2.1 General

All the reactions were carried out under aerobic conditions. [Mn^III₂Mn^II₄O₂(piv)₁₀(4-Me-py)_2.5(PivH)_1.5] (2) was obtained as reported [3d]. Elemental analyses for C, H and N were carried out at the Institute for Inorganic Chemistry at Karlsruhe Institute of Technology.

2.2 Preparation

[Mn₁₁Dy(O)₈(OH)(piv)₁₆(NO₃)(CH₃CN)]·2CH₃CN·½C₇H₁₆ (2·2CH₃CN·½C₇H₁₆): a stirred slurry of [Mn₆O₂(Piv)₁₀(4-Me-py)_2.5(PivH)_1.5] (0.20 g, 0.11 mmol) in MeCN (10 ml) was heated to 70 °C, followed by addition of Dy(NO₃)₃·6H₂O (0.20 g, 0.44 mmol), resulting in a dark-brown solution after 20 min. After stirring under reflux for an additional 30 min, the solution was cooled to room temperature and divided between five small (8 ml) vials, each with 2 ml of solution. Each of these vials was placed into a larger (25 ml) vial containing 2 ml of heptane and the larger vial was sealed. After 2–3 days some white microcrystalline powder appeared on the walls and bottom of the small vials. At this point each large vial was opened every day to check for monocrystals with a microscope and then resealed. After 7–8 days the white material disappeared and brown crystals began to appear. After a further 7 days the brown crystals were collected by filtration, washed with MeCN + H₂O (1:1) to remove residual traces of the (water-soluble) white impurity, and dried in air. A similar yield of the final crystals was obtained after more than 4–5 weeks if the big vials were not opened during the crystallization period. With the procedure which is to briefly open the big vial every day, the crystallisation period can be shortened to 2 weeks. Probably, this procedure, in addition to faster evaporation of solvent, facilitates also the release of the pressure which may speed up the crystallisation. Combined yield from all vials = 0.065 g (46.0% based on Mn). Calc. for C_82.1H_149.8DyMn₁₁NO₄₄ (= 2·0.3 C₇H₁₆): C 37.61, H 5.76, N 0.53%; found: C 37.47, H 5.82, N 0.47%. IR (KBr disk, cm⁻¹): 3430 (s), 2965 (s), 2932 (s), 2908 (s), 2323 (w), 1554 (vs), 1485 (vs), 1461 (s), 1431 (vs), 1382 (s), 1360 (s), 1303 (s), 1230 (vs), 1032 (w), 939 (m), 893 (m), 800 (s), 785 (m), 665 (s), 623 (s), 587 (s), 458 (w).

[Mn₁₁Tb(O)₈(OH)(piv)₁₆(NO₃)(CH₃CN)]·½CH₃CN·¾C₇H₁₆ (1·½CH₃CN·¾C₇H₁₆): this compound as brown crystals was obtained using the same procedure as for 2 with Tb(NO₃)₃·6H₂O in place of Dy(NO₃)₃·6H₂O. Total yield: 0.060 g (43.0% based on Mn). Calc. for C_82.1H_149.8TbMn₁₁NO₄₄ (= 1·0.3 C₇H₁₆): C 37.66, H 5.77, N 0.53%; found: C 37.48, H 5.79, N 0.47%. IR (KBr disk, cm⁻¹): 3431 (s), 2964 (s), 2932 (s), 2907 (s), 2323 (w), 1553 (vs), 1485 (vs), 1461 (s), 1431 (vs), 1381 (s), 1359 (s), 1302 (s), 1229 (vs), 1032 (w), 938 (m), 893 (m), 799 (s), 785 (m), 664 (s), 623 (s), 587 (s), 457 (w).

