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

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


S1. Synthesis and Separation of Dy2ScN@C80
Dy2ScN@C80 was synthesized in a modified Krätschmer-Huffman fullerene generator by vaporizing composite graphite rods (φ 6 × 100 mm) containing a mixture of Dy2O3, Sc2O3, guanidine thiocyanate (GT, as solid nitrogen source 1 ) and graphite powder with the addition of 180 mbar He as described previously. 2 To investigate the effect of Dy-Sc ratio on the formation of Dy3-xScxN@C80 (x=0-3), syntheses by using mixture of Dy2O3, Sc2O3, GT and graphite powder with different molar ratios of Dy-Sc were carried out. The as-produced soot was Soxhlet-extracted by CS2 for 24 h, and the resulting brown-yellow solution was distilled to remove CS2 and then immediately re-dissolved in toluene and subsequently passed through a 0.2 μm Telflon filter for HPLC separation. The isolation of Dy2ScN@C80 was performed by multi-step HPLC. The purities of the isolated Dy2ScN@C80 was further checked by laser desorption/ionization time-of-flight (LDI-TOF) mass spectroscopic (MS) analysis (Bruker autoflex). Figure S1 shows the HPLC profiles of the fullerene mixture extracted from Dy2O3-Sc2O3-GT with different Dy-Sc ratios. The MS spectra were shown in Figure S2. The result indicates that the relative yield of Dy2ScN@C80 is enhanced with the reducing of Dy-Sc ratio, a ratio of Dy:Sc:GT:C=1:0.5:2.5:7.5 is recommended for the higher selectivity in the synthesis of Dy2ScN@C80.

S2. X-ray Crystallographic Analysis of Dy2ScN@C80
Crystal growth of Dy2ScN@Ih(7)-C80۰Ni II (OEP)۰2(C6H6) was accomplished by layering benzene solution of Ni II (OEP) over a solution of Dy2ScN@Ih(7)-C80 in CS2. After the two solutions diffused together over a period of one month, small black crystals (0.2 x 0.1 x 0.1 mm 3 ) suitable for X-ray crystallographic study formed. X-ray diffraction data collection for the crystal was carried out at 100 K at the BESSY storage ring (BL14.3, Berlin-Adlershof, Germany) 3 using a MAR225 CCD detector, λ = 0.89429 Å. Processing diffraction data was done with XDSAPP2.0 suite. 4 The structure was solved by direct methods and refined using all data (based on F 2 ) by SHELX 2016. 5 Hydrogen atoms were located in a difference map, added geometrically, and refined with a riding model. The data can be obtained free of charge from The Cambridge Crystallographic Data Centre with CCDC No. 1547067. Figure S5 shows the location of the main site of the Dy2ScN cluster in the Ih(7)-C80. Figure S6

S3. Configuration of the M2ScN cluster in M2ScN@C80-Ih: experiment versus theory
Extended DFT studies of M3N@C80-Ih molecules with different metals (M = Sc, Y, Lu) reported earlier showed that the M3N cluster has two especially stable configurations (conformers) inside the C80-Ih fullerene cage with C3 and Cs symmetry. 6,7 The structures of the conformers are shown in Figs. S7 and S8 for Y3N@C80-Ih (as DFT computations with Dy are severely complicated and because Y has similar ionic radius and chemical properties to Dy, we use Y as model for Dy). In the C3-conformer, all metal atoms are equivalent and have quasi-η 6 coordination to one of the cage the hexagons (metal atoms is somewhat displaced from the center of the hexagon towards one of the pentagon/hexagon edges). In the Cs conformer, two metal atoms have similar quasi-η 6 coordination as in the C3-conformer, whereas the third metal atom on the symmetry plane is coordinated to the carbon atom on the pentagon/hexagon/hexagon junction. At the PBE/TZ2P level of theory, C3 conformer is more stable than Cs-conformer of M3N@C80-Ih by 4.6 and 8.8 kJ/mol for M = Sc and Y, respectively. Figure S7. DFT-optimized molecular structure of Y3N@C80 with C3-symmetric configuration. The molecule is shown in three projections, C3 axis is perpendicular to the plane of the cluster and passes through nitrogen and two carbon atoms of the cage. Hexagons with quasi-η 6 coordination of Y atoms are shown in pink, other cage carbons are grey. Y-N bond length is 2.060 Å, the Y3N cluster is slightly pyramidal (nitrogen is 0.083 Å above the plane of metal atoms). Figure S8. DFT-optimized molecular structure of Y3N@C80 with Cs-symmetric configuration. The molecule is shown in three projections, symmetry plane is perpendicular to the plane of the cluster and passes through nitrogen and one of the Y atoms. Hexagons with quasi-η 6 coordination of Y as well as the fragment of the cage with close Y-C contacts are shown in pink, other cage carbons are grey. Y-N bond lengths are 2.064 Å and 2×2.066 Å, the Y3N cluster is more pyramidal than in the C3-symmetric conformer (nitrogen is 0.199 Å above the plane of metal atoms).
Substitution of one of the Y atoms in C3-Y3N@C80 by Sc leads to one possible conformer of Y2ScN@C80.
Cs-Y3N@C80 has two non-equivalent Y atoms and hence can lead to two conformers of Y2ScN@C80. However, in the course of DFT optimization, both Cs-derived conformers of Y2ScN@C80 converged to the same structure. Thus, we obtained two conformers of Y2ScN@C80-Ih, one derived from the C3-symmetric arrangement of the M3N cluster inside the cage, and another one derived from the Cs-configuration. At the PBE/TZ2P level, the former is more stable by 6.3 kJ/mol. Both structures are shown in Figure S9 in comparison to the Dy2ScN cluster sites determined experimentally in Dy2ScN@C80-Ih. As can be seen, experimental configurations of the cluster correspond reasonably well to DFT-optimized ones. Furthermore, the site with higher occupancy in the X-ray structure corresponds to the most stable conformer of Y2ScN@C80. It shows that disorder in the experimental structure has intrinsic thermodynamic reasons caused by co-existence of similar low-energy conformations of the cluster inside the fullerene cage. Note that the energy difference between C3-and Cs-derived conformers of Y2ScN@C80 is 6.3 kJ/mol in favor of the C3-derived structure, which correlates with the higher occupancy of the corresponding configuration in Dy2ScN@C80.

