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Relaxation of magnetization in DyM2N@C80 and Dy2MN@C80 (M = Sc, Y, La, Lu) series correlates, respectively, with the mass and size of the diamagnetic metal M.

Enlarging the quantum coherence times and gaining control over quantum effects in real systems are fundamental for developing of quantum technologies. Molecular electron spin qubits are particularly promising candidates for the realization of quantum information processing due to their modularity and tunability, but there is a constant search for tools to increase their quantum coherence times. Here we present how mechanochemical dilution of active spin qubits in the diamagnetic zirconium-MOF matrix, in synergy with controlled encapsulation of fullerene guest, results in a significant increase in relaxation times and better qubit performances of the moderately porous MOF qubit array candidate. 10% diluted copper(II)-porphyrins as potential molecular spin qubits were incorporated in polymorphic PCN-223 and MOF- 525. Spin properties of this hybrid molecular spin qubit frameworks were studied by continuous-wave and pulse electron spin resonance/electron paramagnetic resonance (ESR/EPR) spectroscopy, showing that both spin-lattice and phase memory electron spin relaxation times, T1 and Tm, respectively, increased by the encapsulation of fullerene molecules into the MOF matrix. Specifically, PCN-223 with a larger filling of fullerene shows better performance in both relaxation times compared with the previously surpassing MOF-525 molecular spin qubit framework.

Dysprosium-oxide clusterfullerene Dy2O@C2v(5)-C80 is a single-molecule magnet with very strong antiferromagnetic superexchange Dy⋯Dy coupling via the μ2-O2− bridge.

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.

Layered rare-earth delafossites $ARX_2$ with $R$ = Yb(III) or Ce(III) have received a lot of interest as potential hosts for a quantum spin-liquid ground state. Some systems of this family that show no long-range order down to the lowest measured temperatures, such as NaYbO$_2$, NaYbS$_2$, and NaYbSe$_2$, are presumed to be in a quantum spin-liquid state. However, other isostructural compounds are known to order antiferromagnetically at subkelvin temperatures. Among them, KCeS$_2$ exhibits stripe-$yz$ magnetic order in the triangular-lattice planes that sets in below 400 mK. Here we investigate the spin-wave spectrum of this ordered phase with powder inelastic neutron scattering and describe it using a model Hamiltonian obtained from first-principles calculations based on the complete $|J,m_J\rangle$ multiplet description of the Ce sites with an anisotropic nearest-neighbor exchange interaction. Combing the current understanding of the exchange interaction in the systems with the effects of texturing in the powder, we have been able to model the inelastic neutron scattering spectrum with high fidelity., 6 pages, 3 figures, accepted to Phys. Rev. B

In this report, we study the ordering of C

Chemically robust single-molecule magnets (SMMs) with sufficiently high blocking temperatures TB are among the key building blocks for the realization of molecular spintronic or quantum computing devices. Such device applications require access to the magnetic system of a SMM molecule by means of electronic transport, which primarily depends on the interaction of magnetic orbitals with the electronic states of the metallic electrodes. Scanning tunneling microscopy in combination with ab initio calculations allows to directly address the unoccupied component of the single-electron molecular orbital that mediates the ferromagnetic exchange coupling between two 4f ions within a lanthanide endohedral dimetallofullerene deposited on a graphene surface. The single-electron metal-metal bond provides a direct access to the molecule's magnetic system in the transport experiments, paving the way for investigation and controlled manipulation of the spin system of individual dimetallofullerene SMMs, essential for molecular spintronics. published

A key parameter for the low-temperature magnetic coupling of in dinuclear lanthanide single-molecule magnets (SMMs) is the barrier $U_{FA}$ resulting from the exchange and dipole interactions between the two $4f$ moments. Here we extend the pseudospin model previously used to describe the ground state of dinuclear endofullerenes to account for variations in the orientation of the single-ion anisotropy axes and apply it to the two SMMs Dy$_2$ScN@C$_{80}$ and Dy$_2$TiC@C$_{80}$. While x-ray magnetic circular dichroism (XMCD) indicates the same $J_z=15/2$ Dy groundstate in both molecules, the Dy-Dy coupling strength and the stability of magnetization is distinct. We demonstrate that both the magnitude of the barrier $U_{FA}$ and the angle between the two $4f$ moments are determined directly from precise temperature-dependent magnetization data to an accuracy better than $1^{\circ}$. The experimentally found angles between the $4f$ moments are in excellent agreement with calculated angles between the quantisation axes of the two Dy ions. Theory indicates a larger deviation of the orientation of the Dy magnetic moments from the Dy bond axes to the central ion in Dy$_2$TiC@C$_{80}$. This may explain the lower stability of the magnetisation in Dy$_2$TiC@C$_{80}$, although it exhibits a $\sim 49\%$ stronger exchange coupling than in Dy$_2$ScN@C$_{80}$., 4 figures, 6 pages

The substitution of scandium in fullerene single‐molecule magnets (SMMs) DySc2N@C80 and Dy2ScN@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 DyLu2N@C80, which shows a higher blocking temperature of magnetization (TB=9.5 K), longer relaxation times, and broader hysteresis than DySc2N@C80 (TB=6.9 K). At the same time, Dy2LuN@C80 was found to have a similar blocking temperature of magnetization to Dy2ScN@C80 (TB=8 K), but substantially different interactions between the magnetic moments of the dysprosium ions in the Dy2MN clusters. Surprisingly, although the intramolecular dipolar interactions in Dy2LuN@C80 and Dy2ScN@C80 are of similar strength, the exchange interactions in Dy2LuN@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.

