analogue, we find that the Ce(III) and Nd(III) analogues show slow relaxation of the magnetization due to the strong axial magnetic anisotropy created by the axial F⁻ ligand. AC magnetic susceptibility data and CASSCF theoretical calculations are employed to understand the single-molecule magnet behavior of 1-Ce and 3-Nd.

Using N-Heterocyclic Carbenes as Weak Equatorial Ligands to Design Single-Molecule Magnets: Zero-Field Slow Relaxation in Two Octahedral Dysprosium(III) Complexes

We report the synthesis, structures, and magnetic investigations of two new octahedral dysprosium complexes, based on the original N-heterocyclic carbene (NHC) tridentate bis(phenoxide) ligand, of the respective formulas mer-[DyL(THF)₂Cl] (1) and mer-[DyL(THF)₃][BPh₄] (2), where L = 1,3-bis(3,5-di-tert-butyl-2-oxidophenyl)-5,5-dimethyl-3,4,5,6-tetrahydropyrimidin-1-ium chloride and THF = tetrahydrofuran. The short Dy-O distances in the axial direction in association with the weak donor ability of the NHC moiety provide a suitable environment for slow relaxation of magnetization, overcoming the previous single-molecule magnets based on NHC ligands.

Effect on the geometry over the slow relaxation of the magnetization in a series of erbium(iii) complexes based on halogenated ligands

Erbium(iii) complexes based on halogenated ligands.

Metal–metal bond in lanthanide single-molecule magnets

This review surveys recent critical advances in lanthanide SMMs, highlighting the influences of metal–metal bonds on the magnetization dynamics.

Studies of the Temperature Dependence of the Structure and Magnetism of a Hexagonal-Bipyramidal Dysprosium(III) Single-Molecule Magnet

The hexagonal-bipyramidal lanthanide(III) complex [Dy(O^tBu)Cl(18-C-6)][BPh₄] (1; 18-C-6 = 1,4,7,10,13,16-hexaoxacyclooctadecane ether) displays an energy barrier for magnetization reversal (U_eff) of ca. 1000 K in a zero direct-current field. Temperature-dependent X-ray diffraction studies of 1 down to 30 K reveal bending of the Cl-Ln-O^tBu angle at low temperature. Using ab initio calculations, we show that significant bending of the O-Dy-Cl angle upon cooling from 273 to 100 K leads to a ca. 10% decrease in the energy of the excited electronic states. A thorough exploration of the temperature and field dependencies of the magnetic relaxation rate reveals that magnetic relaxation is dictated by five mechanisms in different regimes: Orbach, Raman-I, quantum tunnelling of magnetization, and Raman-II, in addition to the observation of a phonon bottleneck effect.

Deciphering the Role of Anions and Secondary Coordination Sphere in Tuning Anisotropy in Dy(III) Air-Stable D5h SIMs*

Precise control of the crystal field and symmetry around the paramagnetic spin centre has recently facilitated the engineering of high-temperature single-ion magnets (SIMs), the smallest possible units for future spin-based devices. In the present work, we report a series of air-stable seven coordinate Dy(III) SIMs {[L₂ Dy(H₂ O)₅ ][X]₃ ⋅L₂ ⋅n(H₂ O), n = 0, X = Cl (1), n=1, X = Br (2), I (3)} possessing pseudo-D_5h symmetry or pentagonal bipyramidal coordination geometry with high anisotropy energy barrier (U_eff ) and blocking temperature (T_B ). While the strong axial coordination from the sterically encumbered phosphonamide, ^t BuPO(NHⁱ Pr)₂ (L), increases the overall anisotropy of the system, the presence of high symmetry significantly quenches quantum tunnelling of magnetization, which is the prominent deactivating factor encountered in SIMs. The energy barrier (U_eff ) and the blocking temperature (T_B ) decrease in the order 3>2>1 with the change of anions from larger iodide to smaller strongly hydrogen-bonded chloride in the secondary coordination sphere, albeit the local coordination geometry and the symmetry around the Dy(III) display only slight deviations. Ab initio CASSCF/RASSI-SO/SINGLE_ANISO calculations provide deeper insights into the dynamics of magnetic relaxation in addition to the role of the secondary coordination sphere in modulating the anisotropy of the D_5h systems, using diverse models. Thus, in addition to the importance of the crystal field and the symmetry to obtain high-temperature SIMs, this study also probes the significance of the secondary coordination sphere that can be tailored to accomplish novel SIMs.

