Covalency versus magnetic axiality in Nd molecular magnets: Nd-photoluminescence, strong ligand-field, and unprecedented nephelauxetic effect in fullerenes NdM2N@C80 (M = Sc, Lu, Y)

Nd-based nitride clusterfullerenes NdM2N@C80 with rare-earth metals of different sizes (M = Sc, Y, Lu) were synthesized to elucidate the influence of the cluster composition, shape and internal strain on the structural and magnetic properties. Single crystal X-ray diffraction revealed a very short Nd-N bond length in NdSc2N@C80. For Lu and Y analogs, the further shortening of the Nd-N bond and pyramidalization of the NdM2N cluster are predicted by DFT calculations as a result of the increased cluster size and a strain caused by the limited size of the fullerene cage. The short distance between Nd and nitride ions leads to a very large ligand-field splitting of Nd3+ of 1100-1200 cm-1, while the variation of the NdM2N cluster composition and concomitant internal strain results in the noticeable modulation of the splitting, which could be directly assessed from the well-resolved fine structure in the Nd-based photoluminescence spectra of NdM2N@C80 clusterfullerenes. Photoluminescence measurements also revealed an unprecedentedly strong nephelauxetic effect, pointing to a high degree of covalency. The latter appears detrimental to the magnetic axiality despite the strong ligand field. As a result, the ground magnetic state has considerable transversal components of the pseudospin g-tensor, and the slow magnetic relaxation of NdSc2N@C80 could be observed by AC magnetometry only in the presence of a magnetic field. A combination of the well-resolved magneto-optical states and slow relaxation of magnetization suggests that Nd clusterfullerenes can be useful building blocks for magneto-photonic quantum technologies.

Carbon cage isomers and magnetic Dy⋯Dy interactions in Dy2O@C88 and Dy2C2@C88 metallofullerenes

Isomers of Dy2O@C88 and Dy2C2@C88 show a strong variation in the type and strength of Dy⋯Dy superexchange interactions and magnetization relaxation rate.

Single-Molecule Magnets DyM2 N@C80 and Dy2 MN@C80 (M=Sc, Lu): The Impact of Diamagnetic Metals on Dy3+ Magnetic Anisotropy, Dy⋅⋅⋅Dy Coupling, and Mixing of Molecular and Lattice Vibrations

The substitution of scandium in fullerene single-molecule magnets (SMMs) DySc2 N@C80 and Dy2 ScN@C80 by lutetium has been studied to explore the influence of the diamagnetic metal on the SMM performance of dysprosium nitride clusterfullerenes. The use of lutetium led to an improved SMM performance of DyLu2 N@C80 , which shows a higher blocking temperature of magnetization (TB =9.5 K), longer relaxation times, and broader hysteresis than DySc2 N@C80 (TB =6.9 K). At the same time, Dy2 LuN@C80 was found to have a similar blocking temperature of magnetization to Dy2 ScN@C80 (TB =8 K), but substantially different interactions between the magnetic moments of the dysprosium ions in the Dy2 MN clusters. Surprisingly, although the intramolecular dipolar interactions in Dy2 LuN@C80 and Dy2 ScN@C80 are of similar strength, the exchange interactions in Dy2 LuN@C80 are close to zero. Analysis of the low-frequency molecular and lattice vibrations showed strong mixing of the lattice modes and endohedral cluster librations in k-space. This mixing simplifies the spin-lattice relaxation by conserving the momentum during the spin flip and helping to distribute the moment and energy further into the lattice.

