Boosting axiality in stable high-coordinate Dy(iii) single-molecule magnets.

A new nine-coordinate, air-stable Dy(iii) single-ion magnet has been successfully isolated. Our in silico studies demonstrate that through carefully modulating the ligand electronics, the axiality can be boosted to generate Ucal barriers of over 600 K.

Single-Molecule Magnets (SMMs) are fascinating molecular systems, which display the ability to block magnetisation via an energy barrier, U eff , resulting in the appearance of magnetic hysteresis of molecular origin. 1 Importantly, the design of viable SMMs strongly correlates with the control of the coordination environment at the level of a single metal ion. 2 The use of Dy(III) to generate a strong axial magnetic anisotropy, 3 a realisation achieved through the vital combination of theory and experiment, has led to a new generation of complexes with impressive energy barriers 4 and high blocking temperatures 5 with coercivity up to 80 K (i.e. above the boiling point of liquid nitrogen). 6 Potential applications will require not only the ability to function at higher temperatures, but also to be chemically stable in air or when exposed to heat. 7 However, finding an approach towards coordination environments that promote strong magnetic behaviour in 4f-SMMs and, at the same time, display robust chemical stability under ambient conditions has only recently begun to be addressed. In this regard, we recently reported two pentagonal bipyramidal Dy(III) single-ion magnets (SMMs containing only one metal ion), [Dy(H 2 O) 5 (HMPA) 2 ]Cl 3 ÁHMPAÁH 2 O and [Dy(H 2 O) 5 (HMPA) 2 ]I 3 Á2HMPA (HMPA = hexamethylphosphoramide), with blocking temperatures of B10 K, and we emphasized the important role of the second coordination sphere in controlling the magnetisation reversal barrier. 8 In fact, complexes with higher coordination numbers (Z9) that also possess high energy barriers are rare and tuning such an environment in a way that promotes high axiality whilst offering good stability to air, heat and moisture is a challenging task. For this reason, we were intrigued by the complexes [Ln III LF](CF 3 SO 3 ) 2 ÁH 2 O (L = 1,4,7,10-tetrakis(2-pyridylmethyl)-1,4,7,10-tetraaza-cyclododecane) and, in particular, the notable absence of the Dy(III) analogue along with the lack of magnetic data on any of the reported complexes. 9 The Dy ion geometry is extremely important in order to obtain higher blocking temperatures and we reasoned that the combination of the pseudo D 4d {DyN 8 } cage with a strong axial ligand should show interesting SMM characteristics. 10 Herein, we report the synthesis, magnetic characterisation and ab initio studies of [Dy III LF](CF 3 SO 3 ) 2 ÁH 2 O (1). Furthermore, we demonstrate an elegant strategy for improving the magnetic behaviour of high-coordinate 4f complexes. By carefully modulating the ligand environment in silico, we show how the calculated energy barrier, U cal , can be increased, thus making 1 an extremely attractive system to probe the effects of the highcoordinate ligand environment on the dynamics of the magnetisation. Compound 1 ( Fig. 1 and Fig. S6, S7, ESI †) was isolated under aerobic conditions from aqueous solution (see ESI †) 9 and the stability of 1 to B350 1C is verified by TGA analysis (Fig. S5, ESI †). We also report the isostructural (but not isomorphous) lanthanum analogue, [La III LF](CF 3 SO 3 ) 2 ÁH 2 O (2) (Table S1 and Fig. S1, S2, S11, ESI †) and the Dy-doped lanthanum analogue (3) (Fig. S4, ESI †). The nine coordinate Dy(III) centre sits on a C 2 symmetry axis, coincident with the Dy-F bond. Continuous shape measures analysis, 11 which estimates the distortion from the perfect polyhedron, gives a value of 1.429 (where 0 corresponds to the ideal structure) for a muffin geometry (Fig. S8 and Tables S4,  S5, ESI †). The ninth coordination site is occupied by a strong electronegative fluoride ion, with a relatively short Dy-F bond length of 2.123(2) Å (Table S3, ESI †). Intermolecular hydrogen bonding between the triflate counter-ions and the water molecule is present (Fig. S9, ESI †). In addition, the C-HÁ Á ÁF intermolecular interactions between neighbouring molecules of 1 create a 1D columnar structure along the c-axis with the closest DyÁ Á ÁDy distance of 7.757 Å (Fig. S10, ESI †).
