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

Abstract

Three isomers of Dy₂O@C₈₈ and two isomers of Dy₂C₂@C₈₈ were synthesized and structurally characterized by single-crystal X-ray diffraction, vibrational spectroscopy, and DFT calculations. Both types of clusterfullerenes feature 4-fold electron transfer to the carbon cage, thus resulting in the same carbon cage isomers identified as C₁(26), C_s(32), and D₂(35). The studies of Dy⋯Dy superexchange interactions in Dy₂O and Dy₂C₂ clusters revealed that the O²⁻ bridge favors antiferromagnetic coupling whereas the acetylide group C₂²⁻ supports ferromagnetic coupling of Dy magnetic moments. The strength of the coupling showed a considerable variability in different cage isomers. All metallofullerenes exhibited slow relaxation of magnetization and magnetic hysteresis. In Dy₂O@C₈₈ isomers the hysteresis remained open up to 7–9 K, while in Dy₂C₂@C₈₈ the hysteresis loops were closed already at 2.5 K. This study demonstrated that both the endohedral bridge between metal atoms and the fullerene cage play an important role in magnetic interactions and relaxation of magnetization.

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Introduction

Endohedral metallofullerenes (EMFs) feature fascinating structural diversity, defined by a broad variability of endohedral species with 1–4 metal ions, which are encapsulated in carbon cages of various shape and size ranging from C₆₆ to C₁₀₈ and beyond.^1–5 In clusterfullerenes, endohedral species also include some non-metal atoms, which acquire a negative charge and serve as bridges between metals.^6,7 The non-metal then defines the names of clusterfullerenes, such as endohedral oxygen in oxide clusterfullerenes^8,9 or endohedral carbon in carbide clusterfullerenes.^10,11

The exploration of oxide clusterfullerenes started with a discovery of Sc₄O_2,3@C₈₀ by Stevenson et al.^12,13 and then continued with a series of Sc₂O@C_2n EMFs with cage sizes from C₇₀ to C₈₂.^14–20 More recently, the focus was shifted to lanthanides, resulting in several M₂O@C_2n EMFs with Ho (C_2n = C₇₄,²¹ C₈₄,²² 4 isomers of C₉₀,²³ and 2 isomers of C₉₂ ²⁴), Dy (C_2n = C₇₂,²⁵ C₇₄,²⁵ C₈₀,²⁶ three isomers of C₈₂ ²⁷), and two isomers of Lu₂O@C₈₀.²⁸ In M₂O@C_2n clusterfullerenes, two rare-earth metal ions (M³⁺) are bridged by the μ₂-O²⁻ ion; the whole M₂O cluster has a formal charge of +4 and is encapsulated in fullerene cages preferring the C_2n⁴⁻ state.

A special interest in Dy-EMFs is motivated by their magnetic properties.²⁹ In lanthanide clusterfullerenes, the non-metal ions bear a large negative charge, which imposes a strong axial ligand field and large magnetic anisotropy of nearby lanthanide ions. At the same time, isolation of endohedral species inside the carbon cage enables rather uncommon and yet simple atomic arrangements, thus creating a platform for the study of magnetic interactions and relaxation phenomena, especially well established for Dy-EMFs. But the carbon cage is not just an inert container for encapsulated clusters. A size and shape of a fullerene and topology of its π-system not only determine the electronic properties of the host but also affect the properties of the guests. An intriguingly strong variation of the magnetic properties found for Dy₂O@C_2n clusterfullerenes with C₇₂–C₈₂ cages^25–27 calls for a systematic study of this factor, and in this work we focus on the larger fullerene cage, C₈₈, for which we isolate three isomers of Dy₂O@C₈₈, determine their molecular structures and analyze magnetic properties.

While oxide clusterfullerenes based on C₈₈ were not reported yet, this cage is known for other EMFs with 4-fold electron transfer, such as dimetallofullerenes Sm₂@C₈₈ ³⁰ and Lu₂@C₈₈,³¹ and carbide clusterfullerenes M₂C₂@C₈₈ (M = Sc,³² Y,³³ Er,³⁴ and Lu;^31,35 see Table 1). The structural studies revealed four cage isomers of C₈₈ in those EMFs, including three classical fullerenes C₁(26), C_s(32), and D₂(35), and one heptagon-containing isomer with C_s symmetry (labeled as C_s(hept)). As both feature 4-fold electron transfer to the fullerene, it is reasonable to expect similarity of the cage structure of oxide and carbide clusterfullerenes, and we anticipated to find these cage isomers for Dy₂O@C₈₈ as well. But this structural similarity also allows a different question to be addressed – how the bridge between two Dy ions affects magnetic properties and in particular Dy⋯Dy coupling. This problem requires a study of different types of clusterfullerenes sharing the same fullerene cages, and therefore we also decided to synthesize Dy₂C₂@C₈₈ isomers for comparison with Dy₂O@C₈₈ counterparts. Furthermore, magnetic properties of Dy₂C₂ clusterfullerenes remain poorly explored, except for a single study of Dy₂C₂@C_s(6)-C₈₂, and thus analysis of the role of acetylide group in Dy₂C₂@C_2n EMFs with different cages is an important task on its own.

Table 1 DFT (PBE/TZ2P) stability row of C₈₈⁴⁻ isomers and corresponding EMF structures

Isomer	C88^4−		Y2O@C88		Y2C2@C88		Known structures	This work
	ΔE (kJ mol^−1)	Gap (eV)	ΔE (kJ mol^−1)	Gap (eV)	ΔE (kJ mol^−1)	Gap (eV)
D 2(35)	0.0	0.59	0.0	0.75	0.0	0.75	Sm2,^30 Lu2C2 ^31	Dy2O, Dy2C2
C s(32)	30.2	0.46	16.5	0.69	13.2	0.69	Er2C2,^34 Lu2C2 ^31	Dy2O, Dy2C2
C 1(26)	28.6	0.69	21.1	0.87	38.5	0.84	Y2C2,^33 Lu2 ^31	Dy2O
C 1(30)	47.7	0.40	36.2	0.59	30.0	0.63
C s(hept)	67.0	0.64	54.0	0.77	57.7	0.79	Sc2C2,^32 Lu2C2 ^35

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Synthesis and separation

For the synthesis of Dy₂O-clusterfullerenes, core-drilled graphite rods filled with Dy₂O₃/graphite powder mixture were evaporated in arc-discharge under He/CO₂ (270/27 mbar) atmosphere. The soot was collected and extracted by carbon disulfide (CS₂) under an argon atmosphere for 12 h. The crude extract, containing mainly empty fullerenes, Dy-monometallofullerenes, and Dy₂O-oxide clusterfullerenes, was treated with TiCl₄ following the method proposed by Shinohara et al.^36,37 While empty fullerenes did not react with TiCl₄, Dy-EMFs formed an insoluble complex and could be separated by filtration and then released by breaking the complex with water (Fig. S1†). Three isomers of Dy₂O@C₈₈ were then isolated from the recovered EMF mixture after several steps of linear and recycling HPLC (Fig. S2†) and characterized by LDI-TOF mass-spectrometry as described in ESI (Fig. S3†). The isomers are denoted as Dy₂O-I, Dy₂O-II, and Dy₂O-III, where the Roman number corresponds to the retention time of a given isomer during HPLC separation.

