Endohedral metallofullerene molecular nanomagnets

Abstract

Magnetic lanthanide (Ln) metal complexes exhibiting magnetic bistability can behave as molecular nanomagnets, also known as single-molecule magnets (SMMs), suitable for storing magnetic information at the molecular level, thus attracting extensive interest in the quest for high-density information storage and quantum information technologies. Upon encapsulating Ln ion(s) into fullerene cages, endohedral metallofullerenes (EMFs) have been proven as a promising and versatile platform to realize chemically robust SMMs, in which the magnetic properties are able to be readily tailored by altering the configurations of the encapsulated species and the host cages. In this review, we present critical discussions on the molecular structures and magnetic characterizations of EMF-SMMs, with the focus on their peculiar molecular and electronic structures and on the intriguing molecular magnetism arising from such structural uniqueness. In this context, different families of magnetic EMFs are summarized, including mononuclear EMF-SMMs wherein single-ion anisotropy is decisive, dinuclear clusterfullerenes whose magnetism is governed by intramolecular magnetic interaction, and radical-bridged dimetallic EMFs with high-spin ground states that arise from the strong ferromagnetic coupling. We then discuss how molecular assemblies of SMMs can be constructed, in a way that the original SMM behavior is either retained or altered in a controlled manner, thanks to the chemical robustness of EMFs. Finally, on the basis of understanding the structure–magnetic property correlation, we propose design strategies for high-performance EMF-SMMs by engineering ligand fields, electronic structures, magnetic interactions, and molecular vibrations that can couple to the spin states.

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Ziqi Hu

Ziqi Hu received his bachelor degree from Shandong University (2013) and PhD from Peking University (2018), under the supervision of Prof. Zujin Shi. He then moved to Spain as a postdoctoral fellow in the Institute for Molecular Science (ICMol), University of Valencia, in collaboration with Prof. Eugenio Coronado. In 2023, he joined Prof. Shangfeng Yang's group in the University of Science and Technology of China (USTC) as an associate researcher. Since his PhD studies, he has been fascinated by the structural and magnetic peculiarities of endohedral metallofullerenes towards their applications in single-molecule magnets and molecular spin qubits.

Shangfeng Yang

Shangfeng Yang received his PhD from Hong Kong University of Science and Technology in 2003. He then joined the Leibniz-Institute for Solid State and Materials Research (IFW) Dresden, Germany, as a Humboldt fellow. In December 2007, he joined the University of Science and Technology of China as a full professor in the Hefei National Laboratory for Physical Sciences at Microscale and the Department of Materials Science and Engineering. His research interests include syntheses of fullerene-based nanocarbons and applications in energy conversion and quantum technology. He was the recipient of the National Science Fund for Distinguished Young Scholars and “Hundreds of Talents Programme” of Chinese Academy of Sciences, and elected as Fellow of RSC (FRSC).

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1. Introduction

Molecular nanomagnets represented by single-molecule magnets (SMMs) are magnetic molecules that possess bistable magnetic states depending on the alignment of the unpaired electrons and are able to maintain magnetization in the absence of an applied magnetic field.¹ This magnetic bistability at the molecular level and not related to a cooperative effect, concomitant with the intriguing quantum phenomena in the dynamics of their magnetization as well as the feasibility of rational design, atomically precise synthesis and multidimensional organizations, enables SMMs to be promising candidates for applications in high-density information storage,¹ spintronic devices² and quantum information technologies.^3,4 Since the discovery of the high-spin manganese cluster Mn₁₂O₁₂(acetate)₁₆ (Mn₁₂Ac) as the first SMM in 1993,⁵ the major challenge for SMMs is their fragile magnetic bistability that is present so far only at cryogenic temperatures, and thus a central topic in the field has always been the exploration of methods to increase the blocking temperature (T_B), up to which the SMM behavior can be observed.

The advent of SMMs initially aroused research interests in multinuclear transition metal cluster compounds with the aim to increase the effective energy barrier to magnetization reversal (U_eff) by increasing the spin ground state and ligand field splitting exerted by the coordinated ligands. Later, it was found that metal complexes containing a single lanthanide (Ln) ion may serve as SMMs with large U_eff in the presence of ligand fields, which stems from the larger magnetic moment and single-ion anisotropy of Ln ions as a result of much stronger spin–orbit coupling (SOC) compared to the transition metal ions.^6–8 This category of Ln-based single-ion magnets (SIMs) constitutes a key part of the whole SMM family and has been receiving much research attention. The fine control of the single-ion anisotropy in SIMs thus becomes feasible through coordination chemistry, for which several design criteria were proposed mainly focusing on the enhancement of ligand fields.^9,10 These synthetic strategies are exemplified, for instance, by introducing cyclopentadienyl (Cp) ligands to ensure an axial anisotropy of a dysprosium metallocene cation [Dy(Cp^ttt)₂]⁺ (Cp^ttt = 1,2,4-tri-tert-butyl Cp), enabling a remarkably high T_B of 60 K at which magnetic hysteresis still persists. Such an extraordinary SMM property has been later improved up to 80 K, exceeding the liquid nitrogen temperature (77 K), by engineering ligand structures to protect spin states from the phonon relaxation bath which is mediated by molecular vibrations.^11,12

Besides the low T_B that hampers the applications of SMMs, another major obstacle to their practical application in information storage is the prevailing chemical instability of organometallic compounds, which precludes their sublimation in order to obtain organized molecular assemblies on surfaces. Thus, inert ligands that are able to protect magnetic Ln ions are necessary. In this context, encapsulating Ln ion(s) into a chemically stable fullerene cage offers an alternative solution. The as-formed endohedral metallofullerenes (EMFs) feature a unique intramolecular host–guest molecular structure, in which specific metal clusters with previously unseen bonding and electronic configurations are stabilized in a way that could not be fulfilled by conventional synthetic routes.^13,14 Since the discovery of the first EMF-SMMs in a mixed trimetallic nitride clusterfullerene (NCF) DySc₂N@C₈₀,¹⁵ EMFs have become a fertile territory in the exploration of high-performance SMMs by providing a rich structural diversity of both the encapsulated species and the host fullerene cages. Apart from metal clusterfullerenes bearing metal clusters in the cage, conventional EMFs based on the encapsulation of single or multiple metal ions only are also found to behave as decent SMMs.^16,17 A recent manifestation demonstrates that a low-coordination monometallic azafullerene Dy@C₈₁N displays a high standardized blocking temperature (T_B,100s, defined as the temperature of 100 s relaxation time T(τ_100s)) of 45 K despite a weak ligand field, highlighting the uniqueness of EMFs in which the outstanding SMM performance is ascribed to the quenching of the extra radical on the cage by nitrogen substitution and the very weak coupling of the molecular vibrations to the spin states.¹⁶ Another notable example lies in the discovery of several dimetallic EMF-SMMs M₂@C₇₉N (M = Dy and Tb) and M₂@C₈₀-R (R = CF₃ and PhCH₂) exhibiting giant coercive field and a high T_B,100s of up to 25.2 K for Tb₂@C₈₀(CH₂Ph), where a single-electron metal–metal bond (SEMB) is stabilized to evoke strong magnetic coupling through quenching the unpaired electron on the cage by nitrogen substitution or exohedral derivatization.^18–22 Remarkably, this structural peculiarity is not an exclusive case in EMFs, yet offers a general synthetic insight and can be extended to strongly coupled mixed-valence dilanthanide SMMs (Cp^iPr5)₂Ln₂I₃ (Ln = Dy and Tb) that hold the current record T_B,100s value of 72 K.²³

Exploiting the high chemical and thermal stability of fullerene structures, neutral EMF-SMMs can be readily processed into organized molecular assemblies, such as sub-monolayer deposition on substrates through sublimation or self-assembly.^24–26 This is in striking contrast to most ionic organometallic Ln-SMMs, which are air- and moisture-sensitive and would decompose upon heating or interacting with the substrates. This merit of EMFs allows a step forward in the field of SMMs by facilitating their further integration into spintronic devices, which would be eventually utilized to write in and read out magnetic information. Thus, EMFs are expected to continue to play a crucial role in the future development of SMMs. Moreover, the structural diversity of EMFs shall lead to further synthetic advancements by presenting new structures that in turn contribute to new physical phenomena in molecular magnetism.

In this review, we present an exhaustive review on all types of EMF-SMMs reported to date, including their syntheses, molecular structures, magnetic properties and organizations into molecular assemblies. We pay special attention to the versatile molecular structures of EMFs to unveil their unique structural features in comparison with conventional organometallic compounds, and manage to disclose the correlation between their structures with the magnetic properties. At the end, we propose design strategies for EMF-SMMs towards improved performance by engineering underlying factors such as ligand fields, electronic structures, magnetic interactions, and molecular vibrations that can couple to the spin states.

2. Syntheses and molecular structures of EMFs

EMFs are typically synthesized by using the Krätschmer–Huffman DC-arc discharge method,²⁷ in which a metal precursor, in the form of metal alloy or metal oxide, is evaporated together with the graphite anode under a helium atmosphere as a cooling gas. Other gases or solid compounds, such as N₂, NH₃, CH₄ and Prussian blue (Fe₄[Fe(CN)₆]₃), can be added as reactive gases and nitrogen sources for the synthesis of a desired EMF.^28–30 The EMF-containing raw soot produced by the DC-arc discharge approach is then extracted using organic solvents, such as CS₂ and ortho-dichlorobenzene (o-DCB), using a Soxhlet extraction or reflux method to separate soluble fullerene-related compounds from other carbon materials. The final step is to isolate isomerically pure EMFs using multi-stage high-performance liquid chromatography (HPLC). Since the production process takes place at very high temperatures (3000–5000 K), the extracted products include a rich variety of empty fullerenes and endohedral metallofullerenes with different structures of the host cages and the encapsulated species. This makes the HPLC isolation a demanding and time-consuming process, but it is still feasible by employing a combination of different modified HPLC columns. Overall, the yields of EMFs in the purified forms are usually very low (in the order of milligram). Efforts have been devoted to increasing their production yields, resulting in some success in the selective synthesis of particular types of EMFs.^20,29–31

The accurate structural determination of the isolated EMFs is achieved by single-crystal X-ray crystallography, for which co-crystals are obtained in the presence of nickel octaethylporphyrin (Ni^II(OEP))³² or decapyrrylcorannulene (DPC)³³ hosts to restrict the rotation of the fullerene cages. For additional structural characterization various spectroscopic techniques including ¹³C NMR, IR and Raman spectroscopies are utilized in aid of DFT calculations. Note that for EMFs containing paramagnetic Ln ions that are of interest for magnetic characterization, it is difficult to record ¹³C NMR spectra due to spectral broadening caused by such magnetic centers. The detailed discussions on the synthesis, separation and structural characterization of EMFs have been summarized in several recent reviews.^{13,14,34–36}

EMFs have versatile molecular structures dependent on the encapsulated species and the outer fullerene cages, and thus the corresponding magnetic properties are tunable upon changing their structures.¹³ For the conventional EMFs based on encapsulation of single or multiple metal ions only, mono-, di- and tri-metallofullerenes can be formed by encaging different numbers (one to three) of metal atoms. In this context, mono- and di-EMFs are of particular interest for the magnetic studies in this review due to their structural diversity, whereas examples of tri-EMFs are very limited.^16,17,37 In fact, mono-EMF La@C₈₂ dates back to a very early period just after the discovery of the empty fullerene C₆₀.^38,39 It should be noted that the encapsulated metal atoms transfer their valence electrons to the host fullerene cage, which is distinct from the situation of endohedral fullerenes encapsulating only nonmetal elements as exemplified by N@C₆₀.⁴⁰ This feature provides another aspect for fine-tuning the magnetic properties of EMFs by altering their electronic structures through nitrogen substitution^41–43 and exohedral functionalization^18,20,44 on the cages.

Alternatively, metal atoms can bond with nonmetal ligands inside fullerene cages to form clusterfullerenes.¹⁴ Starting from a coincidental discovery of the nitride clusterfullerene (NCF) Sc₃N@C₈₀,²⁸ which has a relatively high yield during the DC-arc discharging process that is inferior to only C₆₀ and C₇₀, various types of clusterfullerenes have been synthesized including carbide,⁴⁵ oxide,⁴⁶ sulfide,²⁹ cyanide⁴⁷ clusterfullerenes, etc., where the nonmetal ligands formally possess negative charges such as N³⁻, C₂²⁻, O²⁻, S²⁻, and CN⁻, respectively. From the point of view of magnetic properties, these clusterfullerenes allow the manipulation of the ligand fields exerted on the Ln ions via coordination chemistry, thus adding another degree of freedom that can be used for the design of EMF-SMMs.

On the other hand, the structures of fullerene cages hosting encapsulated metal species are diverse not only in cage size but also in cage isomerism. The reported EMFs to date have a cage size ranging very broadly from C₆₀ in Li@C₆₀ cations to C₁₀₈ in Y₂C₂@C₁₀₈.^48,49 The large cage family of EMFs, considering numerous isomers for the same cage size involving different connection ways of pentagons and hexagons, is further expanded by breaking the famous isolated-pentagon rule (IPR).⁵⁰ Among them, the most notable example is the highly symmetric icosahedral I_h(7)-C₈₀ due to its exceptional stability after accepting six electrons from the encapsulated species, based on which various EMF-SMMs are constructed.^17,51,52 These rich cage structural features provide the feasibility of engineering ligand fields around metal ions by the control of metal–cage interaction. Furthermore, the configuration of the encapsulated species may be influenced by the structural variation of the cage, in a way that the cluster geometry or the metal–metal distance is changed, which enables the manipulation of ligand fields or magnetic exchange interactions. Molecular structures of representative EMFs of interest for magnetic studies in this review are illustrated in Fig. 1.

Fig. 1 Molecular structures of representative EMF-SMMs. Green: Dy, cyan: Tb, dark blue: Sc, blue: N, red: O, magenta: F, and gray: C.

3. Magnetic characterization of EMF-SMMs

The majority of SMMs are characterized using the conventional superconducting quantum interference device (SQUID) magnetometers. There are several metrics to evaluate the performance of an SMM. Here we summarize and explain these different metrics, and unify common characterization of the static magnetism and the dynamic behavior. When it comes to the magnetic characterization of EMFs, special care should be undertaken mainly owing to their low yields, which may lead to various challenges in sample preparation, measurement and data analysis. We try to clarify some practical concerns in these steps and discuss detailed issues that need to be taken into account.

The low sample amount of EMFs (usually around 1 mg) makes the precise determination of the sample mass difficult, which normally requires a sample preparation method by drop-casting from CS₂ solution of an EMF into a diamagnetic propylene capsule.¹⁸ Another method utilizes paramagnetic Al foil as the sample holder with its well-characterized magnetic behaviors.^22,53 In any case, background correction is necessary to accurately record the magnetization signal of the measured EMF. Since the EMF samples are mainly prepared in powder rather than in crystalline forms for magnetic characterization studies, the fullerene molecules are strongly disordered such that the measured values of magnetization should be doubled due to an isotropic distribution of easy axes of the molecules.^18,54 It becomes impossible to precisely determine the sample mass when it is less than 0.1 mg. Under this circumstance, a standard quartz sample holder can be used for a vibrating sample magnetometer (VSM) SQUID, which has a negligible diamagnetic background signal at helium temperatures.⁵⁵ Valuable information can still be obtained in this context by relying on the shapes, instead of the absolute values, of the variable-field magnetic susceptibility and variable-temperature magnetization data.

One of the most straightforward ways to identify an SMM is to record a magnetic hysteresis loop at a given temperature, which presents a magnetic memory effect that comes from the magnetic bistability. The opening of the hysteresis loops up to a certain temperature has been well-used as one definition of T_B. However, this hysteretic behavior is highly dependent on the sweep rate of the applied magnetic field during the measurement, such that the temperature at which hysteresis persists is not parameter-free. Another definition of T_B is derived from the bifurcation point of the zero-field cooling/field cooling (ZFC/FC) magnetic susceptibility curves. Similarly, this bifurcation temperature relies on the experimental temperature sweep rate. Thus, the comparison of the T_B values among different SMMs, determined either as hysteresis temperature or ZFC/FC bifurcation temperature, should be done with caution. Apart from T_B, the width of the hysteresis loop (i.e. coercive field, H_c) is equally important, which is the measure of the ability of an SMM to withstand while being demagnetized, and thus it would directly affect the stability and reliability of magnetic information that can be stored. The coercive field is mainly governed by the quantum tunneling effect that takes place close to zero magnetic field. This again is related to the sweep rate of the applied magnetic field.