Terminal Ligand and Packing Effects on Slow Relaxation in an Isostructural Set of [Dy(H2 dapp)X2 ]+ Single Molecule Magnets*

We report three structurally related single ion Dy compounds using the pentadentate ligand 2,6-bis((E)-1-(2-(pyridin-2-yl)-hydrazineylidene)ethyl)pyridine (H2 dapp) [Dy(H2 dapp)(NO3 )2 ]NO3 (1), [Dy(H2 dapp)(OAc)2 ]Cl (2) and [Dy(H2 dapp)(NO3 )2 ]Cl0.92 (NO3 )0.08 (3). The (H2 dapp) occupies a helical twisted pentagonal equatorial arrangement with two anionic ligands in the axial positions. Further influence on the electronic and magnetic structure is provided by a closely associated counterion interacting with the central N-H group of the (H2 dapp). The slow relaxation of the magnetisation shows that the anionic acetates give the greatest slowing down of the magnetisation reversal. Further influence on the relaxation properties of compounds1 and 2 is the presence of short nitrate-nitrate intermolecular ligand contact opening further lattice relaxation pathways.

A Cost-Effective Semi-Ab Initio Approach to Model Relaxation in Rare-Earth Single-Molecule Magnets

We discuss a cost-effective approach to understand magnetic relaxation in the new generation of rare-earth single-molecule magnets. It combines ab initio calculations of the crystal field parameters, of the magneto-elastic coupling with local modes, and of the phonon density of states with fitting of only three microscopic parameters. Although much less demanding than a fully ab initio approach, the method gives important physical insights into the origin of the observed relaxation. By applying it to high-anisotropy compounds with very different relaxation, we demonstrate the power of the approach and pinpoint ingredients for improving the performance of single-molecule magnets.

Insights on the coupling between vibronically active molecular vibrations and lattice phonons in molecular nanomagnets

Spin-lattice relaxation is a key open problem to understand the spin dynamics of single-molecule magnets and molecular spin qubits. While modelling the coupling between spin states and local vibrations allows to determine the more relevant molecular vibrations for spin relaxation, this is not sufficient to explain how energy is dissipated towards the thermal bath. Herein, we employ a simple and efficient model to examine the coupling of local vibrational modes with long-wavelength longitudinal and transverse phonons in the clock-like spin qubit [Ho(W₅O₁₈)₂]^9-. We find that in crystals of this polyoxometalate the vibrational mode previously found to be vibronically active at low temperature does not couple significantly to lattice phonons. This means that further intramolecular energy transfer via anharmonic vibrations is necessary for spin relaxation in this system. Finally, we discuss implications for the spin-phonon coupling of [Ho(W₅O₁₈)₂]^9- deposited on a MgO (001) substrate, offering a simple methodology that can be extrapolated to estimate the effects on spin relaxation of different surfaces, including 2D materials.

Magnetic Properties and Second Harmonic Generation of Noncentrosymmetric Cyanido-Bridged Ln(III)-W(V) Assemblies

One-dimensional zigzag cyanido-bridged coordination polymers have been prepared as a result of self-assembly of lanthanide(III) ions with octacyanidotungstate(V) anions in the presence of N,N-dimethylacetamide (dma). All compounds crystallized in noncentrosymmetric space group P2₁ with a molecular formula of [Ln^III(dma)₅][W^V(CN)₈] [Ln = Gd (1), Tb (2), Dy (3), Ho (4), Er (5), Tm (6), Yb (7), Lu (8), or Y (9)]. Magnetic studies revealed weak antiferromagnetic interactions through Ln^III-NC-W^V bridges and the formation of ferrimagnetically coupled chains at very low temperatures. Moreover, temperature dependencies of magnetic susceptibilities were fitted using the crystal field parameters for Ln(III) ions, determined by the ab initio calculations, yielding magnetic coupling constants in the range of -1 to -5 cm^-1. The wide optical transparency of 1-9 has been determined using solid state absorption spectroscopy. Samples exhibited second harmonic (SH) generation properties with SH susceptibilities ranging from 4.7 × 10^-12 to 9.4 × 10^-11 esu due to the presence of nonlinear optical susceptibility tensor elements (χ_ijk) χ_zxx, χ_zyy, χ_zzz, χ_zxy, χ_yyz, χ_yzx, χ_xyz, and χ_xzx, corresponding to space group P2₁. The determined values were also compared with the results of theoretical calculations and previous reports, indicating a potential relationship between the type of lanthanide ion and the SH intensity.

