Unravelling the role of spin-vibrational coupling in designing high-performance pentagonal bipyramidal Dy(iii) single ion magnets

At the cutting edge of high-performance single-molecule magnets (SMMs) lie lanthanide-based complexes, renowned for their potent magnetic anisotropy. SMMs containing one metal centre are defined as single-ion magnets (SIMs). The performance of SMMs is measured generally via the barrier height for magnetisation reversal (Ueff) and blocking temperature (TB), below which the magnetisation is fully frozen. To enhance the Ueff and TB values in lanthanide-based SMMs, the static crystal field splitting of mJ levels has been effectively adjusted through ligand design, leveraging the oblate/prolate ground state 4f electron density shape. However, the maximum fine-tuning achievable through ligand design, known as the axial limit, has already been reached in this class of compounds. This necessitates new design principles to enhance SMM characteristics to better suit end-user applications. Among other avenues that can be explored to improve SMM characteristics, a deeper understanding of spin-phonon coupling is critical to advancing TB values. However, there are only a handful of examples where this has been deciphered. In this work, using a combination of DFT and ab initio CASSCF calculations, we have performed spin-phonon calculations on five classes of pentagonal bipyramidal Dy(iii) SIMs exhibiting TB values in the range of 4.5 K to 36 K ([Dy(bbpen)Br] (1, H2bbpen = N,N'-bis(2-hydroxybenzyl)-N,N'-bis(2-methylpyridyl)ethylenediamine), [Dy(OCMe3)Br(THF)5][BPh4] (2) [Dy(OSiMe3)Br(THF)5] [BPh4] (3), [Dy(LN5)(Ph3SiO)2](BPh4)·CH2Cl2 (4) and [L2Dy(H2O)5][I]3·L2·H2O (5, L = tBuPO(NHiPr)2)). Unlike the method employed elsewhere for the calculation of spin-phonon coupling, in this work, we have employed a set of criteria and intuitively selected vibrational modes to perform the spin-phonon coupling analysis. The approach provided here not only reduces the computational cost significantly but also suggests chemical intuition to improve the performance of this class of compounds. Our calculations reveal that low-energy vibrational modes govern the magnetisation relaxation in these SIMs. A flexible first coordination sphere found on some of the complexes was found to be responsible for low-energy vibrations that flip the magnetisation, reducing the TB values drastically (complexes 2 and 3). On the other hand, a rigid first coordination sphere and a stiff ligand framework move the spin-vibrational coupling that causes the relaxation to lie beyond the secondary coordination sphere, resulting in an increase in TB values. Our calculations also reveal that not only the atoms in the first coordination sphere but also those in the secondary coordination sphere affect the performance of the SMMs. Learning from this exercise, we have undertaken several in silico models based on these vibrations to improve the TB values. Some of these predictions were correlated with literature precedents, offering confidence in the methodology employed. To this end, our comprehensive investigation, involving twenty-three molecules/models and five sets of geometries for pentagonal bipyramidal Dy(iii) single-ion magnets (SIMs), unveils a treasure trove of chemically sound design clues, poised to enhance the TB values in this fascinating molecular realm.

Magnetic anisotropy in octahedral Dy(III) and Yb(III) complexes

New organophosphate complexes [Ln(dippH)3(dippH2)3]·(H2O)6, (Ln = Dy, Yb and Y; dippH2 = 2,6-diisopropylphenyl phosphate), displaying octahedral coordination geometry around the metal ion, exhibit unusual slow relaxation of magnetisation, which is investigated through experimental studies and ab initio CASSCF calculations.

Can Iron-Porphyrins Behave as Single-Molecule Magnets?