A more reliable definition of T_B, at which 100 s magnetic relaxation time (τ) is determined from the decay of magnetization, is free of experimental parameters and thus serves as a golden standard for SMMs in current state-of-the-art research.¹ This demagnetization at a given temperature follows an exponential decay of magnetization M over time

M(t) = M_eq + (M₀ − M_eq)exp[−(t/τ)^β] (1)

where M_eq and M₀ denote the equilibrium and initial magnetizations, respectively. It is very common that the demagnetization deviates from the single exponential decay (β = 1) due to the change of the relaxation rate over time, which is presumably caused by the local dipolar change thereof.²¹ Instead, a stretched exponential function is often used (0 < β < 1) to fit the decay curve that in turn gives the τ value (>10 s) at a given temperature. In this review, for consistency we denote the temperature of 100 s relaxation time T(τ_100s) as T_B,100s, and refer to other critical metrics of T_B as hysteresis temperature (T_B,hys) and bifurcation temperature in ZFC/FC curves (T_B,ZFC), respectively. Understanding the temperature dependence of the magnetic relaxation is a fundamental subject in the field of SMMs. This behavior can be described by a single or a combination of several possible relaxation mechanisms as follows

τ⁻¹ = τ_QTM⁻¹ + A_HT + CTⁿ + τ₀⁻¹ exp(−U_eff/T) (2)

where the first term denotes the temperature-independent quantum tunneling of magnetization (QTM) which causes a spin flip within the ground doublet, and the rest three terms represent the direct, Raman and Orbach mechanisms. The analysis of the well-known Orbach process following an Arrhenius-type relationship determines the effective energy barrier U_eff, which is another key factor of an SMM related to the relaxation of magnetization through the excited state. However, relaxation may occur via under-barrier pathways, including the Raman process with the assistance of phonons, thus resulting in a low T_B. Blocking the phonon-induced relaxation process has now become a central topic in SMM research. This involves the design strategy of decoupling spin states from molecular vibrations, providing not only theoretical insights^56–60 but also experimental evidence to show that sparse phonon spectra are crucial.^61–63

In addition to demagnetization measurements which normally determine τ > 10 s, the full characterization of the magnetic relaxation with τ spanning over a large range from 10⁻³ s to 1 s requires the dynamic studies by alternating current (AC) magnetometry. These AC measurements could be done in the absence of a static magnetic field with the variable frequency of the AC field in the range of 1–1000 Hz, and give rise to frequency-dependent in-phase (χ′) and out-of-phase (χ′′) susceptibilities, from which τ can be determined at different temperatures by fitting the data using a generalized Debye model. The exceptionally low yields of EMFs, however, often impede the accurate characterization using AC susceptibility to record the Orbach process for the determination of U_eff. This problem becomes worse when the slow magnetic relaxation is extended to high temperatures (>50 K), at which the sensitivity becomes lower since the out-of-phase signal χ′′ almost vanishes based on the small population difference between spin states separated by a weak (∼5 Oe) driving AC field.^16,64

Alternatively, magnetic characterization of an SMM can also be performed via X-ray circular magnetic dichroism (XMCD) experiments on the atomic level. This advanced element-specific technique relies on X-ray absorption spectroscopy (XAS) for an SMM at the Ln M_4,5 edge, allowing for the unambiguous determination of the magnetic properties at its Ln origin, from which field-dependent XMCD hysteresis loops are extracted. Moreover, detailed atomic information, such as the expected values of the spin quantum number, angular momentum and the exact magnetic moment, can be precisely obtained by applying XMCD sum rules at the Ln edge, offering an in-depth insight into the magnetic behaviors of an SMM. It is noteworthy that much less sample is required for XMCD measurements compared to the amount used for commercial SQUID magnetometers, which is suitable for EMF-SMMs with low yields. However, the much noisier magnetic signal from XMCD measurements hampers the characterization of SMMs with weak coercive fields and low remanence at relatively high temperatures.

4. Categories of EMF-SMMs

4.1 Clusterfullerenes

4.1.1 Metal nitride clusterfullerenes (NCFs).
4.1.1.1 NCFs as single-ion magnets. The advent of trimetallic nitride clusterfullerenes (NCFs) showing the composition of (M₁³⁺)_x(M₂³⁺)_3−x(N³⁻)@C_2n⁶⁻ (M₁/M₂ = rare earth metals, Ti, V; x = 1–3),^31,65–71 with Sc₃N@I_h(7)-C₈₀ as an elegant example,²⁸ has opened up a new avenue for EMF research by offering a possibility to construct metal clusters inside the carbon cages. It is noteworthy that in this family of compounds, the most stable configuration of the encapsulated nitride cluster is a planar one, thus inducing a strong cluster size-dependent selection of preferential fullerene cages, which move from the most prevalent C₈₀ to C₈₈ and even to C₉₆ as the radius of the metal ion increases.^32,72–74 From the magnetic point of view, the single-ion anisotropy of a magnetic Ln ion can thus be tailored by the encapsulated N³⁻ ligand and the outer cage coordination. To understand this feature in NCFs employing the trimetallic nitride template, the simplest model is a single-ion magnet (SIM) with only one magnetic center. This calls for a mixed trimetallic nitride through substituting one diamagnetic Sc³⁺ ion in Sc₃N@C₈₀ by a magnetic Ln³⁺ ion. In this regard, Dy³⁺ and Tb³⁺ with the oblate 4f electron density strongly facilitate axial single-ion anisotropy and thus are the most prevalent building blocks to design SMMs.⁷⁵ Specifically, Dy³⁺ has an odd number of f electrons (f⁹) with the ground multiplet of ⁶H_15/2. This follows the Kramers theorem which indicates that the degeneracy of the ground doublet (m_J = ±15/2) cannot be lifted in the absence of a magnetic field. In contrast, the non-Kramers ion Tb³⁺ is an even-number system without fundamental degeneracy. This leads to a tunnel splitting between the two lowest spin states and often gives rise to fast magnetic relaxation when the strict axiality is broken by low-symmetry ligand fields. As a result, majority of SIMs are based on Dy³⁺.^76,77

Following this strategy, the first EMF-SMM was reported by Gerber et al. in 2012 for DySc₂N@C₈₀, in which the nitrogen ligand (N³⁻) imposes a strong ligand field around Dy³⁺ to achieve axial magnetic anisotropy.¹⁵ This results in a magnetic hysteresis as shown in Fig. 2a that persists up to 5 K using a SQUID magnetometer at a slow magnetic field sweep rate of 1.3 mT s⁻¹. The hysteresis loop shows a clear drop in the low-field region with a butterfly shape, which indicates a fast QTM process typical of SIMs. This magnetic behavior is also confirmed by element-specific XMCD measurement, which shows hysteresis of the 4f spin and orbital moment in Dy³⁺ (Fig. 2b). Despite this, slow magnetic relaxation with τ exceeding 2000 s has been evidenced at zero field. The QTM effect can be effectively quenched by applying a magnetic field of 0.3 T, which facilitates the determination of T_B,100s = 4.6 K. Such an effect is also suppressed by diluting DySc₂N@C₈₀ within a diamagnetic C₆₀ matrix to greatly reduce intermolecular interactions. As a result, τ > 20 000 s is determined at zero field.

Fig. 2 (a) Magnetic hysteresis loops for DySc₂N@C₈₀ (the molecular structure is shown in the inset) recorded using SQUID magnetometry at 2–5 K with a field sweep rate of 1.3 mT s⁻¹. (b) Comparison of the magnetic hysteresis loops for DySc₂N@C₈₀ recorded by SQUID and XMCD magnetometry at 2 K. Reproduced with permission from ref. 15 (Copyright 2012, American Chemical Society). (c) Out-of-phase magnetic susceptibility χ′′ of DySc₂N@C₈₀ measured in zero field in the 2–60 K range. The inset shows Cole–Cole plots. The solid lines are fits by the generalized Debye model. (d) Magnetization relaxation times of DySc₂N@C₈₀ at temperatures of 2–87 K. Zero-field values are shown as full dots and in-field (0.2 T) values are denoted as open dots. Relaxation times for non-diluted DySc₂N@C₈₀ are shown in black, and the values for diluted samples are shown in blue (diluted with MOFs) and green (diluted with polystyrene, PS). Reproduced from ref. 64.

Since this first discovery, the magnetic behaviors of DySc₂N@C₈₀ have been extensively studied. Using the XMCD technique, the same group reported that X-rays lead to an increased relaxation rate of magnetization, which is induced by the resonant absorption of the X-ray irradiation and is dependent on its dose.⁸⁰ This additional demagnetization upon X-ray irradiation is helpful in understanding the thinner XMCD magnetic hysteresis compared to that recorded by using conventional SQUID magnetometry. An in-depth research of DySc₂N@C₈₀, focusing on its powder and single-crystal samples, as well as with solid dilutions in three different diamagnetic matrices, demonstrates that the dilution enlarges the hysteresis loops in the low-field region.⁶⁴ In this context, the use of a polystyrene diamagnetic matrix is the most effective approach, which steers the QTM resonance from 150 mT in an undiluted sample to <1 mT. This change of the zero-field tunneling resonance width upon dilution significantly affects the relaxation rates and can be understood with the aid of an analysis of dipolar field distributions. Surprisingly, magnetic relaxation of DySc₂N@C₈₀ can be accessed by AC magnetometry in a very broad temperature range from 2 to 87 K (Fig. 2c and d). Magnetic relaxation up to such a high temperature is caused by the absence of a fast and linear Orbach process usually observed for other SMMs.

The single-ion anisotropy of Dy³⁺ can be manipulated in this type of NCF when Sc³⁺ is replaced by other diamagnetic rare earth metal ions such as Y³⁺ and Lu³⁺. This is essentially due to the inner strain of the trimetallic cluster that is controlled by the sizes of different metals. Note that DyLa₂N@C₈₀ cannot be synthesized since the encapsulated cluster is too large to maintain a planar configuration. It has been shown that introducing a larger Lu³⁺ ion leads to a shorter Dy–N bond and hence a stronger ligand field than in DySc₂N@C₈₀.⁷⁸ Consequently, improved SMM properties are observed for DyLu₂N@C₈₀ with a T_B,ZFC of 9.5 K in comparison with that of its traditional scandium congener (7 K). This study also points out that the mass of the diamagnetic metal ion is another important factor governing the SMM properties of NCFs by influencing cluster-based vibrations, which is achieved via a strong mixing of the local cluster vibrations with acoustic phonons, thus eventually affecting the magnetic relaxation. This observation has further been analyzed systematically in DyM₂N@C₈₀ (M = Sc, Y and Lu), which reveals that a larger size of M leads to stronger ligand fields in the order of Y > Lu > Sc. Moreover, magnetic behaviors are found to be correlated with the mass of M. This results in the improved SMM properties, both in terms of hysteresis at higher temperature and longer relaxation times, in the order of Lu > Y > Sc (Fig. 3a and c, Table 1).⁷⁹ A similar conclusion was also obtained by Wang et al. showing a larger opening of hysteresis in DyY₂N@C₈₀ compared to that of DySc₂N@C₈₀.⁸¹

Fig. 3 (a) Magnetic hysteresis loops of DyLu₂N@C₈₀/Lu₃N@C₈₀ measured at 2 K and compared with those of DySc₂N@C₈₀ and DySc₂N@C₈₀ diluted with Lu₃N@C₈₀ in a 1 : 1 ratio. Sweep rate: 2.9 mT s⁻¹. The inset shows the determination of the bifurcation temperature, T_B,ZFC, from the temperature dependence of the magnetic susceptibility with a temperature sweep rate of 5 K min⁻¹. (b) Magnetic hysteresis loops for Dy₂MN@C₈₀ (M = Sc, Y, La, Lu) at 2 K (2.1 K for the La case) with a field sweep rate of 2.9 mT s⁻¹. (c) and (d) Magnetization relaxation times of DyM₂N@C₈₀ (M = Sc, Y, Lu) (c) and of Dy₂MN@C₈₀ (M = Sc, Y, La, Lu) (d). The insets in (c) and (d) show enlargement of high-temperature parts. Reproduced from (a) ref. 78 and (b)–(d) ref. 79.

Table 1 An exhaustive list of clusterfullerene SMMs reported to date

Type	EMF	T B,100s [K]	T B,hys [K](dH/dt) [mT s^−1]^c	T B,ZFC [K](dT/dt)^d [K min^−1]	U eff [K]	ΔEAFM–FM [K]	Ref.
a The value of TB,100s is determined under an applied magnetic field of 0.2 T. b Field-induced SMMs. c The value in the bracket indicates the field sweep rate (mT s^−1) used to record hysteresis loops. d The value in the bracket indicates the temperature sweep rate (K min^−1) used to record ZFC/FC curves.
NCF-SIMs	DySc2N@D3(6140)-C68	2.3^a	5 (2.9)	3.8 (5)	23.6	—	84
	DySc2N@D5h(6)-C80	3.6^a	7 (2.9)	5.9 (5)	17.7	—	84
	DySc2N@Ih(7)-C80	4.6^a	7 (2.9)	6.9 (5)	23.6	—	15 and 64
	DyY2N@Ih(7)-C80	∼6^a	8 (2.9)	8.4 (5)	929	—	79
	DyLu2N@Ih(7)-C80	∼6.5^a	9 (2.9)	9.5 (5)	24.2	—	78 and 79
	HoSc2N@Ih(7)-C80^b	—	—	—	16.5	—	85
NCFs with multiple magnetic metals	Dy2ScN@Ih(7)-C80	5.0	7 (2.9)	8 (5)	10.7/1735	8.1	95
	Dy2YN@Ih(7)-C80	∼3.5	5 (2.9)	4.7 (5)	43.8/680	1.4	79
	Dy2LaN@Ih(7)-C80	∼2	4 (2.9)	3.3 (5)	—	−1.2	79
	Dy2LuN@Ih(7)-C80	5.2	8 (2.9)	8 (5)	4.3	4.3	78 and 79
	Dy2GdN@Ih(7)-C80	∼1.5	∼1.8 (5.3)	—	15.1	—	96
	DyErScN@Ih(7)-C80	∼4.5	9 (33)	∼8 (3)	12.5	7.0	97
	Tb2ScN@Ih(7)-C80	0.4	∼0.4 (3.3)	—	1/10.5/56.4	9.4	98
	Dy2ScN@D5h(6)-C80	2.6	7 (2.9)	5.3 (5)	8.4	—	84
	Dy2ScN@Ds(51 365)-C84	∼1.8	5 (2.9)	3.3 (5)	—	—	84
	Dy3N@Ih(7)-C80	—	∼2 (0.8)	—	—	3.5	93
CYCFs	TbCN@C2v(19 138)-C76^b	—	—	—	12	—	99
	TbCN@C2(5)-C82^b	—	—	—	10–20	—	100
	TbCN@Cs(6)-C82^b	—	—	—	10–20	—	100
	TbCN@C2v(9)-C82^b	—	—	—	10–20	—	100
OCFs	Dy2O@Cs(10 528)-C72	3.4	7 (2.9)	8 (5)	—	2.2	55
	Dy2O@C2(13 333)-C74	5.0^a	14 (2.9)	14 (5)	—	∼0.1	55
	Dy2O@C2v(5)-C80	3.2	6 (2.9)	11 (5)	25.9	−26.6	101
	Dy2O@Cs(6)-C82	2.8	6 (2.9)	10 (5)	10.8	−10.8	102
	Dy2O@C3v(8)-C82	5.9	7 (2.9)	9 (5)	7.8	−7.8	102
	Dy2O@C2v(9)-C82	3.7	7 (2.9)	8 (5)	18.6	−18.6	102
	Dy2O@C1(26)-C88	6.0	8 (2.9)	10.5 (5)	20.4	−23.7	103
	Dy2O@Cs(32)-C88	4.6^a	8 (2.9)	8.5 (5)	—	−0.6	103
	Dy2O@D2(35)-C88	3.9	8 (2.9)	8.5 (5)	—	5.2	103
SCFs	Dy2S@Cs(10 528)-C72	—	3.0 (8.33)	—	—	—	29
	Dy2S@Cs(6)-C82	—	3.0 (8.33)	—	17.8	15.8	29 and 104
	Dy2S@C3v(8)-C82	2.0	5 (8.33)	4.0 (5)	6.0	9.2	29 and 104
	DyScS@Cs(6)-C82	∼4	9 (10)	7.3 (5)	15.2	—	105
	DyScS@C3v(8)-C82	∼2	9 (10)	7.3 (5)	6.5	—	105
CCFs	DyYTiC@Ih(7)-C80	∼5^a	7 (2.9)	8 (5)	14.9	—	106
	Dy2TiC@Ih(7)-C80	1.7	3 (5)	—	9.5	12.2	107
	Dy2TiC2@Ih(7)-C80	—	1.8 (5)	—	—	—	107
	Dy2TiC@D5h(6)-C80	—	1.8 (5)	—	—	—	107
	Dy2C2@Cs(6)-C82	—	3.0 (8.33)	—	17.4	17.4	29
	Dy2C2@Cs(32)-C88	—	2.1 (2.9)	—	—	9.1	103
	Dy2C2@D2(35)-C88	—	2.1 (2.9)	—	—	4.7	103

---

In addition to the encapsulated diamagnetic metal that plays an important role in determining the single-ion anisotropy and thus the SMM properties of NCFs, the cage structure is expected to be another degree of freedom that can be used for chemical design towards such a goal. In this line, it is the carbon ring motifs coordinating to the metal inside the cage that are of significance to the single-ion anisotropy and ligand fields, which include various binding sites such as a hexagon, pyracylene, and a fused-pentagon in a cage violating the isolated pentagon rule (IPR).^82,83 However, the number of mixed-metal NCFs based on fullerene cages instead of I_h(7)-C₈₀ is rather limited, partly due to the exceptional stability and high yield of C₈₀⁶⁻ and also associated with the synthetic difficulty in HPLC separation of NCFs with different metallic clusters inside the same cage. Popov et al. reported the synthesis of DySc₂N nitride clusterfullerenes with different carbon cages, including D₃(6140)-C₆₈ and D_5h(6)-C₈₀ as well as the well-studied I_h(7)-C₈₀.⁸⁴ Magnetic characterization of this series of NCFs shown in Fig. 4a and c indicates cage-dependent SMM properties, with the I_h(7)-C₈₀ case as the best SMM featuring the broadest hysteresis loop at 2 K, the longest relaxation times and the highest bifurcation temperature (T_B,ZFC) of 7 K in ZFC/FC curves, the D_5h(6)-C₈₀ fullerene as the intermediate one with T_B,ZFC = 5.9 K followed by the D₃(6140)-C₆₈ non-IPR cage with only 3.8 K.