Air-Stable Chiral Single-Molecule Magnets with Record Anisotropy Barrier Exceeding 1800 K

Design and synthesis of air-stable and easily tailored high-performance single-molecule magnets (SMMs) are of great significance toward the implementation of SMMs in molecular-based magneto-electronic devices. Here, by introducing electron-withdrawing fluorinated substituents on equatorial ligand, two chiral Dy(III) macrocyclic complexes, RRRR-Dy-D_6hF₁₂ (1) and SSSS-Dy-D_6hF₁₂ (2), with a record anisotropy barrier exceeding 1800 K and the longest relaxation time approaching 2500 s at 2.0 K for all known air-stable SMMs, were obtained. The nearly perfect axiality of the ground Kramers doublet (KD) enables the open hysteresis loops up to 20 K in the magnetically diluted sample. It is notable that they are structurally rigid with high thermal stability and the apical ligand can be tailored to carry proper surface-binding groups. This finding not only improves the magnetic properties for air-stable SMMs but also provides a new avenue for deposition of SMMs on surfaces.

Near-Infrared Emissive Cyanido-Bridged {YbFe2} Molecular Nanomagnets Sensitive to the Nitrile Solvents of Crystallization

One of the pathways toward luminescent single-molecule magnets (SMMs) is realized by the self-assembly of lanthanide(3+) ions with cyanido transition metal complexes. We report a novel family of emissive SMMs, {YbIII(4-pyridone)4[FeII(phen)2(CN)2]2}(CF3SO3)3·solv (solv = 2MeCN, 1·MeCN; 2AcrCN, 1·AcrCN; 2PrCN, 1·PrCN; 2MalCN·1MeOH; 1·MalCN; MeCN = acetonitrile, AcrCN = acrylonitrile, PrCN = propionitrile, MalCN = malononitrile). They are based on paramagnetic YbIII centers coordinating diamagnetic [FeII(phen)2(CN)2] metalloligands but differ in the nitrile solvents of crystallization. They exhibit a field-induced slow magnetic relaxation dominated by a Raman process, without an Orbach relaxation as indicated by AC magnetic data and the ab initio calculations. The Raman relaxation is solvent-dependent as represented by the power “n” of the BRamanTn contribution varying from 3.07(1), to 2.61(1), 2.37(1), and 1.68(4) for 1·MeCN, 1·PrCN, 1·AcrCN, and 1·MalCN, respectively, while the BRaman parameter adopts the opposite trend. This was correlated with the variation of phonon modes schemes, including the number of available vibrational modes and their energies, dependent on the increasing complexity of the applied nitrile. 1·MeCN and 1·MalCN show the additional T-independent relaxation assignable to dipole-dipole interactions as confirmed by its suppression in 1·AcrCN and 1·PrCN revealing longer Yb–Yb distances and the disappearance in the LuIII-diluted 1·MeCN@Lu. All compounds exhibit YbIII–centered near-infrared photoluminescence sensitized by organic ligands.

Spectroscopic Investigation of a Metal-Metal-Bonded Fe6 Single-Molecule Magnet with an Isolated S = 19/2 Giant-Spin Ground State