Dy₂C₂-clusterfullerenes were synthesized by a similar arc-discharge process, but using He atmosphere with the addition of N₂ (180/10 mbar). The CS₂ extract of the soot in this case contained mainly empty fullerenes, Dy-monometallofullerenes, Dy₃N-nitride clusterfullerenes, and Dy₂C₂-carbide clusterfullerenes. Following the SAFA approach developed by Stevenson et al.,^38–40 the extract was re-dissolved in toluene and reacted with dried diamino silica gel (DASG). Empty fullerenes, Dy-monometallofullerenes, and Dy₂C₂-clusterfullerenes reacted with amino groups and were trapped by DASG, whereas less reactive Dy₃N@C_2n clusterfullerenes mainly remained in solution. The DASG with immobilized fullerenes was then filtered and washed with CS₂, which resulted in the release of Dy₂C₂@C_2n, whereas Dy-monometallofullerenes and main part of empty fullerenes remained trapped (Fig. S4†). Two isomers of Dy₂C₂@C₈₈ denoted as Dy₂C₂-I and Dy₂C₂-II (the Roman numbers correspond to the retention time), were then isolated by HPLC (Fig. S5†) and characterized by LDI-TOF mass-spectrometry as described in ESI† (Fig. S6).

Molecular structures

Single-crystal X-ray diffraction

Molecular structures of Dy₂O-I, Dy₂C₂-I, Dy₂C₂-II, and Dy₂O-III were established by single-crystal X-ray diffraction (SC-XRD). The crystals were obtained by layering fullerene solutions in CS₂ (for Dy₂C₂-I) or toluene (other EMFs) with a benzene solution of nickel octaethylporphyrin (NiOEP) in glass tubes. After slow diffusion of solutions during 3–4 weeks, fullerene·NiOEP co-crystals were obtained as black blocks on the tube walls. X-ray diffraction data collection was carried out at 100 K using synchrotron irradiation at the BESSY storage ring (BL14.2, Berlin-Adlershof, Germany).⁴¹ XDSAPP2.0 suite was employed for data processing.^42,43 The structures were solved by direct methods and refined by SHELXL-2018.⁴⁴ Hydrogen atoms were added geometrically and refined with a riding model. In each structure, the fullerene molecule is supported by one NiOEP molecule, which is the typical packing character of fullerene·NiOEP co-crystals.^45–47 The endohedral units showed a considerable disorder as is common in EMF crystallography. However, in all crystals we could identify one major site with enhanced occupancy, which allowed discussion of the cluster shape and internal position inside the fullerene if not precise geometry parameters. Additional crystal data can be found in ESI† (Table S1 and Fig. S7, S8).

Dy₂O-I (Dy₂O@C₁(26)-C₈₈). The asymmetric unit contains half NiOEP molecule, two halves of fullerene molecule with 0.5 occupancies, half benzene molecule and two halves of toluene molecule with 0.5 occupancies. The intact NiOEP molecule is generated from the half NiOEP molecule with its image by the crystal mirror plane, which coincides with the NiOEP molecule's mirror symmetry plane. The two halves of the fullerene cage and their images by the crystal mirror plane are correlated by the crystal mirror plane as two enantiomers of the chiral C₁(26)-C₈₈ fullerene cage (Fig. 1a). The encapsulated Dy₂O cluster is disordered, however with high occupancies of 0.35 and 0.40 (out of 0.50) for the two main metal sites. The occupancies of the four remaining minor sites are 0.03–0.09 (Fig. 1a). The main site has Dy–O bond lengths of 2.019(4) and 2.050(4) Å, the Dy1–O–Dy2 angle of 166.0(2)°, and Dy1⋯Dy2 distance of 4.0386(9) Å.

Fig. 1 SC-XRD structures of Dy-EMFs co-crystallized with NiOEP. (a) Dy₂O-C₁(26); (b) Dy₂C₂-C_s(32); (c) Dy₂C₂-D₂(35); (d) Dy₂O-D₂(35). In each figure, coordination of the fullerene with the major site of the endohedral cluster to NiOEP is shown on the left, whereas all metal sites in endohedral clusters with their site occupancies and selected geometrical parameters are shown on the right. Note that in (a), (c), and (d), only one from two overlapping fullerene enantiomers is shown.

Dy₂C₂-I (Dy₂C₂@C_s(32)-C₈₈). The asymmetric unit contains one intact NiOEP molecule, one intact fullerene molecule, one ordered benzene molecule and a disordered solvent molecule. The ordered fullerene cage is assigned as C_s(32)-C₈₈. The encapsulated Dy₂C₂ cluster is considerably disordered with 11 Dy sites, which are grouped into two regions with net occupancy of 1 in each of them. The main Dy sites in each group, Dy1 (0.60) and Dy2 (0.34)/Dy10 (0.31), have sufficiently high occupancy to allow the discussion of the cluster geometry. The C₂ unit is refined as ordered, with the C–C bond length of 1.20(2) Å. In the main sites, the Dy₂C₂ cluster has a butterfly shape, in which Dy1–C distances are 2.48(2) and 2.49(2), the angle between two Dy-C₂ planes is 150°, and the Dy⋯Dy distances are 4.54(2) Å (Dy1⋯Dy2), and 4.47(2) Å (Dy1⋯Dy10).

Dy₂C₂-II (Dy₂C₂@D₂(35)-C₈₈) and Dy₂O-III (Dy₂O@D₂(35)-C₈₈). The fullerene·NiOEP·2C₇H₈ crystals of both compounds are essentially isostructural. The asymmetric unit contains one half NiOEP molecule with unit site occupancy, two halves of fullerene molecule in half (0.5) site occupancy, and two disordered toluene molecules. The fullerene cage is assigned to the D₂(35)-C₈₈ isomer. Positions of its two enantiomers related by the crystallographic mirror symmetry plane overlap, resulting in the overall carbon cage disorder.