Fig. 4 (a) Magnetic hysteresis loops for different Dy-Sc NCFs, with the DySc₂N cluster encapsulated inside D₃(6140)-C₆₈, D_5h(6)-C₈₀ and I_h(7)-C₈₀ cages, measured at 2 K with a field sweep rate of 2.9 mT s⁻¹. (b) Magnetic hysteresis loops for NCFs, with the Dy₂ScN cluster encapsulated inside D_5h(6)-C₈₀, I_h(7)-C₈₀ and C_s(51 365)-C₈₄ cages, measured at 2 K with a field sweep rate of 2.9 mT s⁻¹. (c) and (d) Magnetization relaxation times of DySc₂N@C_2n (2n = 68, 80 (two isomers)) (c) and of Dy₂ScN@C_2n (2n = 84, 80 (two isomers)) (d). Reproduced from ref. 84.

The possibility to construct NCF-based SIMs using other anisotropic Ln³⁺ ions, instead of Dy³⁺, has also been explored. AC measurements of HoSc₂N@I_h(7)-C₈₀ reveal that it is a field-induced SMM, that is, slow relaxation of magnetization is only shown in the presence of an applied DC field.⁸⁵ Although it is not a “genuine” SMM that functions at zero field, relaxation times in the order of milliseconds are determined below 6 K. The much faster relaxation rate of HoSc₂N@C₈₀ in comparison with that of DySc₂N@C₈₀ is attributed to its low-symmetry ligand field imposed by the cage which efficiently promotes the magnetic relaxation in the non-Kramers SIM. Similar to Dy-NCFs discussed above, the metal-dependent single-ion anisotropy of HoM₂N@C₈₀ (M = Sc, Lu, Y) was studied by paramagnetic ¹³C NMR studies, XMCD analysis and ligand field calculations using a point-charge model.⁸⁶ The results indicate that despite the same magnetic ground state of Ho³⁺ with |m_J| = 8 in these molecules, chemical shifts and ligand fields are strongly dependent on the size of the M³⁺ ion, which is consistent with the conclusion extracted from DyM₂N@C₈₀.⁷⁹ Furthermore, an interesting behavior was revealed for HoLu₂N@C₈₀, in which the encapsulated cluster can be oriented in a magnetic field since the Ho magnetic moment aligns along the Ho-N axis due to the strong ligand field.⁸⁷ Thus, a hopping motion of the cluster is possible upon applying external magnetic fields, and the activation energy associated with such a process can be determined for HoLu₂N@C₈₀ as well as for TbSc₂N@C₈₀, providing insights into the cluster–cage binding interaction.

Popov et al. systematically studied MSc₂N@C₈₀, using paramagnetic NMR combined with point-charge calculations, with M including all lanthanides (M = La, Ce, Pr, Nd, Tb, Dy, Ho, Er, Tm, Lu) that can be introduced into NCFs.⁸⁸ The ⁴⁵Sc NMR spectra are especially useful for the study of the magnetic properties of these NCF-based SIMs. The interpretation of these spectra accomplished by the point-charge model shows a strong axial ligand field generated by the short M–N bond length in each case. This leads to an easy-axis magnetic anisotropy for the lanthanide ions with an oblate shape of the 4f density (Ce³⁺, Pr³⁺, Nd³⁺, Tb³⁺, Dy³⁺, and Ho³⁺), and an easy-plane anisotropy for prolate lanthanide ions Er³⁺ and Tm³⁺.

4.1.1.2 NCFs with multiple magnetic metal ions. Soon after the discovery of DySc₂N@C₈₀ as the first EMF-SMM, its single-ion anisotropy was investigated by Chibotaru et al. through ab initio calculations, revealing a large effective barrier exceeding 1000 K.⁸⁹ This high height of the barrier, however, does not simply guarantee a high blocking temperature due to the fast QTM in the ground doublet as discussed above, which is further facilitated by hyperfine coupling to nuclear spins.^1,90 How to inhibit QTM has been central to the studies of SMMs directed towards magnetic bistability at high temperatures. To this end, the local symmetry of the coordination environment is found to be crucial to suppress QTM by minimizing the transverse ligand fields and reducing the mixing between different m_J states.⁹ Another synthetic strategy is to design a di-nuclear SMM in which simultaneous reversal of magnetic moments on both lanthanide ions becomes difficult due to magnetic exchange interaction (or magnetic coupling) between them.^91,92 However, it is challenging in conventional organometallic compounds to achieve strong magnetic exchange between lanthanide ions having well-shielded 4f electrons. The confined sub-nanospace provided by a rigid fullerene cage, on the other hand, offers a possibility to enforce close proximity of Ln ions in an encapsulated metal cluster so as to enhance their magnetic coupling.

An ab initio investigation of the dinuclear Dy₂ScN@C₈₀ shows an exchange splitting with an energy barrier of ∼8 cm⁻¹, which is expected to efficiently block the QTM process at low temperatures, and thus may give rise to a high-performance SMM with a long magnetic relaxation time and large magnetic remanence.⁸⁹ Indeed, this prediction was later confirmed by magnetic characterization showing a much wider magnetic hysteresis at 2 K in contrast to the butterfly-shaped hysteresis of mononuclear DySc₂N@C₈₀.⁹³ The suppressed QTM in Dy₂ScN@C₈₀, as predicted by Chibotaru et al.,⁸⁹ is ascribed to a ferromagnetic coupling between two Dy³⁺ ions in the molecule. As a result, a 100 s blocking temperature T_B,100s in the absence of a magnetic field is determined to be about 5.5 K. The angle between the magnetic moments on the two Dy sites can be precisely determined from temperature-dependent magnetization curves, in excellent agreement with the theoretical result showing that the quantization axes of the two Dy ions are collinear with the two Dy–N bonds.⁹⁴ Slow magnetic relaxation of DySc₂N@C₈₀ at higher temperatures can be probed by AC magnetometry up to 76 K.⁹⁵ A remarkably high effective barrier U_eff of 1735 K is extracted from the temperature dependence of τ, which exhibits an Orbach process functioning above 60 K. This thermally activated relaxation process is understood by ab initio calculations, and takes place via the fifth-excited Kramers doublet of the single-ion ligand field splitting in Dy₂ScN@C₈₀.

Similar to monodysprosium NCFs, the role that diamagnetic metals play in the SMM properties can be studied in didysprosium NCFs, where intramolecular magnetic coupling between two Dy³⁺ ions is of particular importance. Substituting Sc with Lu in Dy₂ScN@C₈₀, a similar bifurcation temperature (T_B,ZFC = 8 K) is obtained for Dy₂LuN@C₈₀, while they differ in the interaction between the magnetic moments of Dy³⁺, leading to different temperature and field dependence of the relaxation times.⁷⁸ In the series of Dy₂MN@C₈₀ (M = Sc, Y, La, and Lu), Dy⋯Dy coupling and magnetic relaxation is mainly controlled by the size of M³⁺.⁷⁹ The hysteresis becomes narrower when the ionic radius of M³⁺ is larger, and the relaxation rate at low temperatures is similar for NCFs entrapping Dy₂ScN and Dy₂LuN, but becomes progressively faster for Dy₂YN and Dy₂LaN with much larger clusters (Fig. 3b and d). These observations are correlated with the strength of Dy⋯Dy coupling, and the corresponding energy difference between ferromagnetic and antiferromagnetic states (ΔE_AFM–FM) changes gradually from 8.1 K to −1.2 K as the size of M³⁺ increases. The mass of M, on the other hand, is less critical for the magnetic properties, meaning that the phonon degrees of freedom do not contribute heavily to the relaxation pathways in didysprosium NCFs compared to the situation in monodysprosium SIMs. Substitution of a diamagnetic Sc³⁺ ion in Dy₂ScN@C₈₀ with Gd³⁺ having half-filled f orbitals was also investigated.⁹⁶ It is demonstrated that the energy of the excited exchange state ΔE_AFM–FM decreases in Dy₂GdN@C₈₀ relative to that in Dy₂ScN@C₈₀. This results in a much faster QTM in Dy₂GdN@C₈₀, as evidenced by its very narrow hysteresis at 1.8 K; this acceleration of magnetic relaxation is due to the fact that the isotropic Gd³⁺ can act as a single-atom catalyst.

The interplay between cage structures and intramolecular magnetic coupling in didysprosium NCFs has been studied by encapsulating Dy₂ScN clusters into I_h(7)-C₈₀, D_5h(6)-C₈₀ and a non-IPR C_s(51 365)-C₈₄ (Fig. 4b and d).⁸⁴ Similar to the result of monodysprosium NCFs employing different host cages, the best SMM properties of the didysprosium compounds are found in I_h(7)-C₈₀, which exhibits the broadest hysteresis and the highest bifurcation temperature T_B,ZFC determined from ZFC/FC curves. The NCF with the non-IPR cage has the worst SMM performance in the series of compounds. This is also verified by the larger U_eff of the Orbach relaxation in I_h(7)-C₈₀via the exchange excited state compared to that in D_5h(6)-C₈₀, whereas shorter relaxation time of Dy₂ScN@C₈₄ precludes the study of its temperature dependence of relaxation time.

Apart from Dy³⁺, the possibility to incorporate another Ln³⁺ into an NCF-based dinuclear SMM has also been explored. A heteronuclear NCF DyErScN@I_h(7)-C₈₀ was reported as an SMM with a broadened hysteresis close to zero field compared to that of DySc₂N@C₈₀ due to the suppressed QTM, which stems from the magnetic exchange interaction between Dy³⁺ and Er³⁺.⁹⁷ The more important feature of this molecule is the luminescent Er³⁺ ion integrated into the cage, which provides an additional function of characteristic Er³⁺ near-infrared emission for the SMM, rendering a bifunctional magneto-luminescent molecule. Incorporation of two non-Kramers Tb³⁺ ions instead of Dy³⁺ leads to a Tb₂ScN@C₈₀ SMM exhibiting magnetic hysteresis at sub-Kelvin temperatures, at which a relaxation time in the order of 100 s can be determined.⁹⁸ Analysis of the temperature dependence of τ indicates an Orbach process with 10 K U_eff arising from the exchange excited state due to magnetic coupling. The prefactor (τ₀ in eqn (1)) is 4 orders of magnitude smaller than that of the Dy congener, which is ascribed to the lack of Kramers protection in Tb₂ScN@C₈₀. The magnetic coupling can be better studied in dinuclear systems with two isotropic Gd³⁺ ions instead of other anisotropic Ln³⁺.¹⁰⁸ Despite the fact that strong axial anisotropy is lacking in Gd³⁺, which is beneficial to the design of an SMM, magnetic characterization of Gd₂ScN@C₈₀ clearly confirms a ferromagnetic coupling between two Gd³⁺ ions, and also suggests a non-negligible anisotropy in the molecule.

The situation gets much more complicated when three magnetic Ln³⁺ ions are embedded simultaneously inside a fullerene cage using the trimetallic nitride template, where various ways of coupling three magnetization moments are possible in the trimetallic triangle. This magnetic coupling was first analyzed in Ho₃N@C₈₀ and Tb₃N@C₈₀ using magnetization curves.¹⁰⁹ The strong ligand fields are able to induce a collinear alignment of the individual moments parallel to the M–N bonds, giving rise to a ferromagnetically coupled net magnetic moment in each case. The ferromagnetic coupling was reported in experiment for Gd₃N@C₈₀,^108,110 as well as in theory for Dy₃N@C₈₀.⁸⁹ The latter is expected to trigger magnetic frustration that can greatly suppress magnetization blocking in the SMM regardless of the exchange barrier. Such a magnetic frustrated state is caused by the quasi-degeneracy of the three exchange multiplets in the ground state, that is, the net magnetic moment of the molecule can be aligned along each of the three Dy–N bonds. These predictions of the magnetic properties for Dy₃N@C₈₀ were later confirmed by experiments showing a very narrow magnetic hysteresis at 2 K, which is caused by the frustrated ground state as one of the simplest realizations of a frustrated and ferromagnetically coupled system.⁹³

4.1.2 Metal cyanide clusterfullerenes (CYCFs). The vast majority of clusterfullerenes reported so far contain more than one metal ion inside the cage. Synthesis of monometallic clusterfullerenes was expected to be challenging since fewer electrons could be transferred from the encapsulated cluster to the outer carbon cage, thus contributing less to the stabilization of this type of host–guest molecule. This paradigm has been broken down with the discovery of the first monometallic cyanide clusterfullerene (CYCF) YCN@C_s(6)-C₈₂ by Yang et al.⁴⁷ X-ray crystallographic study shows a triangular cluster geometry which transfers two electrons to the cage, thus facilitating its encapsulation into the popular C₈₂ fullerene with the stable 2-charged state which shares a similar electronic structure with mono-EMFs M@C₈₂ bearing a divalent metal ion (M = Sm, Eu, Yb).^111–115 This monometallic CYCF opens up a new avenue for the design of EMF-SIMs.

To this end, Tb³⁺ with large magnetic anisotropy was later introduced to form TbCN@C₂(5)-C₈₂.¹¹⁶ The same group further synthesized terbium-CYCF based on three isomers of C₈₂, namely C₂(5), C_s(6) and C_2v(9), all adopting a triangular cluster geometry as illustrated in Fig. 5a–c.¹⁰⁰ Variable-temperature magnetization measurements with the aid of a noncollinear magnetic moment model, which considers isotropic distribution of magnetic moments, reveal a magnetic ground state of |m_J| = 6 for each case. AC susceptibility studies demonstrate field-induced SIM properties for all these series of compounds (Fig. 5d–f). Remarkably, it is found that as the isomeric structure of the C₈₂ cage varies from C₂(5) to C_s(6) and to C_2v(9), the Tb–N distance becomes shorter, and the relaxation time increases accordingly, which is likely attributed to the enhanced ligand fields imposed on the Tb³⁺ ion. Thus, this direct correlation between the magnetic properties and the cluster geometry indicates a facile approach to fine-tune single-ion anisotropy by changing the cage structure in these SIMs. Indeed, upon further varying the host cage from the popular C₈₂ to a non-IPR C_2v(19 138)-C₇₆, the embedded TbCN cluster becomes nearly linear instead of maintaining the triangular geometry.⁹⁹ This geometric change is relevant to the strong metal–cage interaction in the presence of the fused-pentagon motif on the cage, as also evidenced by a combined experimental and theoretical study on CYCFs encapsulating a LuCN cluster into C₇₆ and C₈₂ cages.¹¹⁷ The field-induced SIM properties were verified by the frequency-dependent out-of-phase susceptibility χ′′ observed in AC measurements for TbCN@C₇₆, from which a shorter relaxation time is extracted in comparison with that of its C₈₂ counterparts. The reason for the faster relaxation rate in CYCFs with a linear cluster is still not clear. The QTM process governed by the local symmetry or spin-phonon coupling mediated by cluster-based vibrations may be accountable for this observation.

Fig. 5 Molecular structures of TbCN@C₂(5)-C₈₂ (a), TbCN@C_s(6)-C₈₂ (b) and TbCN@C_2v(9)-C₈₂ (c). Out-of-phase AC magnetic susceptibility of TbCN@C₂(5)-C₈₂ (d), TbCN@C_s(6)-C₈₂ (e) and TbCN@C_2v(9)-C₈₂ (f) at 1.8–6 K. Reproduced from ref. 100.

Although no further CYCF-based SIMs have been reported to date besides TbCN@C_76,82, synthetic efforts have been devoted in the field to expand this family of molecules by introducing different lanthanide metals and fullerene cages. In this regard, Dy-based CYCFs are of particular interest owing to their Kramers ion nature, which competes with non-Kramers Tb³⁺ and is usually associated with the suppressed QTM process. By employing Prussian blue as a cheap solid cyanide/nitrogen dual-source, Dy-containing CYCFs can be readily synthesized with high yields.³⁰ X-Ray crystallographic studies of the three isomers of DyCN@C₈₂ indicate the triangular geometry of the embedded cluster which is tunable upon varying the isomeric structure of the cage. Recently, the host cage of CYCFs was extended to C₈₄ with two isomers C₂(13) and C_2v(17), while the metals involved encompass Y, Dy and Tb.¹¹⁸ The missing C_2v(17)-C₈₄, which had never been reported before both in empty fullerenes and EMFs, can be interconverted from the C₂(13)-C₈₄ isomer through two steps of Stone–Wales transformation. This demonstrates the advantage of the monometallic cyanide cluster in stabilizing novel fullerene structures. The subtle difference in the ionic radii of Y³⁺, Dy³⁺, and Tb³⁺ gives rise to a noticeable change in the metal–cage interaction, which can also be varied within different isomeric cages. Thus, the metal–cage interactions and the related single-ion anisotropy, if a magnetic Ln ion is introduced, can be altered via both the encapsulated cluster and host cage.

