High blocking temperatures for DyScS endohedral fullerene single-molecule magnets

Dy-based single-molecule magnets (SMMs) are of great interest due to their ability to exhibit very large thermal barriers to relaxation and therefore high blocking temperatures. One interesting line of investigation is Dy-encapsulating endohedral clusterfullerenes, in which a carbon cage protects magnetic Dy3+ ions against decoherence by environmental noise and allows for the stabilization of bonding and magnetic interactions that would be difficult to achieve in other molecular architectures. Recent studies of such materials have focused on clusters with two Dy atoms, since ferromagnetic exchange between Dy atoms is known to reduce the rate of magnetic relaxation via quantum tunneling. Here, two new dysprosium-containing mixed-metallic sulfide clusterfullerenes, DyScS@Cs(6)–C82 and DyScS@C3v(8)–C82, have been successfully synthesized, isolated and characterized by mass spectrometry, Vis-NIR, cyclic voltammetry, single crystal X-ray diffractometry, and magnetic measurements. Crystallographic analyses show that the conformation of the encapsulated cluster inside the fullerene cages is notably different than in the Dy2X@Cs(6)–C82 and Dy2X@C3v(8)–C82 (X = S, O) analogues. Remarkably, both isomers of DyScS@C82 show open magnetic hysteresis and slow magnetic relaxation, even at zero field. Their magnetic blocking temperatures are around 7.3 K, which are among the highest values reported for clusterfullerene SMMs. The SMM properties of DyScS@C82 far outperform those of the dilanthanide analogues Dy2S@C82, in contrast to the trend observed for carbide and nitride Dy clusterfullerenes.

The first stage HPLC separation was performed on a 5PYE column (10 mm x 250mm, Cosmosil Nacalai Tesque) with toluene as the eluent. Figure S2 shows the first stage HPLC chromatogram of extract sample. Two fractions were collected, A and B, respectively; both containing DyScS@C 82 . After that, fraction A was injected into a Buckyprep column (10 mm x 250mm, Cosmosil Nacalai Tesque) for the second stage separation with toluene as the eluent ( Figure S3a). Fraction A1 was collected and then injected into a Buckyprep-M column (10 mm x 250mm, Cosmosil Nacalai Tesque) with a toluene mobile phase. Fraction A1-1 containing both Sc 2 S@C 82 and DyScS@C 82 was then collected ( Figure S3b). In order to remove Sc 2 S@C 82 , the fourth stage separation for A1-1 was carried out using a 5PBB column (4.9 mm x 250mm, Cosmosil Nacalai Tesque) with a toluene mobile phase, in which pure DyScS@C 82 (I) was obtained ( Figure S3c). In addition, fraction B was also injected into a Buckyprep column (10 mm x 250mm, Cosmosil Nacalai Tesque) for the second stage separation with toluene as the eluent ( Figure S4a). Fraction B1 was collected and re-injected into a Buckyprep-M column (10 mm x 250mm, Cosmosil Nacalai Tesque) with a toluene mobile phase. Fraction B1-1 containing Sc 2 S@C 82 and DyScS@C 82 was then collected ( Figure S4b). Similarly, the final step separation was conducted on a 5PBB column (4.9 mm x 250mm, Cosmosil Nacalai Tesque) with a toluene mobile phase to obtain pure DyScS@C 82 (II) ( Figure S4c). The purity of the isolated DyScS@C 82 (I, II) were confirmed by the single peak on the final-stage HPLC chromatograms and MALDI-TOF mass spectrometry ( Figure S5).        Table S2). These results verified that, even though the HOMO and LUMO for M 2 X@C s (6)-C 82 and M 2 X@C 3v (8)   under a magnetic field of 0.3 T. These measurements were performed both after cooling in zero magnetic field (ZFC) and after cooling in a 0.3 T magnetic field (FC).
The magnetic blocking temperature T B was taken as the maximum in the ZFC measurement. Figure S10. Dependence of the 2 K magnetic hysteresis loops on the field sweep rate. More hysteresis is seen when the field is swept faster, as is expected for single-molecule magnets. S11 Here, the blocking temperature T B is defined as the peak temperature of χ ZFC while warming at a rate of 5 K min -1 . b The 100 s blocking temperature T B,100 is the temperature at which 100 s relaxation time is observed.
Lastly, magnetic saturation-relaxation experiments were performed to obtain magnetic relaxation times of each isomer at several temperatures, both at 0 T and at 0.3 T. In each case, the sample was magnetized to 5 T at a given temperature for five minutes, and then field was then brought down to either 0 T or 0.3 T at a rate of 20-70 mT s -1 , and the magnetization as a function of time was recorded. The resulting decay curves were fit to a stretched exponential decay function: where the left side is the magnetization M as a function of time t, normalized by the t = 0 magnetization M 0 . τ is the relaxation time, b is a positive number between 0 and 1, and y 0 is the normalized magnetization at t = ∞. τ, b, and y 0 are the fit parameters.

S12
The results of these fits are given in Tables S4 -S7 and Figures S9, S10, S11, and S13.
For very long relaxation times in a magnetic field, fits to equation S1 can sometimes suffer from high correlations between the fit parameters. To remedy this, the 1.8 K data of isomer 1 was fit using both relaxation data and field application data, as shown in Figure S. The field application data was taken by cooling the sample in zero field, and then applying a 0.3 T and measuring magnetization as a function of time. The eventual saturation magnetization of this process should match the final magnetization of the saturation decay data, so these two processes can be fit together to obtain accurate relaxation times. The field application data was fit to: Where M 0 is the initial magnetization of the decay data set (the same value as in equation S1), and M 0 ʹ is the initial magnetization of the field application data set. The fit parameters τ , b, and y 0 have the same meanings as in equation S1, and these values are constrained to be equal for the two data sets. a Field decay and field-application were simultaneously fit for this temperature S13 b Field application data was not available at 2K, but the relaxation time is long, causing an unstable fit to (S1). To reduce correlations, y 0 was fixed to a value interpolated from the other temperatures using the Curie law.    Figure S11. Saturation-decay data with fits to equation S1 (solid lines) for DyScS@C s (6)-C 82 at 0 T. S14 Figure S12. Saturation-decay data with fits to equation S1 (solid lines) for DyScS@C s (6)-C 82 at 0.3 T. Figure S13. Combined fit of saturation-relaxation and field application data for DyScS@C s (6)-C 82 at 0.3 T at 1.8 K. S15 Figure S14. Saturation-decay data with fits to equation S1 (solid lines) for DyScS@C 3v (8)-C 82 at 0 T. Figure S15. Saturation-decay data with fits to equation S1 (solid lines) for DyScS@C 3v (8)-C 82 at 0 T. S16 Figure S16. Arrhenius plot of relaxation times for DyScS@C s (6)-C 82 and DyScS@C 3v (8)-C 82 , with shown fits to the Orbach relaxation mechanism (main text equation 1). The fit parameters are supplied in Table S8.