A Molecular [ Mn 14 ] Coordination Cluster Featuring Two Slowly Relaxing Nanomagnets

Single molecule magnets (SMMs) could become the carriers of qubits in quantum computation. A major goal is the synthesis of molecules containing two well-defined SMMs. The use of a new polypyrazol ligand, H4L, has enabled us to synthesize a cluster with SMM behavior containing two quasi independent, slowly relaxing [Mn7] clusters. The dynamics of the magnetization within this species has been studied through ultra-low temperature magnetization and specific heat measurements. The later demonstrate that both cluster subunits of the molecule behave as anisotropic S = 11/2 spins. Molecular nanomagnets occupy a central position among molecular materials that will shape the future of nanotechnology.[1] These species are coordination clusters of paramagnetic (3d and/or 4f) metals, exhibiting a range of spin states as a result of intramolecular magnetic exchange. Some of them feature large spin ground states and Ising-type zero-field splitting (ZFS), which confer them the potential of retaining the orientation of their molecular magnetic moment along the direction of the easy anisotropy axis. These molecules, now called single-molecule magnets (SMMs),[2, 3] have become suitable candidates to become qubits in quantum computation (QC).[4] In this regard, a key step was the demonstration that the tunnelling may be biased by the weak magnetic exchange between two SMMs within a supramolecular dimer,[5] which causes the quantum entanglement of the wave functions of both clusters, as demonstrated through HF-EPR.[6] Entanglement is of utmost relevance if spin clusters are to be considered as possible 2qubit quantum gates for the realization of QC.[7, 8] More recently, entanglement has been found between two fragments linked covalently within the same molecule, such as an Mn12 ring described as two half-rings each with a S = 7/2 spin state,[9] or a Mn6 cluster consisting of two S = 6 metal triangles. In these two cases, a weak ferromagnetic interaction couples both parts of the molecule. Stable molecular objects exhibiting such properties are much more interesting as potential quantum gates than supramolecular assemblies. However, molecular ‘pairs of magnets’ are hard to prepare by design and are thus extremely scarce, as compared with the large number and variety of reported SMMs,[10] more easily obtained by serendipity. Our group has been engaged in the production of discrete coordination assemblies consisting in pairs of well-defined cluster nanomagnets, which we have termed ‘molecular cluster pairs’ (MCPs), as a promising strategy to access coordination chemistry-based 2qubit quantum gates. With this goal, ligands have been specifically designed to favour the aggregation of metals as two separate groups while maintaining them together within the same molecule,[11] or as a way to link two preformed clusters to each other.[12] We now report here the use of the ligand H4L (2,6−bis(5−(2−hydroxyphenyl)−pyrazol−3−yl)−pyridine,[13] Scheme I) in a reaction with Mn ions, which promotes the agreggation of paramgentic centers into two [Mn7] clusters, while also ensuring that these are kept together within a molecular species. The product is a salt with formula [Mn14O2(OH)4(OMe)4(OAc)2(L)2(HL)4(H2L)2(MeOH)2(H2O)6](AcO)2 (1) that contains a covalently linked pair of cluster nanomagnets; we also demonstrate in this paper that the slow relaxation of the magnetization of 1 is due to the individual properties of the [Mn7] fragments, which amounts to having two SMMs within one molecular cation. Recent work has revealed that the product from reactions of H4L with Mn(II)/Mn(III)/AcO− mixtures heavily depends on the solvent used, consisting of a [Mn4] and a [Mn10] cluster when using acetone or THF, respectively.[14] It was thus expected that a solvent with versatile coordination abilities would help to express further the structural diversity of the products resulting from this reaction system. Indeed, mixing NBu4MnO4, Mn(AcO)2·4H2O and H4L (with 6:1:1.5 molar ratio) in MeOH led to crystals of 1 after layering the resulting dark brown solution with Et2O. This product is drastically different from the clusters previously characterized, although with some common local structural features (see below) and incorporates bridging methoxide groups. In this reaction the comproportionation between Mn(VII) and Mn(II) is exploited to facilitate the formation of a majority of Mn(III) ions. Likewise, the oxide ions liberated from MnO4 furnish the necessary base for the (partial) deprotonation of H4L and some molecules of MeOH. A balanced reaction for the formation of 1 may 12 NBu4MnO4 + 58 Mn(AcO)2·4H2O + 40 H4L + 30 MeOH → 5 [Mn14O2(OH)4(OMe)4(OAc)2L2(HL)4(H2L)2(MeOH)2(H2O)6](AcO)2 + 12 NBu4AcO + 92 AcOH + 250 H2O (1) N N HN NH N OH HO

ABSTRACT.Single molecule magnets (SMMs) could become the carriers of qubits in quantum computation.A major goal is the synthesis of molecules containing two well-defined SMMs.The use of a new polypyrazol ligand, H 4 L, has enabled us to synthesize a cluster with SMM behavior containing two quasi independent, slowly relaxing [Mn 7 ] clusters.The dynamics of the magnetization within this species has been studied through ultra-low temperature magnetization and specific heat measurements.The later demonstrate that both cluster subunits of the molecule behave as anisotropic S = 11/2 spins.
