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

Pressure-Induced Structural, Optical and Magnetic Modifications in Lanthanide Single-Molecule Magnets

Lanthanide Single-Molecule Magnets are fascinating objects that break magnetic performance records with observable magnetic bistability at the boiling temperature of liquid nitrogen, paving the way for potential applications in high-density data storage. The switching of lanthanide SMM has been successfully achieved using several external stimuli such as redox reaction, pH titration, light irradiation or solvation/desolvation thanks to the high sensitivity of the magnetic anisotropy to any structural change in the lanthanide surrounding. Nevertheless, the use of applied high pressure as an external stimulus is largely underused, especially considering that it can be combined with high pressure X-ray diffraction to establish a complementary structure-property relationship. This Concept article summarizes the few relevant examples of investigations of lanthanide SMMs under applied high pressure, provides conclusions on the effect of such stimulus on molecular structures and magnetic anisotropy, and finally draws perspective on the future development of magnetic measurements under applied pressure.

A highly anisotropic family of hexagonal bipyramidal Dy(III) unsaturated 18-crown-6 complexes exceeding the blockade barrier over 2700 K: a computational exploration

In the present work, we have explored a series of unsaturated hexa-18-crown-6 (U18C6) ligands towards designing highly anisotropic Dy(III) based single-ion magnets (SIMs) with the general formula [Dy(U18C6)X2]+ (where U18C6 = [C12H12O6] (1), [C12H12S6] (2), [C12H12Se6] (3), [C12H12O4S2] (4), [C12H12O4Se2] (5) and X = F, Cl, Br, I, OtBu and OSiPh3). By analysing the electronic structure, bonding and magnetic properties, we find that the U18C6 ligands prefer stabilising the highly symmetric eight-coordinated hexagonal bipyramidal geometry (HBPY-8), which is the source of the near-Ising type anisotropy in all the [Dy(U18C6)X2]+ complexes. Moreover, the ability of sulfur/selenium substituted U18C6 ligands to stabilize the highly anisotropic HBPY-8 geometry makes them more promising towards engineering the equatorial ligand field compared to substituted saturated 18C6 ligands where the exodentate arrangement of the S lone pairs results in low symmetry. Magnetic relaxation analysis predicts a record barrier height over 2700 K for [Dy(C12H12O6)F2]+ and [Dy(C12H12S6)X2]+ (where X = F, OtBu and OSiPh3) complexes, nearly 23% higher than those of the top performing Dy(III) based SIMs in the literature.

Effect of coordinated anions on ferromagnetically coupled Dy2 zero-field single-molecule magnets

A new hydrazone Schiff base ligand was condensed from 2-hydroxy-3-methoxybenzaldehyde and pyrimidine-4-carbohydrazide {H2L = (E)-N'-(2-hydroxy-3-methoxybenzylidene)pyrimidine-4-carbohydrazide}, which was used to assemble two new Dy2 complexes Dy2L2(DMF)2(NO3)2 (1) and Dy2L2(DMF)2(AcO)2 (2). Notably, the coordinated anions have a subtle effect on the coordination configurations of the Dy3+ ions and the magnetic properties of the two Dy2 complexes. The Dy3+ ions in 1 and 2 have the same N2O5 coordination environment but show the triangular dodecahedron and the biaugmented trigonal prism coordination configurations, respectively. Magnetic measurements revealed that both 1 and 2 have intramolecular ferromagnetic interactions between the Dy3+ ions and show single-molecule magnet behaviors at 0 Oe, with Ueff/k values of 58.2 K for 1 and 59.9 K for 2. These magnetic properties may be explained by theoretical calculations.

The prediction of single-molecule magnet properties via deep learning

This paper uses deep learning to present a proof-of-concept for data-driven chemistry in single-molecule magnets (SMMs). Previous discussions within SMM research have proposed links between molecular structures (crystal structures) and single-molecule magnetic properties; however, these have only interpreted the results. Therefore, this study introduces a data-driven approach to predict the properties of SMM structures using deep learning. The deep-learning model learns the structural features of the SMM molecules by extracting the single-molecule magnetic properties from the 3D coordinates presented in this paper. The model accurately determined whether a molecule was a single-molecule magnet, with an accuracy rate of approximately 70% in predicting the SMM properties. The deep-learning model found SMMs from 20 000 metal complexes extracted from the Cambridge Structural Database. Using deep-learning models for predicting SMM properties and guiding the design of novel molecules is promising.

Understanding Single-Molecule Magnet properties of lanthanide complexes from 4f orbital splitting

We present an approach for connecting the magnetic anisotropy of lanthanide mononuclear complexes with their f-orbital splitting for both idealized and real coordination environments. Our proposal is straightforward to apply and provides sensible estimations of the energy spacing of the ground multiplet for axial magnetic systems. This energy splitting controls Single-Molecule Magnet properties of lanthanide complexes, determining key parameters such as the demagnetization energy barrier (Ueff). Importantly, this approach is consistent with the current paradigm of oblate and prolate preferences for the distribution of the f-electron density, but delivers a finer description for ions belonging to the same group (e.g. the oblates TbIII and DyIII). The model provides simple explanations for some general trends observed experimentally (e.g. the low barriers for ErIII complexes in comparison to DyIII or the large barriers observed for cyclopentadienyl DyIII complexes in comparison with other ligands based on organometallic rings), contributing as a valuable tool to expand our description of ligand field effects in lanthanide-based SMMs.

Influence of symmetry on the magneto-optical properties of a bifunctional macrocyclic DyIII complex

In this work, a novel complex, [Dy(LPr)(NO3)2]·(H2O)·(NO3) (1), containing a highly distorted macrocyclic ligand (LPr) and weak axial anions (NO3-), was synthesized and characterized. Even though this coordination environment is not ideal for maximizing the magnetic anisotropy of a DyIII ion, a magneto-structural analysis reveals that the high distortion of the macrocycle promotes a disposition of the hard plane and easy axis opposite to the expected one. This results in a quite symmetrical environment which allows obtaining a field induced SMM behaviour. The magnetic relaxation properties of this complex were rationalized with the aid of ab initio multireference calculations. Moreover, 1 showed the characteristic emission bands of DyIII ion, indicating that the macrocyclic ligand acts as an efficient sensitizer in the energy transfer process to the emissive state of the DyIII ion. Due to the symmetric environment of 1, the Y/B intensity ratio (0.61) results in CIE coordinates (0.278; 0.314), close to those of the white light region. To gain further insight into the mechanism leading to the luminescence properties, ab initio calculations were performed to elucidate the key factors controlling the Y/B intensity ratio in this bifunctional complex.