The study of magnetic properties, especially the magnetic anisotropy of iron-porphyrin complexes employing multiconfigurational methods, is quite challenging due to many strongly correlated electrons in nearly degenerate orbitals. However, a prerequisite for observing the magnetic anisotropy and slow magnetization relaxation, the zero-field splitting parameter, D, was experimentally observed decades ago for halide-based axially ligated penta-coordinate Fe(III)-porphyrins. In these complexes, the signs of D were reported mostly as positive; in a few cases, inconclusive signs of the D parameter were also mentioned. However, no ab initio calculations have been reported to shed light on this. Deciphering the electronic structure of these penta-coordinated complexes employing the complete active space self-consistent field method and N-electron valence second-order perturbation theory, we confirm the positive D values. However, a negative D value is highly desired to observe the single-molecule magnet properties without an external magnetic field, which we observed in the Fe(II)-porphyrin complexes with axial imidazole ligands instead of halide ligands. The detailed analysis of the multireference wave functions unravels the role of axial ligands in determining the sign and magnitude of the D parameters.

Strategies to quench quantum tunneling of magnetization in lanthanide single molecule magnets

Enhancing blocking temperature (T_B) is one of the holy grails in Single Molecule Magnets(SMMs), as any future potential application in this class of molecules is directly correlated to this parameter. Among many factors contributing to a reduction of T_B value, Quantum Tunnelling of Magnetisation (QTM), a phenomenon that is a curse or a blessing based on the application sought after, tops the list. Theoretical tools based on density functional and ab initio CASSCF/RASSI-SO methods have played a prominent role in estimating various spin Hamiltonian parameters and establishing the mechanism of magnetization relaxation in this class of molecules. Particularly, various strategies to quench QTM effects go hand-in-hand with experiments, and different methods proposed to quell QTM effects are scattered in the literature. In this perspective, we have explored various approaches that are proposed in the literature to quench QTM effects, and these include the role of (i) local symmetry of lanthanides, (ii) super-exchange interaction in {3d-4f} complexes, (iii) direct-exchange interaction in {radical-4f} and metal-metal bonded complexes to suppress the QTM, (iv) utilizing external stimuli such as an electric field or pressure to modulate the QTM and (v) avoiding QTM effects by stabilising toroidal states in 4f and {3d-4f} clusters. We believe the strategies summarized here will help to design new-generation SMMs.

Lanthanide Single-molecule Magnets: Synthetic Strategy, Structures, Properties and Recent Advances

Single-molecule magnets (SMMs) show wide potential applications in the field of ultrahigh-density storage materials, quantum computing, spintronics, and so on. Lanthanide (Ln) SMMs, as an important category of SMMs, open up a promising prospect due to their large magnetic moments and huge magnetic anisotropy. However, the construction of high performance for Ln SMMs remains an enormous challenge. Although remarkable advances are focused on the topic of Ln SMMs, the research on Ln SMMs with different nuclear numbers is still deficient. Therefore, this review summarizes the design strategies for the construction of Ln SMMs, as well as the metal skeleton types. Furthermore, we collect reported Ln SMMs with mononuclearity, dinuclearity, and multinuclearity (three or more Ln spin centers) and the SMM properties including energy barrier (U_eff ) and pre-exponential factor (τ₀ ) are described. Finally, Ln SMMs with low-nuclearity SMMs, especially for single-ion magnets (SIMs), are highlighted to understand the correlations between structures and magnetic behavior of the detail SMM properties are described. We expect the review can shed light on the future developments of high-performance Ln SMMs.