The metal-metal-bonded molecule [Bu₄N][(^HL)₂Fe₆(dmf)₂] (Fe₆) was previously shown to possess a thermally isolated spin S = ¹⁹/₂ ground state and found to exhibit slow magnetization relaxation below a blocking temperature of ∼5 K [J. Am. Chem. Soc. 2015, 137, 13949-13956]. Here, we present a comprehensive spectroscopic investigation of this unique single-molecule magnet (SMM), combining ultrawideband field-swept high-field electron paramagnetic resonance (EPR) with frequency-domain Fourier-transform terahertz EPR to accurately quantify the spin Hamiltonian parameters of Fe₆. Of particular importance is the near absence of a 4th-order axial zero-field splitting term, which is known to arise because of quantum mechanical mixing of spin states on account of the relatively weak spin-spin (superexchange) interactions in traditional polynuclear SMMs such as the celebrated Mn₁₂-acetate. The combined high-resolution measurements on both powder samples and an oriented single crystal provide a quantitative measure of the isolated nature of the spin ground state in the Fe₆ molecule, as well as additional microscopic insights into factors that govern the quantum tunneling of its magnetization. This work suggests strategies for improving the performance of polynuclear SMMs featuring direct metal-metal bonds and strong ferromagnetic spin-spin (exchange) interactions.

Mononuclear Dysprosium Alkoxide and Aryloxide Single-Molecule Magnets

Recent studies have shown that mononuclear lanthanide (Ln) complexes can be high‐performing single‐molecule magnets (SMMs). Recently, there has been an influx of mononuclear Ln alkoxide and aryloxide SMMs, which have provided the necessary geometrical control to improve SMM properties and to allow the intricate relaxation dynamics of Ln SMMs to be studied in detail. Here non‐aqueous Ln alkoxide and aryloxide chemistry applied to the synthesis of low‐coordinate mononuclear Ln SMMs are reviewed. The focus is on mononuclear Dy^III alkoxide and aryloxide SMMs with coordination numbers up to eight, covering synthesis, solid‐state structures and magnetic attributes. Brief overviews are also provided of mononuclear Tb^III, Ho^III, Er^III and Yb^III alkoxide and aryloxide SMMs.

Modulating the magnetization dynamics in Ln-Cu-Rad hetero-tri-spin complexes through cis/trans coordination of nitronyl nitroxide radicals around the metal center

Self-assembling the novel nitronyl nitroxide radical NIT-3Py-5-Ph (2-(5-phenyl-3-pyridyl)-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide) with Ln(hfac)3·2H2O and Cu(hfac)2 (hfac = hexafluoroacetylacetonate) resulted in two heterometallic complexes with formula [LnCu(hfac)5(NIT-3Py-5-Ph)2] (Ln = Gd 1, Dy 2), in which two NIT-3Py-5-Ph radicals are coordinated with the LnIII ion via their nitroxide units in the cis-arrangement manner and the CuII ion is ligated by the pyridyl N donors of the radicals. Interestingly, when the phenyl group of NIT-3Py-5-Ph was replaced with a p-pyridyl group, a new family of 2D networks, namely, {[Ln(hfac)3][Cu(hfac)2]2(NIT-3Py-5-4Py)2}n (Ln = Gd 3, Tb 4, Dy 5; NIT-3Py-5-4Py = 2-(5-(4-pyridyl)-3-pyridyl)-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide) was obtained. In the 2D sheet, each NIT-3Py-5-4Py ligand serves as a μ3-bridge to bind one LnIII center by the aminoxyl moiety and two CuII ions through two pyridine groups to form a 2D structure. The LnIII ion is coordinated by two NO units of two radicals in a trans configuration. DC magnetic measurements indicate that ferromagnetic LnIII-NO exchange occurs in 1-5. AC studies reveal that 2 displays slow relaxation of the magnetization while no such magnetic relaxation is found in complex 5. The observed different magnetic relaxation behaviors of two Dy analogues could be attributed to the different coordination modes of NO groups of the radicals, and the coordination geometry of the Dy center is from C2v in 2 to D2d in 5.

Correlating axial and equatorial ligand field effects to the single-molecule magnet performances of a family of dysprosium bis-methanediide complexes