Understanding electrostatics and covalency effects in highly anisotropic organometallic sandwich dysprosium complexes [Dy(CmRm)2] (where R = H, SiH3, CH3 and m = 4 to 9): a computational perspective

In this article, we have thoroughly studied the electronic structure and 4f-ligand covalency of six mononuclear dysprosium organometallic sandwich complexes [Dy(CmRm)2]n+/- (where R = H, SiH3, CH3; m = 4 to 9; n = 1, 3) using both the scalar relativistic density functional and complete active space self-consistent field (CASSCF) and N-electron valence perturbation theory (NEVPT2) method to shed light on the ligand field effects in fine-tuning the magnetic anisotropy of these complexes. Energy decomposition analysis (EDA) and ab initio-based ligand field theory AILFT calculations predict the sizable 4f-ligand covalency in all these complexes. The analysis of CASSCF/NEVPT2 computed spin-Hamiltonian (SH) parameters indicates the stabilization of mJ |±15/2〉 for [Dy(C4(SiH3)4)2]- (1), [Dy(C5(CH3)5)2]+ (2) and [Dy(C6H6)2]3+ (3) complexes with the Ucal value of 1867.5, 1621.5 and 1070.8 cm-1, respectively. On the other hand, we observed mJ |±9/2〉 as the ground state for [Dy(C7H7)2]3- (4) and [Dy(C8H8)2]- (5) complexes with significantly smaller Ucal values of 237.1 and 38.6 cm-1 respectively. For the nine-membered ring [Dy(C9H9)2]+ (6) complex, we observed the stabilization of the mJ |±1/2〉 ground state, with the first excited state being located ∼29 cm-1 higher in energy. AILFT-NEVPT2 ligand field splitting analysis indicates that the presence of π-type 4f-ligand interactions in complexes 1-3 help generate the axial-ligand field, while the δ-type interactions in complexes 4-5 generate the equatorial ligand field despite the ligands approaching from the axial direction. As the ring size increases, φ-type interactions dominate, generating a pure equatorial ligand field stabilising mJ |±1/2〉 as the ground state for 6. Calculations suggest that the nature of the ligand field mainly governs the Ucal values in the following order: 4f-Lσ > 4f-Lπ > 4f-Lδ > 4f-Lφ. Calculations were performed by replacing ligands with CHELPG charges to access the crystal field (CF) effects which suggests the stabilization of pure mJ |±15/2〉 in all the charge-embedded models (1Q-6Q). Our findings point out that the crystal field and ligand field effects complement each other and generate a giant barrier for magnetic relaxation in the small ring complexes 1-3, while a relatively weak crystal field and adverse 4f-Lδ/4f-Lφ interactions diminish the SMM behaviour in the large ring complexes 4-6.

Theoretical Magnetic Relaxation and Spin-Phonon Coupling Study in a Series of Molecular Engineering Designed Bridged Dysprosocenium Analogues

A detailed computational study of hypothetical sandwich dysprosium double-decker complexes, bridged by various numbers of aliphatic linkers, was performed to evaluate the effect of the structural modifications on their ground-state magnetic sublevels and assess their potential as candidates for single-molecule magnets (SMMs). The molecular structures of seven complexes were optimized using the TPSSh functional, and the electronic structure and magnetic properties were investigated using the complete active space self-consistent field method (CASSCF). Estimates of the magnetic moment blocking barrier (Ueff) and blocking temperatures (TB) are reported. In addition, a new method based on computed derivatives of effective demagnetization barriers Ueff with respect to vibrational normal modes was introduced and applied to evaluate the impact of spin-phonon coupling on the SMM properties. On the basis of the computed parameters, we have identified promising candidates with properties superior to those of the existing single-molecule magnets.

Spin-state energetics and magnetic anisotropy in penta-coordinated Fe(III) complexes with different axial and equatorial ligand environments

The penta-coordinated trigonal-bi-pyramidal (TBP) Fe(III) complex (PMe₂Ph)₂FeCl₃ shows a reduced magnetic anisotropy in its intermediate-spin (IS) state as compared to its methyl-analog (PMe₃)₂Fe(III)Cl₃. In this work, the ligand environment in (PMe₂Ph)₂FeCl₃ is systematically altered by replacing the axial -P with -N and -As, the equatorial -Cl with other halides, and the axial methyl group with an acetyl group. This has resulted in a series of Fe(III) TBP complexes modelled in their IS and high-spin (HS) states. Lighter ligands -N and -F stabilize the complex in the HS state, while the magnetically anisotropic IS state is stabilized by -P and -As at the axial site, and -Cl, -Br, and -I at the equatorial site. Larger magnetic anisotropies appear for complexes with nearly degenerate ground electronic states that are well separated from the higher excited states. This requirement, largely controlled by the d-orbital splitting pattern due to the changing ligand field, is achieved with a certain combination of axial and equatorial ligands, such as -P and -Br, -As and -Br, and -As and -I. In most cases, the acetyl group at the axial site enhances the magnetic anisotropy compared to its methyl counterpart. In contrast, the presence of -I at the equatorial site compromises the uniaxial type of anisotropy of the Fe(III) complex leading to an enhanced rate of quantum tunneling of magnetization.

Hybrid Molecular Magnets with Lanthanide- and Countercation-Mediated Interfacial Electron Transfer between Phthalocyanine and Polyoxovanadate