Molecular Lanthanide Switches for Magnetism and Photoluminescence

Solvation of [(CNT)Ln(η⁸ -COT)] (Ln=La, Ce, Nd, Tb, Er; CNT=cyclononatetraenyl, i.e., C₉ H₉ ^- ; COT=cyclooctatetraendiid, i.e., C₈ H₈ ^2- ) complexes with tetrahydrofuran (THF) gives rise to neutral [(η⁴ -CNT)Ln(thf)₂ (η⁸ -COT)] (Ln=La, Ce) and ionic [Ln(thf)_x (η⁸ -COT)][CNT] (x=4 (Ce, Nd, Tb), 3 (Er)) species in a solid-to-solid transformation. Due to the severe distortion of the ligand sphere upon solvation, these species act as switchable luminophores and single-molecule magnets. The desolvation of the coordinated solvents can be triggered by applying a dynamic vacuum, as well as a temperature gradient stimulus. Raman spectroscopic investigations revealed fast and fully reversible solvation and desolvation processes. Moreover, we also show that a Nd:YAG laser can induce the necessary temperature gradient for a self-sufficient switching process of the Ce(III) analogue in a spatially resolved manner.

Theoretical Investigation of Single-Molecule-Magnet Behavior in Mononuclear Dysprosium and Californium Complexes

Early-actinide-based (U, Np, and Pu) single-molecule magnets (SMMs) have yet to show magnetic properties similar to those of highly anisotropic lanthanide-based ones. However, there are not many studies exploring the late-actinides (more than half-filled f shells) as potential candidates for SMM applications. We computationally explored the electronic structure and magnetic properties of a hypothetical Cf(III) complex isostructural to the experimentally synthesized Dy(dbm)₃(bpy) complex (bpy = 2,2'-bipyridine; dbm = dibenzoylmethanoate) via multireference methods and compared them to those of the Dy(III) analogue. This study shows that the Cf(III) complex can behave as a SMM and has a greater magnetic susceptibility compared to other experimentally and computationally studied early-actinide-based (U, Np, and Pu) magnetic complexes. However, Cf spontaneously undergoes α-decay and converts to Cm. Thus, we also explored the isostructural Cm(III)-based complex. The computed magnetic susceptibility and g-tensor values show that the Cm(III) complex has poor SMM behavior in comparison to both the Dy(III) and Cf(III) complexes, suggesting that the performance of Cf(III)-based magnets may be affected by α-decay and can explain the poor performance of experimentally studied Cf(III)-based molecular magnets in the literature. Further, this study suggests that the ligand field is dominant in Cf(III), which helps to increase the magnetization blocking barrier by nearly 3 times that of its 4f congener.

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 Archetypal Homoleptic Lanthanide Quadruple-Decker-Synthesis, Mechanistic Studies, and Quantum Chemical Investigations

Reduction of [SmIII (COT1,4-SiiPr3 )(BH4 )(thf)] (COT1,4-SiiPr3 =1,4-(i Pr3 Si)3 C8 H6 ) with KC8 resulted in [SmIII/II/III (COT1,4-SiiPr3 )4 ], the first example of a homoleptic lanthanide quadruple-decker. As indicated by an analysis of the bond metrics in the solid-state, the inner Sm ion is present in the divalent oxidation state, while the outer ones are trivalent. This observation could be confirmed by quantum chemical calculations. Mechanistic studies revealed not only insight into possible formation pathways of [SmIII/II/III (COT1,4-SiiPr3 )4 ] but also resulted in the transformation to other mixed metal sandwich complexes with unique structural properties. These are the 1D-polymeric chain structured [KSmIII (COT1,4-SiiPr3 )]n and the hexametallic species [(tol)K(COT1,4-SiiPr3 )SmII (COT1,4-SiiPr3 )K]2 which were initially envisioned as possible building blocks as part of different retrosynthetically guided pathways that we developed.

Radical-Bridged Ln4 Metallocene Complexes with Strong Magnetic Coupling and a Large Coercive Field

Inducing magnetic coupling between 4f elements is an ongoing challenge. To overcome this formidable difficulty, we incorporate highly delocalized tetrazinyl radicals, which strongly couple with f-block metallocenes to form discrete tetranuclear complexes. Synthesis, structure, and magnetic properties of two tetranuclear [(Cp*₂ Ln)₄ (tz^. )₄ ]⋅3(C₆ H₆ ) (Cp*=pentamethylcyclopentadienyl; tz=1,2,4,5-tetrazine; Ln=Dy, Gd) complexes are reported. An in-depth examination of their magnetic properties through magnetic susceptibility measurements as well as computational studies support a highly sought-after radical-induced "giant-spin" model. Strong exchange interactions between the Ln^III ions and tz^. radicals lead to a strong magnet-like behaviour in this molecular magnet with a large coercive field of 30 kOe.

