Molecular Anisotropy Analysis of Single-Ion Magnets Using an Effective Electrostatic Model

Tailoring single-ion magnet properties of coordination polymer C11H18DyN3O9 (Dy-CP) using the radial effective charge model (RECM) and superposition model (SPM)

We investigate Dy-based coordination polymer C11H18DyN3O9 (Dy-CP) exhibiting single-ion magnet (SIM) properties, e.g., quantum tunnelling of magnetization (QTM), magnetic anisotropy, magnetic relaxation, and effective energy barrier (Ueff). To elucidate the underlying mechanisms, crystal field parameters (CFPs) for Dy3+ ions were modelled using the radial effective charge model (RECM) and superposition model (SPM), and the computational packages SIMPRE and SPECTRE. The modelled CFPs enable the prediction of the energy levels and associated wave functions, which successfully explain the field-induced Dy-CP SIM properties. The so-calculated magnetic susceptibility and isothermal magnetization match the experimental data reasonably well. The smaller energy separations of the first (Δ0-1 ∼ 31 cm-1) and the second (Δ0-2 = 74 cm-1) excited Kramers doublets suggest small Ueff = 65 cm-1 for Dy-CP. The magnetic moments of Dy3+ ions exhibit an easy-axis type magnetic anisotropy in the ground state, but change orientation in the excited states due to mixing of states from different Kramers doublets. Low-symmetry CF components play a crucial role in connecting different |±MJ〉 states within the ground multiplet, resulting in QTM and magnetic relaxation to the ground state occurring via the excited states. The RECM and SPM calculated CFP sets are standardized employing the 3DD package to enable meaningful comparison and assessing their mutual equivalence. The results demonstrate the correlation between structural and electronic features of the molecule and site symmetry and distortion of the local coordination polyhedra with SIM properties, offering insights for rational design of new SIMs. The importance of considering low-symmetry aspects in CFP modelling for accurate predictions of magnetic properties is highlighted. This study provides deeper understanding of field-induced behaviour in rare-earth-based SIMs and approaches for rationalization of experimentally measured SIMs' properties.

Gas-Phase Formation of 1,3,5,7-Cyclooctatetraene (C8H8) through Ring Expansion via the Aromatic 1,3,5-Cyclooctatrien-7-yl Radical (C8H9•) Transient

Gas-phase 1,3,5,7-cyclooctatetraene (C₈H₈) and triplet aromatic 1,3,5,7-cyclooctatetraene (C₈H₈) were formed for the first time through bimolecular methylidyne radical (CH)-1,3,5-cycloheptatriene (C₇H₈) reactions under single-collision conditions on a doublet surface. The reaction involves methylidyne radical addition to the olefinic π electron system of 1,3,5-cycloheptatriene followed by isomerization and ring expansion to an aromatic 1,3,5-cyclooctatrien-7-yl radical (C₈H₉^•). The chemically activated doublet radical intermediate undergoes unimolecular decomposition to 1,3,5,7-cyclooctatetraene. Substituted 1,3,5,7-cyclooctatetraene molecules can be prepared in the gas phase with hydrogen atom(s) in the 1,3,5-cycloheptatriene reactant being replaced by organic side groups. These findings are also of potential interest to organometallic chemists by expanding the synthesis of exotic transition-metal complexes incorporating substituted 1,3,5,7-cyclooctatetraene dianion (C₈H₈^2-) ligands and to untangle the unimolecular decomposition of chemically activated and substituted 1,3,5-cyclooctatrien-7-yl radical, eventually gaining a fundamental insight of their bonding chemistry, electronic structures, and stabilities.

Multifunctionality of the [C2mim][Ln(fod)4] series (Ln = Nd–Tm except Pm): magnetic, luminescence and thermochemical studies

The [C2mim][Ln(fod)4] series presents a rare and reversible polymorphism, NIR and visible emission as well as SMM behavior. The varieties of physical behaviors make these compounds suitable for potential technological and/or biomedical applications.