Electronic Structure and Photoluminescence Properties of Eu(η9-C9H9)2

The electronic structure of Eu²⁺ compounds results from a complex combination of strongly correlated electrons and relativistic effects as well as weak ligand-field interaction. There is tremendous interest in calculating the electronic structure as nowadays the Eu²⁺ ion is becoming more and more crucial, for instance, in lighting technologies. Recently, interest in semiempirical methods to qualitatively evaluate the electronic structure and to model the optical spectra has gained popularity, although the theoretical methods strongly rely upon empirical inputs, hindering their prediction capabilities. Besides, ab initio multireference models are computationally heavy and demand very elaborative theoretical background. Herein, application of the ligand-field density functional theory (LFDFT) method that is recently available in the Amsterdam Modeling Suite is shown: (i) to elucidate the electronic structure properties on the basis of the multiplet energy levels of Eu configurations 4f⁷ and 4f⁶5d¹ and (ii) to model the optical spectra quite accurately if compared to the conventional time-dependent density functional theory tool. We present a theoretical study of the molecular Eu(η⁹-C₉H₉)₂ complex and its underlying photoluminescence properties with respect to the Eu 4f-5d electron transitions. We model the excitation and emission spectra with good agreement with the experiments, opening up the possibility of modeling lanthanides in complex environment like nanomaterials by means of LFDFT at much-reduced computational resources and cost.

Magnetic anisotropy of iridium dimers on two-dimensional materials

The magnetic anisotropy energy of Ir₂ dimers on germanene with different adsorption sites and areal densities.

Single Molecule Magnetism with Strong Magnetic Anisotropy and Enhanced Dy∙∙∙Dy Coupling in Three Isomers of Dy-Oxide Clusterfullerene Dy2O@C82

A new class of single-molecule magnets (SMMs) based on Dy-oxide clusterfullerenes is synthesized. Three isomers of Dy2O@C82 with C s(6), C 3v(8), and C 2v(9) cage symmetries are characterized by single-crystal X-ray diffraction, which shows that the endohedral Dy-(µ2-O)-Dy cluster has bent shape with very short Dy-O bonds. Dy2O@C82 isomers show SMM behavior with broad magnetic hysteresis, but the temperature and magnetization relaxation depend strongly on the fullerene cage. The short Dy-O distances and the large negative charge of the oxide ion in Dy2O@C82 result in the very strong magnetic anisotropy of Dy ions. Their magnetic moments are aligned along the Dy-O bonds and are antiferromagnetically (AFM) coupled. At low temperatures, relaxation of magnetization in Dy2O@C82 proceeds via the ferromagnetically (FM)-coupled excited state, giving Arrhenius behavior with the effective barriers equal to the AFM-FM energy difference. The AFM-FM energy differences of 5.4-12.9 cm-1 in Dy2O@C82 are considerably larger than in SMMs with {Dy2O2} bridges, and the Dy∙∙∙Dy exchange coupling in Dy2O@C82 is the strongest among all dinuclear Dy SMMs with diamagnetic bridges. Dy-oxide clusterfullerenes provide a playground for the further tuning of molecular magnetism via variation of the size and shape of the fullerene cage.

Mixed dysprosium-lanthanide nitride clusterfullerenes DyM2N@C80-Ih and Dy2MN@C80-Ih (M = Gd, Er, Tm, and Lu): synthesis, molecular structure, and quantum motion of the endohedral nitrogen atom

Systematic exploration of the synthesis of mixed-metal Dy-M nitride clusterfullerenes (NCFs, M = Gd, Er, Tm, Lu) is performed, and the impact of the second metal on the relative yield is evaluated. We demonstrate that the ionic radius of the metal appears to be the main factor allowing explanation of the relative yields in Dy-M mixed-metal systems with M = Sc, Lu, Er, and Gd. At the same time, Dy-Tm NCFs show anomalously low yields, which is not consistent with the relatively small ionic radius of Tm³⁺ but can be explained by the high third ionization potential of Tm. Complete separation of Dy-Gd and Dy-Er, as well as partial separation of Dy-Lu M₃N@C₈₀ nitride clusterfullerenes, is accomplished by recycling HPLC. The molecular structures of DyGd₂N@C₈₀ and DyEr₂N@C₈₀ are analyzed by means of single-crystal X-ray diffraction. A remarkable ordering of mixed-metal nitride clusters is found despite similar size and electronic properties of the metals. Possible pyramidalization of the nitride clusters in these and other nitride clusterfullerenes is critically analyzed with the help of DFT calculations and reconstruction of the nitrogen inversion barrier in M₃N@C₈₀ molecules is performed. Although a double-well potential with a pyramidal cluster structure is found to be common for most of them, the small size of the inversion barrier often leads to an apparent planar structure of the cluster. This situation is found for those M₃N@C₈₀ molecules in which the energy of the lowest vibrational level exceeds that of the inversion barrier, including Dy₃N@C₈₀ and DyEr₂N@C₈₀. The genuine pyramidal structure can be observed by X-ray diffraction only when the lowest vibrational level is below the inversion barrier, such as those found in Gd₃N@C₈₀ and DyGd₂N@C₈₀. The quantum nature of molecular vibrations becomes especially apparent when the size of the inversion barrier is comparable to the energy of the lowest vibrational levels.