An alternative strategy to modify the cluster geometry was realized by exohedral functionalization on the cage via high-temperature trifluoromethylation.^119,120 This leads to the synthesis of multi-trifluoromethylated CYCFs based on C₈₂ and C₈₄. Different derivatized products, including YCN@C₈₂(CF₃)_16/18 and YCN@C₈₄(CF₃)_16/18, have been structurally characterized using X-ray crystallography. These compounds are stabilized by the formation of isolated C=C bonds and benzenoid rings on the fullerene cages after CF₃ addition, which is able to localize the metal atoms within a particular fragment of the cage. Moreover, the encapsulated YCN cluster with triangular geometry can be further altered depending on the exohedral addition pattern. This shall allow the manipulation of the single-ion anisotropy for Dy³⁺- or Tb³⁺-based CYCFs and thus would certainly stimulate further studies on their SMM properties.

4.1.3 Metal oxide clusterfullerenes (OCFs). Considering the strong ligand field strategy directed at enhancing single-ion anisotropy and the effective barrier of magnetization reversal, it is reasonable to choose a stronger ligand over N³⁻ and CN⁻ in clusterfullerenes as discussed above. This leads to the entrapment of O²⁻ as a nonmetal inside the cage with higher electronegativity. The as-formed oxide clusterfullerenes (OCFs) were first synthesized by Balch et al. in tetrametallic molecules Sc₄O₂@C₈₀ and Sc₄O₃@C₈₀ with the oxygen atoms as μ₃-bridging ligands.^121,122 Note that since scandium has the smallest covalent radius among the family of rare-earth metals, these tetrametallic oxide clusters are limited cases so far, which precludes the synthesis of Ln-congeners with much larger encapsulated clusters that are of interest in this review from the magnetic point of view. The same group later reported another simpler form of OCFs Sc₂O@C_s(6)-C₈₂ consisting of a slightly bent dimetallic oxide cluster, whose electronic structure can be described as (Sc³⁺)₂O²⁻@C₈₂⁴⁻.⁴⁶ The formal four-electron transfer from the cluster suggests that fullerene cages that can form stable tetraanions are suitable hosts in this type of OCF. Indeed, a series of OCFs entrapping Sc₂O clusters within a variety of fullerenes ranging from C₇₀ to C₈₂ were reported by Chen and Feng et al., in which CO₂ is found to boost the yields of OCFs during the arc-discharging production process.^123–129 This template of OCFs can also be extended to lanthanide metals,^130–132 with a notable example of M₂O@C₂(13 333)-C₇₄ (M = Tb, Ho, Lu) featuring a linear M₂O cluster inside the non-IPR fullerene cage.^133–135 Understanding the interplay between the cluster geometry and the cage structure would be crucial to explore their magnetic properties.

Magnetic studies on this type of OCF started from a theoretical work focused on the single-ion anisotropy of heterometallic compounds DyMO@C_2n (M = Sc, Lu; 2n = 72, 76, 82), where diamagnetic rare-earth metal ions are used in conjunction with anisotropic Dy³⁺ to avoid the relaxation pathway through low-lying exchange excited states that are induced by generally weak 4f–4f magnetic coupling.¹³⁶ As expected from a more electronegative O²⁻ compared to N³⁻, ab initio calculations show a strong splitting of the ⁶H_15/2 ground multiplet for Dy³⁺ in each case. Detailed analysis of the wavefunctions of the doublets and the transition probability among them indicates that QTM can be quenched up to the third-excited doublet in the series of compounds. A very large effective barrier U_eff exceeding 2000 K is determined in DyScO@C₈₂. This highly axial anisotropy is expected to give rise to a strong SIM. However, heteronuclear OCFs have not yet been synthesized due to the difficulties both in synthesis and in separation. It should be noted that the overall yields of OCFs are much lower than those for NCFs, and the mixture of Dy₂O, Sc₂O and DyScO species makes the HPLC separation process a challenging task. Thus, one has to focus on the homonuclear system at this stage, where two magnetic Dy³⁺ ions are involved simultaneously. In this context, enhancing magnetic coupling interaction between two Dy³⁺ ions becomes crucial to suppress QTM as discussed in the above section on NCFs with multiple magnetic metal ions (4.1.1.2). Indeed, oxygen-bridged dinuclear compounds in various organometallic SMMs have been demonstrated to induce strong coupling between the two Dy³⁺ ions via superexchange interactions.^137–141

To start with the discussion of the magnetic properties for these dinuclear Dy-SMMs, their low-energy spin states can be generally described using the following spin Hamiltonian

Ĥ_spin = Ĥ_LF1 + Ĥ_LF2 − 2j₁₂Ĵ₁Ĵ₂ + Ĥ_ZEE (3)

where the first two terms are the single-ion ligand-field Hamiltonian for the i-th dysprosium site, and are obtained from ab initio calculations of the two Dy fragments substituting the other Dy³⁺ by a diamagnetic metal ion such as Y³⁺; the third term represents the magnetic coupling interaction between the two Dy³⁺ magnetic moments Ĵ_i with j₁₂ as the coupling constant; and the last term represents the Zeeman effect upon applying a magnetic field. The total magnetic coupling j₁₂ is often treated in the literature, for simplicity, as an effective scalar term stemming from isotropic interaction, rather than a more complex anisotropic tensor.¹⁴² This information can be either derived from the fitting of the isothermal magnetization and variable-temperature magnetic susceptibility curves, or from the analysis of temperature-dependent relaxation times correlating exchange excited states (with the energy of ΔE_AFM–FM) with U_eff in the Orbach relaxation process. This total coupling consists of dipolar and exchange contributions, j_dip and j_exch. The dipolar term is dependent on the distance and relative orientation of the magnetic moments (easy axis of each metal ion) that are extracted from structure and ab initio calculations. The exchange term, determined as the difference of j₁₂ and j_dip, represents magnetic interaction at a chemical origin as a result of orbital overlap between two metal ions, either in a direct way (Heisenberg exchange) or transferred by the bridging ligand (superexchange). Note that instead of the situation in Eqn 3 where lanthanide moment Ĵ is used, another convention of magnetic coupling Hamiltonian employs a projection of pseudospin S̃_i = 1/2 for the i-th magnetic metal center. To avoid ambiguity, therefore, we compare the corresponding energy difference between ferromagnetic (FM) and antiferromagnetic (AFM) states (ΔE_AFM–FM) throughout this review. Under the −2j₁₂Ĵ₁Ĵ₂ convention illustrated in eqn (3), this energy splitting for a didysprosium system can be computed as

ΔE_AFM–FM = 225j₁₂ cos(α) (4)

where α is the angle between quantization axes of two Dy³⁺ ions derived from single-ion anisotropy calculations, and the factor of 225 results from their m_J = ±15/2 ground state.

The first magnetically characterized OCF-based SMMs were reported in 2019 including three isomers of Dy₂O@C₈₂ with C_s(6), C_3v(8) and C_2v(9) cage symmetries.¹⁰² As illustrated in Fig. 6a–c, each of these molecules possesses a slightly bent shape for the encapsulated Dy₂O cluster which features unusually short Dy–O bonds of ≈2.0 Å, resulting in a very strong magnetic anisotropy of Dy ions with their magnetic moments aligning along the Dy–O bonds. Dy₂O@C₈₂ isomers show SMM behaviors with a broad magnetic hysteresis at low temperature (2 K), which persists up to 6–7 K using a field sweep rate of 2.9 mT s⁻¹ (Fig. 6d–f). The opening of the hysteresis loop close to zero field is clear evidence of effective quenching of QTM by magnetic coupling of two Dy³⁺, in contrast to the butterfly-shaped hysteresis observed for NCF-based SIMs.^15,81 A more interesting feature in Dy₂O@C₈₂ isomers lies in the inflection of their hysteresis loops. The abrupt drop of magnetization at zero field at 2 K, noticeable in the C_2v(9) case, arises from QTM that is not completely quenched by magnetic coupling. The inflections away from the zero-field region, on the other hand, are ascribed to the Zeeman splitting of the energy of the FM and AFM states in the presence of a certain magnetic field, at which the crossing point is found between these spin states. It should be noted that this inflection phenomenon is much more obvious than that in the hysteresis of the ferromagnetically coupled Dy₂ScN@C₈₀,⁹⁵ in which the FM state is more likely to be the ground state at a certain molecular orientation without level crossing due to its stronger Zeeman response. Therefore, the complex feature of hysteresis indicates an antiferromagnetically coupled system for Dy₂O@C₈₂. The particular field of inflection can then be used to determine ΔE_AFM–FM as well as the coupling constant j₁₂ combining eqn (3) and (4). Alternatively, the coupling situation can be understood, as discussed above, by the fitting of magnetization curves using eqn (3) and (4), or by the study of their relaxation mechanisms applying eqn (2) and (4). The latter gives the Orbach relaxation process via the FM excited state at low temperatures with U_eff corresponding to ΔE_AFM–FM. The value of ΔE_AFM–FM is thus determined as −7.8 to −18.6 K, suggesting that the Dy⋯Dy exchange coupling in Dy₂O@C₈₂ is the strongest at this time among all dinuclear Dy SMMs with diamagnetic bridges.^{137,138,143–145}

Fig. 6 Molecular structures of Dy₂O@C_s(6)-C₈₂ (a), Dy₂O@C_3v(8)-C₈₂ (b) and Dy₂O@C_2v(9)-C₈₂ (c). Magnetic hysteresis curves of Dy₂O@C_s(6)-C₈₂ (d), Dy₂O@C_3v(8)-C₈₂ (e) and Dy₂O@C_2v(9)-C₈₂ (f) in the range of 1.8–7 K using a field sweep rate of 2.9 mT s⁻¹. The insets represent their corresponding ZFC/FC curves at an applied magnetic field of 0.2 T with a temperature sweep rate of 5 K min⁻¹. Reproduced from ref. 102.

The possibility of putting Dy₂O clusters into other fullerene cages has been explored, discovering two non-IPR cages C_s(10 528)-C₇₂ and C₂(13 333)-C₇₄ as suitable hosts.⁵⁵ The fused-pentagon moieties in these cages govern the positions of Dy³⁺ inside thanks to the strong metal–cage interaction, and the geometry of the Dy₂O cluster is controlled in this way, which is bent within C₇₂ but becomes linear in C₇₄. The cage-dependent cluster geometry greatly affects the SMM behaviors of these two OCFs. Both molecules show open magnetic hysteresis at 1.8 K but with very different shapes. In the case of Dy₂O@C₇₂, the hysteresis loop is typical of an antiferromagnetically coupled SMM featuring quenched QTM in the absence of field and an inflection in the presence of field, similar to the situation of the abovementioned Dy₂O@C₈₂ isomers.¹⁰² In contrast, Dy₂O@C₇₄ exhibits an SIM-like hysteretic behavior which is almost closed at zero field due to the strong QTM. Detailed analysis reveals that in this dinuclear Dy-SMM, the ferromagnetic dipolar coupling is nearly completely counterbalanced by the antiferromagnetic Dy–O–Dy superexchange interaction, thus leading to decoupled Dy moments that are accountable for such a SIM-like hysteresis. Although the relaxation rate of Dy₂O@C₇₄ is fast at zero field, slow relaxation (with τ > 40 s) can be observed up to 6 K at a finite magnetic field of 0.2 T or 0.8 T. The magnetic hysteresis remains open up to 14 K in Dy₂O@C₇₄ and up to 7 K in Dy₂O@C₇₂ at a field sweep rate of 2.9 mT s⁻¹. The former value is the highest hysteresis temperature among all clusterfullerenes reported so far.

Compared to that of Dy₂O@C₈₂, even stronger Dy⋯Dy coupling was found by Popov et al. in Dy₂O@C_2v(5)-C₈₀.¹⁰¹ The ΔE_AFM–FM determined by the fitting of magnetization data shows a very large value of −26.6 K (the dipolar and exchange contributions are 3.9 and −30.5 K, respectively), which is also consistent with the U_eff of 25.9 K extracted from the temperature dependence of magnetic relaxation time. Dy₂O@C₈₀ has a broad hysteresis at 1.8 K opening between −5 T and 5 T and with a coercive field of 0.65 T. A pronounced inflection of the hysteresis loop upon decreasing the field is observed, which is related to the level crossing between AFM and FM states. The magnetic hysteresis persists until 6 K using a field sweep rate of 2.9 mT s⁻¹, while the bifurcation temperature T_B,ZFC is determined as 11 K from ZFC/FC measurements with a temperature sweep rate of 5 K min⁻¹.

Recently, this family of OCF-SMMs has been further extended to three C₈₈ isomers with cage symmetries of C₁(26), C_s(32), and D₂(35).¹⁰³ All isomers of Dy₂O@C₈₈ display slow relaxation of magnetization and magnetic hysteresis. The latter measure of SMMs can be observed up to 7–9 K at 2.9 mT s⁻¹ sweep rate. It is worth noting that Dy₂O@C₈₈ represents EMF-SMMs possessing the largest carbon cages to date. The three isomers of Dy₂O@C₈₈ also allows for the study of their SMM properties as a function of the isomeric fullerene cage. Similar to the above analysis of other OCF-SMMs with smaller cages, it seems clear that the O²⁻ bridge favors antiferromagnetic exchange coupling between the two Dy³⁺ ions. The strength of Dy⋯Dy superexchange interactions, however, differs significantly upon varying the isomeric structure of the C₈₈ cage. The comparative analysis of all nine OCF-SMMs reported so far reveals that only Dy₂O@D₂(35)-C₈₈ has a moderately positive ΔE^exch_AFM–FM value of 2.0–3.2 K, considering only superexchange interactions without the contribution from the dipolar terms. All the other eight molecules feature a negative exchange term, which ranges from the modest −2.2 K in the case of C₇₂ to very large −27.3 K in C₁(26)-C₈₈ and −30.5 K in C₈₀, with the latter two being the strongest Dy⋯Dy interactions in all didysprosium compounds reported by far. Further enhancing the magnetic coupling in Dy-OCFs is definitely a research direction aimed at increasing the blocking temperature of this type of SMM. Despite the fact that unfortunately no clear structural correlation of the exchange coupling strength is concluded in the present literature for Dy-OCFs, the structural diversity of the fullerene cage would become a rich playground to achieve such a goal in future studies.

4.1.4 Metal sulfide clusterfullerenes (SCFs). Replacing the oxygen atom in OCFs by a sulfur atom, a new type of metal sulfide clusterfullerene (SCF) can be constructed in the form of M₂S@C_2n (M = Sc, Ti, Y, Dy, Er, Lu; 2n = 70–82) with a similar electronic structure to that of OCFs. The first SCFs M₂S@C_3v(8)-C₈₂ (M = Sc, Y, Dy, Lu) were synthesized by Dunsch et al. using guanidium thiocyanate (CH₅N₃·HSCN) as a solid sulfur source during the arc-discharging production process, and were characterized by various spectroscopic techniques in combination with DFT calculations.¹⁴⁶ Very soon after this first discovery, Echegoyen et al. reported the synthesis of a series of scandium sulfide clusterfullerenes Sc₂S@C_2n (2n = 80–100) by introducing SO₂ as the sulfur source, among which Sc-SCFs based on two isomers of C₈₂, with the cage symmetries of C_s(6) and C_3v(8), have been isolated and spectroscopically characterized.¹⁴⁷ The molecular structures of the two isomers of Sc₂S@C₈₂ were then determined crystallographically to show significantly bent Sc₂S clusters inside the fullerene cages.¹⁴⁸ Later, it was found in the crystal structure that this bent shape is maintained inside a C_s(10 528)-C₇₂ cage violating the isolated-pentagon rule.¹⁴⁹ Following this synthetic strategy, Sc₂S clusters can be entrapped in an even smaller non-IPR C₂(7892)-C₇₀ cage, which is closely connected with the previously reported C_s(10 528)-C₇₂ by a direct insertion of a C₂ unit.¹⁵⁰ This sulfide template can be extended to Er-SCFs employing the two most stable C₈₂ isomers (C_s(6) and C_3v(8)),¹⁵¹ and is also able to stabilize transition metal-only clusters inside a fullerene cage, forming Ti₂S@D_3h(5)-C₇₈.¹⁵² DFT calculations of the latter suggest an almost linear geometry of the Ti₂S cluster which transfers six electrons to the cage due to the tetravalent oxidation state of titanium, distinct from the four-electron transfer in conventional SCFs encaging trivalent rare-earth metal ions.