Single Mn Atom Doping in Chiral Sensitive Assembled Gold Clusters to Molecular Magnet

Chiral stirred optical and magnetic properties, through the doping of assembled ultrasmall metal clusters (AMCs), are promising discernment to rivet the molecule-like quantum devices. Here, the single manganese (Mn) atom doping and assembly of the gold cluster (Au₈), leading to the chirality driven magnetism, has been achieved through a ligand-mediated growth. The X-ray absorption near edge structure and electron paramagnetic resonance studies corroborate the tetrahedral coordinated local structure of Mn dopant in the Au host. The optical and vibrational circular dichroic analysis affirms the modulation of chirality (negative to positive) in the presence of the Mn. A distinct ferromagnetic hysteresis loop at 300 K shows Mn ridden chiral sensitive ferromagnetism in contrary to the ligand influenced superparamagnetic undoped AMCs. The spin-polarized density functional theory level of calculations reveal the partial overlapping of spin-up and -down density of states in the doped AMCs, attributing to the ferromagnetic nature as like a molecular magnet suitable for the opto-spintronics application.

Derivation of Lanthanide Series Crystal Field Parameters From First Principles

Two series of lanthanide complexes have been chosen to analyze trends in the magnetic properties and crystal field parameters (CFPs) along the two series: The highly symmetric LnZn₁₆ (picHA)₁₆ series (Ln=Tb, Dy, Ho, Er, Yb; picHA=picolinohydroxamic acid) and the [Ln(dpa)₃ ](C₃ H₅ N₂ )₃ ⋅3H₂ O series (Ln=Ce-Yb; dpa=2,6-dipicolinic acid) with approximate three-fold symmetry. The first series presents a compressed coordination sphere of eight oxygen atoms whereas in the second series, the coordination sphere consists of an elongated coordination sphere formed of six oxygen atoms. The CFPs have been deduced from ab initio calculations using two methods: The AILFT (ab initio ligand field theory) method, in which the parameters are determined at the orbital level, and the ITO (irreducible tensor operator) decomposition, in which the problems are treated at the many-electron level. It has been found that the CFPs are transferable from one derivative to another, within a given series, as a first approximation. The sign of the second-order parameter B 0 2 differs in the two series, reflecting the different environments. It has been found that the use of the strength parameter S allows for an easy comparison between complexes. Furthermore, in both series, the parameters have been found to decrease in magnitude along the series, and this decrease is attributed to covalent effects.

Metal-ligand pair anisotropy in a series of mononuclear Er-COT complexes

Synthetic control of the crystal field has elevated lanthanides to the forefront of single-molecule magnet (SMM) research, yet the resultant strong, predictable single-ion anisotropy has thus far not translated into equally impressive molecule-based magnets of higher dimensionality. This roadblock arises from the dual demands made of the crystal field: generate anisotropy and facilitate magnetic coupling. Here we demonstrate that particular metal-ligand pairs can dominate the single-ion electronic structure so fully that the remaining coordination sphere plays a minimal role in the magnitude and orientation of the magnetic anisotropy. This Metal-Ligand Pair Anisotropy (MLPA) effectively separates the crystal field into discrete components dedicated to anisotropy and magnetic coupling. To demonstrate an MLPA building unit, we synthesized four new mononuclear complexes that challenge the electronic structure of the iconic lanthanocene ([Ln(COT)2]+; COT2- = cyclooctatetraene dianion) complex which is known to generate strong anisotropy with Ln = Er3+. Variation in symmetry and coordination strength for Er(COT)I(THF)2 (THF = tetrahydrofuran) (1), Er(COT)I(Py)2 (Py = pyridine) (2), Er(COT)I(MeCN)2 (MeCN = acetonitrile) (3), and Er(COT)(Tp*) (Tp* = tris(3,5-dimethyl-1-pyrazolyl)borate) (4) shows that the Er-COT unit stabilizes anisotropy despite deliberate de-optimization. All four half-sandwich complexes display SMM behavior with effective energy barriers of U eff = 95.6(9), 102.9(3.1), 107.1(1.3), and 133.6(2.2) cm-1 for 1-4 by a multi-relaxation-process fitting. More importantly, the basic state splittings remain intact and the anisotropy axes are within several degrees of normal to the COT2- ring according to complete active space self-consistent field (CASSCF) calculations. Further investigation of the MLPA conceptual framework is warranted as it can provide building units with well-defined magnetic orientation and strength. We envision that the through-barrier processes observed herein, such as quantum tunneling, can be mitigated by formation of larger clusters and molecule-based materials.