For 1, the eight Kramers Doublets (KDs), corresponding to the 6 H 15/2 ground state, span an energy range of 808 K (see ESI † for computational details). The transverse components of the ground state (m J = AE15/2) are found to be negligible (g xx = 0.006, g yy = 0.012, Table S7, ESI †), establishing a strong magnetic anisotropy axis (g zz = 19.837), lying along the Dy-F bond (Fig. S28, ESI †). This can be explained using LoProp 12 charges computed using the CASSCF wavefunction. The charge on the axial F atom is found to be nearly three times larger compared to the nitrogen atoms of the cage ligand, (Fig. S28, ESI †) and this dictates the direction of g zz axis. Similarly, the axial nature is also observed for the first and second exited states (m J = AE13/2, g xx = 0.212, g yy = 0.228, g zz = 16.800 and m J = AE11/2, g xx = 0.468 g yy = 0.583, g zz = 13.380, respectively, Table S7, ESI †), which are found to lie at 185 K and 381 K, respectively above the ground state. Notably, the larger g xx /g yy values obtained for the third-exited state (m J = AE9/2; AE1/2, g xx = 5.213 g yy = 5.565, g zz = 8.350) yield a larger magnetic moment matrix element of 1.8 m B (Fig. 2) which is sufficient to promote magnetic relaxation via this state, giving the maximum calculated relaxation barrier (U cal ) of B527 K. It is important to note that a small transverse magnetic moment is calculated for the first three KDs (3.1 Â 10 À3 , 7.3 Â 10 À2 and 1.7 Â 10 À1 m B , respectively), suggesting the presence of weak Quantum Tunnelling of the Magnetisation (QTM) and again, relaxation via the third exited state. The Orbach processes related to the m J and m J + 1 excited states of opposite magnetization for the first four KDs are found to be very small (o0.16, Fig. 2). Furthermore, thorough analysis of the g-tensor (Table S7, ESI †) reveals axiality up to the third excited state (KD4).
The dc magnetic susceptibility measurements for 1 (Fig. S13, ESI †) show that the experimental w M T value of 14.1 cm 3 mol À1 K (at 300 K) is in close agreement with the theoretical value (14.2 cm 3 mol À1 K) for a single Dy(III) ion ( 6 H 15/2 , S = 5/2, L = 5, g = 4/3). Upon cooling, w M T decreases steadily to a value of 11.1 cm 3 mol À1 K at 20 K, due to thermal depopulation of the m J levels, before increasing to 12.0 cm 3 mol À1 K at 2.8 K. This low temperature increase is consistent with the presence of weak ferromagnetic intermolecular interactions. Furthermore, the w M T data of the diluted sample 3 instead decreases between 50-2 K, which further supports the hypothesis of weak ferromagnetic intermolecular interactions in 1 (Fig. S14, ESI †). Alternating current (ac) susceptibility measurements between 0.6-800 Hz, under zero external dc field, were performed in order to investigate the dynamics of the magnetisation for 1 and the Dy-doped lanthanum analogue, 3. Under zero external dc field, the out-of-phase, w M 00 magnetic susceptibility data exhibit welldefined maxima as a function of frequency ( Fig. 3 and Fig. S17, ESI †) and temperature with w M 00 peaks clearly observable up to 12 K for 1 (Fig. S15, ESI †) and up to 20 K for 3 (Fig. S16, ESI †).  For 1, the plots of w M 0 and w M 00 vs. temperature show a rapid increase in the low temperature region (Fig. S15, ESI †). Additionally, the low temperature set of peaks in the w M 00 (v) curves exhibit little temperature dependence (Fig. 3 upper), which could be attributed to faster relaxation effects (QTM). 13 For the diluted sample 3, the w M 00 (T) maxima under zero dc field, are shifted to higher temperatures and the signal at lower temperatures is significantly reduced, suggesting a slower relaxation of the magnetisation (Fig. S16, ESI †). The relaxation times, t, were extracted from the fit of the Argand plots of w M 00 vs. w M 0 using the generalized Debye model (Fig. S18, ESI †). 14 The a parameters found are relatively large in the range of 0.01-0.29 (2-13 K) for 1, and 0.01-0.41 (6-22 K) for 3, indicating a relatively wide distribution of relaxation times. 1 Thus, the Arrhenius plots are fitted considering more than one possible relaxation process yielding an energy barrier of U eff = B110 K for 1 (Fig. S19 and Table S9, ESI †) and U eff = B290 K for the diluted sample 3 (Fig. S20 and Table S9, ESI †). Importantly, it should be noted that these values are among the highest for high-coordinate lanthanide single-ion magnets (see Table S6, ESI †). To explore the role of low-lying vibrational levels that could enhance relaxation and lower the U cal barrier, we analysed the N-Dy-F bending mode which lies at 115 cm À1 (Fig. S29, ESI †). Calculations performed on selected vibrational modes corresponding to this frequency reveal a significant reduction in the estimated barrier height (see Fig. S29, ESI †).