Positions of endohedral clusters inside the fullerene are also very similar in the two structures. Dy atoms are disordered, but show enhanced occupancies of 0.28/0.34 (out of 0.50) for the main metal sites, which are located on one of the two-fold axes of the D₂-symmetric fullerene cage. In Dy₂C₂@D₂(35)-C₈₈, the C₂ unit has the bond length of 1.23(1) Å, and the main site of the Dy₂C₂ cluster has a slightly bent butterfly shape, with Dy–C bond lengths of 2.401(6), 2.393(6), 2.417(6), and 2.433(7) Å, the angle between Dy1-C₂ and Dy2-C₂ planes of 161.4(4)°, and Dy1⋯Dy2 distance of 4.602(2) Å. In Dy₂O@D₂(35)-C₈₈, Dy–O bond lengths in the main site are 2.061(3) and 2.109(3) Å, the Dy1–O–Dy2 angle is 173.9(2)°, and Dy1⋯Dy2 distance is 4.164(2) Å.

DFT calculations

Crystallographic studies were augmented by extensive DFT calculations of Y₂O@C₈₈ and Y₂C₂@C₈₈ for the four lowest-energy C₈₈⁴⁻ isomers, including D₂(35), C_s(32), C₁(26), and C₁(30), and also for C_s(hept), which was earlier found in some C₈₈-based EMFs.^32,35 For each cage isomer, we first used Fibonacci sampling to generate 120 starting structures with different orientations of the Y₂O endohedral cluster^27,48 and then performed their complete optimization, which gave several unique conformers (Fig. S9†). For Y₂C₂@C₈₈, the reduced set of starting coordinates based on Y₂O@C₈₈ conformers was used, in which oxygen atom was replaced by the acetylide group. Relative energies of the most stable conformers for each cage isomer are listed in Table 1, more detailed data can be found in ESI.† The conformers of Y₂O@C₈₈ and Y₂C₂@C₈₈ were then re-optimized with Dy replacing Y (Fig. 2). Since Y³⁺ and Dy³⁺ have similar ionic radii, the structure and relative energies are very similar, and the following discussion is based on Y analogs.

Fig. 2 DFT-optimized molecular structure of Dy-EMFs (the lowest-energy conformers). Dy – green, O – red, C – gray.

The most stable isomers of C₈₈⁴⁻, Y₂O@C₈₈, and Y₂C₂@C₈₈ all have the D₂(35)-C₈₈ cage. For Y₂O@C₈₈, the calculations revealed only four unique conformers, of which two are 34 kJ mol⁻¹ higher in energy than the two most stable ones. The structure of the lowest-energy conformer corresponds to the main site in SC-XRD structures of Dy₂O-D₂(35) and Dy₂C₂-D₂(35) with the metal atoms aligned along the C₂ axis of the cage. The Y₂O cluster in this conformer is linear, but attains the Y–O–Y angles of 166° and 155° in higher-energy conformers. Likewise, the Y₂C₂ cluster is planar in the most stable conformer of Y₂C₂@D₂(35)-C₈₈. Interestingly, the optimized Y⋯Y distance in Y₂O@C₈₈ is 0.436 Å shorter than in Y₂C₂@C₈₈ (4.206 Å versus 4.642 Å; compare to experimental values of 4.164(2) Å and 4.602(2) Å in Dy analogs), which leads to the shorter distance between the metal and the coordinated hexagon in Y₂C₂@C₈₈ (2.015 Å) than in Y₂O@C₈₈ (2.167 Å) and makes the fullerene cage in Y₂C₂@C₈₈ longer by 0.133 Å (8.673 Å versus 8.540 Å measured as the distance between centroids of Y-coordinated hexagons). A considerable variation of the fullerene size depending on the endohedral species was observed earlier in La₂@D₅(450)-C₁₀₀ compared to La₂C₂@D₅(450)-C₁₀₀, but in that case it was the carbide clusterfullerene which had the shorter length, whereas the La-C₆ distance was identical in both structures, and the whole effect could be explained by a stronger Coulomb repulsion between La ions when not mediated by the acetylide group.⁴⁹

The next in the stability row are Y₂O@C₈₈ and Y₂C₂@C₈₈ isomers based on the C_s(32)-C₈₈ cage. The conformer survey of Y₂O@C_s(32)-C₈₈ gave 6 unique structures, of them three are almost isoenergetic within 4 kJ mol⁻¹ and separated from other conformers by a gap of 25 kJ mol⁻¹. The Y₂O/Dy₂O cluster in all of them is nearly linear with the M–O–M angle of 174–179°. For Y₂C₂@C_s(32)-C₈₈, the lowest-energy conformer has the same position of metal atoms as in the most stable conformer of Y₂O@C₈₈ and corresponds to the main site in the SC-XRD structure of Dy₂C₂-C_s(32) and Lu₂C₂@C_s(32)-C₈₈.³¹ The cluster is planar and is located on the symmetry plane of the fullerene cage.

Y₂O@C₁(26)-C₈₈ is found to be the third most stable isomer of Y₂O@C₈₈. The endohedral cluster is located rather freely, with 9 unique conformers spread in the energy range of 57 kJ mol⁻¹, of which six fall into the window of 15 kJ mol⁻¹. The major site in the SC-XRD structure of Dy₂O-C₁(26) corresponds to the second conformer with the relative energy of 1.1 kJ mol⁻¹. The Y–O–Y angle in this structure is 157°, but the Y₂O cluster appears to be rather flexible with the angle varying strongly between conformers.

To summarize, the cage structures identified in this work for Dy₂O@C₈₈ and Dy₂C₂@C₈₈ by SC-XRD correspond to the most stable cage isomers, whereas locations of the endohedral cluster, at least in their major crystallographic sites, correspond to the lowest-energy conformers. The disorder in the crystal structures may be partially caused by the conformational freedom as DFT predicts several structures with close energies. The relative energies of C₁(30) and C_s(hept) isomers are not prohibitively high, and their formation should be considered as plausible, although they were not found in this work. A deeper study of other cage isomers and their thermodynamic functions may be required to fully disclose the stability row, but this exercise goes beyond the scope of this work.

Spectroscopic properties

While the SC-XRD is the golden standard of the molecular structure determination, a disorder may pose a serious problem for the structure elucidation and even reduce the reliability of the fullerene isomer assignment of EMFs. The high structural sensitivity of UV-Vis-NIR absorption spectra makes them a convenient complimentary technique, which can help resolving questionable structural assignments. If endohedral clusters are not contributing to the frontier orbitals, the absorption spectra of EMFs are dominated by π → π* excitations of the carbon cage. As a result, the spectra of EMFs with different metals or even different types of endohedral clusters may be very similar when they have the same fullerene isomer in the same formal charge state. In particular, close similarity of the spectra can be expected for the same isomers of carbide and oxide clusterfullerenes, as well as of dimetallofullerenes with divalent metals, as they all share the formal fullerene charge of 4−. The exact similarity, however, is expected only if the cluster is not involved at all, which is often not the case. Thus, different positions of the endohedral metal atoms (i.e. different conformers) may also contribute to the distinctions between the spectra.