A series of {V₁₂}-nuclearity polyoxovanadate cages covalently functionalized with one or sandwiched by two phthalocyaninato (Pc) lanthanide (Ln) moieties via V-O-Ln bonds were prepared and fully characterized for paramagnetic Ln = Sm^III-Er^III and diamagnetic Ln = Lu^III, including Y^III. The LnPc-functionalized {V₁₂O₃₂} cages with fully oxidized vanadium centers in the ground state were isolated as (nBu₄N)₃[HV₁₂O₃₂Cl(LnPc)] and (nBu₄N)₂[HV₁₂O₃₂Cl(LnPc)₂] compounds. As corroborated by a combined experimental (EPR, DC and AC SQUID, laser photolysis transient absorption spectroscopy, and electrochemistry) and computational (DFT, MD, and model Hamiltonian approach) methods, the compounds feature intra- and intermolecular electron transfer that is responsible for a partial reduction at V(3d) centers from V^V to V^IV in the solid state and at high sample concentrations. The effects are generally Ln dependent and are clearly demonstrated for the (nBu₄N)₃[HV₁₂O₃₂Cl(LnPc)] representative with Ln = Lu^III or Dy^III. Intramolecular charge transfer takes place for Ln = Lu^III and occurs from a Pc ligand via the Ln center to the {V₁₂O₃₂} core of the same molecule, whereas for Ln = Dy^III, only intermolecular charge transfer is allowed, which is realized from Pc in one molecule to the {V₁₂O₃₂} core of another molecule usually via the nBu₄N⁺ countercation. For all Ln but Dy^III, two of these phenomena may be present in different proportions. Besides, it is demonstrated that (nBu₄N)₃[HV₁₂O₃₂Cl(DyPc)] is a field-induced single molecule magnet with a maximal relaxation time of the order 10^-3 s. The obtained results open up the way to further exploration and fine-tuning of these three modular molecular nanocomposites regarding tailoring and control of their Ln-dependent charge-separated states (induced by intramolecular transfer) and relaxation dynamics as well as of electron hopping between molecules. This should enable us to realize ultra-sensitive polyoxometalate powered quasi-superconductors, sensors, and data storage/processing materials for quantum technologies and neuromorphic computing.

Unraveling the Contributions to Spin-Lattice Relaxation in Kramers Single-Molecule Magnets

The study of how spin interacts with lattice vibrations and relaxes to equilibrium provides unique insights into its chemical environment and the relation between electronic structure and molecular composition. Despite its importance for several disciplines, ranging from magnetic resonance to quantum technologies, a convincing interpretation of spin dynamics in crystals of magnetic molecules is still lacking due to the challenging experimental determination of the correct spin relaxation mechanism. We apply ab initio spin dynamics to a series of 12 coordination complexes of Co²⁺ and Dy³⁺ ions selected among ∼240 compounds that largely cover the literature on single-molecule magnets and well represent different regimes of spin relaxation. Simulations reveal that the Orbach spin relaxation rate of known compounds mostly depends on the ions' zero-field splitting and little on the details of molecular vibrations. Raman relaxation is instead found to be also significantly affected by the features of low-energy phonons. These results provide a complete understanding of the factors limiting spin lifetime in single-molecule magnets and revisit years of experimental investigations by making it possible to transparently distinguish Orbach and Raman relaxation mechanisms.

Single-Molecule Magnetism in Linear Fe(I) Complexes with Aufbau and Non-Aufbau Ground States

With the ongoing efforts on synthesizing mononuclear single-ion magnets (SIMs) with promising applications in high-density data storage and spintronics devices, the linear or quasi-linear Fe(I) complexes emerge as the enticing candidates possessing large unquenched angular momentum. Herein, we have studied five experimentally synthesized linear Fe(I) complexes to uncover the origin of single-molecule magnetic behavior of these complexes. To begin with, we benchmarked the methodology on the experimentally and theoretically well-studied complex [Fe(C(SiMe₃)₃)₂]^-1 (1) (SiMe₃ = trimethylsilyl), which is characterized with a large spin-reversal barrier of 226 cm^-1. Subsequently, the spin-phonon coupling coefficients are calculated for the low-frequency vibrational modes to understand the relaxation mechanism of the complex. Furthermore, the two Fe(I) complexes, that is, [Fe(cyIDep)₂]⁺¹ (2) (cyIDep = 1,3-bis(2',6'-diethylphenyl)-4,5-(CH₂)₄-imidazole-2-ylidene) and [Fe(sIDep)₂]⁺¹ (3) (sIDep = 1,3-bis(2',6'-diethylphenyl)-imidazolin-2-ylidene), are studied that are experimentally reported with no SIM behavior under ac or dc magnetic fields; however, they exhibit large opposite axial zero field splitting (-62.4 and +34.0 cm^-1, respectively) from ab initio calculations. We have unwrapped the origin of this contrasting observation between experiment and theory by probing their magnetic relaxation pathways and the pattern of d orbital splitting. Additionally, the two experimentally synthesized Fe(I) complexes, that is, [(η⁶-C₆H₆)FeAr*-3,5-Pr₂ⁱ] (4) (Ar*-3,5-Pr₂ⁱ = C₆H-2,6-(C₆H₂-2,4,6-Pr₃ⁱ)₂-3,5-Pr₂ⁱ) and [(CAAC)₂Fe]⁺¹ (5) (CAAC = cyclic (alkyl) (amino)carbene), are investigated for SIM behavior, since there is no report on their magnetic anisotropy. To this end, complex 4 presents itself as the possible candidate for SIM.

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.

Modulating Two Pairs of Chiral DyIII Enantiomers by Distinct β-Diketone Ligands to Show Giant Differences in Single-Ion Magnet Performance and Nonlinear Optical Response

Using Dy(dbm)₃(H₂O) and Dy(btfa)₃(H₂O)₂ to react with enantiopure N-donors, (-)/(+)-4,5-pinenepyridyl-2-pyrazine (L_R/L_S), respectively, two pairs of chiral Dy^III enantiomers, Dy(dbm)₃L_R/Dy(dbm)₃L_S (R-1-Dy/S-1-Dy) and Dy(btfa)₃L_R/Dy(btfa)₃L_S (R-2-Dy/S-2-Dy) were obtained, wherein one of the benzene rings of dbm^- (dibenzoylmethanate) in R-1-Dy/S-1-Dy is displaced by the -CF₃ group of btfa^- (4,4,4-trifluoro-1-phenyl-1,3-butanedionate) in R-2-Dy/S-2-Dy. Interestingly, this substitution results not only in giant differences in their single-ion magnetic (SIM) performances but also in their completely different nonlinear optical (NLO) responses. R-1-Dy presents a large effective energy barrier (U_eff = 265.47 K) under zero applied field, being more than 4 × R-2-Dy (61.40 K). The discrepancy on their magnetic performances has been further elucidated by ab initio calculations. Meanwhile, R-1-Dy/S-1-Dy display the strongest third-harmonic generation responses (35/33 × α-SiO₂) among the known lanthanide NLO-active coordination compounds (CCs). On the contrary, R-2-Dy/S-2-Dy exhibit moderate second-harmonic generation responses (0.65/0.70 × KDP). These results not only give the first example of the CCs with both SMM/SIM behavior and a THG response but also provide an efficient strategy for achieving the function regulation and switch in multifunctional CCs.