Solvato Modulation of the Magnetic Memory in Isotopically Enriched Erbium Polyoxometalate

Single-Molecule Magnet (SMM) property is by essence molecular, while commonly measured in solid crystalline state. Solvent crystallization molecules are usually neglected in the analysis and interpretation of solid-state properties. The solvation/desolvation process in the polyoxometalate(POM)-based Na₉ [Er(W₅ O₁₈ )₂ ] ⋅ 35 H₂ O SMM demonstrates that the dehydrated form relaxes more than 1000 times faster than the initial state, while the rehydration process allows the quasi complete recovering of the initial magnetic behaviour. This dehydration process is monitored by thermogravimetric analysis (TGA) and temperature-dependent X-ray powder diffraction, and rationalized by periodic quantum chemical calculations evidencing the tremendous role of the labile water molecules in the stability of the edifice. Ab-initio calculations highlight that sodium ions localization in the structure drive the magnetic responses. Isotopic enrichment with nuclear spin free (¹⁶⁶ Er, I=0) Er^III ions shows that the relaxation dynamics in the quantum regime depends on the nuclear spin.

Electronic Structure of Ytterbium(III) Solvates-a Combined Spectroscopic and Theoretical Study

The wide range of optical and magnetic properties of lanthanide(III) ions is associated with their intricate electronic structures which, in contrast to lighter elements, is characterized by strong relativistic effects and spin-orbit coupling. Nevertheless, computational methods are now capable of describing the ladder of electronic energy levels of the simpler trivalent lanthanide ions, as well as the lowest energy term of most of the series. The electronic energy levels result from electron configurations that are first split by spin-orbit coupling into groups of energy levels denoted by the corresponding Russell-Saunders terms. Each of these groups are then split by the ligand field into the actual electronic energy levels known as microstates or sometimes m_J levels. The ligand-field splitting directly informs on the coordination geometry and is a valuable tool for determining the structure and thus correlating the structure and properties of metal complexes in solution. The issue with lanthanide complexes is that the determination of complex structures from ligand-field splitting remains a very challenging task. In this paper, the optical spectra-absorption, luminescence excitation, and luminescence emission-of ytterbium(III) solvates were recorded in water, methanol, dimethyl sulfoxide (DMSO), and N,N-dimethylformamide (DMF). The electronic energy levels, that is, the microstates, were resolved experimentally. Subsequently, density functional theory calculations were used to model the structures of the solvates, and ab initio relativistic complete active space self-consistent field calculations (CASSCF) were employed to obtain the microstates of the possible structures of each solvate. By comparing the experimental and theoretical data, it was possible to determine both the coordination number and solution structure of each solvate. In water, methanol, and N,N-dimethylformamide, the solvates were found to be eight-coordinated and have a square antiprismatic coordination geometry. In DMSO, the speciation was found to be more complicated. The robust methodology developed for comparing experimental spectra and computational results allows the solution structures of homoleptic lanthanide complexes to be determined.