Magnetic hysteresis is demonstrated for monolayers of the single‐molecule magnet (SMM) Dy2ScN@C80 deposited on Au(111), Ag(100), and MgO|Ag(100) surfaces by vacuum sublimation. The topography and electronic structure of Dy2ScN@C80 adsorbed on Au(111) were studied by STM. X‐ray magnetic CD studies show that the Dy2ScN@C80 monolayers exhibit similarly broad magnetic hysteresis independent on the substrate used, but the orientation of the Dy2ScN cluster depends strongly on the surface. DFT calculations show that the extent of the electronic interaction of the fullerene molecules with the surface is increasing dramatically from MgO to Au(111) and Ag(100). However, the charge redistribution at the fullerene‐surface interface is fully absorbed by the carbon cage, leaving the state of the endohedral cluster intact. This Faraday cage effect of the fullerene preserves the magnetic bistability of fullerene‐SMMs on conducting substrates and facilitates their application in molecular spintronics., Monolayers of Dy2ScN@C80 exhibit magnetic hysteresis on Au, Ag, and MgO|Ag substrates. The substrates influence the ordering of the endohedral cluster, but do not affect the width of the hysteresis. The carbon cage protects the endohedral magnetic cluster and thus ensures that it sustains magnetic bistability.

Dysprosium oxide clusterfullerenes Dy2O@Cs(10528)–C72 and Dy2O@C2(13333)–C74 are synthesized and characterized by single-crystal X-ray diffraction. Carbon cages of both molecules feature two adjacent pentagon pairs. These pentalene units determine positions of endohedral Dy ions hence the shape of the Dy2O cluster, which is bent in Dy2O@C72 but linear in Dy2O@C74. Both compounds show slow relaxation of magnetization and magnetic hysteresis. Nearly complete cancelation of ferromagnetic dipolar and antiferromagnetic exchange Dy…Dy interactions leads to unusual magnetic properties. Dy2O@C74 exhibits zero-field quantum tunneling of magnetization and magnetic hysteresis up to 14 K, the highest temperature among Dy-clusterfullerenes.

We report on the discovery and detailed exploration of the unconventional photo-switching mechanism in metallofullerenes, in which the energy of the photon absorbed by the carbon cage π-system is transformed to mechanical motion of the endohedral cluster accompanied by accumulation of spin density on the metal atoms. Comprehensive photophysical and electron paramagnetic resonance (EPR) studies augmented by theoretical modelling are performed to address the phenomenon of the light-induced photo-switching and triplet state spin dynamics in a series of YxSc3−xN@C80 (x = 0–3) nitride clusterfullerenes. Variable temperature and time-resolved photoluminescence studies revealed a strong dependence of their photophysical properties on the number of Sc atoms in the cluster. All molecules in the series exhibit temperature-dependent luminescence assigned to the near-infrared thermally-activated delayed fluorescence (TADF) and phosphorescence. The emission wavelengths and Stokes shift increase systematically with the number of Sc atoms in the endohedral cluster, whereas the triplet state lifetime and S1–T1 gap decrease in this row. For Sc3N@C80, we also applied photoelectron spectroscopy to obtain the triplet state energy as well as the electron affinity. Spin distribution and dynamics in the triplet states are then studied by light-induced pulsed EPR and ENDOR spectroscopies. The spin–lattice relaxation times and triplet state lifetimes are determined from the temporal evolution of the electron spin echo after the laser pulse. Well resolved ENDOR spectra of triplets with a rich structure caused by the hyperfine and quadrupolar interactions with 14N, 45Sc, and 89Y nuclear spins are obtained. The systematic increase of the metal contribution to the triplet spin density from Y3N to Sc3N found in the ENDOR study points to a substantial fullerene-to-metal charge transfer in the excited state. These experimental results are rationalized with the help of ground-state and time-dependent DFT calculations, which revealed a substantial variation of the endohedral cluster position in the photoexcited states driven by the predisposition of Sc atoms to maximize their spin population., Photoexcitation mechanism of YxSc3−xN@C80 metallofullerenes is studied by variable-temperature photoluminescence, advanced EPR techniques, and DFT calculations, revealing photoinduced rotation of the endohedral cluster.