[Mn₁₁Ho(O)₈(OH)(piv)₁₆(NO₃)(CH₃CN)]·2CH₃CN·½ C₇H₁₆ (3·2CH₃CN·½C₇H₁₆): this compound as brown crystals was obtained using the same procedure as for 2 with Ho(NO₃)₃·6H₂O in place of Dy(NO₃)₃·6H₂O. Yield: ∼0.055 g (39.0% based on Mn). Calc. for C_81.4H_148.2HoMn₁₁NO₄₄ (= 3·0.2 C₇H₁₆): C 37.40, H 5.71, N 0.53%; found: C 37.23, H 5.78, N 0.46%. IR (KBr disk, cm⁻¹): 3419 (s), 2964 (s), 2932 (s), 2907 (s), 2320 (w), 1553 (vs), 1485 (vs), 1460 (s), 1430 (vs), 1381 (s), 1359 (s), 1302 (s), 1228 (vs), 1032 (w), 938 (m), 893 (m), 799 (s), 785 (m), 667 (s), 623 (s), 587 (s), 457 (w).

[Mn₁₁Y(O)₈(OH)(piv)₁₆(NO₃)(CH₃CN)]·2CH₃CN·½ C₇H₁₆ (4·2CH₃CN·½C₇H₁₆): this compound as brown crystals was obtained using the same procedure as for 2 with Y(NO₃)₃·6H₂O in place of Dy(NO₃)₃·6H₂O. Yield: ∼0.050 g (35.7% based on Mn). Calcd for C_82.1H_149.8YMn₁₁NO₄₄ (= 4·0.3 C₇H₁₆): C 38.70, H 5.92, N 0.55%; found: C 38.51, H 6.11, N 0.46%. IR (KBr disk, cm⁻¹): 3412 (s), 2965 (s), 2932 (s), 2907 (s), 2319 (w), 1551 (vs), 1486 (vs), 1460 (s), 1431 (vs), 1379 (s), 1359 (s), 1302 (s), 1229 (vs), 1033 (w), 938 (m), 892 (m), 797 (s), 782 (m), 663 (s), 620 (s), 585 (s), 458 (w).

2.3 Magnetic measurements

The magnetic susceptibility measurements were carried out on polycrystalline samples using a Quantum Design SQUID magnetometer MPMS XL over the temperature range 1.8–300 K for dc applied fields up to 7 T. Alternating current (ac) susceptibility measurements were performed with an oscillating field of 3 Oe and ac frequencies ranging from 1 to 1500 Hz. M versus H measurements were performed at 100 K to check for the presence of ferromagnetic impurities and none were found. The magnetic data were corrected for the sample holder and the diamagnetic contribution.

2.4 Crystal structure determinations

Data for compounds 1-3 were collected at 100 K on a Bruker SMART Apex CCD diffractometer using graphite-monochromated MoKα radiation. Semiempirical absorption corrections were made using SADABS [8a]. The structures were solved using direct methods, followed by full-matrix least-squares refinement against F² (all data) using SHELXTL [8b]. Anisotropic refinement was used for all ordered non-H atoms; organic H atoms were placed in calculated positions. Disordered t-Bu groups were refined with isotropic partial methyl carbon atoms, using geometrical restraints. One disordered lattice MeCN in the lattice of compounds 1 and 2 could not be refined satisfactorily and was handled using the SQUEEZE option in PLATON [9]. Lattice heptane molecules were disordered over special positions, and were refined with half-occupancy C atoms with geometrical similarity restraints. Crystals of 4 diffracted with rather low intensity; however their unit cell showed that they were isotypic to 2 and 3. Since the crystals can lose lattice solvent rather readily on exposure to air, the compositions and formula weights of the samples used in the magnetic measurements were estimated from microanalytical data, particularly when these came from different batches from those used for the structure determinations.

Crystallographic data (excluding structure factors) for the structures in this paper have been deposited with the Cambridge Crystallographic Data Centre as supplementary publication nos. CCDC 862345-862347. Copies of the data can be obtained, free of charge, on application to CCDC, 12 Union Road, Cambridge CB2 1EZ, UK: http://www.ccdc.cam.ac.uk/cgi-bin/catreq.cgi, data_request@ccdc.cam.ac.uk, or fax: +44 1223 336033.