S4. DC magnetometry and relaxation times
DC magnetization measurements were performed using a Quantum Design VSM MPMS3 magnetometer. The sample drop-casted from CS2 solution into a standard powder sample holder (note that cocrystallization with Ni II (OEP) was used only for X-ray diffraction studies, whereas magnetic properties were studied for the pristine Dy2ScN@C80). To measure relaxation time in dc mode, the sample was first magnetized to the saturation at 5 T, then the field was swept as fast to B = 0 T or B = 0.2 T, and then the decay of magnetization was recorded. Decay curves were fitted using stretched exponential function: where τ is the relaxation time and y0 is an equilibrium magnetization at the given field and temperature.

S5. Ab initio calculations
Ab initio energies and wave functions of CF multiplets for the Dy2ScN@C80 molecule have been calculated using the quantum chemistry package MOLCAS 8.0. Each Dy(III) atom in the system was treated independently, while the second Dy ion was substituted by f-electron free Yttrium. Single point complete active space self-consistent field with spin-orbit interactions calculations (CASSCF/SO-RASSI) level of theory was employed to derive ab initio values (Tables S3-S5). The maximum ground state J = 15/2 results in eight low-lying Kramers doublets. The active space of the CASSCF calculations includes eleven active electrons and the seven active orbitals (e.g. CAS (11,7)). All 21 sextet states and 224 quartets and only 490 doublets were included in the state-averaged CASSCF procedure and were further mixed by spin-orbit coupling in the RASSI procedure. VDZ quality atomic natural extended relativistic basis set (ANO-RCC) was employed. The single ion magnetic properties and CF parameters were calculated with use of SINGLE_ANISO module. The CFs were used to construct a model Zeeman Hamiltonian with |J,mJ> basis. Based on this Hamiltonian transition probabilities were estimated using PHI code. The ground magnetic state of both Dy ions is Jz = ±15/2, orientation the anisotropy axes in the Dy2ScN cluster is depicted in Figure  S10.