To assess the strength of the intermolecular interactions, further calculations were performed which yielded small dipolar and intermolecular magnetic exchange couplings (0.02 cm À1 and 0.08 cm À1 respectively). These are expected to further enhance relaxation (see Fig. S30, ESI †). 15 Magnetisation vs. field hysteresis loops were performed on 1 and 3 in light of the large energy barriers observed. Low-temperature hysteresis studies were performed on a single crystal of 1 using an array of micro-SQUIDs. 16 The increase in coercivity with decreasing temperature (Fig. 4) and increasing scan rate (Fig. S26, ESI †) confirms 1 to be a SMM.
The M vs. H loops suggest the presence of QTM and have steps that are somewhat smeared out at low temperatures, possibly due to a distribution of local environments (e.g. disordered solvent molecules, crystals defects) and/or intermolecular interactions. For the diluted powder sample 3 more pronounced butterfly-like loops are observed until 3 K (average sweep rate of B10 mT s À1 ) (Fig. S27, ESI †). The promising magnetic properties and the high stability of 1, combined with the ability to modify either the axial ligand or the polydentate cage ligand, led us to study the effect on the magnetic dynamics of modulating the ligand environment in silico (Fig. 5). To do this, we have created a family of different model systems and used ab initio calculations to show how the ligand electronics can be used to tune and improve the relaxation properties (Fig. S31, S32 and Table S8, ESI †).
Substitution of the axial F À ion by monodentate formate or substituted carboxylates (models 2-4 Fig. 5) destroys the U cal barrier. These weaker axial groups reduce the crystal field splitting significantly, leading to smaller barrier heights ( Fig. 5 and Fig. S31, ESI †) and due to smaller charges compared to the nitrogen atoms of the polydentate ligand, the g zz direction changes (Fig. S32, ESI †). Stronger ligands ( À OR, models 1, 5 and 6 Fig. 5) maintain the g zz direction, but with smaller U cal values than 1. This suggests that axial substitution is detrimental in 1 with the F À ion being the most promising, as was recently shown by Norel et al. 17 We reasoned that if the coordination by the ligand nitrogen atoms is weakened, this should further enhance the barrier height, by moving towards a pseudo Dy-F environment. 18 Hence, we have substituted the -ortho and -para H atoms of the pyridinic ring with strong electron withdrawing groups (models 7-9 Fig. 5). For these models, the computed transverse anisotropy (see Table S8, model-7, model-8 and model-9, ESI †) is found to be significantly reduced, causing an impressive increase to give a U cal energy barrier of 645 K (for X = F, Z = F, Y = H, see Fig. 5).  Furthermore, the transverse matrix elements for the transition magnetic moments are reduced (see Fig. S31, ESI †) and hence the probability of QTM/TA-QTM is decreased. This suggests a promising route to realise higher barriers for magnetization reversal. Importantly, the models investigated were designed taking into consideration their likely future experimental realisation; i.e. they do not show strong steric hindrance and/or have low coordination numbers. To check further the effect of the transverse field we have rotated the -N 4 plane by AE6 degrees in a model complex (Fig. S33, ESI †) and in the presence of the strong axial F ion, changes in the calculated U cal values are found to be negligible (Fig. S34, ESI †). Efforts are currently underway to synthesise substituted analogues of the polydentate cage ligand in our laboratory and as a proof-of-concept we also report the crystal structure of a new ligand (Fig. S12 and Table S2, ESI †) where the electron withdrawing CN group, has been included in the ortho position of each pyridinic ring (Fig. 5  model-8, Fig. S31, S32 and Table S8, ESI †). Hence, future work will focus on the realisation of the above exciting family of complexes with high energy barriers along with good air and heat stability. The

Conflicts of interest
There are no conflicts to declare.