Recent advances in single molecule magnetism of dysprosium-metallofullerenes

This article outlines the magnetic properties of single molecule magnets based on Dy-encapsulating endohedral metallofullerenes. The factors that govern these properties, such as the influence of different non-metal species in clusterfullerenes, the cage size, and cage isomerism are discussed, as well as the recent successful isolation of dimetallofullerenes with unprecedented magnetic properties. Finally, recent advances towards the organization of endohedral metallofullerenes in 1D, 2D, and 3D ordered structures with potential for devices are reviewed.

Carbide clusterfullerene DyYTiC@C80 featuring three different metals in the endohedral cluster and its single-ion magnetism

Carbide clusterfullerene DyYTiC@C80-Ih with three different metal atoms in the endohedral cluster is obtained by arc-discharge synthesis with methane as reactive gas and is successfully isolated by HPLC. The compound shows single-molecule magnetism (SMM) with magnetic hysteresis below 8 K. The SMM properties of DyYTiC@C80 are compared to those of DySc2N@C80 and the influence of the central atom in the endohedral cluster is analyzed.

Strong carbon cage influence on the single molecule magnetism in Dy-Sc nitride clusterfullerenes

Magnetic properties of endohedral metallofullerenes with nitride clusters DySc2N and Dy2ScN and different carbon cages are studied by SQUID magnetometry. All molecules behave as single molecule magnets (SMMs) and exhibit magnetic hysteresis. It is found that the blocking temperature of magnetization and relaxation times strongly depend on the fullerene cage, with the C80-Ih isomer offering the best SMM properties.

Magnetization relaxation in the single-ion magnet DySc2N@C80: quantum tunneling, magnetic dilution, and unconventional temperature dependence

Quantum tunneling and relaxation of magnetization in single molecule magnet DySc₂N@C₈₀ is thoroughly studied as a function of magnetic dilution, temperature, and magnetic field.

Relaxation of magnetization in endohedral metallofullerenes DySc₂N@C₈₀ is studied at different temperatures, in different magnetic fields, and in different molecular arrangements. Magnetization behavior and relaxation are analyzed for powder sample, and for DySc₂N@C₈₀ diluted in non-magnetic fullerene Lu₃N@C₈₀, adsorbed in voids of a metal–organic framework, and dispersed in a polymer. The magnetic field dependence and zero-field relaxation are also studied for single-crystals of DySc₂N@C₈₀ co-crystallized with Ni(ii) octaethylporphyrin, as well as for the single crystal diluted with Lu₃N@C₈₀. Landau–Zener theory is applied to analyze quantum tunneling of magnetization in the crystals. The field dependence of relaxation rates revealed a dramatic dependence of the zero-field tunneling resonance width on the dilution and is explained with the help of an analysis of dipolar field distributions. AC magnetometry is used then to get access to the relaxation of magnetization in a broader temperature range, from 2 to 87 K. Finally, a theoretical framework describing the spin dynamics with dissipation is proposed to study magnetization relaxation phenomena in single molecule magnets.

Selective arc-discharge synthesis of Dy2S-clusterfullerenes and their isomer-dependent single molecule magnetism

