Shape-adaptive single-molecule magnetism and hysteresis up to 14 K in oxide clusterfullerenes Dy2O@C72 and Dy2O@C74 with fused pentagon pairs and flexible Dy–(μ2-O)–Dy angle

Clusterfullerenes Dy2O@C72 and Dy2O@C74 demonstrate a fine balance of exchange and dipolar interactions and slow relaxation of magnetization.


Synthesis and separation S2
Single-crystal X-ray analysis S4 DFT-based Molecular Dynamics S5

Measurements of magnetic properties S9
ZFC and FC measurements S10 Magnetization relaxation times S13 Ab initio calculations of ligand-field splitting S19 Fitting of magnetization curves S20

Experimental and simulated (M/H)T curves S21
DFT-optimized Cartesian coordinates S22

References S26
Electronic Supplementary Material (ESI) for Chemical Science. This journal is © The Royal Society of Chemistry 2020

DFT-based molecular dynamics
DFT-based Born-Oppenheimer molecular dynamics (BOMD) simulations were performed for Y2O@C72 and Y2O@C74 analogs with atomic masses of Dy assigned to Y. Single point energies and forces were calculated at the PBE/TZ2P level using Priroda code. 3 These forces were used to propagate the system in the canonical ensemble (NVT) using Nose-Hoover algorithm as implemented in the Python Atomic Simulation Environment libraries (ASE 3.0). 4 The thermostat temperature was set to 300 K with the characteristic coupling time of 10 fs. The trajectories were propagated for 100 ps using the initial DFT-optimized coordinates as starting points and initial velocities assigned randomly from Maxwell-Boltzmann distribution at 300 K. These trajectories were used to evaluate the spatial distribution of O and Dy atoms at a given unit volume inside the fullerene with discretization of 0.042 × 0.042 × 0.042 Å 3 . The probability isosurfaces obtained by this approach for Y2O@C72 and Y2O@C74 are plotted in Figure S4. Metal atoms oscillate only near their optimized positions. Oxygen atoms exhibit higher mobility in the plane perpendicular to the Dy-Dy axis. Figure S4. Spatial distribution of the probability density for Dy and O atoms in Dy2O@C72 and Dy2O@C74 as determined from molecular dynamics simulations at T = 300 K. Displacements of carbon atoms are not shown. Two isosurfaces show high probability (solid) and low probability (transparent) volumes.

IR spectra
IR spectra of Dy2O@C72,74 samples drop-casted on KBr substrates were measured at room temperature with Vertex 80 FTIR spectrometer (Bruker) equipped with Hyperion microscope. The spectra were computed using two approaches: in a static approach, molecular coordinates were optimized and then hessian was computed analytically along with derivatives of dipole moment with respect to cartesian coordinates. In molecular dynamics approach, time dependence of the x, y, and z components of the dipole moment obtained in DFT-based molecular dynamics simulations were Fourier-transformed to give corresponding spectra. DFT-computed spectra agree well with the experimental ones. Of particular interest is the identification of the vibrations of the Dy2O cluster. In the mid-IR range, DFT calculations shows that the Dy−O antisymmetric stretching mode should have relatively high intensity. In the experimental spectra these vibrations can be assigned to medium-intensity absorption bands at 680-700 cm −1 (marked by arrows in Fig. S5).

Measurement of magnetic properties
Magnetic properties were measured with MPMP 3 system (Quantum Design). The samples for magnetic measurements were prepared by drop-casting CS2 solution of metallofullerenes directly onto quartz sample holders. Each sample contained ca 0.1 mg of dried fullerene after evaporation of CS2. As fullerene molecules are strongly disordered in powders (unless co-crystallization agents are used), magnetic measurements of such powder samples do not require encapsulation in diamagnetic matrix. Besides, quartz holders have negligible diamagnetic signal at helium temperature, which eliminates the need for diamagnetic correction at low temperatures. Since mass of the sample could not be determined precisely, in the fitting of magnetization curves we relied on the shape of the curves rather than on the absolute values. Figure S8. Magnetization curves of Dy2O@C72 (left, 6 and 7 K) and Dy2O@C74 (right, 1.8 K and 14 K), the insets zoom into the region near zero field demonstrating opening of the hysteresis. Magnetic field sweep rate 2.9 mT/s.