In silico design criteria for high blocking barrier uranium (III) SIMs

A combination of DFT and ab initio CASSCF/PT2 calculations on U(III) fictitious models and numerous reported X-ray structures unveils several geometries from coordination number 1 to 12 that can be targeted to design potential U(III) SIMs with attractive barrier heights. Among the geometries studied, the T-shaped and capped pentagonal antiprism geometries yield values exceeding 1500 cm^-1 - a value that is elusive for any uranium SIMs.

The coexistence of long τQTM and high Ueff as a concise criterion for a good single-molecule magnet: a theoretical case study of square antiprism dysprosium single-ion magnets

A systematic theoretical study is performed on a group of 16 square antiprism dysprosium single-ion magnets. Based on ab initio calculations, the quantum tunneling of magnetization (QTM) time, i.e., τ_QTM, and effective barrier of magnetic reversal, U_eff, are theoretically predicted. The theoretical τ_QTM is able to identify the ones with the longest QTM time with small numerical deviations. Similar results occur with respect to U_eff too. The systems possessing the best single-molecule magnet (SMM) properties here are just the ones having both the longest τ_QTM and the highest U_eff, from either experiment or theory. Thus, our results suggest the coexistence of long τ_QTM and high U_eff to be a criterion for high-performance SMMs. Although having its own limits, this criterion is easy to be applied in a large number of systems since both τ_QTM and U_eff could be predicted by theory with satisfactory efficiency and reliability. Therefore, this concise criterion could provide screened candidates for high-performance SMMs quickly and, hence, ease the burden of further exploration aiming for a higher degree of precision. This screening is important since the further exploration could easily demand tens or even hundreds of ab initio calculations for a single SMM. A semi-quantitative crystal field (CF) analysis is performed and shown here to be capable of indicating the general trends in a more chemically intuitive way. This analysis could help to identify the most important coordinating atoms for both diagonal and non-diagonal CF components. Thus, it could give some direct clues for improving the SMM properties: reducing the distance of the axial atom to the central ion, rotating the axial atom closer to the easy axis or increasing the amount of its negative charge. Correspondingly, opposite operations on the equatorial atom could give the same result.

Effect of an axial coordination environment on quantum tunnelling of magnetization for dysprosium single-ion magnets with theoretical insight

Herein, we report two mononuclear dysprosium complexes [Dy(H₄L){B(OMe)₂(Ph)₂}₂](Cl)·MeOH (1) and [Dy(H₄L){MeOH)₂(NCS)₂}](Cl) (2) [where H₄L = 2,2'-(pyridine-2,6-diylbis(ethan-1-yl-1-ylidene))bis(N-phenylhydrazinecarboxamide)] with different axial coordination environments. The structural analysis revealed that the pentadentate H₄L ligand binds through the equatorial position in both complexes. In complex 1, the axial positions are occupied by bidentate dimethoxydiphenyleborate [B(OMe)₂(Ph)₂]^-. On the other hand, in complex 2, one axial position is occupied by two NCS^- and one MeOH molecule while another MeOH molecule is coordinated to the other axial position. Magnetic measurements disclose the presence of field-induced slow relaxation of magnetization with an energy barrier of U_eff = 30 K for 1 whereas no such effective barrier was observed in complex 2. Detailed analysis of field and temperature dependence of the relaxation time confirms the major role of Raman, QTM, and direct processes rather than the Orbach process in complex 1. It was observed that [B(OMe)₂(Ph)₂]^- provides higher axial anisotropy which slows down the QTM process (relaxation time for the QTM process is 2.70 × 10^-5 s) in 1 as compared to NCS anions and MeOH molecules in 2 (1.03 × 10^-8 s), and is responsible for the absence of an effective energy barrier in the latter complex as confirmed by ab initio calculations. The calculations also show that the presence of a large bidentate dimethoxydiphenyleborate ligand in axial positions may result in high-performance Dy-based single-ion magnets.

Pseudo-mono-axial ligand fields that support high energy barriers in triangular dodecahedral Dy(iii) single-ion magnets

Air-stable triangular dodecahedral Dy(iii) single-ion magnets with pseudo-mono-axial linear ligand fields exhibit high energy barrier exceeding 600 K, which represent the highest energy barrier for mononuclear SMMs with triangular dodecahedron.

The interpretation and prediction of lanthanide single-ion magnet from ab initio electronic structure calculation: The capability and limit

Single-molecule magnet (SMM) is a fascinating system holding the potential of being revolutionary micro-electronic device in information technology. However current SMMs are still far away from real-life application due to...

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.

Understanding the Magnetic Anisotropy for Linear Sandwich [Er(COT)]+-based Compounds: A Theoretical Investigation

A series of linear sandwich single-ion magnets containing [Er(COT)]+ fragment were selected to probe the magneto-structural correlations using ab initio methods. For prolate shaped ErIII ion, an equatorially coordinating geometry...

A conjugated Schiff-base macrocycle weakens the transverse crystal field of air-stable dysprosium single-molecule magnets

The dominance of a self-condensed conjugated macrocycle over a [2 + 2] conventional macrocycle in weakening the transverse crystal field and boosting axiality provides a new route to construct high-performance air-stable lanthanide SMMs.

Largely Enhancing the Blocking Energy Barrier and Temperature of a Linear Cobalt(II) Complex through the Structural Distortion: A Theoretical Exploration

Complete-active-space self-consistent field and N-electron valence second-order perturbation theory have both been employed to investigate the magnetic anisotropy of one two-coordinate cobalt(II) compound via altering the Co-C bond lengths and twist angle φ. The calculated energy barrier U_eff decreases with the decrease in the Co-C bond lengths due to the gradually increasing interaction between the 3d orbitals of Co^II and the coordination ligand field and then to the decrease in the ground orbital angular moment L of Co^II. Thus, we cannot improve U_eff simply by shortening the Co-C bond lengths. However, by rotating the twist angle φ from 60 to 0°, it is surprising to find that the energy barrier and blocking temperature can be enhanced up to 1559.1 cm^-1 and 90 K, respectively, with φ = 0°, which are prominent even among lanthanide-based single-molecule magnets.