3.1 Structural analysis

The complexes were structurally characterized using single crystal X-ray crystallography. The details of crystallographic data and structure refinement parameters are summarized in Table 1. Compounds 2-4 crystallize isotypically in the monoclinic space group P2₁/n with Z = 4, compound 1 in P2₁/c with Z = 4. Nonetheless, the molecular structure of the Mn₁₁Tb complex in 1 is very similar to those in 2 and 3, both in terms of atomic connectivity and the orientation of the Mn^III Jahn-Teller elongation axes.

The structure of the compound 2 will be discussed in detail as a representative example (Fig. 1). The oxidation states of the Mn centres were determined by bond-valence sum (BVS) calculations [10], with Mn(1), Mn(2) and Mn(5)-Mn(11) assigned as Mn^III, and Mn(3) and Mn(4) as Mn^II. The Mn centres all have octahedral coordination geometries except for Mn(11), which is square-pyramidal. The high spin Mn^III ions all show the expected Jahn-Teller elongations. The assignments of O(1)-O(6) as (μ₄-O)²⁻, O(8) and O(9) as (μ₃-O)²⁻, and of O(7) as (μ₃-OH)⁻ were also confirmed by BVS calculations and the H-atom on O(7) could be located and refined.

The Mn₁₁Dy core of 2 is closely related to that of our previously reported “bell-shaped” Mn₁₁Ln₂ complexes [3d,7] and its core is compared with that of the Mn₁₁Gd₂ compound in Fig. 1. The Mn^III and Mn^II centres again form the shell of the bell with Mn(1) at the apex, Mn(2)-Mn(5) at the shoulder of the bell, and the remaining six Mn^III centres forming the rim of the bell. Although the two Mn^II centres in 2 are once again located on the shoulder of the bell, they are now on opposite sides of the bell, whereas in the Mn₁₁Gd₂ compound they were on the same side and linked by a pivalate bridge. Dy(1) is nine-coordinate and is connected to each of the eleven Mn centres through the six (μ₄-O), the two (μ₃-O) and the (μ₃-OH) bridges to give a rather irregular coordination polyhedron (Fig. 2). The Mn₁₁Dy core can thus be considered as derived from the “bell-shaped” Mn₁₁Ln₂ core [3d,7], but with the second Dy at the end of the bell's “clapper” cut off (Scheme 1).

Of the sixteen pivalate ligands, the unusual (μ₄,η²,η²) bridging mode, which was seen in the Mn₁₁Ln₂ compounds [3d,7], is observed for one pivalate ligand. Five further pivalates adopt a (μ₃,η²,η¹) triply-bridging mode, while the remaining pivalates and a NO₃⁻ anion form simple syn,syn-bridges between pairs of metal centres. The octahedral coordination of Mn(7) is completed by a coordinated acetonitrile molecule. The molecules are well separated within the crystal structure and no intermolecular hydrogen bonds were observed in the crystal packing.

3.2 Magnetic properties

The dc magnetic susceptibility data for compounds 1-4 were collected in the 1.8–300 K temperature range under a field of 0.1 T (Fig. 3). The dc magnetic data, together with the Weiss constants obtained from Curie-Weiss plots using the data above 130 K, are summarized in Table 2. The χT vs T plots for all compounds show similar profiles with the χT product decreasing in a monotonic fashion over the full temperature range indicating the presence of dominant antiferromagnetic (AF) interactions. The room temperature χT value of 30.06 cm³ K mol⁻¹ in 4 is lower than the expected value for nine Mn^III and two Mn^II non-interacting ions (35.75 cm³ K mol⁻¹), suggesting that the overall AF interactions present between the constituent Mn ions are relatively strong. This is supported by the relatively large and negative value for the Weiss constant of −50.9 K (Table 2) and also by the small magnitude of the magnetization at 2 K under a 7 T field, 7.0 μ_B, which is significantly lower than that (46 μ_B) calculated for a parallel alignment of all the spins (Fig. S1). Furthermore, extrapolation of the in-phase susceptibility product (χ’T) of 4 at very low temperature approaches 2.4 cm³ K mol⁻¹ (Fig. S2), suggesting a small spin ground state of S ≈ 2 in this compound.

