Fulvalene as a platform for the synthesis of a dimetallic dysprosocenium single-molecule magnet

A series of fulvalene-supported dimetallic dysprosium metallocene SMMs provides a roadmap to poly-cationic dysprosocenium single-molecule magnets.


Introduction
Observations of magnetic bistability in structurally well-dened, monodisperse nanomaterials have stimulated considerable interest in technology based on the quantum properties of atoms and molecules. For example, the demonstration of magnetic memory in single holmium atoms on surfaces has introduced potential for the fabrication of data storage devices with capacities surpassing those of conventional technology. 1,2 Molecule-based magnetic materials offer similar opportunities, accompanied by the advantage that their electronic structure can be tuned using imaginative synthetic chemistry. Recent advances include magnetic molecules incorporated into spintronic devices or used as the basis of quantum algorithm operations. [3][4][5] The magnetic hysteresis properties of single-molecule magnets (SMMs) have also been acclaimed as a possible source of novel data storage materials and, while such applications may eventually be possible, certain obstacles must rst be overcome. [6][7][8][9][10] Challenges to the implementation of SMMbased technology include that: (1) all known systems require cooling with cryogens in order to show hysteresis; (2) uniform nano-structuring of SMMs on surfaces is difficult, and; (3) the chemical stability of SMMs throughout surface deposition processes and, subsequently, in a device environment is not guaranteed, regardless of whether or not the bulk material itself is air-sensitive. However, encouraging progress has been made, such as the discovery of magnetic hysteresis in an SMM at 80 K, 11 i.e. above the boiling point of liquid nitrogen, and elegant surface studies of some SMMs have demonstrated the singlemolecule origins of the hysteresis. 12 The advances made to date strengthen the motivation for further research into SMMs, particularly the exploration of new synthetic strategies that aim to increase the temperatures at which these materials function. Considerable effort has been invested into maximizing the effective energy barrier to reversal of the magnetization (U eff ) and the magnetic blocking temperature (T B ). A few highly anisotropic metal ions have proven to be important as the basic ingredient in an SMM, with dysprosium being the most popular and terbium, erbium and cobalt(II) also playing prominent roles. [13][14][15][16][17][18][19][20][21] In the case of Dy 3+ , a 4f 9 ion with oblate spheroidal electron density, successful SMM synthesis strategies tend to produce compounds in which the metal occupies a coordination environment with a strong and highly axial crystal eld. [22][23][24] This approach partly explains why the highest-performing SMMs are based on metallocene cations of the type [Dy(h 5 -Cp R ) 2 ] + , where the bulky cyclopentadienyl ligands [Cp R ] À provide the strong, axial crystal eld whilst also blocking the formation of any deleterious equatorial crystal eld. 6,11,[25][26][27][28][29] Previous work on sandwich SMMs constructed with erbium-COT (COT ¼ cyclo-octatetraenyl) 30,31 and terbium-phthalocyanine 32,33 building blocks has shown that the parameters U eff and T B increase when two or more blocks are linked to form multidecker sandwich complexes. We therefore reasoned that improvements in the SMM properties of dysprosocenium cations might be possible if closely related polymetallic versions could be synthesized. To investigate this idea, we targeted the synthesis of a dimetallic dysprosocenium cation by replacing a cyclopentadienyl ligand with a bicyclopentadienyl ligand, also known as fulvalenyl or pentafulvalenyl, in which two cyclopentadienyl rings share an exocyclic carbon-carbon bond. 34 Dinucleating fulvalenyl ligands have been used extensively in transition metal sandwich chemistry, 35 with recent examples including macrocyclic poly(ferrocenyl) compounds with potential applications as molecular electronic materials. 36,37 In contrast, the use of such ligands in f-element chemistry is uncommon, and in the case of the lanthanides was, hitherto, limited to the dimetallic divalent compounds [M(THF)(h 5 :h 5 -Fv tttt )] 2 with M ¼ Sm, Eu or Yb. 38
The molecular structures of all three compounds were determined by single-crystal X-ray diffraction ( Fig. 1 and Table S1 †). The structure of 1 consists of two similar half-sandwich units in which each dysprosium is ligated by one cyclopentadienyl unit of the Fv tttt ligand in an h 5 -manner, with additional coordination by two k 3 -borohydride ligands and a THF ligand (Fig. 1). The Dy1-C distances are in the range 2.607(4)-2.698(4)Å and the distance from Dy1 to the fulvalenyl C 5 centroid is 2.361(1)Å; the analogous distances for Dy2 are essentially the same (Table S2 † In compound 2, the two unique halves of the molecule each consist of a dysprosium centre sandwiched between an h 5 -Cp* ligand and an h 5 -Fv tttt ligand, with bridges between the metal atoms occurring via both borohydride ligands. The change in the bonding mode of the borohydride ligands in 2 as compared to those in 1 is presumably a consequence of the spatial demands of the Cp* ligands. For Dy1, the bond distances to the Cp* ligand are in the range 2.643(3)-2.667(2)Å and those to the fulvalenyl ligand are 2.630(2)-2.704(4)Å, with associated Dy1centroid distances of 2.362(1)Å and 2.378(1)Å, respectively; the corresponding distances involving Dy2 are not signicantly different (Table S3 †). The metallocene bending angles subtended at Dy1 and Dy2 are 137.913(1) and 139.143(1) , respectively. The bridging borohydride ligands in 2 greatly reduce the extent of twisting between the two halves of the Fv tttt ligand relative to 1, as shown in the C2-C1-C6-C7 torsional angle of 30.0(4) . The Dy/Dy separation is, at 4.148(1)Å, also markedly shorter than that in 1. The IR absorptions for the borohydride ligands occur in the rangeỹ ¼ 2124-2473 cm À1 (Fig. S2 †).