Cubic $f$-electron compounds commonly exhibit highly anisotropic magnetic phase diagrams consisting of multiple long-range ordered phases. Field-driven metamagnetic transitions between them may depend not only on the magnitude, but also on the direction of the applied magnetic field. Examples of such behavior are plentiful among rare-earth borides, such as $R{\mathrm{B}}_{6}$ or $R{\mathrm{B}}_{12}$ ($R$ = rare earth). In this work, for example, we use torque magnetometry to measure anisotropic field-angular phase diagrams of La-doped cerium hexaborides, ${\mathrm{Ce}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{B}}_{6}$ ($x=0,0.18,0.28,0.5$). One expects that field-directional anisotropy of phase transitions must be impossible to understand without knowing the magnetic structures of the corresponding competing phases and being able to evaluate their precise thermodynamic energy balance. However, this task is usually beyond the reach of available theoretical approaches, because the ordered phases can be noncollinear, possess large magnetic unit cells, involve higher-order multipoles of $4f$ ions rather than simple dipoles, or just lack sufficient microscopic characterization. Here we demonstrate that the anisotropy under field rotation can be qualitatively understood on a much more basic level of theory, just by considering the crystal-electric-field scheme of a pair of rare-earth ions in the lattice, coupled by a single nearest-neighbor exchange interaction. Transitions between different crystal-field ground states, calculated using this minimal model for the parent compound ${\mathrm{CeB}}_{6}$, possess field-directional anisotropy that strikingly resembles the experimental phase diagrams. This implies that the anisotropy of phase transitions is of local origin and is easier to describe than the ordered phases themselves.

Yb- and Ce-based delafossites were recently identified as effective spin-1/2 antiferromagnets on the triangular lattice. Several Yb-based systems, such as NaYbO2, NaYbS2, and NaYbSe2, exhibit no long-range order down to the lowest measured temperatures and therefore serve as putative candidates for the realization of a quantum spin liquid. However, their isostructural Ce-based counterpart KCeS2 exhibits magnetic order below TN = 400 mK, which was so far identified only in thermodynamic measurements. Here we reveal the magnetic structure of this long-range ordered phase using magnetic neutron diffraction. We show that it represents the so-called 'stripe-yz' type of antiferromagnetic order with spins lying approximately in the triangular-lattice planes orthogonal to the nearest-neighbor Ce–Ce bonds. No structural lattice distortions are revealed below TN, indicating that the triangular lattice of Ce3+ ions remains geometrically perfect down to the lowest temperatures. We propose an effective Hamiltonian for KCeS2, based on a fit to the results of ab initio calculations, and demonstrate that its magnetic ground state matches the experimental spin structure., This project was funded in part by the German Research Foundation (DFG) under the individual research Grant IN 209/9-1, via the project C03 of the Collaborative Research Center SFB 1143 (project-id 247310070) at the TU Dresden, and the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter—ct.qmat (EXC 2147, project-id 390858490). SA thanks A Popov (IFW, Dresden) and M Vojta (TU Dresden) for fruitful discussions and acknowledges financial support from the German Research Foundation (DFG) under Grant No. AV 169/3-1. We also acknowledge V Joyet and S Djellit for technical assistance and Institut Laue-Langevin, Grenoble (France) for providing neutron beam time.

Encapsulation and confinement of fullerene guests in metal-organic frameworks (MOFs) lead to a novel class of crystalline fulleretic materials with unique physicochemical properties and a broad field of potential applications. The control over the amount of target guests confined in the MOF structure remains a significant challenge, which is particularly pronounced in the confinement of hardly accessible fullerene derivatives. The main strategies used in constructing fulleretic composites are limited by the solubility of components used and solvent versus guest competition for inhabitation of the framework voids. As mechanochemical procedures often overcome these issues, we developed here solvent-free processing by ball milling to gain control over the encapsulation of bulky and rigid C60-fullerene into a sodalite MOF with large cages and narrow cage-apertures. A rapid, green, efficient, and stoichiometry-controlled mechanochemical processing afforded four model C60@zeolitic-imidazolate framework 8 (ZIF-8) crystalline materials containing target 15, 30, 60, and 100 mol % of fullerene entrapped in the accessible cages of the model sodalite zeolitic-imidazolate framework 8 (ZIF-8), in stark contrast to the solution-based strategies that resulted in almost no loading. Varying the fullerene content affects the framework’s vibrational properties, color and luminescence of the composites, and the electron-dose radiation stability. The computational and spectroscopic studies show that the fullerene is accommodated in the cage’s center and that the cage-to-cage transport is a hardly feasible and energetically unfavored process. However, the fast release of C60 molecules from ZIF-8 can be effectively controlled by the pH. The entrapment of fullerene molecules in ZIF-8 resulted in their effective isolation even in higher loadings, paving the way to other tunable porous fulleretics containing single-molecule magnets or nanoprobes available on low scales.