Treatment of the new methanediide-methanide complex [Dy(SCS)(SCSH)(THF)] (1Dy, SCS = {C(PPh2S)2}2-) with alkali metal alkyls and auxillary ethers produces the bis-methanediide complexes [Dy(SCS)2][Dy(SCS)2(K(DME)2)2] (2Dy), [Dy(SCS)2][Na(DME)3] (3Dy) and [Dy(SCS)2][K(2,2,2-cryptand)] (4Dy). For further comparisons, the bis-methanediide complex [Dy(NCN)2][K(DB18C6)(THF)(toluene)] (5Dy, NCN = {C(PPh2NSiMe3)2}2-, DB18C6 = dibenzo-18-crown-6 ether) was prepared. Magnetic susceptibility experiments reveal slow relaxation of the magnetisation for 2Dy-5Dy, with open magnetic hysteresis up to 14, 12, 15, and 12 K, respectively (∼14 Oe s-1). Fitting the alternating current magnetic susceptibility data for 2Dy-5Dy gives energy barriers to magnetic relaxation (U eff) of 1069(129)/1160(21), 1015(32), 1109(70), and 757(39) K, respectively, thus 2Dy-4Dy join a privileged group of SMMs with U eff values of ∼1000 K and greater with magnetic hysteresis at temperatures >10 K. These structurally similar Dy-components permit systematic correlation of the effects of axial and equatorial ligand fields on single-molecule magnet performance. For 2Dy-4Dy, the Dy-components can be grouped into 2Dy-cation/4Dy and 2Dy-anion/3Dy, where the former have almost linear C[double bond, length as m-dash]Dy[double bond, length as m-dash]C units with short average Dy[double bond, length as m-dash]C distances, and the latter have more bent C[double bond, length as m-dash]Dy[double bond, length as m-dash]C units with longer average Dy[double bond, length as m-dash]C bonds. Both U eff and hysteresis temperature are superior for the former pair compared to the latter pair as predicted, supporting the hypothesis that a more linear axial ligand field with shorter M-L distances produces enhanced SMM properties. Comparison with 5Dy demonstrates unusually clear-cut examples of: (i) weakening the equatorial ligand field results in enhancement of the SMM performance of a monometallic system; (ii) a positive correlation between U eff barrier and axial linearity in structurally comparable systems.

Strong Equatorial Crystal Field Enhances the Axial Anisotropy and Energy Barrier for Spin Reversal Process in Yb2 Single Molecule Magnets

The importance of equatorial crystal fields on magnetic anisotropy of ytterbium single molecule magnets (SMMs) is observed for the first time. Herein, we report three similar dinuclear ytterbium complexes with the formula [Yb₂ (3-OMe-L)₂ (DMF)₂ (NO₃ )₂ ]⋅DMF (1), [Yb₂ (3-H-L)₂ (DMF)₂ (NO₃ )₂ ]⋅DMF⋅H₂ O (2), and [Yb₂ (3-NO₃ -L)₂ (DMF)₂ (NO₃ )₂ ] (3), [where 3-X-H₂ L=N'-(2-hydroxy-3-X-benzylidene)picolinohydrazide, X=OMe (1), H (2) NO₂ (3)]. Detailed magnetic measurements reveal the presence of weak antiferromagnetic interactions between the Yb centers and a field-induced slow relaxation of magnetization in all complexes. A higher energy barrier for spin reversal was observed for complex 1 (U_eff =50 K) and it decreases in the order of 2 (47 K) to 3 (40 K). Notably, complex 1 shows a remarkable energy barrier within the frequency range of 1-850 Hz reported for Yb-based SMMs. Further, ab initio calculations show a higher axial anisotropy and lower quantum tunneling of magnetization (QTM) in the ground state for 1 compared to 2 and 3. It was also observed that the presence of a strong crystal field in the equatorial plane (when the ∡ O1-Yb-O3 bond angle is close to 90°) enhances the axial anisotropy and improves the SMM behavior in the studied complexes. Both the experimental and theoretical analysis of relaxation dynamics discloses that Raman and QTM play major role on slow relaxation process for all complexes. To provide more insight into the exchange interactions, broken-symmetry DFT calculations were performed.

Alignment of axial anisotropy of a mononuclear hexa-coordinated Co(ii) complex in a lattice shows improved single molecule magnetic behavior over a 2D coordination polymer having a similar ligand field

The parallel orientation of the anisotropic axes minimizes the transverse component and slow down the relaxation process and results in a higher energy barrier in 0D complex as compared to 2D framework where anisotropic axes are randomly oriented.