Molecular nanomagnets occupy a central position among molecular materials that will shape the future of nanotechnology. [1]These species are coordination clusters of paramagnetic (3d and/or 4f) metals, exhibiting a range of spin states as a result of intramolecular magnetic exchange.Some of them feature large spin ground states and Ising-type zero-field splitting (ZFS), which confer them the potential of retaining the orientation of their molecular magnetic moment along the direction of the easy anisotropy axis.These molecules, now called single-molecule magnets (SMMs), [2,3] have become suitable candidates to become qubits in quantum computation (QC). [4]In this regard, a key step was the demonstration that the tunnelling may be biased by the weak magnetic exchange between two SMMs within a supramolecular dimer, [5] which causes the quantum entanglement of the wave functions of both clusters, as demonstrated through HF-EPR. [6]Entanglement is of utmost relevance if spin clusters are to be considered as possible 2qubit quantum gates for the realization of QC. [7,8] More recently, entanglement has been found between two fragments linked covalently within the same molecule, such as an Mn 12 ring described as two half-rings each with a S = 7/2 spin state, [9] or a Mn 6 cluster consisting of two S = 6 metal triangles.In these two cases, a weak ferromagnetic interaction couples both parts of the molecule.Stable molecular objects exhibiting such properties are much more interesting as potential quantum gates than supramolecular assemblies.However, molecular 'pairs of magnets' are hard to prepare by design and are thus extremely scarce, as compared with the large number and variety of reported SMMs, [10] more easily obtained by serendipity.Our group has been engaged in the production of discrete coordination assemblies consisting in pairs of well-defined cluster nanomagnets, which we have termed 'molecular cluster pairs' (MCPs), as a promising strategy to access coordination chemistry-based 2qubit quantum gates.With this goal, ligands have been specifically designed to favour the aggregation of metals as two separate groups while maintaining them together within the same molecule, [11] or as a way to link two preformed clusters to each other. [12]We now report here the use of the ligand H 4 L (2,6−bis(5−(2−hydroxyphenyl)−pyrazol−3−yl)−pyridine, [13] Scheme I) in a reaction with Mn ions, which promotes the agreggation of paramgentic centers into two [Mn 7 ] clusters, while also ensuring that these are kept together within a molecular species.The product is a salt with formula [Mn 14 O 2 (OH) 4 (OMe) 4 (OAc) 2 (L) 2 (HL) 4 (H 2 L) 2 (MeOH) 2 (H 2 O) 6 ]-(AcO) 2 (1) that contains a covalently linked pair of cluster nanomagnets; we also demonstrate in this paper that the slow relaxation of the magnetization of 1 is due to the individual properties of the [Mn 7 ] fragments, which amounts to having two SMMs within one molecular cation.