Symmetry strategies for high performance lanthanide-based single-molecule magnets

Toward promising candidates of quantum information processing, the rapid development of lanthanide-based single-molecule magnets (Ln-SMMs) highlights design strategies in consideration of the local symmetry of lanthanide ions. In this review, crystal-field theory is employed to demonstrate the electronic structures according to the semiquantitative electrostatic model. Then, specific symmetry elements are analysed for the elimination of transverse crystal fields and quantum tunnelling of magnetization (QTM). In this way, high-performance Ln-SMMs can be designed to enable extremely slow relaxation of magnetization, namely magnetic blocking; however, their practical magnetic characterization becomes increasingly challenging. Therefore, we will attempt to interpret the experimental behaviours and clarify some issues in detail. Finally, representative Ln-SMMs with specific local symmetries are summarized in combination with the discussion on the symmetry strategies, and some of the underlying questions are put forward.

Understanding the Magnetic Anisotropy toward Single-Ion Magnets

Single-molecule magnets (SMMs) can retain their magnetization status preferentially after removal of the magnetic field below a certain temperature. The unique property, magnetic bistable status, enables the molecule-scale SMM to become the next-generation high-density information storage medium. SMMs' new applications are also involved in high-speed quantum computation and molecular spintronics. The development of coordination chemistry, especially in transition metal (3d) and lanthanide (4f) complexes, diversifies SMMs by introducing new ones. In both 3d and 4f SMMs, the ligands play a fundamental role in determining the SMMs' magnetic properties. The strategies for rationally designing and synthesizing high-performance SMMs require a comprehensive understanding of the effects of a crystal field. In this Account, we focus mainly on the magneto-structural correlations of 4f or 3d single-ion magnets (SIMs), within which there is only one spin carrier. These one-spin carrier complexes benefit from getting rid of exchange interactions and relatively large distances of magnetic centers in the lattice, providing the ease to construct high-performance SIMs from the crystal field perspective. We will briefly introduce the crystal field approach for 4f or 3d complexes and then the magnetic anisotropy analysis via the displaced-charge electrostatic model. This idea has been proposed for years, and the related work is also highlighted. The angular-resolved magnetometry method, predominating in determining the magnetic anisotropic axes direction, is discussed. We also give a brief introduction of the quantum chemistry ab initio method, which has shown to be powerful in understanding the magnetic anisotropy and low-lying states. In the constructing and characterizing part, we give an overview of the SIMs based on lanthanide and transition ions, reported by our group in the past 5 years. In the 4f-SIMs survey, we discuss how β-diketonates and cyclomultienes, and their combination, as ligands to influence magnetic anisotropy and provide some suggestion on designing SIMs based on different lanthanide ions. In the 3d-SIMs survey, we fully discuss the correlation between zero-field-splitting parameter D and molecular geometrical angle parameters. Finally, we lay out the challenges and further development of SIMs. We hope the understanding we provide about single-ion magnetic properties will be helpful to design high-performance SMMs.

