Bis-Monophospholyl Dysprosium Cation Showing Magnetic Hysteresis at 48 K

Single-molecule magnets (SMMs) have potential applications in high-density data storage, but magnetic relaxation times at elevated temperatures must be increased to make them practically useful. Bis-cyclopentadienyl lanthanide sandwich complexes have emerged as the leading candidates for SMMs that show magnetic memory at liquid nitrogen temperatures, but the relaxation mechanisms mediated by aromatic C5 rings have not been fully established. Here we synthesize a bis-monophospholyl dysprosium SMM [Dy(Dtp)2][Al{OC(CF3)3}4] (1, Dtp = {P(CtBuCMe)2}) by the treatment of in-situ-prepared “[Dy(Dtp)2(C3H5)]” with [HNEt3][Al{OC(CF3)3}4]. SQUID magnetometry reveals that 1 has an effective barrier to magnetization reversal of 1760 K (1223 cm–1) and magnetic hysteresis up to 48 K. Ab initio calculation of the spin dynamics reveals that transitions out of the ground state are slower in 1 than in the first reported dysprosocenium SMM, [Dy(Cpttt)2][B(C6F5)4] (Cpttt = C5H2tBu3-1,2,4); however, relaxation is faster in 1 overall due to the compression of electronic energies and to vibrational modes being brought on-resonance by the chemical and structural changes introduced by the bis-Dtp framework. With the preparation and analysis of 1, we are thus able to further refine our understanding of relaxation processes operating in bis-C5/C4P sandwich lanthanide SMMs, which is the necessary first step toward rationally achieving higher magnetic blocking temperatures in these systems in the future.


Crystallography
The crystal data for 1 and [NEt3H][Al{OC(CF3)3}4] are compiled in Table S1. Data for crystals of 1 were collected using a Rigaku Oxford Diffraction FR-X diffractometer with a HyPix 6000HE photon counting detector and VariMax TM micro focus optics with Cu Kα radiation (λ = 1.54178 Å). Crystals of [NEt3H][Al{OC(CF3)3}4] were examined using a Rigaku Oxford Diffraction Supernova diffractometer with a CCD area detector and micro focus optics with Mo Kα radiation (λ = 0.71073 Å). Intensities were integrated from data recorded on 1° frames by ω rotation. Cell parameters were refined from the observed positions of all strong reflections in each data set.
A multi-scan (1) or Gaussian grid face-indexed ([NEt3H][Al{OC(CF3)3}4]) absorption correction with a beam profile was applied. 1 The initial structure was solved using ShelXT 2 and the model was refined by full-matrix least-squares on all unique F 2 values using ShelXL, 3 with anisotropic displacement parameters for all nonhydrogen atoms, and with constrained riding hydrogen geometries; Uiso(H) was set at 1.2 (1.5 for methyl groups) times Ueq of the parent atom. The largest features in final difference syntheses were close to heavy atoms and were of no chemical significance. CrysAlisPro 1 was used for control and integration, and SHELX 2,3 was employed through OLEX2 4 for structure solution and refinement. ORTEP-3 5     S6 Figure S4. 13

Magnetic measurements
Magnetic measurements were performed using a Quantum Design MPMS-XL7 superconducting quantum interference device (SQUID) magnetometer. 31.6 mg of a crystalline sample was crushed with a mortar and pestle under an inert atmosphere, and then loaded into a borosilicate glass NMR tube along with 15.4 mg powdered eicosane, which was then evacuated and flame-sealed to a length of ca. 5 cm. The eicosane was melted by heating the tube gently with a low-power heat gun in order to immobilize the crystallites. The NMR tube was then mounted in the center of a drinking straw using friction by wrapping it with Kapton tape, and the straw was then fixed to the end of the sample rod. The measurements were corrected for the diamagnetism of the straw, borosilicate tube and eicosane using calibrated blanks, and the intrinsic diamagnetism of the sample using Pascals constant. 7     We then integrate the distribution function in order to determine the exponentially symmetric bounds ± required for any given choice of : By definition, → 0 for → 1 as this defines purely single exponential relaxation, and increases with increasing and approaches → ∞ as → 0 when the distribution of relaxation times becomes infinitely broad (Figure S18 S14). We fit the empirical relationship between and with the function ≈  with cc-pVTZ 17 and the remaining atoms with cc-pVDZ. 18 Empirical dispersion corrections (gd3) 19 were also accounted for. At the optimized geometry, explicit calculation of the Hessian reveals that it is a true local minimum with all frequencies positive and forces zero. The optimized geometry is a good match with the experimental crystal structure of 1, with a minimized RMSD value of 0.25 Å. 20 In this case we have not calibrated the vibrational frequencies to the IR spectrum of 1, and rather have opted for a fully ab initio calculation in this case.
To determine the spin-phonon coupling of each vibrational mode, we distort the molecule along the normal mode coordinate and perform CASSCF-SO calculations, as described above (except that in this case we use the atomic-compact Cholesky decomposition (acCD) method to generate an auxiliary basis to use the resolution of the identity (RI) approximation), 21 at each point. Assuming the harmonic approximation for each mode, we calculate the thermally averaged displacement at 150 K and displace the molecule up to ±16×, ±10×, ±7× the zeropoint displacement (ZPD) for modes 1 -3, respectively, ±5× ZPD for modes 4 and 5, ±4× ZPD for modes 6 -8, ±3× for modes 9 -13, ±2× ZPD for modes 14 -41, and ±1.5× ZPD for the remaining modes. We calculate the S21 electronic structure with CASSCF-SO at 4 evenly spaced points in both positive and negative directions, and then fit the changes in the crystal field parameters (compared to those calculated at the equilibrium geometry) to cubic polynomials. The method as described here differs from that employed in our original work on [Dy(Cp ttt )2][B(C6F5)4], 22 and so we have repeated the calculations using the revised methodology (we have retained the originally-reported calibration of the vibrational mode energies to the IR and Raman spectra). Hence, we have also calculated the thermally averaged displacement at 150 K and displace the molecule up to ±14×, ±12×, ±8×, ±7×, ±6 ZPD for modes 1 -5, respectively, ±5× ZPD for modes 6 -8, ±4× ZPD for mode 9, ±3× for modes 10 -13, ±2× ZPD for modes 14 -43, and ±1.5× ZPD for the remaining modes. The states at the equilibrium geometry are very similar to those reported previously (Table S6), 22 and the relaxation rates are now in better agreement with the experiment ( Figure S16).
Following our previously described method, 22 we calculate the transition rates from single-phonon processes between each state in the crystal field eigenbasis of the geometry-optimized molecule (here we have applied a magnetic field of 2 Oe along the main magnetic axis to replicate the experimental AC field). However, here we have employed quadruple precision arithmetic throughout, and tested if there is any effect of allowing temperaturedependence in the spin-phonon coupling parameters by altering the vibrational displacement as a function of temperature and determining the appropriate crystal field parameters from the cubic polynomials: we find no difference compared with using a fixed set of spin-phonon coupling matrix elements. Diagonalization of the master matrix gives the relaxation rates, where one is zero corresponding to thermodynamic equilibrium, one is slow corresponding to relaxation over the barrier and the remaining 14 are fast, corresponding to spin motion on either side of the barrier.
We have calculated the strength of the modifications to the crystal field parameters 23 for each vibrational mode, where the parameters below are in Wybourne notation.