For compounds 1–3, the experimental χT product observed at 300 K is in good agreement with the sum of the value of 4 (30.06 cm³ K mol⁻¹) and the Curie constant of single Tb^III, Dy^III and Ho^III ions, respectively (Table 2). In order to assess the interaction between the paramagnetic Ln^III and the Mn₁₁ unit, we can subtract the molar susceptibility contribution of the Y^III analogue from the susceptibilities of 1-3. The ‘subtracted’ χT product increases with decreasing temperature (Fig. S3) suggesting that the single Ln^III ion is ferromagnetically coupled to the Mn₁₁ unit. This is in line with the fact that the Weiss constants of 1-3 are much less negative than that of the diamagnetic Y^III analogue 1. The ferromagnetic interaction between Ln^III and the Mn₁₁ unit is undoubtedly of smaller magnitude than the AF interactions amongst the Mn^II/III ions in the shell.

The field dependence of the magnetization at low temperatures for each of the compounds 1-3 shows a relatively fast increase of the magnetization at low fields, followed by an almost linear increase without clear saturation up to 7 T, where it reaches 14.8, 14.5, and 12.3 μ_B for 1, 2 and 3, respectively (Fig. S1). This observation is indicative of the presence of magnetic anisotropy and/or excited levels mixing into the ground state.

As a result of the magnetic anisotropy present in these compounds, the ac susceptibility measurements were checked under zero dc field. There is only a very weak out-of-phase signal shown above 1.8 K for compound 4, while for 1, 2 and 3 out-of-phase signals are clearly detected below 3 K (Fig. S4). The frequency dependent out-of-phase signals suggest that all these compounds exhibit slow relaxation of its magnetization. The weak slow relaxation observed in compound 4 results from the small contribution of the spin ground state (S ≈ 2) arising from the strong AF couplings between the Mn ions. The significant enhancement to the relaxation observed on incorporation of the 4f ions in place of the Y^III is similar to what we observed for the Mn₄Ln₅ compounds [3e].

In order to confirm SMM behaviour present in these compounds, single crystal magnetization measurements were performed using an array of micro-SQUIDs at temperatures down to 40 mK [11]. Below 1.0 K hysteresis loops are seen in magnetization vs field studies whose coercivities increase with decreasing temperature and increasing sweeping rate (Fig. 4 and Fig. S5). The shape and the width of hysteresis loops observed for the Mn₁₁Tb (1) and Mn₁₁Dy (2) compounds are rather similar in that the coercivity remains narrow at low fields indicating fast tunnelling occurs at H = 0, but the Mn₁₁Ho compound 3 has a somewhat larger coercivity suggesting less tunnelling at H = 0 in this case. The tunnelling at H = 0 present in the Mn₁₁Tb (1) and Mn₁₁Dy (2) compounds is strong enough to make it impossible to obtain a reliable Arrhenius plot, even though slow relaxation is seen. However, for the Mn₁₁Ho compound 3, the dc magnetization decay could be monitored with time, with the resulting effective energy barrier and the relaxation time of 6.0 K and 8.6 × 10⁻⁴ s, respectively (Fig. 5). Since there are no obvious pathways for intermolecular interactions the observed hysteresis results from intramolecular slow relaxation of the magnetization.