Recently, several putative quantum spin liquid (QSL) states were discovered in ${\tilde S} = 1/2$ rare-earth based triangular-lattice antiferromagnets (TLAF) with the delafossite structure. A way to clarify the origin of the QSL state in these systems is to identify ways to tune them from the putative QSL state towards long-range magnetic order. Here, we introduce the Ce-based TLAF KCeS$_2$ and show via low-temperature specific heat and $\mu$SR investigations that it yields magnetic order below $T_{\mathrm N} = 0.38$ K despite the same delafossite structure. We identify a well separated ${\tilde S} = 1/2$ ground state for KCeS$_2$ from inelastic neutron scattering and embedded-cluster quantum chemical calculations. Magnetization and electron spin resonance measurements on single crystals indicate a strong easy-plane $g$~factor anisotropy, in agreement with the ab initio calculations. Finally, our specific-heat studies reveal an in-plane anisotropy of the magnetic field-temperature phase diagram which may indicate anisotropic magnetic interactions in KCeS$_2$., Comment: submission to Scipost Physics

Detailed electronic structure of single atomic magnets is a crucial bit in the further understanding and design of a new generation of monoatomic magnetic elements on surfaces and in molecules. Control and manipulation of the single atomic state, as well as long relaxation of magnetization, have been demonstrated for lanthanide atoms on carefully chosen supporting substrates. However, these convincing experiments are puzzling by insufficient theoretical description, usually omitting the valence electrons of lanthanide atoms. In this work, starting with an idea of the inevitable need of local d- and p-shell electrons for a proper description of the magnetic states of lanthanide atoms, we rationalized the electronic structure and magnetic properties of Ho atom on the MgO substrate using ab initio multiconfigurational approaches. By doing so, we obtained the solution which complements experimental observations without any assumptions and has been able to pin-point the atomic state which most likely to be responsible for the exceptional magnetic properties of Ho on MgO. This study demonstrates that new paradigms are needed for understanding and interpretation of the lanthanide single-atomic magnets.

Engineering intramolecular exchange interactions between magnetic metal atoms is a ubiquitous strategy for designing molecular magnets. For lanthanides, the localized nature of 4f electrons usually results in weak exchange coupling. Mediating magnetic interactions between lanthanide ions via radical bridges is a fruitful strategy towards stronger coupling. In this work we explore the limiting case when the role of a radical bridge is played by a single unpaired electron. We synthesize an array of air-stable Ln2@C80(CH2Ph) dimetallofullerenes (Ln2 = Y2, Gd2, Tb2, Dy2, Ho2, Er2, TbY, TbGd) featuring a covalent lanthanide-lanthanide bond. The lanthanide spins are glued together by very strong exchange interactions between 4f moments and a single electron residing on the metal–metal bonding orbital. Tb2@C80(CH2Ph) shows a gigantic coercivity of 8.2 Tesla at 5 K and a high 100-s blocking temperature of magnetization of 25.2 K. The Ln-Ln bonding orbital in Ln2@C80(CH2Ph) is redox active, enabling electrochemical tuning of the magnetism., Dilanthanide complexes that possess radical bridges exhibit enhanced magnetic exchange coupling, affording molecular magnets with high blocking temperatures. Here, the authors explore a series of dilanthanide-encapsulated fullerenes where the radical bridge is taken to its limit and the role is played by a single unpaired electron.

With single-molecule magnets research on the rise as a result of recent advantages in the field, like remarkable high blocking temperatures up to 60 Kelvin [Nature, 548, 439, 2017], gigantic coercivity up to 80 Tesla [Nat Commun., 10, 571, 2019], magnetization stability in the thin films, further applications are seriously in the scope. The possible venue here is to develop a theory of magnetic moment manipulation and control at the microscopic level. Theory of optimal control in quantum dynamics in complex systems is well-developed. For example, the uses of density matrix techniques have been well summarized already in the early ‘60s by Fano, Haar, and many others. Thus, in many respects, the task is to reframe that research into the language of the problem at hand, and into familiar terms for the community. Recently, it was already proven the Redfield reduced density matrix techniques are applicable for slow-relaxing single-molecule magnets [Nat Commun., 8, 14620, 2017]. In our recent contribution[PCCP,20, 11656, 2018], we have outlined the use of Lindblad dynamics in combination with a few axioms in the rationalization of the relaxation behavior of single-molecule magnets. In this report we put this approach in the context of the magentodynamics theory, showing the close connection to the Landau-Lifshitz-Gilbert model and presenting further elaboration for the proposed method.

The ordering of endohedral clusterfullerenes Sc3N@C80 and YSc2N@C80 co-crystallized with Ni(OEP) and isolated complexes with Ni(OEP) have been investigated theoretically. Having used multiple orientations of M3N clusters inside the cages with Fibonacci sampling, we describe the effect of intermolecular interactions on the orientation of the endohedral cluster.

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.

The magnetic ordering and bistability of one-dimensional chains of endofullerene Dy2ScN@C80 single-molecule magnets (SMMs) packed inside single-walled carbon nanotubes (SWCNTs) have been studied using high-resolution transmission electron microscopy (HRTEM), X-ray magnetic circular dichroism (XMCD), and ab initio calculations. X-ray absorption measurements reveal that the orientation of the encapsulated endofullerenes differs from the isotropic distribution in the bulk sample, indicating a partial ordering of the endofullerenes inside the SWCNTs. The effect of the one-dimensional packing was further investigated by ab initio calculations, demonstrating that for specific tube diameters, the encapsulation is leading to energetically preferential orientations of the endohedral clusters. Additionally, element-specific magnetization curves reveal a decreased magnetic bistability of the encapsulated Dy2ScN@C80 SMMs compared to the bulk analog.