Recent work has revealed that the product from reactions of H 4 L with Mn(II)/Mn(III)/AcO − mixtures heavily depends on the solvent used, consisting of a [Mn 4 ] and a [Mn 10 ] cluster when using acetone or THF, respectively. [14]It was thus expected that a solvent with versatile coordination abilities would help to express further the structural diversity of the products resulting from this reaction system.Indeed, mixing NBu 4 MnO 4 , Mn(AcO) 2 •4H 2 O and H 4 L (with 6:1:1.5 molar ratio) in MeOH led to crystals of 1 after layering the resulting dark brown solution with Et 2 O.This product is drastically different from the clusters previously characterized, although with some common local structural features (see below) and incorporates bridging methoxide groups.In this reaction the comproportionation between Mn(VII) and Mn(II) is exploited to facilitate the formation of a majority of Mn(III) ions.Likewise, the oxide ions liberated from MnO 4 − furnish the necessary base for the (partial) deprotonation of H 4 L and some molecules of MeOH.A balanced reaction for the formation of 1 may be written (eq.1), although it is clear that other chemical processes also take place in solution, not unveiled in the solid phase.
Compound 1 is a salt of two AcO − anions and a [Mn 14 ] 2+ complex cation (Fig. 1).The latter is a coordination cluster of fourteen Mn(II/III) ions distributed into two well differentiated and symmetry related groups of seven metals.Within each [Mn 7 ] fragment, the donors of four distinct, partially deprotonated long-distance link between both well-defined clusters of the molecule.The metal topology within each aggregate (Fig. 1, bottom) may be described as a puckered pentagon in form of capped square, linked through the "capping" metal to a Mn 2 metal pair acting as a "tail".It contains six Mn ions in the oxidation state +3 and one in the oxidation state +2 (Mn1).This assignment was decided on the basis of BVS, charge balance considerations and the metric parameters and coordination geometries around the metal ions.Indeed, Mn3 to Mn7 exhibit Jahn-Teller elongated (distorted) coordination geometries, while Mn2 exhibits axially elongated square pyramidal coordination.All H 2 O and MeOH molecules occupy axial sites, the rest of these positions being occupied by pyridyl or pyrazolyl moieties, µ 3 −OH − , µ−OH − or µ−MeO − (the latter two in very distorted situations, corresponding to Mn6 to O18 and Mn5 to O16, respectively).Low valent Mn1 is in a distorted pentagonal bipyramidal geometry.The structure of the complex in 1 underscores the dual function that H 4 L may play in its various deprotonated forms.First, it is a highly versatile donor, here exhibiting four different coordination modes (Scheme II), none of which coincident with the four previously observed. [13,14] his confers to the ligand the ability to form metal aggregates with a large variety of structures.On the other hand, the presence of two groups of donor atoms separated by a spacer that not always coordinates (in 1 it does for only half of the ligands) adds the potential of linking covalently two distant entities, as revealed here with the formation of the first MCP with H 4 L. The cation of 1 is only the eighth [Mn 14 ] cluster reported, since the first example was published in 2002 [15] (full list of references in the SI).
Variable temperature bulk magnetic susceptibility measurements (from 2 to 300 K) show the presence of exchange coupling   This minimum is followed by a maximum of 33.8 cm 3 Kmol −1 at 6 K and finally, χ M T reaches 28.0 cm 3 Kmol −1 at 2 K.These data suggest the presence of a high molecular spin ground state.Further insights into this ground state were obtained through AC susceptibility measurements, shown in the inset of Fig. 2. Between 3 and 10 K, the equilibrium susceptibility χ Τ can be determined from measurements performed at sufficiently low frequencies (223 Hz in this experiment).It obeys the Curie-Weiss law χ' = C/(T−θ) with C = 33.8cm 3 Kmol −1 and θ = −0.066K (Fig. S1).The Curie constant is compatible [16] with either a total S = 15/2 ground state for the whole molecule, or with two S = 11/2 spins embodied inside the cluster, both with g = 2.The isothermal (T = 2 K) magnetization clearly favours the scenario of two quasi-independent S = 11/2 units in the molecule of 1 (Fig. S2).The goal of performing coherent manipulation of molecular spins, as is necessary for applications in QC, underscores the importance of understanding the magnetic relaxation mechanisms.Relaxation times, τ, can be obtained by varying the frequency of the AC susceptibility experiments.Data measured down to 400 mK reveal the existence of frequency dependent maxima in the χ' and χ" vs T plots (χ' and χ" are the in-phase and out-of-phase components of the dynamical susceptibility, respectively; Fig. 2, inset).The results confirm that 1 exhibits the slow relaxation of the magnetization that is typical of SMMs.As a first approximation, the maxima of the χ" vs T plots correspond to the condition τ = 1/ω.