Similar to OCF-SMMs with strong magnetic coupling between two Dy³⁺ ions, Dy-SCFs are of particular interest for magnetic studies. By using Dy₂S₃ as a solid source of metal and sulfur, and adding methane to a reactive atmosphere so as to reduce the formation of empty fullerenes in the arc-discharging process, Dy-SCFs can be selectively synthesized as the main fullerene products.²⁹ Among them, two C₈₂ isomers (C_s(6) and C_3v(8)) and C_s(10 528)-C₇₂ have been successfully isolated, and the structures of the former two isomers were unambiguously determined by single-crystal XRD characterization to reveal significantly bent Dy₂S clusters inside the cages. All these three molecules exhibit magnetic hysteresis at low temperatures, with the C_3v(8)-C₈₂ case being the best SMM showing open hysteresis up to 4 K using a field sweep rate of 8.33 mT s⁻¹ and T_B,ZFC = 4 K at a temperature sweep rate of 5 K min⁻¹ in ZFC/FC measurements. Its dynamic magnetic properties can be studied by DC and AC susceptibility measurements in the temperature range from 1.6 K to 70 K. This exceptional slow magnetic relaxation up to high temperatures enables the determination of three Orbach relaxation processes with U_eff of 10.5, 48 and 1232 K, respectively. The first energy barrier is associated with the magnetic exchange excited state similar to that for Dy-OCFs; the intermediate barrier can be ascribed to the local vibrational mode of librating the Dy₂S cluster within the cage, while the highest value matches the excited doublet in the single Dy³⁺ ligand field. On the other hand, Dy₂S@C_s(6)-C₈₂ has a faster magnetic relaxation featuring two barriers of 15.2 and 523 K, corresponding to relaxation via the exchange excited state and via the excited doublet in ligand field splitting, respectively. Comparing the magnetic behaviors of these SCFs with their OCF counterparts, it is evident that generally weaker SMM performance can be found in SCFs. This disparity originates from the lower electronegativity and the larger covalent radius of sulfur. The latter results in the bent shape of the cluster instead of nearly linear one usually observed in OCFs; and the former means that a weaker ligand field is imposed by S²⁻ in comparison with that by O²⁻. Nevertheless, Dy-SCFs still have the longest relaxation times and the highest energy barriers compared to other Dy-SMMs that contain a sulfur bridge.^153–155 This is because sulfur possesses a larger negative charge inside the fullerene, while the Dy–S bond length is also considerably shorter, thus giving rise to a strong ligand field.

The two isomers of Dy₂S@C₈₂ were further magnetically characterized at sub-Kelvin temperature, which shows broad hysteresis at 0.41 K with two clear QTM steps (one at zero field and the other at a certain field) in each case (Fig. 7c and d).¹⁰⁴ This allows a detailed analysis of the level crossing for different orientations in the presence of an applied magnetic field, providing precise information on the strength of Dy⋯Dy interactions in Dy₂S@C₈₂. The derived ΔE_AFM–FM values are 15.4 K and 7.3 K for C_s and C_3v isomers, respectively, which are in line with the results extracted from the fitting of temperature dependence of relaxation times as discussed above.²⁹ It is worthwhile to note that while the O²⁻ bridge facilitates an antiferromagnetically coupled system in Dy-OCFs, a ferromagnetically coupled ground state is found for Dy-SCFs. The sub-Kelvin temperatures enable the determination of relaxation times by DC demagnetization measurements. The QTM regime is thus achieved, rendering long relaxation times near 900 s and 3200 s for C_s and C_3v isomers. This QTM process is related to the situation where the two Dy³⁺ magnetic moments flip simultaneously as an entity.

Fig. 7 Molecular structures of Dy₂S@C_s(6)-C₈₂ (a) and Dy₂S@C_3v(8)-C₈₂ (b). Magnetic hysteresis loops of Dy₂S@C_s(6)-C₈₂ (c) and Dy₂S@C_3v(8)-C₈₂ (d) at 0.41 K and compared to some higher-temperature curves recorded until the hysteresis is closed. Field sweep rates 2.9 mT s⁻¹ for T = 2 K and above, and 3.3 mT s⁻¹ for T = 0.41 K. QTM₀, QTM_A, and asterisk denote the features appearing because of the level crossing in Zeeman energies. Magnetic hysteresis loops of DyScS@C_s(6)-C₈₂ (e) and DyScS@C_3v(8)-C₈₂ (f) at 2–9 K with a sweep rate of 10 mT s⁻¹. Reproduced from (c) and (d) ref. 104 and (e) and (f) ref. 105.

Substituting one Dy³⁺ by a diamagnetic Sc³⁺ ion in these two isomers of Dy₂S@C₈₂ further leads to two SIMs.¹⁰⁵ Magnetic characterization of these DyScS@C₈₂ isomers shows an open magnetic hysteresis even at zero field at 2 K, indicating a quenched QTM effect compared to that of Dy-NCFs featuring a nearly closed hysteresis loop at zero field (Fig. 7e and f).⁷⁶ The hysteresis of DyScS@C₈₂ is open until 9 K in each case, where a fast field sweep rate of 10 mT s⁻¹ is used. The bifurcation temperatures determined from ZFC/FC curves are both around 7.3 K. This better SMM performance of DyScS@C₈₂ than Dy₂S@C₈₂ suggests potential interest in future magnetic studies of DyScO@C₈₂ with an even stronger axial ligand field.¹³⁶

4.1.5 Metal carbide clusterfullerenes (CCFs). Another type of clusterfullerenes isostructural and isoelectronic to OCFs and SCFs is metal carbide clusterfullerenes (CCFs) M₂C₂@C_2n (M = rare earth metals; 2n = 68–108) featuring a C₂²⁻ bridging ligand.^{45,48,156–159} CCFs are the second family of clusterfullerenes after NCFs, which was first discovered in 2001 by Wang et al. in Sc₂C₂@D_2d(23)-C₈₄.¹⁶⁰ Over the past two decades, an increasingly large number of CCFs have been synthesized with a rich variety of structures both for the encapsulated clusters and for the host fullerene cages. The interplay between the host and guest has been disclosed to show a structural transformation from a bent butterfly cluster shape in small cages to a linear geometry in large fullerenes thanks to the cage compression effect.¹⁶¹ Despite the plethora of structural studies on CCFs with a C₂²⁻ bridge, one of the few CCF-SMMs that have been reported to date includes Dy₂C₂@C_s(6)-C₈₂.²⁹ This molecule exhibits similar SMM performance to Dy₂S@C_s(6)-C₈₂ discussed above, showing a narrow magnetic hysteresis at 1.8 K which persists up to 3 K with a field sweep rate of 8.33 mT s⁻¹. AC susceptibility measurements reveal an effective barrier, corresponding to the exchange excited state, of 17.4 K in Dy₂C₂@C_s(6)-C₈₂, which is comparable to the value of 15.2 K determined for Dy₂S@C_s(6)-C₈₂. Note that inside the same C_s(6)-C₈₂ cage, the two Dy³⁺ magnetic moments in Dy₂C₂ and Dy₂S are ferromagnetically coupled, whereas an antiferromagnetically coupled ground state is identified for Dy₂O.¹⁰² Similar observations were found for the two isomers of Dy₂C₂@C₈₈ with cage symmetries of C_s(32) and D₂(35), which also show significantly narrower magnetic hysteresis loops compared to those of their Dy₂O counterparts.¹⁰³ Thus, a general conclusion can be drawn from the comparative studies that, given the same cage structure, OCFs have better SMM performance than SCFs and OCFs. This is very likely due to the stronger single-ion anisotropy and stronger superexchange interaction in the presence of an O²⁻ bridging ligand.

In addition to the C₂²⁻ bridging ligand, metal carbide containing a single C atom is also available within the fullerenes. This type of clusterfullerene was first synthesized by Popov et al. in Lu₂TiC@I_h(7)-C₈₀ having a μ₃-carbide ligand and mimics the structure of M₃N@C₈₀ (M = rare earth metals) NCFs.¹⁶² The tetravalent oxidation state of Ti gives rise to a Ti=C double bond in the former. As a result, both of these clusterfullerenes feature a cluster-to-cage six-electron transfer. Replacing the diamagnetic Lu³⁺ by Dy³⁺ leads to two dinuclear Dy-SMMs Dy₂TiC@C₈₀ with the cage symmetries of I_h(7) and D_5h(6) that are structurally characterized by spectroscopic methods.¹⁰⁷ The two isomers display similar hysteresis loops at 1.8 K. The hysteresis of the I_h(7) isomer can be observed up to 3 K using 5 mT s⁻¹ field sweep rate, showing a much weaker SMM performance compared to that of Dy₂ScN@C₈₀ (T_B,hys = 7 K at 2.9 mT s⁻¹ sweep rate), despite a stronger magnetic coupling found for Dy₂TiC@C₈₀.⁹⁵ This may be explained by a larger deviation of the orientation of the Dy magnetic moments from the Dy–C bond axes.⁹⁴ Adding one more carbon atom in the encapsulated cluster, Dy₂TiC₂@C₈₀ only exhibits a narrow hysteresis at 1.8 K. An SIM can also be constructed in DyYTiC@C₈₀ that contains three different metals, with two being diamagnetic.¹⁰⁶ Similar to DySc₂N@C₈₀,¹⁵ a butterfly-shaped hysteresis is observed for DyYTiC@C₈₀ at 1.8 K, which is open up to 7 K at 2.9 mT s⁻¹ sweep rate.

The trimetallic carbide can be further extended to a special case of Dy₃C₂@C₈₀ reported recently by Yang et al., in which a three-center single-electron metal–metal bond is disclosed within the triangular Dy₃ plane with very short Dy–Dy distances of ∼3.4 Å.¹⁶³ A similar trimetallic single-electron bond was later unveiled in Er₃C₂@C₈₀.¹⁶⁴ This peculiar metal–metal bonding character is distinct from the situation in Sc₃C₂@C₈₀ where the unpaired electron is localized on the C₂ unit,^165–167 and thus is expected to evoke strong magnetic coupling between three Ln ions, which has just been confirmed very recently in a trinuclear gadolinium organometallic compound with a giant S = 11 ground state.¹⁶⁸

4.2 Conventional EMFs

4.2.1 Monometallofullerenes (mono-EMFs). Coming back from clusterfullerenes with complex structures of the encapsulated species, we now focus on a simpler and conventional category of EMFs in which only metal atom(s) can be entrapped within the fullerene cage. To construct novel EMF-based SIMs, it is a natural idea to choose monometallofullerenes (mono-EMFs) encapsulating merely one metal ion inside a carbon cage. In fact, this simplest form of EMFs dates back to the discovery of empty fullerene and has a relatively high yield, in particular M@C₈₂ (M = rare earth metals).³⁹ The majority of mono-EMFs contain trivalent lanthanide ions, such as La³⁺, Ce³⁺, Pr³⁺, Nd³⁺, Gd³⁺, Tb³⁺, Dy³⁺, Ho³⁺, and Er³⁺. Thus, the cage is paramagnetic in the presence of an unpaired electron. On the other hand, if an encapsulated Ln³⁺ possesses partially filled 4f orbitals, its intrinsic magnetic properties are of particular interest. In this context, the magnetic properties are more complex since it is inevitably affected by the magnetic coupling with the unpaired electron on the cage. Early-stage research studies on the magnetic properties of these mono-EMFs mainly aimed at the determination of their effective magnetic moments using a SQUID magnetometer, which is either extracted by the Curie–Weiss law or from the fitting isothermal magnetization with the Brillouin function.¹⁶⁹ For instance, the magnetization of Gd@C₈₂ measured at different temperatures gives an effective magnetic moment of 7.70 μ_B, which is slightly smaller than that of the free Gd³⁺ ion with an ⁸S_7/2 ground state (μ_eff = 7.94 μ_B) in the absence of orbital angular momentum (L) due to its half-filled 4f-shell.¹⁷⁰ This reduction of the magnetic moment is explained by the antiferromagnetic coupling between Gd³⁺ (S_Gd = 7/2) and the unpaired electron on the cage (S_cage = 1/2), and was later confirmed by high-frequency electron paramagnetic resonance (EPR) spectroscopy indicating an antiferromagnetically coupled S = 3 ground state.¹⁷¹ Other lanthanide ions with nonvanishing orbital moment further complicate the determination of the magnetic moment of a mono-EMF.¹⁷² Although a systematic SQUID study on a series of mono-EMF compounds M@C₈₂ (M = Gd, Ho, Tb, Dy, Er) suggests noticeable magnetic anisotropy for each molecule from isothermal magnetization, as a function of applied magnetic field divided by temperature (H/T), no magnetic hysteresis has been observed down to 1.8 K in all cases.¹⁷³

It is reasonably expected that the unpaired electron on the cage of these trivalent mono-EMFs could be detrimental to their magnetic stability that intrinsically originated in the anisotropic Ln ions, such as Dy³⁺. This can be rationalized by considering that on the one hand, the cage spin is weakly coupled with the encapsulated magnetic metal, which is sensitive to the subtle variations in the environment, such as lattice phonons and intermolecular interaction in a powder form. This strong molecular interaction is even able to induce dimerization of a relatively unstable Y@C_s(6)-C₈₂ isomer in its cocrystal with Ni(OEP).¹⁷⁴ The harmful influence of the open-shell cage on the metal, on the other hand, is aggravated due to the fact that the charge and the associated spin are actually delocalized on the cage, and thus numerous cage-based molecular vibrations can easily affect the spin state of the whole molecule. Very often these vibrations are able to accelerate magnetic relaxation and need to be carefully engineered at molecular and atomic levels. In fact, mono-EMFs represent an ideal case in which the Ln ion is coordinated with only one rigid carbon cage ligand, thus resulting in an ultralow phonon density of state involving metal-based vibrations. Only three vibrational modes are present in mono-EMFs in which the metal ion oscillates along the x-, y- and z-axes.⁸³ This extraordinarily low-coordination environment, being inaccessible via conventional synthetic strategies since Ln ions always tend to have large coordination numbers, resembles the cases where single Ln atoms (Ho and Dy) are attached on graphene or metallic surfaces.^175–177 Thanks to the reduced spin-phonon coupling as a result of low coordination, these single-atom magnets display magnetic bistability at an atomic level despite the large strength difference of ligand fields imposed by distinct surfaces.

Extracted from the above analysis, mono-EMFs are a promising platform to design SMMs, yet it is crucial to quench the unpaired electron on the cage which can then be used as a diamagnetic matrix for the Ln ion, with the aim to protect the spin state against the influence from the open-shell carbon cage. Such a goal can be realized by encapsulating divalent metals, such as Eu²⁺, Sm²⁺ and Yb²⁺. While the latter possesses fully occupied f orbitals (f¹⁴), Eu²⁺ has a half-filled f⁷ configuration and thus is considered to be isotropic at its atomic origin but slightly anisotropic in real molecules.¹⁷⁸ Sm²⁺, on the other hand, could be interesting from the magnetic point of view. ¹³C NMR spectra also show changes in chemical shifts due to the paramagnetic lanthanide ion.^111,179,180 However, it is not anisotropic enough to induce SMM behaviors. Thus, one has to again resort to trivalent mono-EMFs employing conventional magnetic Ln ions such as Dy³⁺ and Tb³⁺. In this context, a possible solution to quench the unpaired electron on the cage is exohedral functionalization via radical addition. This strategy can be achieved either by in situ derivatization during the arc-discharging process or by chemical reaction during extraction of the raw soot using organic solvents, affording covalent modifications of the cage with trifluoromethyl,^181,182 dichlorophenyl,^44,183–185 benzyl,^186,187 and other radical groups.^188,189 Not only mono-EMF derivatives have been reported based on the most popular C₈₂ cages, but also various unstable fullerenes can be stabilized in this way, such as La@C₇₂-C₆H₃Cl₂ having a non-IPR cage and “missing” mono-EMFs like M@C₇₄ and M@C₇₀ (M = Y, La). The successful syntheses of these otherwise unstable species evidence the stabilization effect induced by radical addition on the open-shell mono-EMFs. The closed-shell carbon cage obtained via this approach also leads to the activation of the luminescence of Er³⁺ in its mono-EMFs due to the enlarged optical band gap upon functionalization.¹⁸⁴

An even more straightforward method to realize the closed-shell fullerene cage in mono-EMFs is in situ nitrogen substitution of the pristine carbon cage, thus producing an azafullerene. Indeed, the idea of azafullerene was first achieved in (C₅₉N)₂ dimers¹⁹⁰ and was later applied in mono-EMF La@C₈₁N together with the synthesis of the pristine La@C₈₂.¹⁹¹ However, this observation of monometallic azafullerene was only suggested by mass spectroscopy. The precise confirmation of its structure had long remained an open question over decades. Recently, such an approach towards a nitrogen-substituted mono-EMF with a closed-shell fullerene cage has been accomplished in La@C₈₁N which is derived from the pristine C_3v-C₈₂ cage.⁴² The closed-shell nature of the azafullerene cage is verified by EPR spectroscopy showing an EPR-silent behavior for La@C₈₁N.

Introducing Dy³⁺ to design a novel SMM, an azafullerene compound Dy@C₈₁N was reported by Coronado et al. very recently based upon C_s-C₈₂.¹⁶ In the structure of the mono-EMF Dy@C₈₁N, the Dy³⁺ ion is asymmetrically coordinated by one side to a hexagonal carbon ring on the cage, while lacking any nonmetal ligand or negative charge on the other side towards the center of the cage. This extraordinary low coordination results in a very weak ligand field causing a small overall splitting (∼230 cm⁻¹) of the ⁶H_15/2 ground multiplet for Dy³⁺, similar to that found for a single Dy atom attached on graphene with the Dy-C₆ ring coordination.¹⁷⁷Ab initio calculations not only confirm the weak ligand field, but also indicate a mixed ground state for Dy³⁺. This special feature of single-ion anisotropy, often associated with weak SMM properties,¹⁹² is in striking contrast to the situation in all high-performance Dy-SMMs, where a pure m_J = ±15/2 ground Kramers doublet and a strongly axial field are always required. Despite this, the DC magnetic characterization of Dy@C₈₁N shows slow magnetic relaxation (with τ > 40 s) up to 60 K (Fig. 8c). Analysis of the temperature dependence of the relaxation times reveals a temperature-independent QTM process below 17 K and a thermally activated Raman-like mechanism at high temperatures. The 100-s blocking temperature T_B,100s, extracted from the fitting of the τ(T⁻¹) curve, is determined as 45 K. This represents a record value among all known EMF-SMMs reported to date, being only behind the cyclopentadienyl (Cp)-based lanthanide complexes.^{11,12,23,193–195} The fast drop of τ due to an Orbach process normally detected for high-performance SMMs is not observed in Dy@C₈₁N even up to 60 K. The lack of the Orbach process was reported before in DySc₂N@C₈₀ as discussed above,⁶⁴ which suggests a weak spin-phonon coupling in this type of EMF-SIMs. Among them, Dy@C₈₁N is even cleaner in terms of relaxation through the phonon bath because it has a minimal number (three) of vibrational modes that can couple to the spin states.