Synthesis of antiaromatic polycyclic hydrocarbons (PHs) is challenging because the high energy of their highest occupied molecular orbital and low energy of their lowest unoccupied molecular orbital cause them to be reactive and unstable. In this work, two large antiaromatic acene analogues, namely, cyclopenta[pqr]indeno[2,1,7-ijk]tetraphene (CIT, 1a) and cyclopenta[pqr]indeno[7,1,2-cde]picene (CIP, 1b), as well as a curved antiaromatic molecule with 48 π-electrons, dibenzo[a,c]diindeno[7,1,2-fgh:7',1',2'-mno]phenanthro[9,10-k]tetraphene (DPT, 1c), are synthesized on the basis of the corona of indeno[1,2-b]fluorene. These three antiaromatic PHs possess a narrow energy gap down to 1.55 eV and exhibit high kinetic stability under ambient conditions. Moreover, these compounds display reversible electron transfer processes in both the cathodic and anodic regimes. Their cation and anion radicals are characterized by in situ vis-NIR absorption and electron paramagnetic resonance spectroelectrochemistry. The X-ray crystallographic analysis confirms that while CIP and CIT manifest planar structures, DPT shows a curved π-conjugated carbon skeleton. The synthetic strategy starting from ortho-substituted benzene units to construct five-membered rings in this work provides a unique entry to novel pentagon-embedding or curved antiaromatic polycyclic hydrocarbons. In addition, besides the detailed chemical and physical investigations, microscale single-crystal fiber field-effect transistors were also fabricated.

A long time ago, Kuhn predicted that long polymers should approach a limit where their global motion is controlled by solvent friction alone, with ruggedness of their energy landscapes having no consequences for their dynamics. In contrast, internal friction effects are important for polymers of modest length. Internal friction in proteins, in particular, affects how fast they fold or find their binding targets and, as such, has attracted much recent attention. Here we explore the molecular origins of internal friction in unfolded proteins using atomistic simulations, coarse-grained models and analytic theory. We show that the characteristic internal friction timescale is directly proportional to the timescale of hindered dihedral rotations within the polypeptide chain, with a proportionality coefficient b that is independent of the chain length. Such chain length independence of b provides experimentally testable evidence that internal friction arises from concerted, crankshaft-like dihedral rearrangements. In accord with phenomenological models of internal friction, we find the global reconfiguration timescale of a polypeptide to be the sum of solvent friction and internal friction timescales. At the same time, the time evolution of inter-monomer distances within polypeptides deviates both from the predictions of those models and from a simple, one-dimensional diffusion model.

Conspectus A characteristic phenomenon of lanthanide–fullerene interactions is the transfer of metal valence electrons to the carbon cage. With early lanthanides such as La, a complete transfer of six valence electrons takes place for the metal dimers encapsulated in the fullerene cage. However, the low energy of the σ-type Ln–Ln bonding orbital in the second half of the lanthanide row limits the Ln2 → fullerene transfer to only five electrons. One electron remains in the Ln–Ln bonding orbital, whereas the fullerene cage with a formal charge of −5 is left electron-deficient. Such Ln2@C80 molecules are unstable in the neutral form but can be stabilized by substitution of one carbon atom by nitrogen to give azafullerenes Ln2@C79N or by quenching the unpaired electron on the fullerene cage by reacting it with a chemical such as benzyl bromide, transforming one sp2 carbon into an sp3 carbon and yielding the monoadduct Ln2@C80(CH2Ph). Because of the presence of the Ln–Ln bonding molecular orbital with one electron, the Ln2@C79N and Ln2@C80(R) molecules feature a unique single-electron Ln–Ln bond and an unconventional +2.5 oxidation state of the lanthanides. In this Account, which brings together metallofullerenes, molecular magnets, and lanthanides in unconventional valence states, we review the progress in the studies of dimetallofullerenes with single-electron Ln–Ln bonds and highlight the consequences of the unpaired electron residing in the Ln–Ln bonding orbital for the magnetic interactions between Ln ions. Usually, Ln···Ln exchange coupling in polynuclear lanthanide compounds is weak because of the core nature of 4f electrons. However, when interactions between Ln centers are mediated by a radical bridge, stronger coupling may be achieved because of the diffuse nature of radical-based orbitals. Ultimately, when the role of a radical bridge is played by a single unpaired electron in the Ln–Ln bonding orbital, the strength of the exchange coupling is increased dramatically. Giant exchange coupling in endohedral Ln2 dimers is combined with a rather strong axial ligand field exerted on the lanthanide ions by the fullerene cage and the excess electron density localized between two Ln ions. As a result, Ln2@C79N and Ln2@C80(CH2Ph) compounds exhibit slow relaxation of magnetization and exceptionally high blocking temperatures for Ln = Dy and Tb. At low temperatures, the [Ln3+–e–Ln3+] fragment behaves as a single giant spin. Furthermore, the Ln–Ln bonding orbital in dimetallofullerenes is redox-active, which allows its population to be changed by electrochemical reactions, thus changing the magnetic properties because the change in the number of electrons residing in the Ln–Ln orbital affects the magnetic structure of the molecule.