Magnetic behavior of the novel pentagonal-bipyramidal erbium(III) complex (Et3NH)[Er(H2DAPS)Cl2]: high-frequency EPR study and crystal-field analysis

We report the synthesis, crystal structure and magnetic properties of the new heptacoordinated mononuclear erbium(III) complex (Et₃NH)[Er(H₂DAPS)Cl₂] (H₄DAPS = 2,6-diacetylpyridine bis-(salicylhydrazone)) (1). The coordination polyhedron around the Er(III) ion features a slightly distorted pentagonal bipyramid formed by the pentagonal N₃O₂ chelate ring of the H₂DAPS ligand in the equatorial plane and two apical chloride ligands. Detailed high-frequency/high-field electron paramagnetic resonance (HF-EPR) studies of 1 result in the precise determination of the crystal field (CF) splitting energies (0, 290 and 460 GHz) and effective g-values of the three lowest Kramers doublets (KDs) of the Er(III) ion. The obtained HF-EPR data are in good agreement with the results from CF analysis for the Er(III) ion based on the simulation of the dc magnetic data of 1. The results from dynamic susceptibility measurements indicate that there is no slow relaxation of magnetisation behaviour. This observation is discussed in terms of the electronic structure of 1 obtained from experimental and theoretical results.

Regulating the magnetic properties of seven-coordinated Dy(III) single-ion magnets through the effect of positional isomers on axial crystal-field

Six Dy(III) single-ion magnets (SIMs) [Dy(n-OMe-bbpen)X] were synthesized by a solvothermal reaction with three positional isomers (ortho, meta, and para) of ligands n-OMe-H₂bbpen and dysprosium halides DyX₃, (n-OMe-H₂bbpen = N,N'-bis(2-hydroxy-n-methoxybenzyl)-N,N'-bis(2-methylpyridyl)ethylenediamine; n = 3, X = Cl, 1; n = 3, X = Br, 2; n = 4, X = Cl, 3; n = 4, X = Br, 4; n = 5, X = Cl, 5; n = 5, X = Br, 6). Dynamic magnetic measurements revealed that the six complexes possess notably different effective barriers of magnetic reversal: 872.0 K (1), 1210.1 K (2), 137.9 K (3), 602.6 K (4), 907.0 K (5) and 1216.7 K (6). 6 showed the best performance as SIMs among the six Dy(III) complexes. Moreover, the magnetic hysteresis loops of 6 remained open at 21 K. The crystal structures indicate the switching of local symmetry around Dy(III) ion, aroused by the variation in intermolecular interactions and steric effects. This switch is primarily correlated with the distinction of magnetic properties. In addition, ab initio calculations confirmed that the different electrostatic potential around Dy(III) ion stemming from the electronic effect of the OMe-substituted group is another factor leading to the distinction in magnetic properties. This work warns us that when designing ligands for Dy-SIMs, the effect of positional isomerism on magnetic performance must be considered, which is one of the factors that can easily be overlooked.

Spin-Phonon Coupling and Slow-Magnetic Relaxation in Pristine Ferrocenium

We report the spin dynamic properties of non‐substituted ferrocenium complexes. Ferrocenium shows a field‐induced single‐molecule magnet behaviour in DMF solution while cobaltocene lacks slow spin relaxation neither in powder nor in solution. Multireference quantum mechanical calculations give a non‐Aufbau orbital occupation for ferrocenium with small first excitation energy that agrees with the relatively large measured magnetic anisotropy for a transition metal S=1/2 system. The analysis of the spin relaxation shows an important participation of quantum tunnelling, Raman, direct and local‐mode mechanisms which depend on temperature and the external field conditions. The calculation of spin‐phonon coupling constants for the vibrational modes shows that the first vibrational mode, despite having a low spin‐phonon constant, is the most efficient process for the spin relaxation at low temperatures. In such conditions, vibrational modes with higher spin‐phonon coupling constants are not populated. Additionally, the vibrational energy of this first mode is in excellent agreement with the experimental fitted value obtained from the local‐mode mechanism.

Combined Experimental and Ab Initio Methods for Rationalization of Magneto-Luminescent Properties of YbIII Nanomagnets Embedded in Cyanido/Thiocyanidometallate-Based Crystals

The ab initio calculations were correlated with magnetic and emission characteristics to understand the modulation of properties of NIR-emissive [Yb^III(2,2'-bipyridine-1,1'-dioxide)₄]³⁺ single-molecule magnets by cyanido/thiocyanidometallate counterions, [Ag^I(CN)₂]^- (1), [Au^I(SCN)₂]^- (2), [Cd^II(CN)₄]^2-/[Cd^II₂(CN)₇]^3- (3), and [M^III(CN)₆]^3- [M^III = Co (4), Ir (5), Fe (6), Cr (7)]. Theoretical studies indicate easy-axis-type ground doublets for all Yb^III centers. They differ in the magnetic axiality; however, transversal g-tensor components are always large enough to explain the lack of zero-dc-field relaxation. The excited doublets lie more than 120 cm^-1 above the ground one for all Yb^III centers. It was confirmed by high-resolution emission spectra reproduced from the ab initio calculations that give reliable insight into energies and oscillator strengths of optical transitions. These findings indicate the dominance of Raman relaxation with the power n varying from 2.93(4) to 6.9(2) in the 4-3-5-1-2 series. This trend partially follows the magnetic axiality, being deeper correlated with the phonon modes schemes of (thio)cyanido matrices.

Improving the single-molecule magnet properties of two pentagonal bipyramidal Dy3+ compounds by the introduction of both electron-withdrawing and -donating groups

Two mononuclear Dy³⁺ compounds [Dy(bmbpen-F)X] (X = Cl, 1; Br, 2) with a pentagonal bipyramidal (PBP) geometry were obtained from N,N'-bis-(5-methyl-2-hydroxybenzyl)-N,N'-bis(5-fluoro-2-methylpyridyl)ethylenediamine (H₂bmbpen-F) and dysprosium halides. The magnetic anisotropy and single-molecule magnet (SMM) behavior of these PBP compounds were regulated by introducing both electron-withdrawing F atoms into the equatorial pyridine rings and electron-donating -CH₃ groups into the axial phenolic hydroxyl rings. The results of magnetic characterization show that 1 and 2 exhibit single molecule magnet behavior with magnetization reversal barriers of 990(13) and 1189(16) K under a zero dc external field and magnetic hysteresis loops up to 26 K and 36 K, respectively. The results of ab initio calculations are consistent with the experimental observations, confirming that the simultaneous introduction of electron-withdrawing groups into the equatorial positions and electron-donating groups into the axial positions can lead to PBP Dy-SMMs with improved properties.