Fig. 8 (a) Magnetic hysteresis loops for Dy@C₈₁N at 1.9–39 K using SQUID magnetometry with a field sweep rate of 3.5 mT s⁻¹. (b) Magnetic hysteresis for Dy@C₈₁N at 5 K recorded by using the XMCD technique. (c) Temperature-dependence of magnetization relaxation times for Dy@C₈₁N and the determination of its blocking temperature T_B,100s = 45 K. The inset shows its molecular structure. (d) Experimental and simulated EPR spectra of Dy@C₈₁N in a toluene solution at 10 K. The inset illustrates the hyperfine structures. Reproduced from ref. 16.

As shown in Fig. 8a, magnetic hysteresis of Dy@C₈₁N was recorded up to 39 K at a magnetic field sweep rate of 3.5 mT s⁻¹, and further persists until 60 K using a faster sweep rate of 100 Oe s⁻¹. Surprisingly, the hysteresis is thin even at the lowest measured temperature of 1.9 K, i.e., with weak coercive field and magnetization remanence. This very special hysteretic feature is further confirmed by element-specific XMCD measurement at the Dy M_4,5 edge (Fig. 8b). The direct process in the presence of a strong applied magnetic field is likely responsible for the usual reduction of magnetic hysteresis due to the strongly mixed ground doublet of Dy³⁺ in the low-coordination environment, whose Zeeman energy is sensitive to the distortion caused by coupling of long-range vibrations to the spin states. The mixing nature of the ground doublet in Dy@C₈₁N also leads to the observation of the EPR signal at 10 K using a conventional X-band spectrometer (Fig. 8d). A strong hyperfine coupling is evidenced for Dy@C₈₁N between the electron spin and the nuclear spin within Dy³⁺, in which the hyperfine constant A_z = 1600 MHz is determined for ¹⁶³Dy. This information extracted from the EPR spectrum, in contrast, is elusive for other Dy-based SMMs due to the fast spin–lattice relaxation arising from the strong spin–orbit coupling in Dy³⁺, which may be ascribed to the well-protected Dy³⁺ spin from the destabilizing interactions with phonons in Dy@C₈₁N at zero or finite magnetic fields where QTM dominates. Taking advantage of the hyperfine structures, it could be feasible to fine-tune magnetic relaxation upon applying magnetic fields, as already shown in SMMs based on Ho³⁺ and Tb³⁺.^196,197

4.2.2 Dimetallofullerenes (di-EMFs). Apart from the single-ion system, introducing another metal ion complicates the electronic and magnetic properties of the molecule. As can be inferred from the above discussions on clusterfullerenes behaving as dinuclear SMMs, the design strategy towards better SMM performance lies in enhancing the magnetic coupling between two Ln ions. Although some success has been achieved by utilizing strong bridging ligands to induce large ligand field splitting and favor superexchange interactions, the coupling is still not strong enough to preserve magnetic bistability up to practically high temperatures (for example, above the liquid nitrogen temperature of 77 K) against relaxation. This is majorly owing to the well-shielded 4f electrons that are not amenable to interacting with other magnetic metal ions.

The goal of strong magnetic coupling can be realized by introducing a N₂³⁻ radical bridge between two Ln³⁺ ions in an organometallic compound due to the rather diffuse unpaired electron from the N₂³⁻ bridge.¹⁹⁸ Such diffuse electron spin is able to strongly interact with the 4f electrons of Ln³⁺, thus giving rise to magnetic hysteresis up to 8.3 K at a sweep rate of 80 mT s⁻¹ when the high-anisotropy Dy³⁺ is incorporated. Better SMM properties are obtained in Tb³⁺–N₂³⁻–Tb³⁺ three-center systems, among which a T_B,100s value of 20 K is determined by employing Cp-based ligands together with the radical bridge.^199,200 An advantageous consequence of the strong magnetic coupling is a broad hysteresis with a large coercive field thanks to the effective quenching of QTM at zero field. This design strategy of radical-bridged dilanthanide compounds as high-performance SMMs has been extensively studied, featuring strong antiferromagnetic or ferromagnetic coupling between the radical and Ln³⁺.^201,202

Taking advantage of fullerene cages with confined nanospace, dimetallofullerenes (di-EMFs) are of particular interest for magnetic studies aiming at direct metal–metal interactions and thus strong magnetic coupling without any nonmetal ligand between the two metals. This ligand-unsupported metal–metal bond can be stabilized in M₂@C₈₂ (M = Sc, Y, Er, Lu), in which each metal adopts the divalent oxidation state, offering one electron to form a σ bond, and as a result the most popular tetravalent C₈₂ cages are favored.^203–205 For I_h(7)-C₈₀ with exceptional stability in a 6-charged state, on the other hand, di-EMFs were initially expected to contain a rare-earth metal with the high oxidation state (+3), as exemplified in La₂@C₈₀. However, the valence state of the metal atom in di-EMFs is in fact determined by its ns²(n − 1)d¹ to ns¹(n − 1)d² excitation energy that corresponds to the metal–metal bonding orbital.^17,203 The relation of this energy to the cage molecular orbitals (MOs) is then crucial to govern the electronic structure of a di-EMF. A peculiar triplet ground state is thus found in theory for M₂@C₈₀ (M = Sc, Y, Gd, Er, Lu) resulting from the half filling of the low-lying bonding MOs of the M₂ dimer to form a single-electron metal–metal bond (SEMB), while the cage possesses another unpaired electron.^206,207 Under this circumstance, M₂ transfers five electrons to the cage, leaving each metal with a formal charge of +2.5. This is akin to the situation of radical-bridged dilanthanide complexes as mentioned above, but with much structural simplicity in which the unpaired electron is shared solely by two metals, instead of being localized on the bridging ligand, affording an M³⁺–e–M³⁺ three-center system.

Preceding the in-depth understanding of the SEMB, such a bonding peculiarity was realized in a stable dimetallic azafullerene M₂@C₇₉N (M = Y, Tb) by Dorn et al., which is derived from the unstable M₂@C₈₀ by quenching its unpaired electron on the cage via nitrogen substitution.⁴¹ The singly-occupied metal–metal bonding molecular orbital (SOMO) is low-lying below the highest occupied MO (HOMO), thus leading to the stabilization of this open-shell molecule. Despite having a SEMB inside the cage, crystallographic study of Tb₂@C₇₉N shows a long Tb–Tb distance of 3.902 Å, even exceeding the sum of the covalent radius of two Tb atoms (3.88 Å), which is likely attributed to the strong Coulombic repulsion within the Tb₂⁵⁺ dimer. The open-shell nature is better understood in an S = 1/2 species, Y₂@C₇₉N, which enables the detection of single electron spin using EPR spectroscopy. The signal is split into three peaks with an intensity ratio of 1 : 2 : 1 arising from the hyperfine interaction of the single electron with the I = 1/2 ⁸⁹Y nuclear spin. A very large hyperfine coupling constant of 81 G (with the isotropic g factor of 1.9740 measured at room temperature) is observed for Y₂@C₇₉N. In comparison, the value is only 3.1 G in a radical-bridged diyttrium compound with a Y³⁺–N₂³⁻–Y³⁺ three-center system. This indicates the substantially stronger interaction between the unpaired electron and metals in di-EMFs containing SEMBs without any nonmetal bridging ligand, which can be evidenced by the sharing of the SOMO by the two metals in Y₂@C₇₉N whereas a SOMO mainly localized on the N₂ unit is found for the radical-bridged diyttrium compound.²⁰⁸

The same group later also synthesized Gd₂@C₇₉N, which was characterized by X- and W-band EPR spectroscopy to show a giant spin ground state of S = 15/2, as a result of strong ferromagnetic coupling between the S =1/2 unpaired electron and two Gd³⁺ ions with S = 7/2.⁴³Ab initio studies of the isoelectronic [Gd₂@C₈₀]⁻ anion suggest that this ferromagnetic coupling arises from Hund's rule, but not from the double exchange mechanism conventionally observed in dinuclear mixed-valence transition-metal compounds.²⁰⁹ The exceptional stability of these SEMB-containing open-shell di-EMFs comes from the low-lying metal–metal bonding orbital as discussed before. Even for La₂@C₈₀ with a relatively high-energy La₂ valence MO, SEMBs can still be stabilized by accepting one electron in such an MO upon reduction, radical addition and light-induced charge separation in an electron donor–acceptor conjugate.^210–213 This is because that the La₂ valence MO becomes the lowest unoccupied MO (LUMO) of the whole molecule. The existence of SEMBs in these cases can be then verified by EPR spectroscopy to show strong hyperfine splitting in the spectra due to the ¹³⁹La nucleus.

The possibility of utilizing SEMB-containing di-EMFs towards high-performance SMMs was explored theoretically by Rajaraman et al.²¹⁴ Broken-symmetry (BS) DFT studies of Gd₂@C₇₉N reveal a very strong ferromagnetic exchange between Gd and the unpaired electron with the coupling constant j_Gd–e (in the −2j_Gd–eS_GdS_e convention) in the order of 200 cm⁻¹. Ab initio calculations performed on the Dy₂@C₇₉N molecule suggest that the exceptionally strong Dy-e magnetic coupling not only quenches QTM but can also increase the effective barrier of magnetization reversal. Thus, Dy₂@C₇₉N is anticipated to be a high-performance SMM. This idea was later realized by Popov et al. in a benzyl monoadduct, instead of substituting one carbon atom by nitrogen on the cage, of Dy₂@C₈₀ to quench the unpaired cage radical so as to obtain air-stable Dy₂@C₈₀(CH₂Ph) containing a SEMB.¹⁸ In this molecule, the magnetic moments of two Dy³⁺ and the unpaired electron align collinearly to form a single spin unit of 21 μ_B. The spin Hamiltonian of this three-center system should be defined as follows derived from eqn (3) in absence of magnetic field

Ĥ_spin = Ĥ_LF1 + Ĥ_LF2 − 2j_Ln–e(Ĵ₁S_e + Ĵ₂S_e) − 2j₁₂Ĵ₁Ĵ₂ (5)

where the first two terms are the single-ion anisotropy of two Dy sites; the third term describes the magnetic coupling between single electrons and Dy considering an equal j_Dy–e for the two metals; and the last term denotes the coupling between two Dy magnetic moments. Notably, the last term can be safely neglected thanks to the overwhelmingly strong Dy-e magnetic coupling over Dy–Dy 4f–4f interaction. The giant Dy-e ferromagnetic coupling is confirmed by the fitting of magnetic susceptibility and magnetic magnetization curves, which jointly yield a large j_Dy–e of 32 cm⁻¹. This results in the exchange-excited state with the energy that essentially matches with the effective barrier U_eff of 613 K extracted from an Orbach relaxation process, in which the spin of one Dy center is flipped (Fig. 9g). Remarkably, QTM is efficiently quenched by the giant magnetic coupling interaction, and a broad hysteresis loop is thus observed at 2 K which closes gradually until 22 K with 2.9 mT s⁻¹ field sweep rate (Fig. 9d). A 100-s blocking temperature T_B,100s of 18 K is obtained for Dy₂@C₈₀(CH₂Ph) from the temperature dependence of relaxation time, while a bifurcation temperature T_B,ZFC of 21.9 K is determined (Fig. 9a). Very similar results were later found for Dy₂@C₇₉N, which shows a slightly larger U_eff of 669 K but a lower T_B,100s of 12 K (Table 2).²² The weaker SMM performance in Dy₂@C₇₉N is due to the faster zero-field QTM at low temperatures, which likely stems from the structural difference in these congeners. In this context, the functional group attached on the cage of Dy₂@C₈₀(CH₂Ph) shall lead to a larger intermolecular distance in a powder sample and thus suppresses the QTM effect.

Fig. 9 (a)–(c) ZFC/FC curves of Dy₂@C₈₀(CH₂Ph) (a), Tb₂@C₈₀(CH₂Ph) (b), and Tb₂@C₇₉N (c). The magnetic field was 0.2–0.3 T, and the temperature sweep rate was 5 K min⁻¹. (d)–(f) Magnetic hysteresis of Dy₂@C₈₀(CH₂Ph) (d), Tb₂@C₈₀(CH₂Ph) (e), and Tb₂@C₇₉N (f). The magnetic field sweep rate was 2.9 mT s⁻¹ in (d) and (f) and 9.5 mT s⁻¹ in (e). (g)–(i) Low-energy part of the spectra of Dy₂@C₈₀(CH₂Ph) (g), Tb₂@C₈₀(CH₂Ph) (h), and Tb₂@C₇₉N (i), using the effective spin Hamiltonian in eqn (5), with transition probabilities visualized as lines of different thickness (thicker lines correspond to higher probabilities), the x axis is the projection of magnetic moment upon the main anisotropy axis, μ_z. A schematic description of the spin alignment in the ground state and exchange-excited states is also shown (Dy and Tb, green arrows; single electron spin, dark blue and red arrows). Reproduced with permission from (a)–(f) ref. 17, (g) ref. 18, (h) ref. 19 and (i) ref. 21.

Table 2 An exhaustive list of conventional EMF-SMMs reported to date

Type	EMF	T B,100s [K]	T B,hys [K] (dH/dt) [mT s^−1]	T B,ZFC [K] (dT/dt) [K min^−1]	U eff [K]	j Ln–e [cm^−1]	Ref.
a Field-induced SMMs. b The value in the bracket indicates the field sweep rate (mT s^−1) used to record hysteresis loops. c The value in the bracket indicates the temperature sweep rate (K min^−1) used to record ZFC/FC curves.
Mono-EMF	Dy@Cs(6)-C81N	45	39 (3.5)/60 (10)	69 (1)	—	—	16
Di-EMFs	Dy2@C80(CH2Ph)	18	22 (2.9)	21.9 (5)	613	32	18
	Dy2@C79N	12	24 (20)	21 (3)	669	32	22
	Tb2@C79N	24	26 (2.9)	28 (5)	757	45	21
	Tb2@C80(CH2Ph)	25.2	27 (9.5)	28.9 (5)	799	55	19
	Tb2@C80(CF3)	25	26 (2.9)	28.5 (5)	801	—	20
	Tb2@C80(CH2Ph)(pyr2)	26.6	28 (2.9)	30.3 (5)	725	—	26
	Ho2@C80(CH2Ph)	—	—	—	334	40	19
	Er2@C80(CH2Ph)^a	—	—	—	—	20	19
	TbGd@C80(CH2Ph)	—	—	14.4 (5)	—	—	19
	TbY@C80(CH2Ph)	—	5 (2.9)	5 (5)	—	35	19
	Nd2@C80(CF3)^a	—	—	—	—	—	217
	Gd2@C79N^a	—	—	—	6.5	175/170	53 and 218
	DyEr@C3v(8)-C82	—	3 (33)	5 (3)	6.4	—	226

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Using the cage derivatization method of benzyl radical addition, a series of air-stable M₂@C₈₀(CH₂Ph) (M₂ = Y₂, Gd₂, Tb₂, Dy₂, Ho₂, Er₂, TbY, TbGd) compounds containing SEMBs have been synthesized.¹⁹ Among them, Tb₂@C₈₀(CH₂Ph) exhibits a gigantic coercive field of 8.2 T at 5 K extracted from its hysteresis loops, which can be recorded without closing up to 27 K at a field sweep rate of 9.5 mT s⁻¹ (Fig. 9e). Analysis of the temperature-dependence of magnetic relaxation time gives a high T_B,100s of 25.2 K and a large U_eff of 799 K (Fig. 9h). Meanwhile, T_B,ZFC of 28.9 K can be extracted from the ZFC/FC curves (Fig. 9b). All these SMM metrics are significantly superior to those of its Dy counterpart, and are similar to the situation of N₂³⁻-radical-bridged dilanthanide compounds in which Tb is also better than Dy.^198,200 In contrast to the worse Tb-SIMs often observed in organometallic compounds, the exceptional SMM behaviors for Tb₂@C₈₀(CH₂Ph) lie in the Kramers Tb³⁺–e–Tb³⁺ three-center system, instead of the single non-Kramers Tb³⁺ ion, in such a way that QTM within the degenerate ground doublet of a strongly coupled system is essentially forbidden. Examining the magnetic properties of di-EMFs containing other anisotropic Ln ions reveals much weaker SMMs for Ho₂ and Er₂ cases. The former shows slow magnetization relaxation below 1 s with non-colinear alignment of the three magnetic moments, while the latter only exhibits field-induced AC signals due to the easy-plane anisotropy of the Er spin. Weaker SMM performance is also observed for the mixed-metal TbGd and TbY compounds, where the blocking temperatures (T_B,ZFC) defined by ZFC/FC measurements are 14 K and 5 K, respectively. It is thus demonstrated that the coupling of the single Ln spin to the electron spin of the SEMB is not sufficiently strong, and the involvement of two anisotropic Ln ions is necessary to construct a remarkably high-performance SMM. When diamagnetic Y³⁺ and Sc³⁺ are introduced into M₂@C₈₀(CH₂Ph) with an M³⁺–e–M³⁺ three-center system, strong hyperfine splitting can be observed in the presence of ⁸⁹Y and ⁴⁵Sc nuclear spins, giving rise to fully-resolved EPR spectra with well-defined transitions between specific electron-nuclear quantum states.^215,216

