A hard molecular nanomagnet from confined paramagnetic 3d-4f spins inside a fullerene cage

Reducing inter-spin distance can enhance magnetic interactions and allow for the realization of outstanding magnetic properties. However, achieving reduced distances is technically challenging. Here, we construct a 3d-4f metal cluster (Dy2VN) inside a C80 cage, affording a heretofore unseen metallofullerene containing both paramagnetic 3d and 4f metal ions. The significantly suppressed 3d-4f (Dy-V) distances, due to the unique cage confinement effect, were observed by crystallographic and theoretical analysis of Dy2VN@Ih(7)-C80. These reduced distances result in an enhanced magnetic coupling (Jtotal, Dy-V = 53.30 cm−1; Jtotal, Dy-Dy = −6.25 cm−1), leading to a high magnetic blocking temperature compared to reported 3d-4f single-molecule magnets and strong coercive field of 2.73 Tesla. Our work presents a new class of single-molecule magnets with both paramagnetic 3d and 4f metals confined in a fullerene cage, offering superior and tunable magnetic properties due to the unique cage confinement effect and the diverse composition of the entrapped magnetic core.

The electrochemical properties of Dy2VN@Ih(7)-C80 were studied by cyclic voltammetry with tetrabutylammonium hexafluorophosphate (TBAPF6) as the supporting electrolyte.The characteristic redox potentials are listed in Table S4.Dy2VN@Ih(7)-C80 has one reversible oxidation process and four reduction processes, in which the first, third and fourth reduction processes are all reversible, and the second reduction process is irreversible.The first oxidation potential and the first reduction potential are 0.05 V and -0.81 V, respectively, the electrochemical bandgap is 0.86 eV, which is in great agreement with its optical bandgap.In comparison to Sc2VN@Ih(7)-C80, both the oxidation potential and reduction potential of Dy2VN@Ih(7)-C80 move to the negative direction, suggesting a stronger electron-donating properties of Dy2VN@Ih(7)-C80.This could be rationalized by considering the larger ionic radius of Dy than Sc and the presumably resulted stronger metalcage interactions in Dy2VN@Ih(7)-C80 than Sc2VN@Ih(7)-C80.

EMF
Sample Preparation.The sample (0.340 mg) for magnetic measurements was prepared by dropcasting carbon disulfide (CS2) solution onto a slice of Al foil (5.413 mg) which is paramagnetic to minimize the background of sample holder.Then, fast evaporation of CS2 afforded black powder.
After that, the Al foil was folded into a small cube and stuck on the inner wall of a plastic straw with very small amount of N grease (less than 1 mg).The mass of the sample was determined by the variation of the Al foil before and after drop-casting.All the mass values were weighed using a Metallo Toledo Ultra-micro balance (1 μg).
Magnetic measurements.Magnetic properties were determined using Quantum Design MPMS3 magnetometer.DC mode was adopted for the measurements of susceptibility and magnetization, while VSM mode was selected for hysteresis, zero-field-cooled (ZFC)/field-cooled (FC) magnetization (ZFC-FC) and magnetization decay measurements.The background of Al foil and Pascal correction were considered when the point-by-point diamagnetic correction was carried on the data.Due to the quantity limitation, alternative current (ac) susceptibility measurement was not conducted.
Relaxation times extraction from decay measurements.Considering the long magnetic relaxation times of Dy2VN@Ih(7)-C80, the relaxation times were determined from the magnetization decay measurements.The sample was first magnetized under 1 kOe dc field for saturation.Then the field was swept to zero as fast as possible and then the decay data was collected.The relaxation times were obtained by fitting the data using equation S1 S6,S7 , where Meq, M0, τ and b are fitting parameters.Figure S5 shows the selected magnetization decay curves and their fittings.Table S7 shows the fitted relaxation times τ under different temperatures.Determination of the effective energy barrier (Ueff).The fitting of the whole dataset of relaxation times τ vs. T -1 could be accomplished by combining Orbach and quantum tunneling of magnetization (QTM) processes using equation S2.The best fit gives the Orbach barrier of U1 = 70.7 K and the QTM relaxation time of τQTM = 1249.8s.The magnetic relaxation in high-temperature range is usually dominated by the Orbach process, thus we also only fit the relaxation times τ vs. T -1 above 6 K.And only Arrhenius fitting of the dataset of relaxation times τ vs. T -1 above 6 K using equation S3 gives the effective exchange barrier of 68.0 K, which is consistent with U1.