Magnetic anisotropy on demand exploiting high-pressure as remote control: an ab initio proof of concept

Lanthanide based single molecule magnets have recently become very promising systems for creating single molecule devices working at high temperatures (nitrogen boiling temperature). However, the variation of the direction of the anisotropy tensor as a function of the applied pressure still represents a quite unexplored field. Application of external pressure can be a promising method toward neat control of magnetic anisotropy and relaxation processes in the bulk phase. Required criteria for being eligible for such systems are as follows: the presence of first excited energy levels with significantly different orientations of its anisotropy tensor; sufficiently low energies of such levels so that they can mix with the ground state; and the possibility of tuning their energies by small geometrical perturbations. The archetype compound {Na[DyDOTA(H2O)]·4H2O} (1) (H4DOTA = 1,4,7,10-tetraazacyclododecane-1,4,7,10-N,N',N'',N'''-tetraacetic acid) fulfils all such criteria. A state-of-the-art in silico proof of concept study on the possibility of controlling the orientation of the anisotropy tensor as a function of pressure in [DyDOTA(H2O)]- by inducing different apical water molecule (AWM) orientations and/or DOTA-induced crystal field is presented.

Structural, magnetic and theoretical analyses of anionic and cationic phthalocyaninato-terbium(III) double-decker complexes: magnetic relaxation via higher ligand-field sublevels enhanced by oxidation

Crystal structural and magnetic analyses were performed for the anionic (1-) and cationic (1+) forms of phthalocyaninato-Tb3+ double-decker single-molecule magnets (SMMs). Both charged species showed slow magnetic relaxations and magnetic hysteresis characteristics for SMMs. 1+ showed longer magnetic relaxation times (τ) and higher activation energy for spin reversal (ΔE) than 1- did. Ligand field (LF) splitting calculated using ab initio methods revealed that the experimental ΔE values in 1- and 1+ were considerably larger than the first excited LF levels but rather close to the higher excited ones, indicating the magnetic relaxation via higher excited states.

Homochiral Dysprosium Phosphonate Nanowires: Morphology Control and Magnetic Dynamics

Controllable synthesis of uniformly distributed nanowires of coordination polymers with inherent physical functions is highly desirable but challenging. In particular, the combination of chirality and magnetism into nanowires has potential applications in multifunctional materials and spintronic devices. Herein, we report four pairs of enantiopure coordination polymers with formulae S-, R-Dy(cyampH)₃  ⋅ CH₃ COOH ⋅ 2H₂ O (S-1, R-1), S-, R-Dy(cyampH)₃  ⋅ 3H₂ O (S-2, R-2), S-, R-Dy(cyampH)₂ (C₂ H₅ COO) ⋅ 3H₂ O (S-3, R-3) and S-, R-Dy(cyampH)₃  ⋅ 0.5C₂ H₅ COOH ⋅ 2H₂ O (S-4, R-4) [cyampH₂ =S-, R-(1-cyclohexylethyl)aminomethylphosphonic acids], which were obtained depending on the pH of the reaction mixtures and the specific carboxylic acid used as pH regulator. Interestingly, compounds 3 were obtained as superlong nanowires, showing 1D neutral chain structure which contains both phosphonate and propionate anion ligands. While compounds 1, 2 and 4 appeared as block-like crystals, superhelices and nanorods, respectively, and exhibited similar neutral chain structures containing only phosphonate ligand. Slow magnetization relaxation characteristic of single-molecule magnet (SMM) behavior was observed for compounds S-1 and S-3. Theoretical calculations were performed to rationalize the magneto-structural relationships.

Structural and magnetic studies of mononuclear lanthanide complexes derived from N-rich chiral Schiff bases

A new family of mononuclear lanthanide complexes with the formula [CeIII(L)(NO3)3(MeOH)] (1) and [LnIII(L)(NO3)3]·MeOH where Ln = Gd (2) or Dy (3) and L = N,N'-bis(pyridin-2-ylmethylene)cyclohexane-1,2-diamine has been obtained with the use of enantiomerically pure Schiff bases. Dynamic magnetic studies indicate that 1-3 present field-induced slow relaxation of the magnetization and their response has been compared with the magnetically diluted complexes 2d and 3d. Structural studies have been carried out by single crystal X-ray and powder diffraction.

The anisotropy of the internal magnetic field on the central ion is capable of imposing great impact on the quantum tunneling of magnetization of Kramers single-ion magnets

In this work, a theoretical method, taking into account the anisotropy of the internal magnetic field (B[combining right harpoon above]int), is proposed to predict the rate of quantum tunneling of magnetization (QTM), i.e., τQTM-1, for Kramers single-ion magnets (SIMs). Direct comparison to both experimental and previous theoretical results of three typical Kramers SIMs indicates the necessity of the inclusion of the anisotropy of B[combining right harpoon above]int for accurate description of QTM. The predictions of the method here are consistent with the theory proposed by Prokof'ev and Stamp (PS). For Kramers SIMs of high magnetic axiality, the QTM rates, predicted by the method here, are almost linearly proportional to the results by the PS method. The dependence of τQTM-1 on various parameters is analyzed for model systems. The averaged magnitude of B[combining right harpoon above]int (Bave) and principal g value of the axial direction (gZ) are the parameters on which τQTM-1 is linearly dependent. The ones on which τQTM-1 is quadratically dependent are gXY, i.e., the principal g value of the transversal direction, and xaniso characterizing the anisotropy of B[combining right harpoon above]int. Compared to Bave and gZ, gXY and xaniso provide a higher order of dependence for QTM. Therefore regulation of the SMM property via introduction of desired values of gXY and xaniso ought to be a strategy more efficient than the one via Bave and gZ. Being different from the one via gXY, the strategy via xaniso to regulate the QTM has been rarely touched upon according to our best knowledge. However, this strategy could also lead to significant improvement since it is the same as gXY in the aspect of the dependence of τQTM-1.