The extraordinary SMM performance of Tb-based di-EMF was then further realized in Tb₂@C₇₉N using an azafullerene to obtain a closed-shell fullerene cage.²¹ Magnetic characterization of Tb₂@C₇₉N indicates similar results yet a slightly weaker SMM in comparison with Tb₂@C₈₀(CH₂Ph). Specifically, Tb₂@C₇₉N exhibits a slightly lower T_B,100s of 24 K and U_eff of 757 K (Fig. 9i). Its hysteresis, albeit broad, has a weaker coercive field of 3.8 T between 1.8 and 10 K, which then closes down up to 26 K at 2.9 mT s⁻¹ sweep rate (Fig. 9f). Similarly, a slightly lower bifurcation temperature T_B,ZFC of 28 K is determined (Fig. 9c). This difference in magnetic properties between di-EMFs with the carbon cage modified by N-substitution and by benzyl addition is consistent with the above discussion on the Dy counterparts. More importantly, ab initio calculations demonstrate that the magnetic moments of Tb ions in Tb₂@C₇₉N are tilted from the Tb–Tb bond by approximately 7°. This slight non-collinearity of the Tb quantization axes may be caused by the strong variation of the electrostatic potential distribution upon replacing one carbon atom by nitrogen, and could contribute to the change of magnetic behaviors. Apart from nitrogen substitution and exohedral benzyl addition on the cage, trifluoromethylation of di-EMF anions was then demonstrated to be a highly selective alternative route to this kind of structures featuring a ferromagnetically coupled M³⁺–e–M³⁺ three-center system.²⁰ Through this method, Tb₂@C₈₀(CF₃) can be readily synthesized as the main reaction product, which behaves as a strong SMM with a broad magnetic hysteresis, a high T_B,100s of 24 K and an effective barrier U_eff of 801 K. Very recently, this method has been applied to stabilize SEMBs within an early lanthanide dimer Nd₂ inside the I_h(7)-C₈₀ and D_5h(6)-C₈₀ cages, making Nd₂@C₈₀(CF₃) based on the I_h(7) isomer a field-induced SMM showing slow relaxation below 3 K.²¹⁷

The magnetic coupling situation in di-EMFs containing SEMBs can be better understood in a Gd³⁺–e–Gd³⁺ system incorporating two nearly isotropic Gd³⁺ ions without spin–orbit coupling. Fitting the magnetic susceptibility and magnetization curves of Gd₂@C₇₉N clearly reveals a giant ferromagnetic Gd–e coupling with a coupling constant of 160–180 cm⁻¹.^53,218 Note that this value is comparable to the result predicted by BS-DFT calculations (∼200 cm⁻¹)²¹⁴ and greatly surpasses the antiferromagnetic coupling constant (−27 cm⁻¹) obtained in the N₂³⁻-radical-bridged digadolinium compound.¹⁹⁸ Such a strong magnetic coupling enables a giant total spin of S = 15/2 for the whole molecule. This high-spin ground state is well separated from the excited states and can be retained even at room temperature. Surprisingly, low temperature AC measurements also disclose that Gd₂@C₇₉N is a field-induced SMM showing slow relaxation of magnetization with the τ values at the millisecond scale at low temperatures below 3 K.²¹⁸

The isotropic nature of the half-filled Gd³⁺ ion precludes the possibility to design a high-performance SMM based on it. This isotropy in the free Gd³⁺ ion is lifted in a coordination compound in the presence of ligand fields, which is ascribed to the mixing of the excited state with the ground multiplet ⁸S_7/2. Note that the splitting of the ground multiplet in this case is very small (in the order of 1 cm⁻¹) compared to that for other anisotropic Ln-based compounds in the same coordination environment (normally 100–1000 cm⁻¹), but matches with the energy scale of conventional X-band EPR (∼0.3 cm⁻¹), which can then be used as a powerful tool to probe the spin states of compounds having Gd³⁺. Despite the fragile magnetic bistability in a slightly anisotropic Gd-SMM, superposition between their two spin states could be created utilizing the pulsed EPR technique, giving rise to a spin qubit candidate showing a quantum coherence effect that could pave a way for quantum information processing.^219–222 Indeed, Gd₂@C₇₉N was found to be an excellent high-spin qubit with microsecond-scale long coherence time at 5 K.⁵³ A more intriguing feature of this molecule lies in its well-defined 16-fold spin sublevels derived from an S = 15/2 high-spin ground state. This allows coherent manipulation of the arbitrary superposition state between each adjacent level pair in a periodic manner, resulting in diverse Rabi oscillations performed at different applied magnetic fields. Gd₂@C₇₉N thus represents the largest-spin molecule that possesses Rabi oscillations reported so far. Aiming at a step forward using SMMs in quantum information technologies, the non-equidistant energy levels and long coherence times in the high-spin Gd₂@C₇₉N fulfill the requirements of Grover's searching algorithm exploiting multi-levels of the anisotropic SMMs,²²³ which has been realized on the nuclear spin of a Tb-SMM.²²⁴

The appealing magnetic properties in these SEMB-containing di-EMFs further stimulated the synthesis of strongly coupled dilanthanide organometallic compounds (Cp^iPr5)₂Ln₂I₃ (Ln = Dy, Tb, Gd) directed at high-performance SMMs.²³ By employing two Cp-based ligands as a source of strong axial ligand fields and three I⁻ anions as bridging ligands, very strong SEMBs are constructed, giving rise to a ferromagnetically coupled high-spin ground state. These features jointly result in an enormous coercive field with a lower bound of 14 T in (Cp^iPr5)₂Dy₂I₃ at 60 K, which surpasses even commercial magnets. Analysis of its relaxation times show a record-high T_B,100s of 72 K, while this value is 65 K for the Tb congener. As a result of strong coupling, their effective barriers U_eff are determined to be as high as 2347 K and 1990 K, respectively. The better SMM performance, compared to that of di-EMFs with the same Ln³⁺–e–Ln³⁺ three-center system (Ln = Tb, Dy) derived from the pristine Ln₂@C₈₀, originates in the stronger magnetic coupling in (Cp^iPr5)₂Ln₂I₃. Fitting the variable-temperature magnetic susceptibility curve of the Gd case using the three-center model gives a giant Gd–e coupling constant of j_Gd–e = 389 cm⁻¹, more than twice the value of 175 cm⁻¹ determined for Gd₂@C₇₉N.⁵³ This strong SEMB can also be evidenced from the short Ln–Ln distances in (Cp^iPr5)₂Ln₂I₃ that are within the sum of covalent radii for each metal atom. In contrast, substantially longer Ln–Ln distances are found for di-EMFs in the presence of strong Coulombic repulsion and metal–cage interactions that tend to separate the two Ln ions.

Extracted from the above comparative analysis, enhancing magnetic coupling in SEMB-containing di-EMFs is key to further improve their SMM properties. Since the previously discussed species are all based on I_h(7)-C₈₀, it seems inevitable to alter the cage structure to achieve this goal. In this context, finding a much smaller cage is a logical next step to enforce close contact of the two encapsulated metals and overcome Coulombic repulsion by the confinement effect. This idea was confirmed theoretically in an actinide di-EMF that direct overlap of 5f orbitals may be realized to form U≡U triple bonds in U₂@C₆₀,²²⁷ while the short U–U distance is not observed in U₂@C₈₀ due to the strong metal–cage interactions.²²⁸ Similar to Ln₂@C₇₉N (Ln = Tb, Dy, Gd) that are of particular interest to molecular magnetism, Ln₂@C₅₉N has been computed to show strong SEMBs.²²⁹Ab initio calculations yield a large Gd–e coupling constant of j_Gd–e = 434.8 cm⁻¹ that is two times larger than the value determined for Gd₂@C₇₉N. Very high effective barriers U_eff are also predicted with values of 1702 and 2160 K for Dy and Tb cases, respectively, comparable to the current record determined in (Cp^iPr5)₂Gd₂I₃.²³

Although these theoretical studies point out a promising future direction, synthesizing di-EMFs with such a small cage based on C₆₀ is not feasible at the current stage of research. By slightly varying the cage size from C₈₀, it has been shown that a SEMB may also be formed in Er₂@C_3v(8)-C₈₂ by electrochemically manipulating the Er–Er bonding orbital.¹⁵¹ Similarly, two isomers of DyEr@C₈₂ with C_3v(8) and C_s(6) cage symmetries were reported, exhibiting cage-dependent magnetic and photoluminescent properties.²²⁶ Magnetic characterization studies indicate that DyEr@C_3v(8)-C₈₂ is an SMM with a thin hysteresis which closes below 3 K at a sweep rate of 33 mT s⁻¹, while DyEr@C_s(6)-C₈₂ is a paramagnet. Theoretical studies suggest the likely presence of SEMBs in these cases and consequently open-shell cage structures.

Very recently, Yang et al. have made a step forward towards the stabilization of SEMBs inside various pristine cages without the need for nitrogen substitution or chemical derivatization.²²⁵ This is accomplished by introducing a transition metal Ti in conjunction with La to form a heterometallic LaTi dimer inside the D_3h(5)-C₇₈, I_h(7)-C₈₀, D_5h(6)-C₈₀ and C_2v(9)-C₈₂ carbon cages, each of which has a formal 6-charged state. After transferring six electrons to the cage, there is one unpaired electron left within the LaTi dimer, creating a SEMB. The La–Ti distances can be largely varied from 4.31 to 3.97 Å upon increasing the cage size from C₇₈ to C₈₂ (Fig. 10a). This uncommon anticorrelation between the cage size and the La–Ti distance suggests that the metal–cage interaction is instead the dominating effect in determining the strength of a SEMB inside medium-size fullerene cages. As shown in Fig. 10b, DFT calculations confirm the existence of SEMBs in each case featuring a metal–metal bonding SOMO, despite the long La–Ti separation due to the much smaller Ti atom, and its increased strength is verified by the gradual shift in the accumulation of electron density towards the center of the LaTi dimer. Interestingly, EPR spectroscopy shows a consecutive enhancement of hyperfine coupling between the unpaired electron and La following the decrease of La–Ti distance (Fig. 10c and d). The strongest coupling is thus found in LaTi@C_2v(9)-C₈₂. By changing metal–metal interactions and magnetic coupling, therefore, this proof-of-concept study offers a possibility to design SMMs, based on other anisotropic lanthanide metals such as Dy and Tb, which show improved performance in comparison with di-EMFs employing a modified I_h(7)-C₈₀ cage.

Fig. 10 (a) Molecular structures of LaTi@D_3h(5)-C₇₈, LaTi@I_h(7)-C₈₀, LaTi@D_5h(6)-C₈₀, and LaTi@C_2v(9)-C₈₂ (from left to right). La: cyan, Ti: violet. Their La-Ti distances are indicated. (b) SOMOs of LaTi@D_3h(5)-C₇₈, LaTi@I_h(7)-C₈₀, LaTi@D_5h(6)-C₈₀, and LaTi@C_2v(9)-C₈₂ (from left to right). (c) Experimental and simulated EPR spectra of LaTi@C_2n (2n = 78, 80 (two isomers), 82) measured in toluene solutions at 243 K. (d) Average hyperfine coupling constant (A_av in MHz) and La-Ti Mayer bond order of LaTi@C_2n (2n = 78, 80 (two isomers), 82) as a function of the La-Ti distance. Reproduced with permission from ref. 225 (Copy right 2023, American Chemical Society).

5. Assemblies of EMF-SMMs

The practical use of SMMs in information storage requires a well-defined molecular array that allows single molecules of interest to be precisely addressed. To this end, SMMs are required at first to be processed into a molecular assembly, such as a 2D monolayer on a substrate, in which sublimation is needed. This means that SMMs should be both chemically and thermally stable. In fact, these features constitute the major advantage of using EMFs as SMMs thanks to their highly robust fullerene structures. In this section, we move from the magnetic properties obtained from molecular ensembles in powder EMF samples towards the feasibility and prospect of their assembled molecular arrangements into different dimensions.

5.1 1D SMM assemblies inside single walled carbon nanotubes (SWCNTs)

With cylindrical empty space, single walled carbon nanotubes (SWCNTs) with a typical diameter range of 1–2 nm are intuitively considered as a suitable container for atoms or molecules to construct a 1D assembly. Spherical EMF molecules, such as Gd@C₈₂ and La₂@C₈₀, usually possess diameters less than 1 nm and can be readily encapsulated into SWCNTs to form a peapod-like hybrid structure, thus enabling single atom imaging of lanthanides that may be transformed into lanthanide atomic wires upon heating.^230–232 Regarding SMMs, nevertheless, very few examples have been demonstrated combining them and SWCNTs, one of which is achieved through attaching bis-phthalocyaninato terbium (TbPc₂) onto the surfaces of SWCNTs, generating supramolecular spin valves with giant magnetoresistance.²³³ On the other hand, encapsulation of SMMs into SWCNTs is expected to give rise to a quasi 1D arrangement in which their SMM properties should be enhanced.²³⁴ A non-1D manifestation is using multi-walled carbon nanotubes (MWCNTs) with large diameters of ∼6.5 nm to accommodate [Mn₁₂O₁₂(O₂CCH₃)₁₆(H₂O)₄] (Mn₁₂Ac, with a diameter of 1.6 nm), whose SMM behaviors are significantly altered inside MWCNTs compared to its bulk properties.²³⁵

The first example to encapsulate EMF-SMMs into SWCNTs was reported by Yamashita et al. focusing on a well-studied NCF-SMM DySc₂N@C₈₀via a sublimation method.²³⁶ Transmission electron microscopy clearly showcases peapod structures wherein the EMF molecules line up in a quasi 1D chain as depicted in Fig. 11a and b. Magnetic characterization of this peapod structure [DySc₂N@C₈₀]@SWCNT by using SQUID magnetometers confirms that its characteristic SMM properties are retained inside SWCNTs with stepwise hysteresis at 1.8 K (Fig. 11c). Remarkably, the coercive field is greatly increased from 0.5 Oe in the bulk measurement to 0.4 T in the peapod structures, and correspondingly a slow relaxation of magnetization is observed in the absence of an external magnetic field with τ of 5650 s determined at 2 K, which is longer than that of DySc₂N@C₈₀ measured as a powder sample.¹⁵ Suppression of QTM by diluting the EMF upon encapsulation into SWCNTs is likely accountable for these improvements in the SMM performance, demonstrating that SWCNTs are able to protect SMMs from the environment in this 1D hybrid system.

Fig. 11 (a) and (b) TEM images and structural model of [DySc₂N@C₈₀]@SWCNT. (c) Magnetic hysteresis loops for DySc₂N@C₈₀ (open circles) and [DySc₂N@C₈₀]@SWCNT (filled circles) at 1.8 K. Arrows indicate the direction of the measurements. Reproduced with permission from ref. 236 (Copy right 2018, American Chemical Society).

At the same time, another NCF bearing two Dy³⁺ ions, Dy₂ScN@C₈₀, was also successfully packed inside SWCNTs.²³⁷ Element-specific XMCD was performed for this hybrid material at the Dy M₅-edge. The results show a deviation in its X-ray absorption spectra from that of an isotropic bulk sample, indicating a preferential orientation of the encapsulated Dy2ScN cluster that partially aligns the magnetization easy axis of the SMM in a 1D chain. This partial ordering of the clusters is also verified by ab initio calculations considering the diamagnetic counterpart Y₂ScN@C₈₀ inside the SWCNTs. Surprisingly and in striking contrast to the situation in mononuclear DySc₂N@C₈₀ packed peapod structures as described above, the broad hysteresis of the bulk Dy₂ScN@C₈₀ sample is not preserved when being filled inside the SWCNTs. Instead, magnetization curves for the Dy₂ScN@C₈₀/SWCNTs hybrid recorded at ∼2 K reveal a reduced magnetic bistability and vanishing hysteretic behavior. Various possible reasons, such as a higher local temperature in XMCD measurements, interaction with conducting electrons in metallic SWCNTs, and dipole–dipole interactions with residue metallic catalyst nanoparticles, were proposed to explain the observed reduction of SMM properties, yet no conclusive rationale has been reached.

5.2 2D SMM assemblies on surfaces

Attaching SMMs onto conducting surfaces to form 2D molecular assemblies is a crucial step forward in the field, in which the inherent magnetic properties of the SMMs should be maintained or precisely controlled.^238–240 Among the plethora of examples of SMMs prepared so far, only a handful of candidates have been studied in surface science, such as Mn₁₂Ac, TbPc₂, and Fe₄, where the XMCD technique is greatly needed.^241–246 Various reasons can be ascribed to the lack of research in this area, majorly including the chemical instability that is often associated with the SMMs which precludes their processability onto surfaces under ultrahigh vacuum conditions at room temperature by sublimation and facilitates the loss of their magnetic bistability due to the detrimental interaction with the surfaces.² EMFs can thus be a suitable candidate in this context.