The synthesis of 1, 2 and [3][B(C 6 F 5 ) 4 ] demonstrates that fulvalenyl ligands can indeed form the structural basis of linked dysprosium metallocenes. In the next stage, our aim was to investigate how the changes in the crystal eld environment experienced by the Dy 3+ centres impact upon the SMM properties.

Magnetic properties
The magnetic properties of 1, 2 and [3][B(C 6 F 5 ) 4 ] were studied in static (DC) and dynamic (AC) magnetic elds using a Magnetic Property Measurement System. The temperature dependence of the product of the molar magnetic susceptibility and temperature, i.e. c M T(T), is consistent with the dimetallic composition of the three compounds. The values of c M T at 300 K are 27.3, 27.2 and 27.5 cm 3 K mol À1 for 1, 2 and [3][B(C 6 F 5 ) 4 ], respectively, are close to the theoretical value of 28.2 cm 3 K mol À1 for a complex containing two weakly interacting Dy 3+ ions with 6 H 15/2 ground multiplets (Fig. S4, S6 and S8 †). 39 The decreases in c M T with temperature for 1 and [3][B(C 6 F 5 ) 4 ] are similar and gradual without featuring a sharp drop at lower temperatures, reaching values of 22.2 and 21.9 cm 3 K mol À1 at 2.0 K. The decrease in c M T with temperature for 2 is similar in the hightemperature regime, however a much more pronounced decrease was observed below 20 K such that a value of 17.5 cm 3 K mol À1 is reached at 2.0 K. The decrease in c M T(T) with decreasing temperature for all three compounds can be accounted for by gradual depopulation of the excited crystal eld levels of the Dy 3+ ions, which may occur concomitantly with antiferromagnetic exchange coupling becoming more prominent as thermal randomization effects diminish, particularly in compound 2. The isothermal eld-dependence of the magnetization, M(H), for each compound also reects the presence of two Dy 3+ ions per complex, reaching values of 9.89, 10.11 and 9.60 Nb at 7 T and 1.9 K for 1, 2 and [3][B(C 6 F 5 ) 4 ], respectively (Fig. S5, S7 and S9 †).