Fig. 3 compares UV-Vis-NIR absorption spectra of Dy-EMFs isolated in this work. The spectrum of Dy₂O-C₁(26) with C₁(26)-C₈₈ cage resembles the spectra reported for Y₂C₂@C₁(26)-C₈₈ ³³ and Lu₂@C₁(26)-C₈₈,³¹ but also that of Er₂C₂@C_s(32)-C₈₈ from ref. 34. Given that the latter is also different from the spectra of other EMFs with C_s(32)-C₈₈ cage, we suggest that the Er₂C₂@C₈₈ identified as the C_s(32) isomer in ref. 34 requires reassignment to C₁(26).

Fig. 3 Vis-NIR absorption spectra of Dy₂O@C₈₈ and Dy₂C₂@C₈₈ isomers measured in toluene solution at room temperature.

The spectrum of Dy₂C₂-C_s(32) is virtually identical to that of Lu₂C₂@C_s(32)-C₈₈ from ref. 31, in agreement with the same fullerene cage determined by SC-XRD for both structures. It also shows a certain similarity to the spectrum of Dy₂O-II, the only compound for which we did not succeed with the SC-XRD structure elucidation. We thus tentatively assign C_s(32) isomer to Dy₂O-II, and further confirm this assignment by IR spectroscopy as discussed below.

In line with the same cage isomerism and metal positions determined by SC-XRD, Dy₂C₂-D₂(35) and Dy₂O-D₂(35) have almost identical absorption spectra. Comparison to the literature data gave rather puzzling results. Our spectra are similar to that of Sm₂@C₈₈-D₂(35)³⁰ with the same fullerene cage as determined in this work, but also show a close resemblance with the spectra of Sc₂C₂@C_s(hept)-C₈₈ ³² and Lu₂C₂@C_s(hept)-C₈₈.³⁵ We thus decided to look for further spectroscopic verification of the fullerene cage structure.

IR spectra are also very sensitive to the molecular structure of the fullerene cage. Besides, they can be predicted by DFT with high accuracy. This good agreement between experiment and theory was used earlier for the correct determination of some EMF structures when SC-XRD data were not available yet.^50–52Fig. 4a compares experimental and calculated spectra of Dy₂C₂-C_s(32) and Dy₂O-C_s(32) (note that calculations were performed for Y analogs, which does not affect the results of comparison because metal-based modes occur at much lower frequencies). For Dy₂C₂-C_s(32), the theory gives very good agreement with the experiment, especially in the range of tangential fullerene modes above 1000 cm⁻¹. For Dy₂O-C_s(32), we averaged the spectra of three low-energy conformers, as their spectra were found to be rather different. After the averaging, reasonable agreement with experimental data was obtained. Note that the spectra of Dy₂C₂-C_s(32) and Dy₂O-C_s(32) with the same fullerene cage are still considerably different, which shows that the internal cluster and position of metal atoms do affect the IR spectra. Earlier we have already seen similar differences in the spectra of EMFs with I_h-C₈₀ fullerene cage and different endohedral units.⁵³

Fig. 4 Experimental and DFT-computed IR spectra: (a) Dy₂O-C_s(32) and Dy₂C₂-C_s(32); (b) Dy₂C₂-D₂(35); (c) Dy₂O-D₂(35). Computations are performed for Y analogs. The inset in (b) shows vibrational displacements of pyracylene fragment responsible for the strong band at 1574 cm⁻¹.

For Dy₂C₂-D₂(35) (Fig. 4b) and Dy₂O-D₂(35) (Fig. 4c), the calculated spectra of D₂(35) isomers show strikingly good agreement with the experimental data, whereas those of C_s(hept) isomers are substantially different. Thus, the IR spectroscopy confirms the cage isomer assignment of Dy₂C₂-D₂(35) and Dy₂O-D₂(35). Both EMFs have a very characteristic absorption band at 1574 cm⁻¹ with a particularly strong intensity considerably exceeding that of all other absorption features. DFT calculations ascribe this band to the stretching vibration of the shortest C=C bonds in the molecule (1.384 Å) located between pentagons in four pyracylene fragments.

Magnetic properties

The isolation of three isomers of Dy₂O@C₈₈ and two isomers of Dy₂C₂@C₈₈ allows us to analyze how the structural peculiarities of endohedral clusters and fullerene cages can affect the magnetic properties of Dy EMFs. The first effect may be addressed by comparing isostructural Dy₂O and Dy₂C₂ compounds, whereas the second one can be considered by comparing different cage isomers with the same endohedral cluster. The role of the non-metal units, such as O²⁻ and C₂²⁻, in the magnetism of EMFs is two-fold: they have a strong influence on the single-ion magnetic anisotropy of Dy ions by providing the main contribution to the ligand field,^54–58 and they play a role of bridges between two Dy ions thus determining the strength of superexchange interactions.^{25,27,57,59–61}

Ab initio calculations

The single-ion anisotropy can be analyzed straightforwardly through multiconfigurational ab initio methods, such as the CASSCF/RASSI approach in Molcas employed in this work.^62,63 We use Dy₂O-D₂(35) and Dy₂C₂-D₂(35) as representative examples as they have the same fullerene cage isomer and identical η⁶-coordination of Dy ion to the carbon cage, and hence the difference between them can be directly ascribed to the different influence of O²⁻ and C₂²⁻ units. Fig. 5 shows the calculated ligand field splitting and orientation of magnetic moments for Dy ions in Dy₂O-D₂(35) and Dy₂C₂-D₂(35). Both O²⁻ and C₂²⁻ impose an axial ligand field on Dy ions, yielding the ground state Kramers doublet (KD) with J_z = ±15/2. The orientation of the quantization axis is also similar in both clusters as it coincides with Dy–O bond in Dy₂O and passes through the center of the acetylide group in Dy₂C₂. However, the ligand-field splitting and the degree of axiality imposed by O²⁻ and C₂²⁻ are very different. On average, the splitting in Dy₂O is twice higher than in Dy₂C₂ (481 cm⁻¹versus 224 cm⁻¹ for the first excited KD and 1494 cm⁻¹versus 780 cm⁻¹ for the whole LF splitting in the ground-state ⁶H_15/2 multiplet). Already for the ground-state KD, the g_x and g_y components of the pseudospin g-tensor in Dy₂C₂@C₈₈ are 50 times larger than in Dy₂O@C₈₈. This indicates that Dy magnetic moments in Dy₂C₂ are more susceptible to perturbations of the magnetic field and hence can relax faster. A purity of the KD states when presented in |m_J〉 basis is also considerably higher in Dy₂O than in Dy₂C₂. In the latter, only the first KD is relatively pure with 99.8% of the |15/2〉 term, whereas already in the second KD the contribution of the leading |13/2〉 term is only 86.5%, and the mixing is further increased in higher-energy KDs. In Dy₂O@C₈₈, the leading term contributions in the four lowest-energy KDs are 100.0% |15/2〉, 99.9% |13/2〉, 97.7% |11/2〉, and 94.3% |9/2〉, and only in the fifth KD the weight decreases below 90%, to 89.2% for |7/2〉. Thus, the Dy₂O cluster with the negative charge localized on the single oxide ion features much stronger axiality than the Dy₂C₂ cluster, in which the negative charge is spread over two carbons.