A method for the selective synthesis of sulfide clusterfullerenes Dy2S@C2n is developed. Addition of methane to the reactive atmosphere reduces the formation of empty fullerenes in the arc-discharge synthesis, whereas the use of Dy2S3 as a source of metal and sulfur affords sulfide clusterfullerenes as the main fullerene products along with smaller amounts of carbide clusterfullerenes. Two isomers of Dy2S@C82 with Cs(6) and C3v(8) cage symmetry, Dy2S@C72-Cs(10528), and a carbide clusterfullerene Dy2C2@C82-Cs(6) were isolated. The molecular structure of both Dy2S@C82 isomers was elucidated by single-crystal X-ray diffraction. SQUID magnetometry demonstrates that all of these clusterfullerenes exhibit hysteresis of magnetization, with Dy2S@C82-C3v(8) being the strongest single molecule magnet in the series. DC- and AC-susceptibility measurements were used to determine magnetization relaxation times in the temperature range from 1.6 K to 70 K. Unprecedented magnetization relaxation dynamics with three consequent Orbach processes and energy barriers of 10.5, 48, and 1232 K are determined for Dy2S@C82-C3v(8). Dy2S@C82-Cs(6) exhibits faster relaxation of magnetization with two barriers of 15.2 and 523 K. Ab initio calculations were used to interpret experimental data and compare the Dy-sulfide clusterfullerenes to other Dy-clusterfullerenes. The smallest and largest barriers are ascribed to the exchange/dipolar barrier and relaxation via crystal-field states, respectively, whereas an intermediate energy barrier of 48 K in Dy2S@C82-C3v(8) is assigned to the local phonon mode, corresponding to the librational motion of the Dy2S cluster inside the carbon cage.

Record-high thermal barrier of the relaxation of magnetization in the nitride clusterfullerene Dy2ScN@C80-Ih

The Dy-Sc nitride clusterfullerene Dy2ScN@C80-Ih exhibits slow relaxation of magnetization up to 76 K. Above 60 K, thermally-activated relaxation proceeds via the fifth-excited Kramers doublet with the energy of 1735 ± 21 K, which is the highest barrier ever reported for dinuclear lanthanide single molecule magnets.

Determining Key Local Vibrations in the Relaxation of Molecular Spin Qubits and Single-Molecule Magnets

To design molecular spin qubits and nanomagnets operating at high temperatures, there is an urgent need to understand the relationship between vibrations and spin relaxation processes. Herein we develop a simple first-principles methodology to determine the modulation that vibrations exert on spin energy levels. This methodology is applied to [Cu(mnt)₂]^2- (mnt^2- = 1,2-dicyanoethylene-1,2-dithiolate), a highly coherent complex. By theoretically identifying the most relevant vibrational modes, we are able to offer general strategies to chemically design more resilient magnetic molecules, where the energy of the spin states is not coupled to vibrations.

Development and applications of the LFDFT: the non-empirical account of ligand field and the simulation of the f-d transitions by density functional theory

Ligand field density functional theory (LFDFT) is a methodology consisting of non-standard handling of DFT calculations and post-computation analysis, emulating the ligand field parameters in a non-empirical way. Recently, the procedure was extended for two-open-shell systems, with relevance for inter-shell transitions in lanthanides, of utmost importance in understanding the optical and magnetic properties of rare-earth materials. Here, we expand the model to the calculation of intensities of f → d transitions, enabling the simulation of spectral profiles. We focus on Eu(2+)-based systems: this lanthanide ion undergoes many dipole-allowed transitions from the initial 4f(7)((8)S7/2) state to the final 4f(6)5d(1) ones, considering the free ion and doped materials. The relativistic calculations showed a good agreement with experimental data for a gaseous Eu(2+) ion, producing reliable Slater-Condon and spin-orbit coupling parameters. The Eu(2+) ion-doped fluorite-type lattices, CaF2:Eu(2+) and SrCl2:Eu(2+), in sites with octahedral symmetry, are studied in detail. The related Slater-Condon and spin-orbit coupling parameters from the doped materials are compared to those for the free ion, revealing small changes for the 4f shell side and relatively important shifts for those associated with the 5d shell. The ligand field scheme, in Wybourne parameterization, shows a good agreement with the phenomenological interpretation of the experiment. The non-empirical computed parameters are used to calculate the energy and intensity of the 4f(7)-4f(6)5d(1) transitions, rendering a realistic convoluted spectrum.