The real (c 0 ) and imaginary (c 00 ) components of the AC magnetic susceptibility were measured for each compound as functions of temperature and AC frequency (n) (Fig. 2, S10-S12, S15-S17, S20-S22 †), using zero DC eld and a small AC eld of 3 Oe. The observation of well-dened maxima in the c 00 (T) and c 00 (n) plots for 1, 2 and [3][B(C 6 F 5 ) 4 ] indicate slow relaxation of the magnetization without the need for an external DC eld. For compound 1, maxima were observed in the c 00 (n) plot from 1.9-14 K before the upper frequency limit of the measurement system is reached (Fig. 2). Up to 6 K, the position of the frequency maximum and, hence, the relaxation time (s), varies only slightly with temperature, suggesting that relaxation via quantum tunnelling of the magnetization (QTM) is dominant in this regime. At higher temperatures, the frequency maximum becomes strongly temperature dependent, which is likely to reect thermally activated relaxation becoming dominant. The relaxation times for each temperature were extracted and plotted as a function of T À1 , revealing that the change from QTM to activated regimes is abrupt (Fig. 2). Fitting the data with the equation , where s 0 À1 and U eff denote the Orbach parameters, C and n denote the Raman parameters, and the rate of QTM is s QTM À1 , gives an energy barrier of U eff ¼ 154(15) cm À1 with s 0 ¼ 3.93(6) Â 10 À11 s, the Raman parameters are C ¼ 8. 16(3) Â 10 À4 s À1 K Àn , n ¼ 5.87(1) and s QTM ¼ 2.31(1) Â 10 À3 s. The AC susceptibility measurements on compounds 2 and [3][B(C 6 F 5 ) 4 ] revealed that slow relaxation of the magnetization occur across wider temperatures ranges of 1.9-55 K and 1.9-72 K, respectively, relative to 1 (Fig. 2). In the case of 2, the c 00 (n) plot consists of well-dened maxima from 1.9 K up to 40 K, and for [3][B(C 6 F 5 ) 4 ] the maxima were observed from 1.9 K up to 60 K. The temperature dependence of the relaxation times for 2 revealed that the system does not cross to a purely temperatureindependent regime even at the lowest measurement temperature (Fig. 2). Hence, it was possible to t the ln s vs. T À1 data for 2 without a QTM term, which produced Orbach parameters of U eff ¼ 252(4) cm À1 , s 0 ¼ 1.94(3) Â 10 À8 s and Raman parameters of C ¼ 4.56 (2) Â 10 À4 s À1 K Àn , n ¼ 4.12 (1). For [3][B(C 6 F 5 ) 4 ], aer a strong dependence of ln s on T À1 in the hightemperature regime, the relaxation time is only weakly temperature-dependent below 5 K. A t of the data for this compound gave U eff ¼ 384(18) cm À1 , s 0 ¼ 1.37(6) Â 10 À8 s, C ¼ 6.55(4) Â 10 À1 s À1 K Àn , n ¼ 2.03(2) and s QTM ¼ 1.39 (6) Â 10 À1 s.
Comparing the U eff parameters for 1, 2 and [3][B(C 6 F 5 ) 4 ] reveals substantial increases on moving through the series. This trend can be understood in a qualitative sense by considering how the composition and geometry of the crystal eld experienced by each Dy 3+ centre varies. Whilst the Dy 3+ ions in all three compounds must experience a dominant axial crystal eld to show any slow relaxation properties in zero DC eld, this is clearly relatively weak in 1 and stronger in 3. The presence of only one cyclopentadienyl group per Dy 3+ in 1 is sufficient to induce SMM behaviour by providing a relatively strong axial crystal eld, but the two borohydride ligands and the THF ligand provide a competing equatorial eld that limits the barrier height. In 2, the additional [Cp*] À ligands strengthen the axial component of the crystal eld whilst simultaneously reducing the number of equatorial ligands, resulting in an increase in the barrier by approximately 100 cm À1 (60%) relative to 1. Upon forming 3, not only is another equatorial borohydride ligand removed from the coordination environment of both Dy 3+ ions, the two metallocene units are also less bent by approximately 7 -8 and the individual cyclopentadienyl donor groups are slightly closer to the metal centres than in 2. Consequently, the barrier height in 3 is approximately 130 cm À1 (50%) greater than that in 2. Furthermore, the ln s versus T À1 data are also consistent with the single-ion QTM being reduced by intramolecular exchange interactions between the Dy 3+ ions. The Dy/Dy distances decrease in the order 1 > 3 > 2, hence the QTM should be slowest in 2, as observed.