Fig. 5 Ligand-field splitting in Dy ions in Dy₂O-D₂(35) (a) and Dy₂C₂-D₂(35) (b) computed at the CASSCF/RASSI level. Insets show fragments of the molecules with atoms surrounding Dy ions. Quantization axes are shown in light blue, Dy – green, O – red, C – gray.

SQUID magnetometry

As follows from the results of ab initio calculations, magnetic ground state of Dy ions in all the studied EMFs is the Ising state with J_z = ± 15/2. It means that the differences in the static low-temperature magnetic behavior of the compounds should be caused by variation in the Dy⋯Dy interactions. The latter can be conveniently addressed by measurements of the temperature dependence of the magnetic susceptibility χ as the shape of the χT product curve exhibits characteristic signatures of interactions between magnetic moments. For two non-interacting moments, the curve should be almost flat with a steep decrease at the lowest temperatures. This is the behavior we observe for Dy₂O-C_s(32) (Fig. 6). For the antiferromagnetic (AFM) coupling, the decrease of χT starts at higher temperatures and is smoother, which corresponds to the behavior found for Dy₂O-C₁(26). Finally, for the ferromagnetically-coupled (FM) moments, the χT curve develops a peak at low temperatures, which matches the behavior of Dy₂O-D₂(35). Thus, from the χT measurements, we infer that the isomers of Dy₂O@C₈₈ represent three different situations of magnetic Dy⋯Dy interactions. For the Dy₂C₂@C₈₈ isomers the situation is different – both Dy₂C₂-C_s(32) and Dy₂C₂-D₂(35) show clear signatures of FM coupling, which is stronger in Dy₂C₂-C_s(32). For all the compounds, the shapes of experimental χT curves are well reproduced by simulations with interaction parameters determined from the fit of magnetization curves as described below.

Fig. 6 Experimental χT curves (dots) and results of simulations (solid lines; red dashed line is calculated for the system of two non-interacting Dy ions) of Dy₂O and Dy₂C₂ EMFs with C₈₈ cages. Magnetic susceptibility is defined as χ = M/H at 0.5 T. Experimental curves are corrected for linear background and scaled to match simulated curves in high-temperature range.

Further details are obtained from isothermal magnetization curves plotted in Fig. 7. All three Dy₂O@C₈₈ isomers show magnetic hysteresis with a closing temperature of around 8–9 K at a sweep rate of 2.9 mT s⁻¹. The hysteresis closing temperature matches the bifurcation temperatures of χ curves measured in zero-field cooled sample (ZFC) and during the in-field cooling (FC) and listed in Table 2 (see also insets in Fig. 7).

Fig. 7 Low-temperature magnetization curves of Dy₂O@C₈₈ and Dy₂C₂@C₈₈ EMFs: Dy₂O-C₁(26) (a and d), Dy₂O-C_s(32) (b), Dy₂O-D₂(35) (c), Dy₂C₂-C_s(32) (e), and Dy₂C₂-D₂(35) (f), sweep rate 2.9 mT s⁻¹. Insets in (a)–(c) show χ_FC and χ_ZFC curves (0.2 T, sweep rate 5 K min⁻¹) and determination of T_B and T_irrev. (d) Shows magnetic hysteresis of Dy₂O-C₁(26) measured in different field ranges at 1.8 K, as well as the derivative of the magnetization curve.

Table 2 Parameters of Dy⋯Dy interactions and magnetic hysteresis in Dy₂O@C₈₈ and Dy₂C₂@C₈₈ EMFs^a,b

	ΔEAFM–FM	j	α (°)	T B	T irrev	T hyst	T B100
a ΔEAFM–FM (cm^−1), j (cm^−1), and α (°) are determined from the fits of magnetization curves. b T B is defined as the peak temperature in χZFC, Tirrev is the bifurcation point between χZFC and χFC curves (both measured with the sweep rate 5 K min^−1), Thyst is the highest temperature at which the hysteresis loop is still open (sweep rate 2.9 mT s^−1), and TB100 is the temperature, at which magnetization relaxation time is 100 s; all temperatures are in K.
Dy2O-C1(26)	−16.5	−0.080	23 ± 1		10.5	8	6.0
Dy2O-Cs(32)	−0.4	−0.002	23 ± 11	5.5	8.5	8	4.6 (0.2 T)
Dy2O-D2(35)	3.6	0.022	43 ± 2	7.5	8.5	8	3.9
Dy2C2-Cs(32)	6.3	0.029	11 ± 3			2.1
Dy2C2-D2(35)	3.3	0.015	0 ± 5			2.1

---

The shapes of hysteresis are quite different between the isomers and reflect the nature of Dy⋯Dy interactions deduced from χT measurements. The most distinctive are the curves measured for Dy₂O-C₁(26). At 1.8 K the hysteresis is open in the whole measurement range from −7 T to +7 T and clearly shows two regimes with a small and large magnetic moment. The low-field regime corresponds to the dominant AFM alignment of the magnetic moments. But when the magnetic field exceeds 2 T, the state with the FM alignment gains lower energy and starts to increase its population, hence causing an increase of the magnetization. This hysteresis shape resembles that found in some other dinuclear Dy complexes with antiferromagnetic coupling,^27,64–71 but the transition between the two states in Dy₂O-C₁(26) occurs at a considerably higher field, pointing to a much stronger Dy⋯Dy coupling in the fullerene.