The behavior in magnetic field of a paramagnetic center is characterized by its $g$ tensor. An anisotropic form of the latter implies different kind of response along different crystallographic directions. Here we shed light on the anisotropy of the $g$ tensor of Yb$^{3+}$ 4$f^{13}$ ions in NaYbS$_2$ and NaYbO$_2$, layered triangular-lattice materials suggested to host spin-liquid ground states. Using quantum chemical calculations we show that, even if the ligand-cage trigonal distortions are significant in these compounds, the crucial role in realizing strongly anisotropic, `noncubic' $g$ factors is played by inter-layer cation charge imbalance effects. The latter refer to the asymmetry experienced by a given Yb center due to having higher ionic charges at adjacent metal sites within the magnetic $ab$ layer, i.e., 3+ nearest neighbors within the ab plane versus 1+ species between the magnetic layers. According to our results, this should be a rather general feature of 4$f^{13}$ layered compounds: less inter-layer positive charge is associated with stronger in-plane magnetic response., 6 pages, 1 figure

The azafullerene Tb-2@C79N is found to be a single-molecule magnet with a high 100-s blocking temperature of magnetization of 24 K and large coercivity. Tb magnetic moments with an easy-axis single-ion magnetic anisotropy are strongly coupled by the unpaired spin of the single-electron Tb-Tb bond. Relaxation of magnetization in Tb-2@C79N below 15 K proceeds via quantum tunneling of magnetization with the characteristic time tau(QTM)=16462 +/- 1230 s. At higher temperature, relaxation follows the Orbach mechanism with a barrier of 757 +/- 4 K, corresponding to the excited states, in which one of the Tb spins is flipped. European Union's Horizon 2020 research and innovation programme, European Research Council [648295]; European Union's Horizon 2020 research and innovation programme, Marie Sklodowska-Curie action [748635]; Deutsche Forschungsgemeinschaft [PO 1602/4-1, 1602/5-1]; Luther & Alice Hamlett Scholarship We acknowledge funding from the European Union's Horizon 2020 research and innovation programme, European Research Council (grant agreement No 648295 to A.A.P.), and Marie Sklodowska-Curie action (grant agreement No. 748635 to S.M.A.), and the Deutsche Forschungsgemeinschaft (grants PO 1602/4-1 and 1602/5-1 to A.A.P.). K.K. acknowledges financial support from a Luther & Alice Hamlett Scholarship. Computational resources were provided by the Center for High Performance Computing at the TU Dresden. We appreciate the help from Dr. Anja U. B. Wolter and Sebastian Gass in magnetic measurements and technical support with computational resources in IFW Dresden by Ulrike Nitzsche.

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.

Encapsulation of magnetic species within robust molecular containers is a natural route towards stable and processable single molecule magnets (SMMs). Air-stability, thermal stability, ability to form thin molecular layers on different substrates are among the critical issues to be addressed. Chemical and thermal stability of fullerenes makes them perfectly suitable for this goal. Fullerenes can encapsulate up to four metal atoms within their inner space, and a number of lanthanide EMFs was found to show SMM behavior.1-5 Besides, EMF-SMMs can form monolayers by sublimation6, 7 or by self-assembly from solution,8 and such monolayers retain their SMM properties on metallic substrates. In this contribution we will highlight recent developments in the field of lanthanide-EMFs with peculiar magnetic properties. 1. Spree, L.; Popov, A. A., Recent advances in single molecule magnetism of dysprosium-metallofullerenes. Dalton Trans. 2019, 48, 2861-2871. 2. Liu, F.; Spree, L.; Krylov, D. S.; Velkos, G.; Avdoshenko, S. M.; Popov, A. A., Single-Electron Lanthanide-Lanthanide Bonds Inside Fullerenes toward Robust Redox-Active Molecular Magnets. Acc. Chem. Res. 2019, 52, 2981-2993. 3. Liu, F.; Velkos, G.; Krylov, D. S.; Spree, L.; Zalibera, M.; Ray, R.; Samoylova, N. A.; Chen, C.-H.; Rosenkranz, M.; Schiemenz, S.; Ziegs, F.; Nenkov, K.; Kostanyan, A.; Greber, T.; Wolter, A. U. B.; Richter, M.; Büchner, B.; Avdoshenko, S. M.; Popov, A. A., Air-stable redox-active nanomagnets with lanthanide spins radical-bridged by a metal-metal bond. Nat. Commun. 2019, 10, 571. 4. Liu, F.; Krylov, D. S.; Spree, L.; Avdoshenko, S. M.; Samoylova, N. A.; Rosenkranz, M.; Kostanyan, A.; Greber, T.; Wolter, A. U. B.; Büchner, B.; Popov, A. A., Single molecule magnet with an unpaired electron trapped between two lanthanide ions inside a fullerene. Nat. Commun. 2017, 8, 16098. 5. Chen, C.-H.; Krylov, D. S.; Avdoshenko, S. M.; Liu, F.; Spree, L.; Yadav, R.; Alvertis, A.; Hozoi, L.; Nenkov, K.; Kostanyan, A.; Greber, T.; Wolter, A. U. B.; Popov, A. A., Selective arc-discharge synthesis of Dy2S-clusterfullerenes and their isomer-dependent single molecule magnetism. Chem. Sci. 2017, 8, 6451-6465. 6. Greber, T.; Seitsonen, A. P.; Hemmi, A.; Dreiser, J.; Stania, R.; Matsui, F.; Muntwiler, M.; Popov, A. A.; Westerström, R., Circular dichroism and angular deviation in x-ray absorption spectra of Dy2ScN@C80 single-molecule magnets on h-BN/Rh(111). Phys. Rev. Mater. 2019, 3, 014409. 7. Westerström, R.; Uldry, A.-C.; Stania, R.; Dreiser, J.; Piamonteze, C.; Muntwiler, M.; Matsui, F.; Rusponi, S.; Brune, H.; Yang, S.; Popov, A.; Büchner, B.; Delley, B.; Greber, T., Surface aligned magnetic moments and hysteresis of an endohedral single-molecule magnet on a metal. Phys. Rev. Lett. 2015, 114, 087201. 8. Chen, C. H.; Krylov, D. S.; Avdoshenko, S. M.; Liu, F.; Spree, L.; Westerström, R.; Bulbucan, C.; Studniarek, M.; Dreiser, J.; Wolter, A. U. B.; Büchner, B.; Popov, A. A., Magnetic hysteresis in self-assembled monolayers of Dy-fullerene single molecule magnets on gold. Nanoscale 2018, 10, 11287-11292.