ZFC and FC measurements
To study blocking of magnetization in Dy-oxide clusterfullerenes, we performed series of measurements to compare temperature dependence of magnetization for the sample preliminary cooled down to 2 K and then measured during warming up (zero-field cooled, ZFC) and, for the same sample, but the measurement is done during cooling the sample down in the applied field. An example of the measurements sequence is shown in Figure S9, which plots temperature, magnetic field, and magnetization as a function of time. At the moment t0, magnetic field is zero, and temperature is 30 K. Between t0 and t1, the sample is cooled down to 2 K in zero field, magnetization is also essentially zero during this temperature sweep. Then, during the [t1,t2] period, the sample is stabilized at T = 2 K for one minute. At the moment t2, the field is ramped to 0.2 T (it takes ca 2 second to reach this field) and the command to start the temperature sweep is initiated. However, at this moment, magnetometer usually starts additional temperature stabilization, which proceeds between t2 and t3, and only then the real temperature sweep is started. Unfortunately, users have no control of the [t2,t3] period, and in the measurements shown in Fig. S10 this period varied randomly from 5 to 70 seconds. Since magnetization of the sample is increasing during the [t2,t3] period, when the temperature sweep starts at the moment t3, magnetization is already not zero, but attains some finite value. Depending on the relaxation time of the sample and [t2,t3] time, the deviation of the magnetization from zero can be from very small to quite significant. Then, between t3 and t4, magnetization is measured during warming the sample up to 30 K (red dots in Fig. S9 and red curves in Fig. S10; this section is referred to as ZFC). Since relaxation of magnetization accelerates with the temperature increase, magnetization (which is smaller than the equilibrium value) first increases till reaches equilibrium value at some temperature, when relaxation become fast enough so that thermodynamic equilibrium is established faster than the temperature is changed. Above this temperature, magnetization decreases with temperature following the equilibrium behavior. After reaching 30 K, the sample is again stabilized between t4 and t5, and then the temperature sweep down to 2 K is started and proceeds between t5 and t6. Magnetization (referred to as FC, blue dots) during this sweep is increasing. At the beginning of the sweep, this increase follows the thermodynamic behavior, but at some temperature relaxation of magnetization becomes slow. Thus, when temperature reaches 2 K, magnetization is smaller than the equilibrium magnetization for this temperature. If the measurement of magnetization is then continued at the constant temperature ([t6, tfin] period), gradual increase of magnetization can be observed. Results of such measurements are usually presented as an overlay of ZFC and FC magnetization curves as a function of temperature (e.g., Fig. S10). At higher temperatures, when relaxation of magnetization is fast and thermodynamic equilibrium is restored faster than the temperature is changed, ZFC and FC curves coincide. When relaxation of magnetization becomes slow at lower temperatures and thermodynamic equilibrium is not restored anymore on the temperature sweep timescale, FZC and FC curves bifurcate. Usually, ZFC curve shows a peak near the bifurcation point, and the temperature of the peak is defined the blocking temperature, TB. Sometimes, ZFC and FC curves also bifurcate above TB, and then the bifurcation point is defined at Tirrev. 8 TB and Tirrev are kinetic parameters and depend on the measurement settings such as magnetic field, temperature sweep rate. Besides, the shape of ZFC curve will also depend strongly on the temperature stabilization time [t2,t3]. For the sake of comparison with other fullerene samples, we report the values measured in a field of 0.2 T with the temperature sweep rate of 5 K/min. Figure S10 compare the measurements for Dy2O@C72 in different fields, and also with different lowest temperature (2 K and 3 K). Figure S11 shows the measurements for Dy2O@C74 in different fields.     Fig. 4 in the manuscript of the field dependence of relaxation times), magnetization of Dy2O@C74 always jumps to a relatively high during the field ramp from zero to the measurement field. As a result, ZFC/FC curves strongly depend on the magnetic field used in the measurements. The higher the field-the more conventional the shapes are.

Magnetization relaxation times
Magnetization decay curve was then fitted with stretched exponential function: Where and 0 are the equilibrium and initial magnetizations, respectively, is a characteristic relaxation time and is an additional parameter that corresponds to the time-dependent decay rate.     Table S6.    Simulations were performed using coupling constants from the fits of magnetization curves (Fig. S15-S16).