Switching of Slow Magnetic Relaxation Dynamics in Mononuclear Dysprosium(III) Compounds with Charge Density

The symmetry around a Dy ion is recognized to be a crucial parameter dictating magnetization relaxation dynamics. We prepared two similar square-antiprismatic complexes, [Dy(LOMe)2(H2O)2](PF6) (1) and Dy(LOMe)2(NO3) (2), where LOMe = [CpCo{P(O)(O(CH3))2}3], including either two neutral water molecules (1) or an anionic nitrate ligand (2). We demonstrated that in this case relaxation dynamics is dramatically affected by the introduction of a charged ligand, stabilizing the easy axis of magnetization along the nitrate direction. We also showed that the application of either a direct-current field or chemical dilution effectively stops quantum tunneling in the ground state of 2, thereby increasing the relaxation time by over 3 orders of magnitude at 3.5 K.

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

The magnetic behaviour of a Dy(LH)3 complex (LH(-) is the anion of 2-hydroxy-N'-[(E)-(2-hydroxy-3-methoxyphenyl)methylidene]benzhydrazide) was analysed in depth from both theoretical and experimental points of view. Cantilever torque magnetometry indicated that the complex has Ising-type anisotropy, and provided two possible directions for the easy axis of anisotropy due to the presence of two magnetically non-equivalent molecules in the crystal. Ab initio calculations confirmed the strong Ising-type anisotropy and disentangled the two possible orientations. The computed results obtained by using ab initio calculations were then used to rationalise the composite dynamic behaviour observed for both pure Dy(III) phase and Y(III) diluted phase, which showed two different relaxation channels in zero and non-zero static magnetic fields. In particular, we showed that the relaxation behaviour at the higher temperature range can be correctly reproduced by using a master matrix approach, which suggests that Orbach relaxation is occurring through a second excited doublet.

Can Non-Kramers Tm(III) Mononuclear Molecules be Single-Molecule Magnets (SMMs)?

In recent years, plentiful lanthanide-based (Tb(III) , Dy(III) , and Er(III) ) single-molecule magnets (SMMs) were studied, while examples of other lanthanides, for example, Tm(III) are still unknown. Herein, for the first time, we show that by rationally manipulating the coordination sphere, two thulium compounds, 1[(Tp)Tm(COT)] and 2[(Tp*)Tm(COT)] (Tp=hydrotris(1-pyrazolyl)borate; COT=cyclooctatetraenide; Tp*=hydrotris(3,5-dimethyl-1-pyrazolyl)borate), can adopt the structure of non-Kramers SMMs and exhibit their behaviors. Dynamic magnetic studies indicated that both compounds showed slow magnetic relaxation under dc field and a relatively high effective energy barrier (111 K for 1, 46 K for 2). Magnetic diluted 1 a[(Tp)Tm0.05 Y0.95 (COT)] and 2 a[(Tp*)Tm0.05 Y0.95 (COT)] even exhibited magnetic relaxation under zero dc field. Relativistic ab initio calculations combined with single-crystal angular-resolved magnetometry measurements revealed the strong easy axis anisotropy and nearly degenerated ground doublet states. The comparison of 1 and 2 highlights the importance of local symmetry for obtaining Tm SMMs.

SIMPRE1.2: Considering the hyperfine and quadrupolar couplings and the nuclear spin bath decoherence

SIMPRE is a fortran77 code which uses an effective electrostatic model of point charges to predict the magnetic behavior of rare-earth-based mononuclear complexes. In this article, we present SIMPRE1.2, which now takes into account two further phenomena. First, SIMPRE now considers the hyperfine and quadrupolar interactions within the rare-earth ion, resulting in a more complete and realistic set of energy levels and wave functions. Second, and to widen SIMPRE's predictive capabilities regarding potential molecular spin qubits, it now includes a routine that calculates an upper-bound estimate of the decoherence time considering only the dipolar coupling between the electron spin and the surrounding nuclear spin bath. Additionally, SIMPRE now allows the user to introduce the crystal field parameters manually. Thus, we are able to demonstrate the new features using as examples (i) a Gd-based mononuclear complex known for its properties both as a single ion magnet and as a coherent qubit and (ii) an Er-based mononuclear complex. © 2016 Wiley Periodicals, Inc.