Solvent responses and substituent effects upon magnetic properties of mononuclear DyIII compounds

Solvent responsive magnets comprise a class of molecule-based materials where lattice solvent driven structural transformation leads to the switching of magnetic properties. Herein, we present a special type of magnet where single-crystal to single-crystal (SCSC) transformations within mononuclear DyIII compounds result in the switching of DyIII single-molecule magnets (SMMs). This structural transformation involves lattice solvents which leads to significant changes in the color and magnetic properties. Additionally, the relaxation dynamics of mononuclear DyIII compounds are perceptibly fine-tuned by the modification of β-diketonate ligands. The uniaxial magnetic anisotropies, magneto-structural correlations and the relaxation mechanism were investigated by magnetic studies and ab initio calculations. These experimental and theoretical studies indicate that compound 2 exhibits the best magnetic properties in compounds 1-4. The experimental observation is supported by the theoretical prediction of QTM time (τZeeQTM) as theτZeeQTM of 2 is remarkably longer than those of the other three compounds by an order of magnitude. This means that, compared with 1, 3, and 4, the magnetic relaxation of 2 is significantly slower. Meanwhile, 2 has the largest value of axial ESP (the axial electrostatic potential), which supports the smallest gXY value in these compounds, resulting in better SMM properties. The present results offer a systematic synthesis regulation to change the magnetization dynamics and further understand magneto-structural correlations for DyIII SMMs.

In Situ Ligand Formation in the Synthetic Processes from Mononuclear Dy(III) Compounds to Binuclear Dy(III) Compounds: Synthesis, Structure, Magnetic Behavior, and Theoretical Analysis

Guided by the self-assembled process and mechanism, the strategy of in situ Schiff base reaction would be capable of bringing a feasible method to construct and synthesize lanthanide compounds with distinct structures and magnetic properties. A mononuclear Dy(III) compound was synthesized through a multidentate Schiff base ligand and a chelating β-diketonate ligand, which was named as [Dy(L)(bppd)]·CH₃OH [1; H₂L = N,N'-bis(2-hydroxy-5-methyl-3-formylbenzyl)-N,N'-bis(pyridin-2-ylmethyl)ethylenediamine and bppd = 3-bis(pyridin-2-yl)propane-1,3-dione]. Furthermore, a new binuclear Dy(III) compound, [Dy₂(H₂Lox)(bppd)₃]·8CH₃OH [2; H₄Lox = N,N'-bis[2-hydroxy-5-methyl-3-(hydroxyiminomethyl)benzyl]-N,N'-bis(pyridin-2-ylmethyl)ethylenediamine], was obtained via an in situ synthetic process. Under similar synthetic conditions, [Dy(L)(ctbd)] [3; ctbd = 1-(4-chlorophenyl)-4,4,4-trifluoro-1,3-butanedione] and [Dy₂(H₂Lox)(ctbd)₃]·CH₃OH·C₄H₁₀O (4) were synthesized by modifying the β-diketonate ligand and in situ Schiff base reaction. Compound 3 is a mononuclear configuration, while compound 4 exhibits a binuclear Dy(III) unit. Therein, formylbenzyl groups of H₂L in 1 and 3 were changed to (hydroxyiminomethyl)benzyl groups in 2 and 4, respectively. In isomorphous 2 and 4, two Dy(III) centers are connected through two phenol O^- atoms of the H₂Lox^2- ligand to form a binuclear structure. Eight-coordinated Dy(III) ions with different distortions can be observed in 1-4. The crystals of 1 and 3 suffered dissolution/precipitation to obtain 2 and 4, respectively. The relationship between the structure and magnetism in compounds 1-4 was discussed through the combination of structural, experimental, and theoretical investigations. Especially, the rates of quantum tunneling of magnetization of 1-4 were theoretically predicted and are consistent with the experimental results. For 2 and 4, the theoretically calculated dipolar parameters J_dip are consistent with the experimental observation of weak ferromagnetic coupling.

The influence of organic bases and substituted groups on coordination structures affording two mononuclear Dy(iii) single-molecule magnets (SMMs) and a novel Dy(iii)–K(i) compound with unusually coordinated fluorine atoms

The different organic bases and substituted groups of auxiliary ligands play an important role in synthetic processes, finally affording distinct structures and magnetic properties.

Two C2v symmetry dysprosium(iii) single-molecule magnets with effective energy barriers over 600 K

Two high-performance C_2v symmetry dysprosium(iii) single-molecule magnets were synthesized. The mechanism of magnetization dynamics was studied in detail.

Switching of easy-axis to easy-plane anisotropy in cobalt(ii) complexes

In situ microcalorimetry monitored assembly and coligand induced switching of the magnetic anisotropy sign have been observed in a β-diketonate-Co(ii) system.

Control of magnetic anisotropy by macrocyclic ligand distortion in a family of DyIII and ErIII single molecule magnets

A family of hexaazamacrocyclic lanthanide complexes, [Ln(Ln)(NCS)3] (LnIII = Dy, Er; n = 1-3) has been synthesized and characterized by single-crystal X-ray diffraction, magnetic measurements and ab initio calculations. Macrocyclic ligands (Ln) differ in the lateral spacers, which are aliphatic chains with two and three carbons (for Ln, n = 1 and 2, respectively), and an aromatic ring for Ln = 3. Modification of the macrocycle spacer tunes planarity and rigidity of the equatorial coordination for both oblate (Dy) and prolate (Er) lanthanide ions. Ac-susceptibility studies showed that four of the six complexes are field induced single molecule magnets (SMMs). Trends in magnetic relaxation properties are rationalized with the aid of ab initio multireference calculations, highlighting the combined influence of macrocycle planarity, lanthanide electronic density distribution and intermolecular interactions for the achievement of slow demagnetization.

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.

Substitution Effects Regulate the Formation of Butterfly-Shaped Tetranuclear Dy(III) Cluster and Dy-Based Hydrogen-Bonded Helix Frameworks: Structure and Magnetic Properties