High magnetization reversal barriers in luminescent dysprosium octahedral and pentagonal bipyramidal single-molecule magnets based on fluorinated alkoxide ligands

We report the synthesis and structures of three luminescent dysprosium(iii) complexes based on fluorinated alkoxide ligands of formulas [Dy(L1)2(THF)4][BPh4]·0.5THF (1), [Dy(L2)2(THF)5][BPh4]·2.5THF (2) and [Dy(L3)2(THF)5][BPh4]·2THF (3) (L1 = (CF3)3CO-, L2 = C6F5C6F4O-, L3 = C6F5C(CH3)O-). Despite the different dysprosium ion geometries (octahedral vs. distorted pentagonal bipyramidal), these systems exhibit a single-molecule magnet (SMM) behavior, but with distinct relaxation dynamics. Moreover, a typical dysprosium-based luminescence is observed for the three complexes, which make them bifunctional magneto-luminescent SMMs. Remarkably, complex 3 exhibits a high anisotropy barrier of 1469 cm-1 and a blocking temperature of 22 K, making it one of the most performant alkoxide-based SMMs with the highest blocking temperature for a luminescent SMM.

Tuning the coordination sphere of octahedral Dy(iii) complexes with silanolate/stannanolate ligands: synthesis, structures and slow relaxation of the magnetization

This study reports four SMMs based on silanolate or stannanolate ligands cis-[Dy(OSiPh3)2(THF)4][BPh4]·THF·C6H6 (1), cis-[Dy(OSnPh3)2(THF)4][BPh4]·THF·C6H6·C6H14 (2), fac-[Dy(OSiPh3)3(THF)3]·THF (3) and fac-[Dy(OSiPh3)3(bipy)(THF)]·THF (4).

Synthesis, structures and magnetic properties of dysprosium(iii) complexes based on amino-bis(benzotriazole phenolate) and nitrophenolates: influence over the slow relaxation of the magnetization

Field-induced slow relaxation in dysprosium amino-bis(benzotriazole) phenolate complexes.

An unusual mechanism of building up of a high magnetization blocking barrier in an octahedral alkoxide Dy3+-based single-molecule magnet

We report a new octahedral luminescent SMM exhibiting massive crystal-field splitting and an anisotropic barrier of 1385 cm⁻¹.

Pseudo-tetrahedral vs. pseudo-octahedral ErIII single molecule magnets and the disruptive role of coordinated TEMPO radical

Tetrahedral Er^III complexes are potential candidates for high-performance single molecule magnets (SMMs).

An approach to estimate the barrier height for magnetisation reversal in {Dy2} SMMs using ab initio calculations

Although ab initio CASSCF calculations yield a good numerical estimate of barrier height for magnetisation reversal for mononuclear Dy(iii) SIMs, obtaining a reliable value for higher nuclearity clusters such as {Dy2} are challenging. By analysing ab initio computed data of thirty-one different {Dy2} SMMs, we propose a model equation that relates the calculated barrier heights to the experimental values and offers a viable way to predict the barrier heights in {Dy2} SMMs.

Blocking like it's hot: a synthetic chemists' path to high-temperature lanthanide single molecule magnets

Progress in the synthesis, design, and characterisation of single-molecule magnets (SMMs) has expanded dramatically from curiosity driven beginnings to molecules that retain magnetization above the boiling point of liquid nitrogen. This is in no small part due to the increasingly collaborative nature of this research where synthetic targets are guided by theoretical design criteria. This article aims to summarize these efforts and progress from the perspective of a synthetic chemist with a focus on how chemistry can modulate physical properties. A simple overview is presented of lanthanide electronic structure in order to contextualize the synthetic advances that have led to drastic improvements in the performance of lanthanide-based SMMs from the early 2000s to the late 2010s.