Heteronuclear Ni(ii)–Ln(iii) (Ln = La, Pr, Tb, Dy) complexes: synthesis and single-molecule magnet behaviour

The crystal structures are reported for three heterometallic Ni₂Ln and a Ni₂Dy₂ complex, using the Schiff base ligand 2-methoxy-6-[(E)-phenyliminomethyl] phenol. Detailed dc and ac magnetic susceptibility studies were reported for all the complexes. The complexes 3 and 4 shows frequency dependent out-of-phase susceptibility signals.

Coherence and organisation in lanthanoid complexes: from single ion magnets to spin qubits

Molecular magnetism is reaching a degree of development that will allow for the rational design of sophisticated systems.

A monometallic lanthanide bis(methanediide) single molecule magnet with a large energy barrier and complex spin relaxation behaviour

We report a dysprosium(iii) bis(methanediide) single molecule magnet (SMM) where stabilisation of the highly magnetic states and suppression of mixing of opposite magnetic projections is imposed by a linear arrangement of negatively-charged donor atoms supported by weak neutral donors. Treatment of [Ln(BIPMTMS)(BIPMTMSH)] [Ln = Dy, 1Dy; Y, 1Y; BIPMTMS = {C(PPh2NSiMe3)2}2-; BIPMTMSH = {HC(PPh2NSiMe3)2}-] with benzyl potassium/18-crown-6 ether (18C6) in THF afforded [Ln(BIPMTMS)2][K(18C6)(THF)2] [Ln = Dy, 2Dy; Y, 2Y]. AC magnetic measurements of 2Dy in zero DC field show temperature- and frequency-dependent SMM behaviour. Orbach relaxation dominates at high temperature, but at lower temperatures a second-order Raman process dominates. Complex 2Dy exhibits two thermally activated energy barriers (U eff) of 721 and 813 K, the largest U eff values for any monometallic dysprosium(iii) complex. Dilution experiments confirm the molecular origin of this phenomenon. Complex 2Dy has rich magnetic dynamics; field-cooled (FC)/zero-field cooled (ZFC) susceptibility measurements show a clear divergence at 16 K, meaning the magnetic observables are out-of-equilibrium below this temperature, however the maximum in ZFC, which conventionally defines the blocking temperature, T B, is found at 10 K. Magnetic hysteresis is also observed in 10% 2Dy@2Y at these temperatures. Ab initio calculations suggest the lowest three Kramers doublets of the ground 6H15/2 multiplet of 2Dy are essentially pure, well-isolated |±15/2, |±13/2 and |±11/2 states quantised along the C[double bond, length as m-dash]Dy[double bond, length as m-dash]C axis. Thermal relaxation occurs via the 4th and 5th doublets, verified experimentally for the first time, and calculated U eff values of 742 and 810 K compare very well to experimental magnetism and luminescence data. This work validates a design strategy towards realising high-temperature SMMs and produces unusual spin relaxation behaviour where the magnetic observables are out-of-equilibrium some 6 K above the formal blocking temperature.

Molecular lanthanide single-ion magnets: from bulk to submonolayers

Single-ion magnets (SIMs) are mononuclear molecular complexes exhibiting slow relaxation of magnetization. They are currently attracting a lot of interest because of potential applications in spintronics and quantum information processing. However, exploiting SIMs in, e.g. molecule-inorganic hybrid devices requires a fundamental understanding of the effects of molecule-substrate interactions on the SIM magnetic properties. In this review the properties of lanthanide SIMs in the bulk crystalline phase and deposited on surfaces in the (sub)monolayer regime are discussed. As a starting point trivalent lanthanide ions in a ligand field will be described, and the challenges in characterizing the ligand field are illustrated with a focus on several spectroscopic techniques which are able to give direct information on the ligand-field split energy levels. Moreover, the dominant mechanisms of magnetization relaxation in the bulk phase are discussed followed by an overview of SIMs relevant for surface deposition. Further, a short introduction will be given on x-ray absorption spectroscopy, x-ray magnetic circular dichroism and scanning tunneling microscopy. Finally, the recent experiments on surface-deposited SIMs will be reviewed, along with a discussion of future perspectives.