Fullerene single molecule magnets (SMMs) DySc2N@C80 and Dy2ScN@C80 are functionalized via a 1,3-dipolar cycloaddition with surface-anchoring thioether groups. The SMM properties of Dy-fullerenes are substantially affected by the cycloaddition. Submonolayers of the physisorbed derivatives exhibit magnetic hysteresis on an Au(111) surface at 2 K as revealed by X-ray magnetic circular dichroism.

The notions of a reaction path and a reaction coordinate are central to chemistry as they provide low-dimensional descriptions of complex molecular processes. Here we discuss how to define, compute, and use the reaction paths for chemical transformations in molecules that are subjected to mechanical stress and thus driven toward regions of conformational space that are otherwise inaccessible both in computational studies and in reality. We further show that the circuitous nature of mechanochemical pathways often makes their one-dimensional description impossible and describe how multidimensional effects can be detected experimentally.

Any single molecular magnets (SMMs) perspective for application is as good as its magnetization stability in ambient conditions. Endohedral metallofullerenes (EMFs) provide a solid basis for promising SMMs. In this study, we investigated the behavior of functionalized EMFs on a gold surface (EMF-L-Au). Having followed the systems molecular dynamics paths, we observed that the chemically locked inner cluster inside fullerene cage will remain locked even at room temperature due to the ligand-effect. We have located multiple possible minima with different charge arrangements between EMF-L-Au fragments. Remarkably, the charge state of the EMF inner cluster remained virtually constant and so magnetic properties are expected to be untouched. © 2018 Wiley Periodicals, Inc.

Single-atom catalysts are of great interest because of their high efficiency. In the case of chemically deposited sp(2) carbon, the implementation of a single transition metal atom for growth can provide crucial insight into the formation mechanisms of graphene and carbon nanotubes. This knowledge is particularly important if we are to overcome fabrication difficulties in these materials and fully take advantage of their distinct band structures and physical properties. In this work, we present atomically resolved transmission EM in situ investigations of single Fe atoms at graphene edges. Our in situ observations show individual iron atoms diffusing along an edge either removing or adding carbon atoms (viz., catalytic action). The experimental observations of the catalytic behavior of a single Fe atom are in excellent agreement with supporting theoretical studies. In addition, the kinetics of Fe atoms at graphene edges are shown to exhibit anomalous diffusion, which again, is in agreement with our theoretical investigations.

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.

Increasing the temperature at which molecules behave as single-molecule magnets is a serious challenge in molecular magnetism. One of the ways to address this problem is to create the molecules with strongly coupled lanthanide ions. In this work, endohedral metallofullerenes Y2@C80 and Dy2@C80 are obtained in the form of air-stable benzyl monoadducts. Both feature an unpaired electron trapped between metal ions, thus forming a single-electron metal-metal bond. Giant exchange interactions between lanthanide ions and the unpaired electron result in single-molecule magnetism of Dy2@C80(CH2Ph) with a record-high 100 s blocking temperature of 18 K. All magnetic moments in Dy2@C80(CH2Ph) are parallel and couple ferromagnetically to form a single spin unit of 21 μB with a dysprosium-electron exchange constant of 32 cm−1. The barrier of the magnetization reversal of 613 K is assigned to the state in which the spin of one Dy centre is flipped., Single molecule magnets have demonstrated promise for information storage, molecular spintronics and quantum computing, but are limited by their low operational temperatures. Here, Popov and coworkers prepare a SMM with a high blocking temperature of 18 K by trapping two lanthanide ions with a single-electron bond inside a fullerene.