Prospecting Lighting Applications with Ligand Field Tools and Density Functional Theory: A First-Principles Account of the 4f(7)-4f(6)5d(1) Luminescence of CsMgBr3:Eu(2+)

The most efficient way to provide domestic lighting nowadays is by light-emitting diodes (LEDs) technology combined with phosphors shifting the blue and UV emission toward a desirable sunlight spectrum. A route in the quest for warm-white light goes toward the discovery and tuning of the lanthanide-based phosphors, a difficult task, in experimental and technical respects. A proper theoretical approach, which is also complicated at the conceptual level and in computing efforts, is however a profitable complement, offering valuable structure-property rationale as a guideline in the search of the best materials. The Eu(2+)-based systems are the prototypes for ideal phosphors, exhibiting a wide range of visible light emission. Using the ligand field concepts in conjunction with density functional theory (DFT), conducted in nonroutine manner, we develop a nonempirical procedure to investigate the 4f(7)-4f(6)5d(1) luminescence of Eu(2+) in the environment of arbitrary ligands, applied here on the CsMgBr3:Eu(2+)-doped material. Providing a salient methodology for the extraction of the relevant ligand field and related parameters from DFT calculations and encompassing the bottleneck of handling large matrices in a model Hamiltonian based on the whole set of 33,462 states, we obtained an excellent match with the experimental spectrum, from first-principles, without any fit or adjustment. This proves that the ligand field density functional theory methodology can be used in the assessment of new materials and rational property design.

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.

The angular overlap model extended for two-open-shell f and d electrons

We discuss the applicability of the Angular Overlap Model (AOM) to evaluate the electronic structure of lanthanide compounds, which are currently the subject of incredible interest in the field of luminescent materials. The functioning of phosphors is well established by the f-d transitions, which requires the investigation of both the ground 4f(n) and excited 4f(n-1)5d(1) electron configurations of the lanthanides. The computational approach to the problem is based on the effective Hamiltonian adjusted from ligand field theory, but not restricted to it. The AOM parameterization implies the chemical bonding concept. Focusing our interest on this interaction, we take the advantages offered by modern computational tools to extract AOM parameters, which ensure the transparency of the theoretical determination and convey chemical intuitiveness of the non-empirical results. The given model contributes to the understanding of lanthanides in modern phosphors with high or low site symmetry and presents a non-empirical approach using a less sophisticated computational procedure for the rather complex problem of the ligand field of both 4f and 5d open shells.

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.

Tailoring the optical properties of lanthanide phosphors: prediction and characterization of the luminescence of Pr(3+)-doped LiYF4

We present a theoretical work detailing the electronic structure and the optical properties of (PrF8)(5-) embedded in LiYF4, complementing the insight with data that are not available by experimental line. The local distortions due to the embedding of the lanthanide ion in the sites occupied in the periodic lattice by smaller yttrium centres, not detectable in regular X-ray analyses, are reproduced with the help of geometry optimization. Then, based on the local coordination environment, the relation structure-optical properties is constructed by Density Functional Theory computations in conjunction with the ligand field theory analyses (LFDFT) determining the [Xe]4f(2)→ [Xe]4f(1)5d(1) transitions. In previous instances we analysed rather symmetric systems, here facing the complexity of low symmetry cases, treated in the Wybourne ligand field parameterization and in the Angular Overlap Model (AOM) frame. A very important improvement at the AOM level is the consideration of the f-d mixing that brings coupling term of odd-even nature, essential for the realistic description of the asymmetric coordination centres. Furthermore, we introduce now a principle for modelling the emission intensity. The results are in agreement with available experimental findings. The relevance of the modelling has a practical face in the rational design of optimal luminescent materials needed in domestic lightening and also an academic side, revisiting with modern computational tools areas incompletely explored by the standard ligand field theories.

Surface aligned magnetic moments and hysteresis of an endohedral single-molecule magnet on a metal

The interaction between the endohedral unit in the single-molecule magnet Dy_{2}ScN@C_{80} and a rhodium (111) substrate leads to alignment of the Dy 4f orbitals. The resulting orientation of the Dy_{2}ScN plane parallel to the surface is inferred from comparison of the angular anisotropy of x-ray absorption spectra and multiplet calculations in the corresponding ligand field. The x-ray magnetic circular dichroism is also angle dependent and signals strong magnetocrystalline anisotropy. This directly relates geometric and magnetic structure. Element specific magnetization curves from different coverages exhibit hysteresis at a sample temperature of ∼4  K. From the measured hysteresis curves, we estimate the zero field remanence lifetime during x-ray exposure of a submonolayer to be about 30 seconds.