Does the thermal evolution of molecular structures critically affect the magnetic anisotropy?

In the absence of a critical phase transition, one can safely use the crystal structure information determined at liquid nitrogen temperature in magnetic anisotropy research.

A dysprosium based single-ion magnet is synthesized and characterized by the angular dependence of the single-crystal magnetic susceptibility. Ab initio and effective electrostatic analyses are performed using the molecular structures determined from single crystal X-ray diffraction at 20 K, 100 K and 300 K. Contrary to the common assumption, the results reveal that the structural thermal effects that may affect the energy level scheme and magnetic anisotropy below 100 K are negligible.

Magnetic anisotropy of endohedral lanthanide ions: paramagnetic NMR study of MSc2N@C80-Ih with M running through the whole 4f row

Paramagnetic and variable temperature 13C and 45Sc nuclear magnetic resonance studies are performed for nitride clusterfullerenes MSc2N@C80 with icosahedral Ih(7) carbon cage, where M runs through all lanthanides forming nitride clusters. The influence of the endohedral lanthanide ions on the NMR spectral pattern is carefully followed, and dramatic differences are found in peak positions and line widths. Thus, 13C lines broaden from 0.01-0.02 ppm in diamagnetic MSc2N@C80 molecules (M = La, Y, Lu) to several ppm in TbSc2N@C80 and DySc2N@C80. Direction of the paramagnetic shift depends on the shape of the 4f electron density in corresponding lanthanide ions. In TmSc2N@C80 and ErSc2N@C80 with prolate 4f-density of lanthanide ions, 13C signals are shifted down-field, whereas 45Sc peaks are shifted up-field versus diamagnetic values. In all other MSc2N@C80 molecules lanthanide ions have oblate-shaped 4f electron density, and the lanthanide-induced shift is negative for 13C and positive for 45Sc peaks. Analysis of the pseudocontact and contact contributions to chemical shifts revealed that the pseudocontact term dominates both in 13C and 45Sc NMR spectra, although contact shifts for 13C signals are also considerable. Point charge computations of the ligand field splitting are performed to explain experimental results, and showed reasonable agreement with experimental pseudocontact shifts. Nitrogen atom bearing large negative charge and located close to the lanthanide ion results in large magnetic anisotropy of lanthanide ions in nitride clusterfullerenes with quasi-uniaxial ligand field.

Improving f-element single molecule magnets

Historical developments, trends, pitfalls and strategies in improving f-element single molecule magnets are described.

Prediction of the quantized axis of rare-earth ions: the electrostatic model with displaced point charges

An electrostatic model with displaced point charges to predict the quantized axis of rare-earth ions is proposed.

Syntheses, structures, and magnetic properties of homodinuclear lanthanide complexes based on dinucleating Schiff base ligands

Two series of homodinuclear lanthanide(iii) complexes were synthesized and characterized. Magnetic studies reveal the weakly antiferromagnetic coupling between paramagnetic Ln ions and enhanced relaxation of magnetization for Dy₂ complexes.

Magnetic and photo-physical investigations into DyIII and YbIII complexes involving tetrathiafulvalene ligand

Three TTF-based complexes have been elaborated using β-diketonate Dy^III and Yb^III precursors. [Yb(tta)₃(L)]·2CH₂Cl₂ enlarges the scarce series of redox-active luminescent single-molecule magnets with correlation between emissive and magnetic properties.