Compounds 1, 2 and [3][B(C 6 F 5 ) 4 ] further illustrate the magneto-structural correlation developed for dysprosium and terbium metallocene SMMs, in which the cyclopentadienyl ligands provide dominant axial crystal elds and the properties are attenuated by the equatorial ligands. 28,40,41 In addition to accounting for the variation in energy barrier across the series, their hysteresis properties can also be interpreted in terms of the molecular structure. Thus, although the cyclopentadienyl ligands dominate the crystal eld, the borohydride and THF ligands provide non-negligible equatorial components, which result in the magnetization versus eld hysteresis occurring as narrow S-shaped curves at 1.9 K and various eld in the range AE5 T with an average scan rate of 23 Oe s À1 for each compound (Fig. S14, S19 and S24 †). There is essentially no hysteresis for 1, however the hysteresis for 2 displays narrow loops centred on eld values of approximately AE1.3 kOe and AE5.0 kOe, respectively, and [3][B(C 6 F 5 ) 4 ] shows a loop around AE1.7 kOe. These subtle effects are presumably a consequence of exchange bias between the Dy 3+ centres affecting the rate of relaxation via QTM, suggesting that the borohydride ligands are effective at transmitting exchange interactions. 42 This proposal is consistent with a recent study of magnetic exchange in [Ln(BH 4 ) 3 ] (Ln ¼ Gd-Tm), in which it was found that {HBH} bridges between the metal centres allow antiferro-or ferro-magnetic exchange, albeit with very small coupling constants. 43

Theoretical analysis
The local magnetic properties of each individual Dy 3+ ion in 1-3 were rst studied. State-averaged complete active space selfconsistent eld (SA-CASSCF) calculations 44-48 followed by restricted active space state interaction treatment of spin-orbit coupling (SO-RASSI) 49 and calculation of local magnetic properties using the SINGLE_ANISO_OPEN module 50,51 were carried out on each ion while the other Dy 3+ ion in the complex was replaced by diamagnetic yttrium. The properties of the eight lowest Kramers doublets (KDs) of each ion are listed in Tables S8-S13. † In each case the ground Kramers doublet (KD) is characterized by a strongly axial g-tensor with small but nonvanishing transverse components. The direction of the principal magnetic axis of each ground KD is determined by an axial-type interaction with the Fv tttt and Cp* ligands (Fig. 3).
The rst-excited local KDs of the two Dy 3+ ions in 1 lie 176 cm À1 and 181 cm À1 above the ground KD. The angles between the principal magnetic axes of the ground and rst excited states are 41.3 and 43.0 , respectively. These relatively large angles should lead to an efficient Orbach mechanism via the rst-excited KD, and an effective barrier corresponding to the energies of the rst excited states. Indeed, the effective barrier height determined from the ts is 154 cm À1 which agrees well with the calculated values. A qualitative ab initio barrier for the relaxation of magnetization was constructed using a well-established methodology, 52 where the relaxation pathway is traced by following large magnitudes of transition magnetic moment matrix elements between different states. The barriers for 1 are shown in Fig. 3 and the quantitative transition magnetic moment matrix elements are listed in Table  S14. † Based on the calculated values, the barrier should be crossed earliest at the rst-excited KD and latest at the hexcited KD. Based on the experimental barrier height, the most likely relaxation takes place via the rst-excited KD.
In 2, the lowest four KDs on each Dy 3+ ion have roughly collinear principal magnetic axes. The calculated transition magnetic moments (Fig. 3 and Table S15 †) predict that the barrier becomes crossed either at the second-(364 cm À1 and 362 cm À1 ) or third-excited (452 cm À1 and 457 cm À1 ) local KDs. The experimentally determined barrier height (252 cm À1 ) is, however, closest to the energies of the rst-excited local KD (214 cm À1 and 208 cm À1 ). The transition matrix elements for an Orbach process via the rst excited KD are, however, not vanishingly small and this mechanism remains plausible. The rst four KDs of Dy1 and the rst three KDs of Dy2 in 3 are also roughly collinear. Based on the transition dipole moments (Fig. 3 and Table S16 †) the barrier is most likely crossed at the second (546 cm À1 and 551 cm À1 ) or third excited KD (667 cm À1 and 666 cm À1 ). The experimentally determined barrier height (384 cm À1 ) is again closest to the energy of the rst excited KD (336 cm À1 and 339 cm À1 ) and, again, an Orbach mechanism via the rst excited KD has non-vanishing transition magnetic moment matrix elements and remains plausible.
Based on the energy of the rst excited KD (which in all cases corresponds to the experimentally determined barrier height), the axiality of the crystal-eld (CF) environments of the Dy 3+ ions clearly increases from 1 to 3. Further to the qualitative analysis of this trend (see above), quantitative insight was obtained by calculating the ab initio CF parameters 53 for each Dy 3+ ion and the results are listed in Tables S17-S19 † using the Iwahara-Chibotaru notation. 54 The effect of the CF can be understood qualitatively by considering the second-rank parameters, summarized in Table 1. The axial B 20 parameters clearly increase from 1 to 2 to 3, which is consistent with the increased axiality of the CF. The parameters should be compared to those calculated for the current benchmark SMM, i.e. the [(C 5 Me 5 )Dy(C 5 i Pr 5 )] + cation, which has an energy barrier of 1540 cm À1 and a blocking temperature of 80 K, 11 also listed in Table 1. It is immediately clear that the axiality falls short of that in [(C 5 Me 5 )Dy(C 5 i Pr 5 )] + and the off-diagonal |B 2AE2 | parameters of 1-3 are much larger. Thus, the equatorial borohydride  ligands in 1-3, and the lack of axial Cp* ligands in 1, clearly lead to much reduced axiality. The non-negligible off-diagonal CF parameters lead to signicant mixing of the different local angular momentum eigenstates dened by some denite angular momentum projection M. This is evident from Tables S20-S25, † which give the projections of the ab initio CF eigenstates on angular momentum eigenstates. The states in the ground KDs have a large contribution from a state with some denite M, but in all cases even the states in the ground KD are signicantly mixed. This is consistent with the effective barrier being crossed at the rst excited local KD in each case.