The generation of two types of complexes with different topological connections and completely different structural types merely via the substitution effect is extremely rare, especially for -CH₃ and -C₂H₅ substituents with similar physical and chemical properties. Herein, we used 3-methoxysalicylaldehyde, 1,2-cyclohexanediamine, and Dy(NO₃)₃·6H₂O to react under solvothermal conditions (CH₃OH:CH₃CN = 1:1) at 80 °C to obtain the butterfly-shaped tetranuclear Dy^III cluster [Dy₄(L¹)₄(μ₃-O)₂(NO₃)₂] (Dy₄, H₂L¹ = 6,6'-((1E,1'E)-(cyclohexane-1,3-diylbis(azanylylidene))bis(methanylylidene))bis(2-methoxyphenol)). The ligand H₂L¹ was obtained by the Schiff base in situ reaction of 3-methoxysalicylaldehyde and 1,2-cyclohexanediamine. In the Dy₄ structure, (L¹)^2- has two different coordination modes: μ₂-η¹:η²:η¹:η¹ and μ₄-η¹:η²:η¹:η¹:η²:η¹. The four Dy^III ions are in two coordination environments: N₂O₆ (Dy1) and O₉ (Dy2). The magnetic testing of cluster Dy₄ without the addition of an external field revealed that it exhibited a clear frequency-dependent behavior. We changed 3-methoxysalicylaldehyde to 3-ethoxysalicylaldehyde and obtained one case of a hydrogen-bonded helix framework, [DyL²(NO₃)₃]_n·2CH₃CN (Dy-HHFs, H₂L² = 6,6'-((1E,1'E)-(cyclohexane-1,3-diylbis(azanylylidene))bis(methanylylidene))bis(2-ethoxyphenol)), under the same reaction conditions. The ligand H₂L² was formed by the Schiff base in situ reaction of 3-ethoxysalicylaldehyde and 1,2-cyclohexanediamine. All Dy^III ions in the Dy-HHFs structure are in the same coordination environment (O₉). The twisted S-shaped (L²)^2- ligand is linked by a Dy(III) ion to form a spiral chain. The spiral chain is one of the independent units that is interconnected to form Dy-HHFs through three strong hydrogen-bonding interactions. Magnetic studies show that Dy-HHFs exhibits single-ion-magnet behavior (U_eff = 68.59 K and τ₀ = 1.10 × 10^-7 s, 0 Oe DC field; U_eff = 131.5 K and τ₀ = 1.22 × 10^-7 s, 800 Oe DC field). Ab initio calculations were performed to interpret the dynamic magnetic performance of Dy-HHFs, and a satisfactory consistency between theory and experiment exists.

Spin dynamics in single-molecule magnets and molecular qubits

Over recent decades, much effort has been made to lengthen spin relaxation/decoherence times of single-molecule magnets and molecular qubits by following different chemical design rules such as maximizing the total spin value, controlling symmetry, enhancing the ligand field or inhibiting key vibrational modes. Simultaneously, electronic structure calculations have been employed to provide an understanding of the processes involved in the spin dynamics of molecular systems and served to refine or introduce new design rules. This review focuses on contemporary theoretical approaches focused on the calculation of spin relaxation/decoherence times, highlighting their main features and scope. Fundamental aspects of experimental techniques for the determination of key Single Molecule Magnet/Spin Qubit properties are also reviewed.

Dysprosium-based complexes with a flat pentadentate donor: a magnetic and ab initio study

The reactivity of the well-known pentadentate N3O2 Schiff base H2L (2,6-bis(2-hydroxyphenyliminomethyl)pyridine) towards a lanthanoid metal, in this case DyIII, has been investigated for the first time. This reactivity markedly depends on the pH of the medium and, accordingly, two different complexes, [Dy(HL)(NO3)2]·H2O (1·H2O) and [Dy(L)(NO3)(EtOH)(H2O)]·2H2O (2·2H2O), could be isolated from dysprosium(iii) nitrate and H2L. In addition, reaction of H2L with dysprosium(iii) chloride in methanol yields [Dy(HL')2][Dy(L)(Cl2)] (3), where H2L' ((6-(2-hydroxyphenyliminomethyl)-2-methoxyhydroxymethyl)pyridine) is an N2O2 hemiacetal donor derived from the partial hydrolysis of the H2L ligand, and subsequent addition of the methanol solvent to the carbonyl group. This latter reaction has been firstly observed for a lanthanoid metal. Single crystal X-ray diffraction studies of 1·1.15Py·0.3CH3C6H5, 2·2H2O and 3 show that the Schiff base is acting as a nearly flat pentadentate donor in all the cases, this behaviour being independent of the deprotonation degree of the phenolic oxygen atoms, both mono- or bisdeprotonated. Complexes 1·1.15Py·0.3CH3C6H5 and 2·2H2O show DyN3O6 cores, with distorted geometries closer to spherical tricapped trigonal prism or spherical capped square antiprism for 1·1.15Py·0.3CH3C6H5 and 2·2H2O, respectively. In the case of 3, the [Dy(HL')2]+ cation shows a dysprosium ion in an N4O4 triangular dodecahedron environment, while the [Dy(L)(Cl2)]- anion displays a DyN3O2Cl2 core with distorted pentagonal bipyramidal geometry. Moreover, attempts to dilute 1·H2O with yttrium yielded single crystals of (Et3NH)[Dy0.09Y0.91(L)(NO3)2] (4), where the Schiff base shows a similar pentadentate coordination mode. Dynamic magnetic studies of 1·H2O, 2·2H2O and 3 show that 2·2H2O and 3 present field-induced slow relaxation of the magnetisation, with Ueff barriers of 46.1(9) and 31.0(7) K for 2·2H2O and 3, respectively, while 1·H2O does not exhibit frequency-dependent peaks of the out of phase susceptibility, even in the presence of an external dc magnetic field. By contrast, the dilute sample 4 behaves as a SIM at zero dc field, with an energy barrier of ca. 49 K. Ab initio calculations using CASSCF methods including spin-orbit effects qualitatively support the obtained magnetic results, indicating that axiality is not the only factor that should be taken into account in order to increase effective energy barriers.

Design of high-temperature f-block molecular nanomagnets through the control of vibration-induced spin relaxation

One of the main roadblocks that still hamper the practical use of molecular nanomagnets is their cryogenic working temperature. In the pursuit of rational strategies to design new molecular nanomagnets with increasing blocking temperature, ab initio methodologies play an important role by guiding synthetic efforts at the lab stage. Nevertheless, when evaluating vibration-induced spin relaxation, these methodologies are still far from being computationally fast enough to provide a useful predictive framework. Herein, we present an inexpensive first-principles method devoted to evaluating vibration-induced spin relaxation in molecular f-block single-ion magnets, with the important advantage of requiring only one CASSCF calculation. The method is illustrated using two case studies based on uranium as the magnetic centre. Finally, we propose chemical modifications in the ligand environment with the aim of suppressing spin relaxation.

Structurally modulated single-ion magnets of mononuclear β-diketone dysprosium(iii) complexes

Four perturbed eight-coordinated mononuclear β-diketone based Dy(iii) SIMs with distinct hydrogen bond interactions and electron delocalization are noteworthily modulated by the aromatic groups of auxiliary ligands.

High performance single-molecule magnets, Orbach or Raman relaxation suppression?

Relaxation mechanisms limiting the blocking temperature for high-performance single molecule magnets (SMMs) are investigated. Best SMMs are limited by the exponential regime. Current ab initio methods can yield accurate estimations for this limit.