S6. Coupling between magnetic moments of Dy ions in Dy2ScN@C80
The system with two Dy centers with magnetic moments J1 and J2 weakly coupled through exchange/dipolar interaction can be described by the following effective spin Hamiltonian: where the HCFi terms are single-ion crystal-field Hamiltonians, and the last term describes the exchange and dipolar interactions between two Dy centers (rather unfortunately, both exchange coupling and the total magnetic moment of lanthanide are traditionally designated as J, so we use the small letter j for the coupling and the capital J for the momentum). In the spirit of the Lines model, both exchange and dipolar interactions are modelled here by a single isotropic coupling parameter j12. In the simulation discussed below, the CF parameters in Eq. S1 and the angle between the main axes of the magnetization of individual Dy centres are obtained from ab initio calculations as described in the previous section, and simulations are performed using the PHI code. To match the experimental energy of the first exchange/dipolar excited state (estimated as 10.7 K from the Arrhenius behavior of the low-temperature relaxation times), the absolute value of the exchange/dipolar parameter j12 should be equal to 0.073 cm −1 . The sign of j12 (and hence the nature of the coupling between the magnetic moments of Dy centers) can be determined from the temperature dependence of χT (Fig. S11) as well as from the magnetization curves (Fig. S12).
By definition, the magnetic susceptibility χ is the derivative of the magnetization M with respect to the magnetic field B, whereas the experimentally measured quantity is the ratio M/B. For small values of B, the ratio and the derivative are quite close, but with the increase of the field a deviation between both quantities can become significant. Therefore, we will use the designation (M/B)T for all experimental curves.
When measured in small fields (0.2 T, 0.5 T, 1 T), the experimental (M/B)T curves show a sharp peak at low temperature, which becomes smaller as the external field is increasing (Fig. S11a). At B = 3 T, the peak is not observed anymore. The same pattern is observed in simulated χT curves for the ferromagnetically-coupled system (j12 = +0.073 cm −1 ). When the magnetic moments of Dy ions are coupled antiferromagnetically (j12 = −0.073 cm −1 ), χT exhibits a gradual increase without a low-temperature peak at any value of the external field (Fig. S11c). Thus, Figure S11 shows that the experimental (M/B)T pattern is reproduced well by the simulation for the ferromagnetically coupled system. Figure S11. (a) Experimentally measured (M/B)T curves (identical to χT curves when measured in low field); (b) simulated χT curves for the ferromagnetically coupled system; (c) simulated χT curves for the antiferromagnetically coupled system.

S17
The ferromagnetic coupling can be also confirmed by the shape of the magnetization curve measured at 8 K (the lowest temperature at which hysteresis is negligible). The simulated magnetization curves are compared to the experimental one at Fig. S12. Whereas the FM-coupled system provides a very good match to the experimental data, the simulated curve for the AFM system deviates significantly.
where r n is the normal of the radius vector connecting two magnetic moments 1 µ and 2 µ , and R12 is the distance between them. The angle between the moments, 116.7°, is taken from ab initio calculations. ΔE dip = 4.6 K is somewhat less than a half of the low-temperature barrier in Dy2ScN@C80. From ΔE dip , the dipolar contribution j12 dip to the j12 constant in eq. (S1) is computed by scaling with the factor of 15 2 •cos(α), where α is the angle between the anisotropy axes of individual Dy ions. For Dy2ScN@C80, this amounts to 0.031 cm −1 .

S18
Low-temperature magnetization curves of Dy2ScN@C80 also show a feature near 1 T, which can be seen below 3-4 K, but is less clear at higher temperatures. Detailed exploration of this feature in experimental curves is hardly possible because of the slow relaxation of magnetization and hence hysteresis observed at the temperatures when this feature is present. Computed thermodynamic magnetization curves also show the presence of the bent in low-T curves (Fig. S13). Figure S14, illustrating Zeeman splitting of the lowest-energy states in Dy2ScN@C80, shows that may be cause be the level crossing of FM and AFM states in a finite field. Since the measurements are performed for the powder sample with random orientations of the Dy2ScN cluster with respect to the external field, position of the level crossing is distributed in a rather large field range.

S19
Excited states of the di-Dy systems in the low-energy part of the spectrum are additive of the values of the constituent single-ions. For instance, 4 states (2 quasi-dublets) with Jz = ± 15/2 for both Dy ions in FM and AFM arrangement, |±15/2, ±15/2 , are followed by 8 |±15/2, ±13/2 and |±13/2, ±15/2 states in which one of the Dy centers has Jz = ± 13/2 (the energies of the quasi-dublets are 418, 425, 460, and 467 cm −1 ; compare to the single-ion KDs with the energies of 418 and 457 cm −1 for Dy2 and Dy1). The next 8 states (4 quasi-dublets) with the energies of 746, 752, 758, and 764 cm −1 correspond to |±15/2, ±11/2 and |±11/2, ±15/2 states (corresponding single-ion state have the energies of 741 and 755 cm −1 ). Two |±13/2, ±13/2 quasi-dublets have the energies of 878 and 885 cm −1 (compare to the sum of the energy of single-ion state, 418+457 = 875 cm −1 ). The density of states is then increasing dramatically at higher energies as more and more mixed states become available in the middle part of the spectrum (Fig. S15). As the model describing coupling of Dy moments (Hamiltonian S1) is most probably oversimplified, we doubt that these mixed states are described reliably. Besides, in weakly coupled system, such as Dy2ScN@C80, relaxation via excited states of the coupled system would require simultaneous flip of the spin of two Dy centers which appears less probable than relaxation via excited states of individual Dy ions. Figure S15. Energy spectrum of the total spin Hamiltonian for Dy2ScN@C80. Although Dy2ScN is not a Kramers system, each vertical line in the spectrum corresponds to de facto to two quasi degenerate states.