S6. Theoretical Analysis.
Ab initio calculations.Ab initio calculations were performed at the CASSCF/SO-RASSI level of theory with the use of SINGLE_ANISO program S15-S17 employing MOLCAS 8.1 program S18 for both magnetic centers to obtain the crystal-field/zero-field parameters for Dy(III) and V(III).The calculation models were built on the crystal structure without further optimization.For the calculation of Dy(III), the other Dy(III) was replaced by diamagnetic Lu(III) and V(III) was replaced by diamagnetic Sc(III).The basis sets for all atoms are atomic natural orbitals from the MOLCAS ANO-RCC library S19,S20 : ANO-RCC-VTZP for Dy(III)/V(III) ions; VTZ for close N and C; VDZ for distant C and diamagnetic Lu(III)/Sc(III).The calculations employed the second order Douglas-Kroll-Hess Hamiltonian, where scalar relativistic contractions were considered in the basis sets and the spin-orbit couplings were handled in the restricted active space state interaction (RASSI-SO) procedure.We have mixed the maximum number of spin-free states which was possible with our hardware (all from 21 sextets, 128 from 224 quadruplets, 130 from 490 doublets for the Dy(III) fragment).Active electrons in seven active spaces include all f electrons (CAS (9, 7)) of Dy (III) in the CASSCF calculation.For the calculation of V(III), two active electrons in five active spaces (CAS (5,2)) was adopted in the CASSCF calculation.Dynamic correlation energy was also be considered using the CASPT2 S21 program.Density functional theory calculations.DFT calculations were performed at the B3LYP, PBE0, TPSSh, and ωB97X-D functionals with the basis function of 6-31G(d) for carbon atom and CEP-4G for metal atoms by using the quantum chemistry package Gaussian 16.S22 The natural bond orbital calculations were performed with NBO 3.0 program S23 also included in Gaussian 16.
The optimized results in Table S8 indicate the spin-ground state of Dy2VN@Ih(7)-C80 with 2S + 1 = 13.The crystal structure of Dy2VN@Ih(7)-C80 is in line with the optimized one (Fig. S6) at the ωB97X-D/6-31G(d)~CEP-4G, which was considered to further understand the electronic structures.The Mulliken atomic spin population in Table S9 means that there are about 2, 5, and 5 unpaired electrons remain at V, Dy1, and Dy1A atoms, respectively, confirmed with the plot of spin density of Dy2VN@Ih(7)-C80 in Fig. S8.On the other hand, in comparison of ground-state electronic configuration of Dy (4f 10 6s 2 ) and Sc (3d 3 4s 2 ) atoms, the NPA results indicate the three-electron transfer of each metal atom leading to the formally six-electron transfer from inner cluster to outer fullerene cage, and there are clear back-donation in 3d and 5d for V and Dy atoms, respectively.The formally electronic structure can be characterized as [(Dy 3+ )2V 3+ N 3-@Ih(7)-C80 6-].Additionally, the metal-nonmetal interaction in inner cluster show clear covalent characters based on the Wiberg bond order calculations.S8.Relative energy (ΔE in kcal·mol -1 ) of optimized Dy2VN@Ih(7)-C80 with different spin multiplicities (2S + 1) at different density functionals and same basis function 6-31G(d)~CEP-4G where S is the spin angular momentum.Supplementary Table S9.Mulliken atomic spin population and natural population analysis (NPA) of Dy2VN in optimized Dy2VN@Ih(7)-C80 with spin-ground state at the ωB97X-D/6-31G(d)~CEP-4G , where the basis function of 6-31G(d) for carbon atom and CEP-4G for metal atoms.
Magnetic interaction fitting.The magnetic states of this three-center spin system can be described with the total spin Hamiltonian (Equation 2) as mentioned in the main text.The calculated crystal field parameters were employed to describe the crystal-field splitting of the single Dy(III) ion.Both the coupling within two Dy centers and the interaction between the Dy center and V center were included into the spin Hamiltonian.The two Dy centers are structurally identical as V-N locates on the crystallographic symmetric plane, thus the interactions between different Dy centers and V center can be considered to be identical.
According to the results from ab initio, the magnetic anisotropy of Dy centers are very close to the Ising limit, while the calculated E/D for V center is 0.31, thus the V center could be treated as isotropic with the average giso = 1.9.Therefore, the exchange interaction between the magnetic centers was considered within the Lines model using the Hamiltonian (Equation 3) in main text, while the dipole−dipole magnetic coupling is treated exactly with the Hamiltonian (Equation S4) as shown below where  ⃗ is a unit vector and |r| is the distance between the magnetic centers.
The fitting was conducted in the POLY_ANISO program 16,17 and only data above 20 K were considered during the fitting.The best fit gave U1, Lines = 63.4K and was well consistent with the energy barrier fitted from data of demagnetization (U1 = 70.7 K).
Supplementary Fig. S9 Orientation of easy axis (dashed lines) of the ground Kramers doublets on two Dy(III) centers and one possible representation of the orientation of the magnetic moments (arrows) on the paramagnetic centers for the ground state in Dy2VN@Ih(7)-C80.Dy: green; N: blue; V: orange.
Supplementary Table S10.Calculated energy levels and g (gx, gy, gz) tensors of the lowest eight Kramers doublets (KDs) on individual Dy(III), and zero-field splitting parameters D, E and g (gx, gy, gz) tensors of the lowest spin-orbit state on individual V(III) in Dy2VN@Ih(7)-C80.

Table S11 .
The obtained energy states based on Lines model and their corresponding g-tensor values.