To obtain the numerical parameters of the coupling, we fitted magnetization curves measured at different temperatures using the effective spin Hamiltonian (1):

Ĥ_spin = Ĥ_LF1 + Ĥ_LF2 − 2j₁₂Ĵ₁·Ĵ₂ + Ĥ_ZEE (1)

where Ĥ_LFi are single-ion ligand-field Hamiltonians of Dy³⁺, j₁₂ is the coupling constant between dysprosium moments, and Ĥ_ZEE is the Zeeman term describing interaction of Dy³⁺ magnetic moments with the external magnetic field. We use ab initio computed ligand field parameters in Ĥ_LFi, and Dy³⁺ moments Ĵ_i are treated in the |J, m_J〉 basis sets of the ⁶H_15/2 multiplet. In the lowest-energy part of the spectrum, the Hamiltonian yields two quasi-doublets associated with ferromagnetic and antiferromagnetic alignment of Dy³⁺ magnetic moments (Fig. S12 in ESI†). The energy difference between them depends on the coupling constant and the angle α between quantization axes of Dy³⁺ ions: ΔE_AFM–FM = 225j₁₂ cos(α), where the coefficient 225 appears because of the use of the full Dy³⁺ momentum in the Hamiltonian (1) and the single-ion ground state with J_z = ±15/2 (see ESI† for more details). In the fitting with PHI code,⁷²j₁₂ and α were treated as free parameters, and computed curves were powder-averaged to be compatible with experimental magnetization curves measured for powder samples. Finally, only experimental points in the field range where hysteresis is very narrow or completely closed were used as the Hamiltonian (1) does not include relaxation processes and hence cannot be used to model magnetic hysteresis. Experimental and fitted magnetization curves are compared in ESI.† Although different conformers of EMF molecules may have somewhat different single-ion LF parameters and LF splitting, our calculations in this work as well as earlier studies^25–27,57 showed that the ground state KD of Dy ions in such EMFs are very close to the pure m_J = ±15/2 state irrespective of the Dy-cage coordination. Furthermore, the energy gap to the first excited KD is so high that only the ground-state KD will have significant population at low temperatures. Thus, it is not expected that the results of simulations with eqn (1) will be noticeably affected by the coexistence of different orientations of endohedral clusters or by accuracy limitations of the ab initio modelling of the LF splitting.

For Dy₂O-C₁(26), the fitting procedure gave α of 23 ± 1° and j₁₂ of −0.08 cm⁻¹, yielding the ΔE_AFM–FM value of −16.5 cm⁻¹, one of the largest interaction energies between Dy magnetic moments in dinuclear {Dy₂} compounds (see ref. 27 for a recent survey). Note that since Dy³⁺ magnetic moments in the Dy₂O-C₁(26) molecule are not collinear, the magnetic moment of the ground AFM state is not zero but amounts to 20 sin(α/2) = 4μ_B. The fitted parameters and Hamiltonian (1) were then used to simulate χT curve, which gave good agreement to the experimental data (Fig. 6), thus confirming the reliable determination of the interaction parameters.

In Dy₂O-C_s(32), the hysteresis shape features a considerable decrease of the magnetization near zero field, which is consistent with the weak Dy⋯Dy interactions. When the coupling is negligible, an additional magnetization relaxation channel via zero-field quantum tunneling of magnetization is open, which results in a drastically reduced remanence. This hysteretic behavior is similar to the recently studied Dy₂O@C₇₄,²⁵ although the QTM signatures in the hysteresis curve of Dy₂O-C_s(32) are less pronounced than in the latter. The fitting of the magnetization curves with Hamiltonian (1) gave the angle of 23 ± 11° and a very small constant j₁₂ of −0.002 cm⁻¹. Note that when the coupling is weak, the dependence of the curves on the angle between magnetic moment is also reduced, thus resulting in a larger uncertainty. The small ΔE_AFM–FM value of only −0.4 cm⁻¹ is in line with the shape of χT curve, which is also well reproduced by simulations.

The shape of the magnetic hysteresis in Dy₂O-D₂(35) resembled that observed for some other dinuclear lanthanide fullerenes with FM coupling, such as Dy₂ScN@C₈₀,⁷³ Tb₂ScN@C₈₀,⁷⁴ and Dy₂S@C₈₂.⁶¹ After the sample is saturated at 7 T, ramping the field down produces only a small decrease of magnetization until reaching zero field. On crossing zero field, a certain decrease of magnetization occurs, which is likely due to the zero-field QTM. But the latter implies simultaneous flip of magnetic moments of both Dy³⁺ ions, and is not very efficient in a strongly coupled system. At a further negative ramping, another kink in the curve is seen at −0.48 T, after which the magnetization drops abruptly. Following earlier studies,^61,74,75 this feature is assigned to the level crossing between the FM and AFM states, which promotes the efficient relaxation of magnetization via the QTM mechanism. Fitting the magnetization curves of Dy₂O-D₂(35) resulted in j₁₂ of 0.022 cm⁻¹, α of 43 ± 2°, and ΔE_AFM–FM of 3.6 cm⁻¹. The angle is unexpectedly large, given that SC-XRD and DFT results agree on the linear shape of the Dy₂O cluster. Yet these parameters also give a good match between simulated and experimental χT curves. The AFM–FM energy difference can be also estimated from the magnetic field of the QTM kink (H_QTM) in the hysteresis curve as ΔE_AFM–FM = 0.935H_QTM[T]μ_Dy[μ_B] (ref. 61), which gives 4.4 cm⁻¹.

In both isomers of Dy₂C₂@C₈₈, only a very narrow opening of the hysteresis is observed at 1.8 K and 2.1 K, and the loop is completely closed by 2.5 K. Fitting of the magnetization curves gives the FM coupling with ΔE_AFM–FM of 6.3 cm⁻¹ in Dy₂C₂-C_s(32) and 3.3 cm⁻¹ in Dy₂C₂-D₂(35). The angle between magnetic moments is only 11 ± 3° in Dy₂C₂-C_s(32) and is nearly 0° in Dy₂C₂-D₂(35) within the uncertainty limit of ±5°.

Magnetization relaxation times

The open magnetic hysteresis indicates that the studied Dy-EMFs are single-molecule magnets,^76–80 and their magnetodynamics was further characterized by measuring the relaxation times τ_M at different temperatures. As the sample amount was not sufficient for AC measurements, only DC technique was employed. The samples were first magnetized at the field of 7 T, then the field was ramped down to zero as fast as possible, and the decay of magnetization was then followed and fitted with a stretched exponential function. The values determined for Dy₂O@C₈₈ isomers are plotted in Arrhenius coordinates in Fig. 8. The DC technique is reliable only for relaxation times longer than 50–100 s, which limits the accessible temperature range to that below T_B.

Fig. 8 Temperature dependence of the magnetization relaxation time measured for Dy₂O@C₈₈ isomers: Dy₂O-C₁(26) (at 0 T), Dy₂O-C_s(32) (0.2 T), and Dy₂O-D₂(35) (0 T). Solid lines are fits with Orbach (Dy₂O-C₁(26)) and Raman mechanisms (Dy₂O-C_s(32) and Dy₂O-D₂(35)).