A remarkably large magnetic anisotropy energy of 305 K is computed by quantum chemistry methods for divalent Fe$^{2+}$ $d^6$ substitutes at Li-ion sites with $D_{6h}$ point-group symmetry within the solid-state matrix of Li$_3$N. This is similar to values calculated by the same approach and confirmed experimentally for linearly coordinated monovalent Fe$^{1+}$ $d^7$ species, among the largest so far in the research area of single-molecule magnets. Our ab initio results therefore mark a new exciting exploration path in the search for superior single-molecule magnets, rooted in the $d_{xy}^{1.5} d_{x^2-y^2}^{1.5} d_{z^2}^1 d_{yz}^1 d_{zx}^1$ configuration of $d^6$ transition-metal ions with linear or quasilinear nearest-neighbor coordination. This $d^6$ axial anisotropy may be kept robust even for symmetries lower than $D_{6h}$, provided the ligand and farther-neighbor environment is engineered such that the $d_{xy}^{1.5} d_{x^2-y^2}^{1.5} d_{z^2}^1 d_{yz}^1 d_{zx}^1$ - $d_{xy}^{1} d_{x^2-y^2}^{1} d_{z^2}^2 d_{yz}^1 d_{zx}^1$ splitting remains large enough., Comment: 5 pages, 1 figure

We report the first example of a donor–acceptor corannulene‐containing hybrid material with rapid ligand‐to‐ligand energy transfer (ET). Additionally, we provide the first time‐resolved photoluminescence (PL) data for any corannulene‐based compounds in the solid state. Comprehensive analysis of PL data in combination with theoretical calculations of donor–acceptor exciton coupling was employed to estimate ET rate and efficiency in the prepared material. The ligand‐to‐ligand ET rate calculated using two models is comparable with that observed in fullerene‐containing materials, which are generally considered for molecular electronics development. Thus, the presented studies not only demonstrate the possibility of merging the intrinsic properties of π‐bowls, specifically corannulene derivatives, with the versatility of crystalline hybrid scaffolds, but could also foreshadow the engineering of a novel class of hierarchical corannulene‐based hybrid materials for optoelectronic devices.

Herein, we report the first example of a crystalline metal-donor-fullerene framework, in which control of the donor-fullerene mutual orientation was achieved through chemical bond formation, in particular, by metal coordination. The (13) C cross-polarization magic-angle spinning NMR spectroscopy, X-ray diffraction, and time-resolved fluorescence spectroscopy were performed for comprehensive structural analysis and energy-transfer (ET) studies of the fulleretic donor-acceptor scaffold. Furthermore, in combination with photoluminescence measurements, the theoretical calculations of the spectral overlap function, Förster radius, excitation energies, and band structure were employed to elucidate the photophysical and ET processes in the prepared fulleretic material. We envision that the well-defined fulleretic donor-acceptor materials could contribute not only to the basic science of fullerene chemistry but would also be used towards effective development of organic photovoltaics and molecular electronics.

Charge migration is a ubiquitous phenomenon with profound implications throughout many areas of chemistry, physics, biology and materials science. The long-term vision of designing functional materials with tailored molecular scale properties has triggered an increasing quest to identify prototypical systems where truly molecular conduction pathways play a fundamental role. Such pathways can be formed due to the molecular organization of various organic materials and are widely used to discuss electronic properties at the nanometer scale. Here, we present a computational methodology to study charge propagation in organic molecular stacks at nano and sub-nanoscales and exploit this methodology to demonstrate that moving charge carriers strongly affect the values of the physical quantities controlling their motion. The approach is also expected to find broad application in the field of charge migration in soft matter systems.

Electron impact study of isomer S 6 -C 60 (CF 3 ) 12 resulted in the ionization efficiency curves (IEC) of singly and doubly charged positive ions and electron capture resonances for negative ones. The appearance energy (AE) values of the fragment C 60 (CF 3 ) n ions appear to correlate linearly with n down to n = 0 (C 60 ion) and its value for each additional act of CF 3 detachment rises by 2–3 eV. Observations of metastable ions reveal several cases of quasi-simultaneous detachment of two CF 3 -groups. Energy shift between ionization energy of S 6 -C 60 (CF 3 ) 12 and AE of the first fragment C 60 (CF 3 ) 11 ion was observed as 8.8 eV for singly and 8.3 eV for doubly charged ions. To rationalize this energy shift a DFT calculation of the orbital energies for the C 60 (CF 3 ) 12 + cation have been carried out and energy gap between HOMO and LUMO orbitals was estimated. High probability of occupation of the localized σ* orbital and CF 3 -elimination require four electron excitation and can be effected via a multielectron transition from the multitude of the densely distributed occupied π orbitals. The analogies with the fragmentation of C 60 with C 2 -elimination are mentioned.

Electron ionization, thermal surface ionization, matrix-assisted laser desorption/ionization, electrospray ionization, and electron capture mass spectrometric techniques have been applied to the analysis of mixtures of trifluoromethylated C 60 derivatives. For the first time ionization energy and electron affinity values for some of the molecules under investigation have been reported. These ionization characteristics have allowed to explain the differences in the results obtained by means of different mass spectral techniques.