Opening Magnetic Hysteresis by Axial Ferromagnetic Coupling: From Mono-Decker to Double-Decker Metallacrown

Combining Ising-type magnetic anisotropy with collinear magnetic interactions in single-molecule magnets (SMMs) is a significant synthetic challenge. Herein we report a Dy[15-MC_Cu -5] (1-Dy) SMM, where a Dy^III ion is held in a central pseudo-D_5h pocket of a rigid and planar Cu₅ metallacrown (MC). Linking two Dy[15-MC_Cu -5] units with a single hydroxide bridge yields the double-decker {Dy[15-MC_Cu -5]}₂ (2-Dy) SMM where the anisotropy axes of the two Dy^III ions are nearly collinear, resulting in magnetic relaxation times for 2-Dy that are approximately 200 000 times slower at 2 K than for 1-Dy in zero external field. Whereas 1-Dy and the Y^III -diluted Dy@2-Y analogue do not show remanence in magnetic hysteresis experiments, the hysteresis data for 2-Dy remain open up to 6 K without a sudden drop at zero field. In conjunction with theoretical calculations, these results demonstrate that the axial ferromagnetic Dy-Dy coupling suppresses fast quantum tunneling of magnetization (QTM). The relaxation profiles of both complexes curiously exhibit three distinct exponential regimes, and hold the largest effective energy barriers for any reported d-f SMMs up to 625 cm^-1 .

Role of Ab Initio Calculations in the Design and Development of Organometallic Lanthanide-Based Single-Molecule Magnets

Single-molecule magnets based on lanthanides are very attractive due to their potential applications proposed in the area of microelectronic devices. Very recent advances in this area are due to the blend of conventional lanthanide chemistry with organometallic ligands, and several breakthrough achievements are attained with this combination. Ab initio methods based on multi-reference CASSCF calculations are playing a vital role in the design and development of such molecules. In this minireview, we aim to appraise various contributions in the area of organometallic lanthanide complexes (those containing lanthanide-carbon bonds) and describe how these robust wavefunction-based methods have played a constructive role not only in rationalizing the observed magnetic properties but also proven to be a potential predictive tool with some selected examples.

A method for extending AC susceptometry to long-timescale magnetic relaxation

As the ability to generate magnetic anisotropy in molecular materials continues to hit new milestones, concerted effort has shifted towards understanding, and potentially controlling, the mechanisms of magnetic relaxation across a large time and temperature space. Slow magnetic relaxation in molecules is highly temperature-, field-, and environment-dependent with the relevant timescale easily traversing ten orders of magnitude for current single-molecule magnets (SMM). The prospect of synthetic control over the nature of (and transition probabilities between) magnetic states make unraveling the underlying mechanisms an important yet daunting challenge. Currently, instrumental considerations dictate that the characteristic relaxation time, τ, is determined by separate methods depending on the timescale of interest. Static and dynamic probe fields are used for long- and short-timescales, respectively. Each method captures a distinct, non-overlapping time range, and experimental differences lead to the possibility of fundamentally different meanings for τ being plotted and fitted globally as a function of temperature. Herein, we present a method to generate long-timescale waveforms with standard vibrating sample magnetometry (VSM) instrumentation, allowing extension of alternating current (AC) susceptometry to SMMs and other superparamagnets with arbitrarily long relaxation time. We fit these data to a generalized Debye model and present a comparison to results obtained from direct current (DC) magnetization decay.

A New Class of Lanthanide Complexes with Three Ligand Centered Radicals: NMR Evaluation of Ligand Field Energy Splitting and Magnetic Coupling

Combination of three radical anionic Ph-BIAN ligands (Ph-BIAN=bis-(phenylimino)-acenaphthenequinone) with lanthanoid ions leads to a series of homoleptic, six-coordinate complexes of the type Ln(Ph-BIAN)₃ . Magnetic coupling data were measured by paramagnetic solution NMR spectroscopy. Combining ¹ H NMR with ² H NMR of partially deuterated compounds allowed a detailed study of the magnetic susceptibility anisotropies over a large temperature range. The observed chemical shifts were separated into ligand- and metal-centered contributions by comparison with the Y analogue (diamagnetic at the metal). The metal-centered contributions of the complexes with the paramagnetic ions could then be separated into pseudocontact and Fermi contact shifts. The latter is large within the Ph-BIAN scaffold, which shows that magnetic coupling is significant between the lanthanide ion and the radical ligand. Pseudocontact shifts were further correlated to structural data obtained from X-ray diffraction experiments. Ligand-field parameters were determined by fitting the temperature dependence of the observed magnetic susceptibility anisotropies. The electronic structure determined by this approach shows, that the Er and Tm analogues are candidates for single molecule magnets (SMM). These results demonstrate the possibilities for the application of NMR spectroscopy in investigations of paramagnetic systems in general and single molecule magnets in particular.