For Dy₂O-C₁(26), the increase of the relaxation time with cooling takes a linear form down to 2.5 K, with the sign of a leveling off at lower temperatures. The linear dependence is a characteristic feature of the Orbach relaxation mechanism with an effective barrier U^eff corresponding to an excited spin state:

τ_M⁻¹(T) = τ₀⁻¹ exp(−U^eff/T). (2)

Fitting of the experimental data with eqn (2) gives U^eff of 20.5 ± 0.3 K (14.2 cm⁻¹) and the attempt time τ₀ of 3.3 ± 0.3 s. The barrier is much smaller than the energies of excited LF states but is close to the ΔE_AFM–FM value determined from the fit of magnetization curves, which suggests that the magnetization reversal in the AFM ground state of Dy₂O-C₁(26) proceeds via sequential flips of individual Dy magnetic moments, including a formation of the FM state after the first flip. The levelling off below 2.5 K may indicate the switch to the simultaneous flip of two Dy moments through a temperature-independent QTM such as observed in Dy₂S@C₈₂ at sub-K temperatures.⁶¹

In Dy₂O-C_s(32), the measurement at zero field showed coexistence of the fast relaxation (presumably a QTM) with a slower thermal process, which makes a determination of τ_M rather ambiguous. As the zero-field QTM can be suppressed by application of a finite magnetic field, the measurements were then performed in the field of 0.2 T. For Dy₂O-D₂(35), the measurements were performed in zero field. Dy₂O-C_s(32) and Dy₂O-D₂(35) show a different temperature dependence of τ_M than Dy₂O-C₁(26), which can be described by a power-law function, τ_M⁻¹(T) = CTⁿ, characteristic for the Raman relaxation mechanism. The fit gives similar parameters for two isomers, C = (1.13 ± 0.05) × 10⁻⁴ s⁻¹ K⁻ⁿ and n = 2.93 ± 0.04 in Dy₂O-C_s(32) and C = (0.67 ± 0.03) × 10⁻⁴ s⁻¹ K⁻ⁿ and n = 3.70 ± 0.04 in Dy₂O-D₂(35). The n values are much smaller than the classical expectation of n = 9 for the Raman process but are consistent with the behaviour of many other Dy-SMM, including Dy-EMFs, also showing smaller exponents in the Raman regime associated with the influence of optical phonons.⁸¹

For both Dy₂C₂@C₈₈ isomers, the relaxation times appeared too short for their reliable determination by DC magnetometry. Since an open magnetic hysteresis requires τ_M of at least a few seconds, a conservative estimation would be 5–10 seconds at 1.8 K. Much faster relaxation of magnetization in Dy₂C₂@C₈₈ when compared to Dy₂O@C₈₈ is in line with the ab initio calculations suggesting a substantially lower axiality in Dy₂C₂ clusters.

Discussion

With the study of Dy₂O@C₈₈ in this work, Dy-oxide clusterfullerenes Dy₂O@C_2n become the most diverse class of Dy-based EMF-SMMs both in terms of the cage size (ranging from C₇₂ to C₈₈) and isomeric composition (C₈₂ and C₈₈ are represented by three isomers each). Table 3 lists the energetic characteristics of Dy⋯Dy interactions and blocking temperatures of magnetization in the Dy₂O@C_2n series and compares the values to other dinuclear Dy-clusterfullerenes.

Table 3 Dy⋯Dy interaction energy and blocking temperature of magnetization in dinuclear Dy-EMFs^a

	ΔE^totAFM–FM	ΔE^dipAFM–FM	ΔE^exchAFM–FM	U ^effexch	T B	T irrev	T B100	Ref.
a ΔE^exchAFM–FM is the difference of ΔE^totAFM–FM and ΔE^dipAFM–FM; U^effexch is the energy barrier of the low-temperature Orbach process assigned to the relaxation via the exchange excitation; ΔEAFM–FM and U^effexch values in cm^−1, temperature in Kelvin. b ΔE^totAFM–FM is determined from the fit of magnetization curves. c ΔE^totAFM–FM is determined as the exchange barrier U^effexch. d ΔE^totAFM–FM is determined from the QTM features in hysteresis curves. e Tw - this work.
Dy2O@Cs(10 528)-C72	1.5^b	3.0	−1.5	—	4.0	8	3.4	25
Dy2O@C2(13 333)-C74	∼0.1^b	2.6	−2.5	—	6.7	14	5.0 (0.2 T)	25
Dy2O@C2v(5)-C80	−18.5^b	2.7	−21.2	18.0	5.0	11	3.2	26
Dy2O@Cs(6)-C82	−7.5^c	3.0	−10.5	7.5	4.4	10	2.8	27
Dy2O@C3v(8)-C82	−5.4^c	2.5	−7.8	5.4	7.4	9	5.9	27
Dy2O@C2v(9)-C82	−12.9^c	2.6	−15.6	12.9	5.8	8	3.7	27
Dy2O@C1(26)-C88	−16.5^b	2.5	−19.0	14.2		10.5	6.0	Tw^e
Dy2O@Cs(32)-C88	−0.4^b	2.3	−2.7	—	5.5	8.5	4.6 (0.2 T)	Tw
Dy2O@D2(35)-C88	3.6^b/4.4^d	2.2	1.4/2.2	—	7.5	8.5	3.9	Tw
Dy2C2@Cs(6)-C82	12.1^c	2.6	9.5	12.1	∼2		—	57
Dy2C2@Cs(32)-C88	6.3^b	1.7	4.6	—	∼2		—	Tw
Dy2C2@D2(35)-C88	3.3^b	1.7	1.6	—	∼2		—	Tw
Dy2S@Cs(6)-C82	11.0^b/10.7^d	2.2	8.5	12.4	∼2		—	57 and 61
Dy2S@C3v(8)-C82	6.4^b/5.1^d	2.3	2.8	4.2	4.0		2.0	57 and 61
Dy2TiC@Ih(7)-C80	8.5^b	3.4	5.1	6.6	∼2		1.7	59 and 82
Dy2ScN@Ih(7)-C80	5.6^c	3.3	2.3	5.6	7.9	8	5.0	56
Dy2LuN@Ih(7)-C80	3.0^c	3.3	−0.3	3.0	7.9	10	5.2	60

---

Our new results demonstrate that that the O²⁻ bridge in Dy₂O cluster can support not only AFM interactions between Dy magnetic moments as in previously studied Dy₂O@C_2n EMFs, but also the FM coupling. It is different from Dy₂-clusterfullerenes with S²⁻, C₂²⁻, C⁴⁻, and N³⁻ bridges, which all favor the FM coupled ground state. Quite unusual is the magnitude of the variation of the Dy⋯Dy interaction energy found in seemingly similar Dy₂O@C₈₈ isomers. Estimation of dipolar contribution to ΔE_AFM–FM shows that ΔE^dip_AFM–FM is positive in all EMFs and falls into the energy range of 1.5–3 cm⁻¹. Thus, the exchange contribution to Dy⋯Dy coupling appears to be responsible for the strong variation of ΔE_AFM–FM. Among the studied Dy₂O@C_2n compounds, only one, Dy₂O@D₂(35)-C₈₈, has moderately positive ΔE^exch_AFM–FM value of 1.4–2.2 cm⁻¹, whereas other 8 feature negative exchange term spanning from the modest −1.5 cm⁻¹ in Dy₂O@C₇₂ to very large −21.2 cm⁻¹ in Dy₂O@C₈₀ and −19.0 cm⁻¹ in Dy₂O@C₁(26)-C₈₈, by far the strongest Dy⋯Dy interactions in all Dy₂-complexes. The data does not present any clear correlation between the structural parameters and the strength of the exchange coupling. The fullerene cage definitively plays an important role, as can be deduced from the considerable variation of the values within the isomeric series, especially for isomers of Dy₂O@C₈₈. However, it is hard to conclude at this moment if this strong influence is caused by the variation of the Dy₂O cluster shape and size in different cages, by indirect interactions via the fullerene π-system, or because different Dy-fullerene coordination sites alter the metal orbital composition and hence modify the superexchange interactions via the O²⁻ bridge. A combined influence of all these factors is likely to play a role.