A submonolayer of a magnetic EMF Gd₃N@C₈₀ was prepared by depositing molecules onto metallic surfaces by thermal evaporation at room temperature.²⁴⁷ Field-, temperature- and angle-dependent XMCD measurements of Gd₃N@C₈₀ on Cu(001) reveal that the magnetic moments of the individual 4f⁷ Gd³⁺ ion couple ferromagnetically to each other. On the other hand, changing the surface to ferromagnetic Ni(001) induces a spin polarization of the Gd³⁺ magnetic moments, enabling the detection of two different Gd species that couple ferromagnetically and antiferromagnetically to the Ni substrate. An indirect exchange mechanism mediated by the fullerene cage is accountable for the magnetic coupling to the substrate, and the different orientations of the cage are likely responsible for the observation of different coupling interactions within the same submonolayer.

The first EMF-SMM for surface science studies was reported by Greber et al. via depositing Dy₂ScN@C₈₀ onto a Rh(111) substrate using the same sublimation method under vacuum.²⁵⁰ A submonolayer is generated in this way, in which the Dy³⁺ magnetic moments are aligned because of the interaction between the SMM and the metallic substrate. The angular anisotropy of X-ray absorption spectra and multiplet calculations indicate that the Dy₂ScN cluster is orientated parallel to the surface. Remarkably, magnetic hysteresis is observed in this submonolayer at ∼ 4 K. The relaxation time is estimated to be about 30 s at zero field, much faster than that measured for powder samples. Despite this reduced magnetic bistability after deposition, which should be partly due to the demagnetization effect caused by X-ray irradiation as mentioned before,⁸⁰ the surface-aligned magnetic ordering and the SMM behaviors in this EMF/Rh submonolayer are observed at one order of magnitude higher sample temperature than that for the transition-metal cluster SMMs.^242–244

This result demonstrates the merit of using EMF-SMMs in surface science and thus has sparked further studies. For instance, employing the same preparation method, the same EMF-SMM Dy₂ScN@C₈₀ was evaporated onto a different surface, h-BN/Rh(111) nanomesh, to form 1.3 monolayers.²⁵¹ Similarly, partial orientations of the encapsulated units and of the magnetic moments are determined by angle-dependent XMCD measurements. It is demonstrated that the monolayers exhibit a larger hysteresis with a coercive field of 0.4 T at 2 K in comparison with the result of Dy₂ScN@C₈₀ on a pure Rh(111) surface. The magnetic behaviors of Dy₂ScN@C₈₀ monolayers on different substrates were then studied, where not only metals like Au(111) and Ag(100) but also insulators such as MgO|Ag(100) were chosen for SMM deposition.²⁴⁸ A strong influence of the surface on the structural ordering of Dy₂ScN@C₈₀ monolayers is revealed. Despite this, their SMM properties are very similar in XMCD studies, all exhibiting broad magnetic hysteresis, with a coercive field of ca. 0.4 T at 2 K (Fig. 12e), that is independent of the substrate. DFT calculations indicate that the charge state of the encapsulated cluster remains intact, which is due to the protection of its electronic and magnetic properties provided by the fullerene, acting as a Faraday cage, against interactions with conducting substrates.

Fig. 12 (a)–(d) Illustrations of Dy₂ScN@C₈₀ (a), functionalized DySc₂N@C₈₀ with a surface-anchoring thioacetate group (b), Dy₂@C₈₀(CH₂Ph) (c), and pyrene-functionalized Tb₂@C₈₀(CH₂Ph). (e)–(h) Magnetic hysteretic behaviors of submonolayers for Dy₂ScN@C₈₀ on Au(111) (e), functionalized DySc₂N@C₈₀ on Au(111) (f), Dy₂@C₈₀(CH₂Ph) on graphene/Ir(111) (g), and pyrene-functionalized Tb₂@C₈₀(CH₂Ph) on HOPG (h). Reproduced with permission from (e) ref. 248, (f) ref. 249, (g) ref. 24 and (h) ref. 26.

Apart from evaporating the pristine EMFs to construct a 2D molecular assembly on surfaces, the chemical possibility to achieve the same goal, using functionalized Dy₂ScN@C₈₀ and DySc₂N@C₈₀ SMMs, was explored by Popov et al.²⁴⁹ This is realized by 1,3-dipolar cycloaddition with surface-anchoring thioether groups (–S–CH₃). Compared to the pristine EMFs, the two functionalized molecules display different magnetic behaviors. In the case of DySc₂N@C₈₀, functionalization increases the bifurcation temperature T_B,ZFC by 1 K, while the shape of hysteresis remains largely unchanged. For Dy₂ScN@C₈₀, the value of T_B,ZFC becomes 4 K smaller and the hysteresis is noticeably thinner after functionalization. The thioether groups make it feasible to link these two functionalized EMF-SMMs to an Au(111) surface by simple physisorption, so as to generate low-coverage self-assembled monolayers (SAMs). XMCD measurements evidence that the magnetic bistability of these EMF-SMMs is retained in SAMs, featuring magnetic hysteresis at 2 K for each case. However, close contact of the fullerene cage with the metallic surface is favored in the preferential horizontal configurations, which is a result of the strong interaction of the fullerene and the linker with the substrate. This feature is expected to facilitate magnetic relaxation in SAMs. Furthermore, calculations indicate a random orientation of the Dy³⁺ magnetic moments at room temperature because of the highly mobile nature of these structures, whereas an orientation parallel to the surface is expected at low temperatures. A similar observation was also found recently for DySc₂N@C₈₀ adsorbed on a Pt(111) surface, which is directly inferred from the X-ray absorption spectra with in-plane polarization and indicates a weak but non-negligible interaction between the encapsulated cluster and the metallic surface.²⁵²

Changing the thioether linker –S–CH₃ to a thioacetate group –S–Ac as the surface-anchoring group (Fig. 12b), cycloadducts of Dy₂ScN@C₈₀ and DySc₂N@C₈₀ SMMs can be grafted on gold via chemisorption, rather than a pure physisorption process, to form self-assembled films with submonolayer coverage.²⁵³ This is realized by dissolving functionalized EMFs in o-dichlorobenzene (o-DCB)/ethanol (10 : 1) upon adding H₂SO₄. The obtained SAMs from solution demonstrate that in both cases the magnetic bistability of bulk samples is maintained and the magnetic moments of the Dy ions are preferentially aligned parallel to the surface. Comparative magnetic studies were performed by XMCD measurements of the grafted SMMs using this facile solution-based procedure and of the pristine EMFs on the substrate prepared by sublimation. It is shown that while this chemical functionalization tends to reduce the SMM properties of Dy₂ScN@C₈₀, magnetic bistability in the on-surface DySc₂N@C₈₀, as can be seen in Fig. 12f, is significantly enhanced with observable magnetic hysteresis up to 10 K. The shielding effect of the carbon cage on the encapsulated magnetic centers also enables robust SMM behaviors that are not hinged upon the metallic substrate.

Moving from the NCFs to SEMB-containing di-EMFs with better SMM performance, the possibility of generating a 2D molecular assembly based on Dy₂@C₈₀(CH₂Ph) was first explored.²⁴ It should be noted that in contrast to the non-derivatized EMFs with the pristine fullerene cages, lower thermal stability of Dy₂@C₈₀(CH₂Ph) precludes its direct deposition on a surface by sublimation. Meanwhile, this functionalized EMF also lacks a surface-anchoring group that is necessary for the formation of self-assembled submonolayers. To this end, a gentle deposition method of electrospray technique was used in the preparation of Dy₂@C₈₀(CH₂Ph) on graphene/Ir(111) as a suitable substrate. Remarkably, the as-formed submonolayer exhibits SMM behaviors that are fully comparable to those observed for the bulk sample. A broad magnetic hysteresis can be recorded by XMCD measurements at 2 K, which persists until around 20 K (Fig. 12g). Moreover, time-dependent XMCD relaxation measurements allow disentanglement of the contribution of the X-ray photon flux to the demagnetization effect. The analysis of its temperature-dependent relaxation times thus gives rise to a high 100-s blocking temperature T_B of 17 K in this surface-supported SMM. In this 2D assembly, scanning tunneling microscopy was applied to directly image the unoccupied single-electron Dy–Dy bonding orbital (LUMO) with the aid of ab initio calculations.²⁵⁴ This result is further validated by changing the encapsulated metal from Dy to Er, which leads to the observation of an energy shift of the metal-based LUMO with respect to the neighboring cage-based orbitals. The energetically and spatially resolved SEMB orbital thus offers a direct access to this exchange-coupled magnetic system in transport experiments.

The bulk studies of di-EMFs indicate the better SMM performance of the Tb³⁺–e–Tb³⁺ three-center system, with Tb₂@C₈₀(CH₂Ph) as an example, than that of its Dy counterpart. In order to obtain its self-assembled monolayers, further exohedral functionalization is necessary. This was done by introducing pyrene groups which show high affinity to graphitic substrates.²⁶ Interestingly, pyrene-functionalized Tb₂@C₈₀(CH₂Ph)(pyr₂) (Fig. 12d) features similar but slightly better SMM performance than Tb₂@C₈₀(CH₂Ph). Higher T_B,100s of 26.6 K and T_B,ZFC of 30.3 K are obtained after functionalization compared to those of Tb₂@C₈₀(CH₂Ph) (T_B,100s = 25.2 K and T_B,ZFC = 28.9 K) determined using the same experimental conditions. Tb₂@C₈₀(CH₂Ph)(pyr₂) SAMs can then be simply constructed by the solution-based preparation procedure on graphitic substrates (graphene and highly oriented pyrolytic graphite HOPG) in an ambient environment. The magnetic bistability of this EMF-SMM is preserved on substrates, showing a broad magnetic hysteresis that closes down up to a very high temperature of 28 K (Fig. 12h), which is a major step forward in the field of on-surface SMMs.

In the case of Tb₂@C₇₉N with a similar three-center system but without the derivatized “branch” outside the cage, the growth of thin films by sublimation under ultra-high vacuum conditions becomes feasible thanks to its sufficient thermal stability. Thus, monolayers of Tb₂@C₇₉N were prepared on Cu(111) and Au(111) substrates.²⁵ While the bulk sample of Tb₂@C₇₉N is a high-blocking temperature (T_B,100s = 24 K) SMM featuring a strongly ferromagnetic coupling between two Tb magnetic moments and the unpaired electron spin, a distinct antiferromagnetically coupled ground state is identified for its monolayers in XMCD studied at the Tb-M_4,5 edge. This results in a non-magnetic state in which magnetization is completely lost, and can be assigned to anionic Tb₂@C₇₉N⁻ species with a doubly-occupied Tb–Tb bonding orbital, likely due to charge transfer from the substrate or trapping of secondary electrons. Since the antiferromagnetic coupling in this non-magnetic state is not strong enough, a metamagnetic transition can be found in the field of 2.5–4 T, where the ferromagnetically coupled state dominates. By depositing Tb₂@C₇₉N on other substrates, such as h-BN|Rh(111) and MgO|Ag(100), the coexistence of neutral and anionic species can be observed, leading to a narrow magnetic hysteresis that persists up to 25 K.

5.3 3D SMM assemblies within metal–organic frameworks (MOFs)

A more complex network of SMMs is a 3D molecular assembly, for which porous metal–organic frameworks can be naturally considered as a suitable host.^255,256 Regarding EMFs, paramagnetic Y₂@C₇₉N was first introduced by Wang et al. inside the pores of a MOF crystal (MOF-177) to show axisymmetric paramagnetic properties.²⁵⁷ These different magnetic properties in the host–guest complex, in comparison with the isotropic system observed for Y₂@C₇₉N both in solution and in powder, suggest that the electron spin can be steered inside the pores of the MOF. The same group later reported that by combining the same MOF-177 and a different paramagnetic EMF Sc₃C₂@C₈₀, the latter is able to act as a spin probe to sensitively detect the pore environment of the MOF.²⁵⁸ On the other hand, gas adsorption can be detected when a pyrene-based covalent organic framework (Py-COF) is introduced as the host.²⁵⁹

By embedding DySc₂N@C₈₀ SMM into the pores of MOF-177, it is demonstrated that the QTM effect at zero field can be effectively suppressed upon encapsulation.²⁶⁰ A similar observation was also found for the same EMF incorporated into a different MOF structure, which is due to the dilution effect that weakens intermolecular interactions.⁶⁴ By incarcerating DySc₂N@C₈₀ into a photo-switchable azobenzene functionalized MOF (^AzoMOF), magnetic hysteresis opens up at zero field at 2 K by suppressing the QTM effect.²⁶¹ More importantly, the hysteresis becomes broader after ultraviolet (365 nm) irradiation. The isomerization of azobenzene groups is expected to change the host–guest interaction between the EMF molecule and the MOF structure, and should be responsible for the enhanced SMM properties.

6. Conclusions and outlook

Since the discovery of DySc₂N@C₈₀ as the first EMF-SMM in 2012, EMFs have constituted an important branch of lanthanide-based SMMs during the last decade as elaborately summarized in this article. For the SMMs that are hinged upon only one magnetic lanthanide ion (SIMs), single-ion anisotropy plays a pivotal role. This factor can be precisely manipulated by engineering the structures of the encapsulated cluster and of the host fullerene cage in various types of clusterfullerene, in which the confinement effect imposed by the carbon cage facilitates strong axial anisotropy towards the nonmetal ligand with a short metal–nonmetal distance. Removing this nonmetal ligand and changing the electronic structure of the fullerene give rise to a low-coordination mono-EMF with a closed-shell cage, where vibrational degrees of freedom are minimized, thus reducing another equally important factor of spin–vibration coupling that is detrimental to magnetic bistability. In these EMF-SIMs, how to effectively suppress QTM in non-diluted bulk samples? To address this critical issue, judicious design of the cluster and cage structures is necessary. Heterometallic oxide clusterfullerenes with the largest possible effective barrier may be a target because their extremely axial ligand field may be able to quench QTM within the highly pure ground doublet m_J = ±15/2 for the encapsulated Dy³⁺ ion. Fine control of the local symmetry of the coordination environment is another possible solution, which nevertheless remains largely unexplored in EMFs. The design strategy for the special case of mono-EMFs with closed-shell fullerene cages, on the other hand, is more straightforward since the cage structure is the only variable factor given the same encapsulated Ln. Here, a fullerene cage with a more rigid metal–cage binding interaction is expected to reduce spin–vibration coupling so as to slow down the magnetic relaxation. To this end, mono-EMFs with non-IPR cages are of particular relevance.

For the SMMs consisting of two magnetic lanthanide ions, magnetic coupling between them becomes a decisive factor governing their magnetic properties by blocking quantum tunneling of magnetization. This factor can be applied in clusterfullerenes by designing different bridging ligands that are able to transfer superexchange interactions as well as by altering the cage structures which in turn fine-tune the cluster geometry. Alternatively, such a goal can be realized in di-EMFs by engineering the electronic structure of the cage to generate single-electron metal–metal bonds (SEMBs), in which the unpaired electron directly couples to the two metals in the absence of any nonmetal bridging ligand. In these dinuclear EMFs, how to enhance magnetic coupling is the key to realize better SMMs. Whether it is feasible to generate an efficient direct Heisenberg exchange, rather than superexchange interaction, in a Ln–Ln bonding system becomes an intriguing aspect. On the other hand, although single-electron Ln–Ln bonds are an eye-catching case, the problem lies in the fact that the Ln–Ln distance is not short enough to induce strong magnetic coupling comparable to that of the best-performing SMM. Changing the host cage to compress the Ln₂ dimer appears to be a promising direction despite its synthetic challenge given that available cage structures are very limited so far.

Another more general consideration is focused on the lanthanide metals. Since now the magnetic bistability of all reported EMF-SMMs comes from Dy³⁺ and Tb³⁺ only, the possibility of exploiting other Ln metals, especially early lanthanides, is of great interest to researchers. These candidates are in fact being widely used in permanent magnets, such as Nd₂Fe₁₄B and SmCo₅. The similarity of single-ion anisotropy between early and late lanthanide ions that differ by seven f electrons may provide a general guidance herein. Beyond single molecular behaviors in bulk, several EMF-SMMs have been further processed into molecular assemblies via sublimation or self-assembly thanks to their rich structural diversity, exceptional magnetic properties and high chemical and thermal robustness. Their intrinsic SMM properties can be largely maintained in these organized structures, showcasing their great potential in information storage where single-molecule addressing is needed. With these exciting advancements, a next step forward would be to construct molecular spintronic devices based on SMMs towards their practical use as magnetic memory units to store information, yet very little is known about the role SMMs can play in this context. To fulfill future advancement directed at high-temperature, processable EMF-SMMs and beyond, there are many open questions remaining to be addressed. These endeavors, from the point of view of synthetic chemistry, shall be undertaken with an emphasis on the new structures, new related physical phenomena as well as the understanding of their interplay at an atomic level.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (51925206, U1932214, and 52302052), the Anhui Provincial Natural Science Foundation (2308085MB33), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB0450301), the Fundamental Research Funds for the Central Universities (20720220009), and the National Synchrotron Radiation Laboratory (KY2060000240)

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