Dinuclear Dy2 Single-Molecule Magnets: Functional Modulation on the Bridging Ligand and Different Relaxation Performances within the Single-Crystal to Single-Crystal System

Crystal structures, single-molecule magnetic behavior, and ab initio calculations of four new phenoxo-bridged dinuclear dysprosium complexes and their gadolinium(III) analogues are explored. Complexes [Dy₂ (DMOMP)₂ (DBM)₄ ]₂ ⋅CHCl₃ (1; DMOMP=1-methyl-3,5-dimethoxy-4-hydroxybenzene, DBM=1,3-diphenylpropane-1,3-dione); [Dy₂ (DMOAP)₂ (DBM)₄ ]₂ ⋅CHCl₃ (2; DMOAP=syringaldehyde); Dy₂ (DMOEP)₂ (DBM)₄ (3; DMOEP=methyl syringate); and solvent-free Dy₂ (DMOMP)₂ (DBM)₄ (4), which is obtained by the transformation of single crystal into single crystal from 1, have nearly identical core structures and only differ in the substituents at the para position of the phenol moieties of the bridging ligand. In this system, the electronic effects are efficiently implemented to significantly modify the ligand field strength and exchange coupling by modulating the substituents on the phenol backbone. The effective energy barrier (U_eff ) of magnetization reversal is improved significantly to fivefold magnitude, at most, and the hysteresis temperature up to 3.5 K by deliberately using the electron-withdrawing substituent to replace the electron-donating one. The origin of the two relaxation processes in 1 is mostly attributed to the existence of two molecules in one unit, which is illuminated by means of the transformation of single crystal into single crystal.

Single Ion Magnets from 3d to 5f: Developments and Strategies

Single-ion magnets (SIMs), exhibiting slow magnetization relaxation in the absence of the magnetic field, originate from their single spin-carrier centre. In pursuit of high-performance magnetic properties, such as high spin-reversal barrier and high blocking temperature, various metal centres were investigated to establish SIMs, including 3d and 5d transition metal ions, 4f lanthanide ions, and 5f actinide ions, which possess unique zero-field splitting and magnetic properties. Therefore, proper ligand field is of great importance to different types of metals. In the given great breakthroughs since the first SIM, [Pc₂ Tb]^- (Pc=dianion of phthalocyanine), was reported, strategies of ligand field design have emerged. In this review, the developments of SIMs with different metal centres are summarized, as well as the possible strategies.

A Dysprosium Metallocene Single-Molecule Magnet Functioning at the Axial Limit

Abstraction of a chloride ligand from the dysprosium metallocene [(Cp^ttt )₂ DyCl] (1_Dy Cp^ttt =1,2,4-tri(tert-butyl)cyclopentadienide) by the triethylsilylium cation produces the first base-free rare-earth metallocenium cation [(Cp^ttt )₂ Dy]⁺ (2_Dy ) as a salt of the non-coordinating [B(C₆ F₅ )₄ ]^- anion. Magnetic measurements reveal that [2_Dy ][B(C₆ F₅ )₄ ] is an SMM with a record anisotropy barrier up to 1277 cm^-1 (1837 K) in zero field and a record magnetic blocking temperature of 60 K, including hysteresis with coercivity. The exceptional magnetic axiality of 2_Dy is further highlighted by computational studies, which reveal this system to be the first lanthanide SMM in which all low-lying Kramers doublets correspond to a well-defined M_J value, with no significant mixing even in the higher doublets.