Magnetic hysteresis and strong ferromagnetic coupling of sulfur-bridged Dy ions in clusterfullerene Dy2S@C82

Two isomers of metallofullerene Dy₂S@C₈₂ with sulfur-bridged Dy ions exhibit broad magnetic hysteresis with sharp steps at sub-Kelvin temperature. Analysis of the level crossing events for different orientations of a magnetic field showed that even in powder samples, the hysteresis steps caused by quantum tunneling of magnetization can provide precise information on the strength of intramolecular Dy⋯Dy inter-actions. A comparison of different methods to determine the energy difference between ferromagnetic and antiferromagnetic states showed that sub-Kelvin hysteresis gives the most robust and reliable values. The ground state in Dy₂S@C₈₂ has ferromagnetic coupling of Dy magnetic moments, whereas the state with antiferromagnetic coupling in C _s and C _3v cage isomers is 10.7 and 5.1 cm^-1 higher, respectively. The value for the C _s isomer is among the highest found in metallofullerenes and is considerably larger than that reported in non-fullerene dinuclear molecular magnets. Magnetization relaxation times measured in zero magnetic field at sub-Kelvin temperatures tend to level off near 900 and 3200 s in C _s and C _3v isomers. These times correspond to the quantum tunneling relaxation mechanism, in which the whole magnetic moment of the Dy₂S@C₈₂ molecule flips at once as a single entity.

Enhancing the barrier height for Yb(III) single-ion magnets by modulating axial ligand fields

The effect of systematic modification of the axial ligand field X on Ueff values in Yb(iii)-based SIMs, [Yb(Ph3PO)4X2]X' (X, X' = NO3 (1), OTf (2) and X = I/Br/Cl; X' = I3 (3)), whose equatorial Ph3PO ligation remains unchanged, has been investigated. Combined magnetic studies coupled with ab initio calculations reveal weakening of the axial ligand fields leading to the increase in the energy barrier, apart from suggesting the operation of different relaxation pathways.

Alignment of Axial Anisotropy in a 1D Coordination Polymer shows Improved Field Induced Single Molecule Magnet Behavior over a Mononuclear Seven Coordinated FeII Complex

Herein, we report a CN-bridged alternating Fe^II -Ni^II 1D chain to ensure the alignment of axial anisotropy and improve the single molecule magnet (SMM) behavior in seven coordinated Fe^II compound. The chain was constructed from hepta coordinated Fe(II) complex as an anisotropic building unit and diamagnetic nickel tetra cyanate as a bridging ligand. The magnetic measurements show the easy-axis anisotropy of the seven coordinated Fe(II) complex and field induced SMM behavior with spin reversal energy barrier U_eff =61(2) K (42 cm^-1 ) and pre-exponential relaxation time τ₀ =1.9×10^-8  s. The detailed analysis of the relaxation dynamics discloses that the Orbach process plays an important role in slow relaxation of magnetization for this compound. Notably, this example represents a remarkable energy barrier observed in hepta coordinated Fe(II) SMMs. The ab initio calculations estimate the magnitude of axial anisotropy and show the parallel orientation of the anisotropic axis throughout the 1D polymeric chain. In addition, it is also reported that the presence of weak π accepter ligands in the distorted axial position enhance the easy-axis anisotropy.

Synthesis, Structure, Magnetic and Photoluminescent Properties of Dysprosium(III) Schiff Base Single-Molecule Magnets: Investigation of the Relaxation of the Magnetization

We report here the synthesis, structure, magnetic and photoluminescent properties of three new bifunctional Schiff-base complexes [Dy(L₁ )₂ (py)₂ ][B(Ph)₄ ]⋅py (1), [Dy(L₁ )₂ Cl(DME)] ⋅ 0.5DME (2) and [Dy(L₂ )₂ Cl] ⋅ 2.5(C₇ H₈ ) (3) (HL₁ =Phenol, 2,4-bis(1,1-dimethylethyl)-6-[[(2-methoxy-5-methylphenyl)imino]methyl]; HL₂ =Phenol, 2,4-bis(1,1-dimethylethyl)-6-[[(2-methoxyphenyl)imino]methyl]). The coordination environment of the Dy³⁺ ion and the direction of the anisotropic axis may be controlled by the combination of the substituent groups of the Schiff bases, the nature of the counter-ions (Cl^- vs. BPh₄ ^- ) and the coordinative solvent molecules. A zero-field slow relaxation of the magnetization is evidenced for all complexes but strong differences in the relaxation dynamics are observed depending on the Dy³⁺ site geometry. In this sense, complex 1 exhibits an anisotropy barrier of 472 cm^-1 _, which may be favourably compared to other related examples due to the shortening of the Dy-O bond in the axial direction. Besides, the three complexes exhibit a ligand-based luminescence making them as bifunctional magneto-luminescent systems.