Comparison of different clusters within one fullerene cage can be used to distinguish the cage and the bridge effects. However, this also appears to be rather ambiguous. For instance, Dy₂C₂@D₂(35)-C₈₈ and Dy₂O@D₂(35)-C₈₈ have very close ΔE_AFM–FM values, but at the same time Dy₂C₂@C₈₈ and Dy₂O@C₈₈ isomers with the C_s(32) cage have different size and the sign of ΔE_AFM–FM. The comparison of Dy₂O@C₈₂, Dy₂C₂@C₈₂, and Dy₂S@C₈₂ with C_s(6) cage isomer shows that the strength and the sign of Dy⋯Dy coupling in Dy₂S and Dy₂C₂ are similar, while Dy₂O counterpart has the opposite sign of ΔE_AFM–FM (Table 3). Finally, in isostructural and isoelectronic Dy₂TiC and Dy₂ScN clusters within the I_h(7)-C₈₀ cage, the superexchange through C⁴⁻ is almost twice stronger than through N³⁻.⁵⁹ Overall, we can conclude that the bridge is certainly crucial in determining the Dy⋯Dy coupling, but not in a very deterministic way as the influence of other factors may be of a comparable magnitude.

The SMM performance of Dy₂-clusterfullerenes does not show an obvious correlation with the Dy⋯Dy coupling strength but is clearly affected by the single-ion magnetic anisotropy. Thus, the blocking and hysteresis closing temperature in dinuclear systems reduces in the following row of the bridge units: O²⁻ ≥ N³⁻ > C⁴⁻ ≥ S²⁻ ≥ C₂²⁻, which corresponds to the decrease of the average ligand-field splitting in these types of clusterfullerenes as predicted by ab initio calculations.^{54,55,57,59,83} Counterintuitively, this conclusion is not directly transferable to analogous mono-nuclear Dy-EMFs. The hysteresis closing temperature in DySc₂N@C₈₀,^45,84 DyLu₂N@C₈₀,⁶⁰ DyY₂N@C₈₀,⁸⁵ DyScS@C₈₂,⁸⁶ and DyYTiC@C₈₀ ⁵⁸ is near 7–8 K irrespective of their non-metal units. The synthesis and studies of mixed-metal oxide and carbide clusterfullerenes with single Dy atom, such as DyScO@C₈₂ and DyScC₂@C₈₂, and the studies of mono-nuclear Dy-SMMs with different cage sizes will be required to fully disclose this phenomenon. However, it can be pointed out that the highest hysteresis closing temperature among Dy₂-clusterfullerenes, 14 K, is found for Dy₂O@C₇₄, in which the Dy⋯Dy coupling is so weak that the compound shows butterfly-shaped hysteresis with pronounced zero-field QTM typical for single-ion SMMs.²⁵

Although the Dy⋯Dy coupling does not seem to correlate with the blocking temperature in Dy₂-clusterfullerenes, it does affect the low-temperature relaxation. The distinct Orbach relaxation mechanism involving the exchange excitation (either FM → AFM or AFM → FM) is observed only in Dy₂-clusterfullerenes with |ΔE_AFM–FM| values exceeding a threshold of 5 cm⁻¹ (e.g., Dy₂O@C₁(26)-C₈₈). For compounds with weaker coupling, the relaxation is better described by the Raman mechanism (as Dy₂O@C_s(32)-C₈₈ and Dy₂O@D₂(35)-C₈₈, Fig. 8).

Conclusions

In this work, we report on the synthesis, isolation and systematic structural studies of endohedral metallofullerenes with Dy₂O and Dy₂C₂ clusters encapsulated within C₈₈ cages. As both clusters transfer four electrons to the fullerene host, they tend to feature the same cage isomers, which were identified by single-crystal X-ray diffraction as C₁(26), C_s(32), and D₂(35) and further supported by spectroscopic studies. These cage isomers correspond to the most stable C₈₈⁴⁻ isomers according to DFT calculations.

The availability of isomeric and isostructural Dy₂O@C₈₈ and Dy₂C₂@C₈₈ EMFs allowed the study of magnetic Dy⋯Dy interactions as a function of the fullerene cage and the bridging unit. We showed that the oxide ion O²⁻ tends to prefer an antiferromagnetic coupling of Dy magnetic moments, whereas the acetylide group C₂²⁻ favors their ferromagnetic coupling. The strength of the interaction is found to vary strongly with the fullerene cage isomerism. All metallofullerenes exhibited single-molecule magnetism with an open magnetic hysteresis but with a considerably different blocking temperature of magnetization. Dy₂C₂@C₈₈ isomers are weak SMMs with hysteresis closing already at 2.5 K, whereas in Dy₂O@C₈₈ isomers the hysteresis remained open up to 7–9 K. This difference in relaxation behavior agrees with the much stronger single-ion magnetic anisotropy in Dy₂O@C₈₈ than in Dy₂C₂@C₈₈ predicted by ab initio calculations.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors acknowledge financial support by Deutsche Forschungsgemeinschaft (grants PO 1602/7-1, LI 3055/3-1, and AV 169/3-1) and the National Science Foundation China (NSFC 91961109 to N. C.). Diffraction data have been collected on BL14.2 at the BESSY II electron storage ring operated by the Helmholtz-Zentrum Berlin; we would particularly like to acknowledge the help and support of Manfred Weiss and his group members during the experiments at BESSY II. Computational resources were provided by the Center for High Performance Computing at the TU Dresden. We appreciate the technical support with computational resources in IFW Dresden by Ulrike Nitzsche. Sandra Schiemenz is acknowledged for the help with spectroscopic measurements, and Dr Anja Wolter-Giraud and Sebastian Gaß are acknowledged for the help with magnetic measurements in IFW Dresden.

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Footnotes

† Electronic supplementary information (ESI) available. CCDC 2175825–2175828. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d2qi01796b

‡ These authors contributed equally.

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