The Mn₁₁Y compound 4 and our previously reported Mn₁₁La₂ complex [7] have similar bell-shaped Mn^III₉Mn^II₂ cores and their rare-earth ions are diamagnetic. Although they both have small spin ground states with S ≈ 2, 4 shows weak out-of-phase signals in its ac susceptibility, whereas the Mn₁₁La₂ does not. These two compounds are respectively isostructural to 2 and to the Mn₁₁Gd₂ complex, for which the Mn₁₁ cores and orientations of the Mn^III Jahn-Teller axes are compared in Fig. 1. Although quantitative analysis of the Jahn-Teller axes is not possible, comparison of the two cores in Fig. 1 suggests that these axes might be better aligned in the Mn₁₁Ln series than in the Mn₁₁Ln₂ one. In the Mn₁₁Ln compounds (Fig. 1, below left), seven of the Jahn-Teller axes are aligned approximately in the direction of the Ln(1)-Mn(1) vector, with only those of Mn(1) and Mn(5) orientated perpendicular to this direction. In the Mn₁₁Ln₂ series (Fig. 1, below right) three such axes, those for Mn(5), Mn(8) and Mn(9), are oriented essentially perpendicular to the other six. This would be in line with the idea that compound 4 should have a larger overall molecular uniaxial anisotropy arising from the tensorial sum of the anisotropies of the individual ions.

It is appropriate at this point to re-examine the coordination polyhedron of the Dy^III ion in 2, which is noticeably oblate, with Dy(1) lying rather close to the plane of the pentagon defined by the oxo ligands O(1), O(2), O(3), O(4) and O(8). In their review of lanthanide anisotropy and single-molecule magnet behaviour, Rinehart and Long point out that such a coordination geometry is rather unusual for Dy^III, with axially-dominated geometries being more common. Such prolate geometries result in uniaxial single-ion anisotropies for ions such as Tb^III and Dy^III, for which the M_J states with high |J| have oblate electron densities [12]. The coordination polyhedra of the lanthanides in 1 and 2 are therefore unlikely to favour uniaxial single-ion anisotropy for their Tb^III or Dy^III ions. Consequently, it is likely that the enhanced SMM behaviour observed for 1 and 2 compared with 4 mainly result from the ferromagnetic coupling of the spins on the Tb^III or Dy^III to the anisotropic Mn₁₁ shells, just as was found for the Mn₁₁Ln₂ compounds [3d,7], rather than from the Ln^III ions making any significant single-ion uniaxial anisotropy to the molecules. The angular electron density distribution for the Ho^III M_J levels with high |J| are such that they are expected to be less destabilised than for Tb^III and Dy^III [12], which might be predicted to improve SMM behaviour for 3 compared to 1 and 2, as is, in fact the case here. Indeed, the oblate coordination polyhedron found for the Ln^III ions in 1-3 is more likely to promote uniaxial single-ion anisotropy for ions such as Er^III or Yb^III [12], but unfortunately it was not possible to isolate such Mn₁₁Ln compounds with lanthanides heavier than holmium.

It is noticeable that no well-resolved steps in the hysteresis loops of compounds 1-3 due to resonant quantum tunnelling of magnetization (QTM) were observed. In a recent report of a Mn₁₂Gd complex, which also has a central lanthanide surrounded by a shell of manganese ions, it was proposed that the number of O²⁻ ions bridging between the manganese and the lanthanide ion(s) in such Mn_xLn_y clusters plays a crucial factor in determining whether well-resolved quantum tunnelling behaviour is observed or not, and that eight such oxo bridges were necessary to observe steps in the hysteresis [3g]. However, in compounds 1-3 we do indeed have eight O²⁻ ions bridging between the manganese centres and the lanthanide ions, but no clear QTM steps can be observed in the hysteresis loops, in contradiction of the perhaps overly simplistic proposal in [3g]. It is unlikely that the number of oxo bridges is the only factor contributing to the presence of quantum tunnelling. The precise structural topologies, the relative orientations of the Jahn-Teller anisotropies of the Mn^III centres, differences in the Mn-O-Mn and Mn-O-Ln angles, and the specific anisotropy brought to the molecule by the rare-earth ion(s) will all influence any quantum behaviour in such compounds.