The effect of intramolecular interaction between the two Dy 3+ ions was studied by the Lines model 55 and the magnetic point-dipole approximation as implemented in the POLY_-ANISO module. 51,56,57 The Lines model describes the exchange interaction in terms of a single phenomenological scalar parameter which was determined by minimizing the standard deviation between the measured and calculated magnetic susceptibilities. Due to the general lack of low-temperature features in the susceptibility of 1 and 3 (Fig. S4, S8 and S28 †), the parameter could only be only reliably determined for 2. The eigenvalues of the Lines exchange operator and the dipolar coupling operator where mapped to an effective Ising-type Hamiltonian of the form: In eqn (1), theS ¼ 1/2 pseudospin operators act on the ground KDs of the two Dy 3+ ions. The dipolar coupling parameters J dipolar are À0.9 cm À1 , À2.5 cm À1 and À1.4 cm À1 for 1-3, respectively, which are consistent with variations in the Dy/Dy distance between the two ions. The exchange parameter J ex determined for 2 is À1.2 cm À1 , hence the total exchange interaction is J tot z À3.7 cm À1 . The absence of bridging borohydride ligands in 1 is likely to result in a vanishingly small J ex parameter relative to 2, which, combined with the smaller J dipolar parameter, provides further support for the idea that the steps in the M(H) hysteresis in 2 and 3 occur as a consequence of exchange-bias effects.  [3][B(C 6 F 5 ) 4 ]), we have shown that a dimetallic dysprosocenium complex can be synthesized. All three fulvalenyl-supported compounds are SMMs in zero applied eld and show appreciable increases in the effective energy barrier to reversal of the magnetization across the series, which more than doubles from 154(15) cm À1 in 1 to 384(18) cm À1 in 3. The improvements in the energy barrier are attributable to the increasingly dominant axial crystal eld provided by the Fv tttt and Cp* ligands balanced against the inuence of the equatorial borohydride ligands. Quantitative support for this magneto-structural correlation was obtained from ab initio calculations, which revealed marked increases in the axial B 20 parameter across the series but also with appreciable non-axial parameters.

Conclusions
It is instructive to consider these results in light of the SMM properties of [(C 5 Me 5 )Dy(C 5 i Pr 5  Dy(C 5 i Pr 5 )(BH 4 )], there many structural features in common with 2 and 3 and yet the energy barrier is a miniscule 7(1) cm À1 in zero eld. 11 This comparison further highlights how the strategy of combining metallocene building blocks to give a dimetallic dysprosocenium cation may improve SMM performance. In contrast, the barrier determined for [(C 5 i Pr 5 ) Dy(BH 4 ) 2 (THF)] in zero eld is 241(7) cm À1 , which is markedly larger than the barrier of 154(15) cm À1 in 1. However, since the Dy-Cp cent distances in the two half-sandwich complexes are very similar, the different barriers are likely to originate from the inuence of the THF ligands. The Dy-O distances in 1 are approximately 0.03-0.08Å shorter than those in its monometallic counterpart, pointing towards a stronger equatorial component of the crystal eld and, therefore, relaxation via an Orbach process with a lower barrier. Looking forward, if a dimetallic dicationic dysprosocenium complex such as [{Dy(h 5 -Cp*)} 2 (h 5 :h 5 -Fv tttt )] 2+ could be synthesized, substantial increases in the axial crystal eld parameters and decreases in the non-axial parameters should combine with the benecial effects of exchange coupling in a dimetallic complex. Whilst substituent-dependent geometric factors will clearly play an important role in determining the properties, a dimetallic dysprosocenium dication can reasonably be anticipated to display enhancements in the energy barrier and blocking temperature relative to the current benchmark SMM.

Conflicts of interest
There are no conicts to declare.