This behavior reveals that the spins flip via a thermally activated mechanism over the magnetic anisotropy barrier.For the simplest Hamiltonian for the isolated ground state with uniaxial anisotropy, H = DS z 2 , the energy barrier for a non-integer spin ground state reads U = (S z 2 -¼)×|D|.Using the activation energy determined from the Arrhenius fit gives D/k B = 0.6 K each of the two S = 11/2 entities.Additional information on the relaxation of these spins was obtained from the dependence of χ' and χ" on frequency at 2 K, which can be described by the Cole-Cole functions (eqs.3  and 4).In these equations, χ S and χ T are the adiabatic (infinite frequency) and isothermal (equilibrium) susceptibility limits, respectively, and the parameter β gives a measure of the distribution of relaxation times within the system (with β = 1 for a single relaxation process).By fitting both components of the susceptibility with these equations (Fig. S3) we find χ S = 1.66 cm 3 mol −1 and β = 0.53.The fact that β < 1, indicating a broad dispersion of τ's, may be due to a distribution of anisotropy parameters or to the presence of various relaxation channels, e.g.associated with close lying excited spin states.The value of χ S provides access to an independent estimation of D as extracted from eq. 5, [16] which applies to two spin subunits within the same molecule.This calculation affords D/k B = 0.57 K, in remarkable agreement with the value obtained from the Arrhenius plot.
The dependence of τ with temperature (from ca 2.7 to 1 K) was determined by fitting the χ' vs T data measured at ν = 3330 Hz with the first of Cole-Cole equations (see above).The number of free parameters was reduced by setting β and χ S equal to the values determined at 2 K, and χ T = C/(T − θ).The data obtained by this method agree very well with the relaxation time values extracted from the maxima of the χ" vs T plots (Arrhenius plot, Fig. 3).Below approximately 1.5 K, τ begins to deviate from the Arrhenius law, thus departing from the pure thermally activated relaxation.The additional data point obtained from C p vs T measurements (see below) confirms this trend, while also indicating that a quantum relaxation mechanism is not yet dominant at 0.7 K. Nonetheless, the isothermal magnetization measured on single crystals at temperatures from 0.2 K to 2 K (Fig. 4) shows hysteresis loops below 1.2 K, confirming the SMM behaviour in 1.The loops widen as T decreases and are smooth, with no clear traces of the steps characteristic of resonant quantum tunnelling within SMMs.
An independent confirmation of this puzzling behavior was obtained from AC susceptibility measurements performed under finite DC magnetic fields.At T = 2 K (Fig. S4), the results show a smooth decline of χ' and χ" upon the increase of the magnetic field, with no indication of the resonant behavior seen in many SMMs. [17,18] his observation becomes even more evident when examining the magnetic field dependence of the relaxation time, τ (Fig. S5), which was obtained from the susceptibility measurements at 2 K using Cole-Cole fits (eqs.3 and 4).The results show that τ is maximum at H = 0, in striking contrast with the pronounced minimum observed for SMMs flipping their spins via quantum tunnelling.The field dependence of τ resembles instead that expected for classical spins.This classical response might be due in part to the presence of an exchange field between the [Mn 7 ] sub-units acting as an effective bias that energetically detunes the spin-up and spin-down states, as previously observed with a su-
H 4 L ligands (see Scheme II for coordination modes) keep the metals together, indirectly through the ligand backbone structure, and directly by means of four −N−N− (from pyrazolyl moieties) and one µ−O (phenolate based) bridges.In addition there are one µ 3 −O 2− (O13), one µ 3 −OH − (O10), one µ−OH − (O17), two µ−MeO − and one µ−AcO − (syn,syn) ligands helping to cement the metals of the aggregate.The coordination is also achieved by three H 2 O, one MeOH and five phenolate terminal groups, each of the latter associated to a bridging pyrazolyl moiety (see above) in the establishment of six-member chelate rings.Finally, one of the HL 3− groups of the [Mn 7 ] fragment reaches out to the other heptanuclear aggregate, chelating one metal of the latter (Mn7) through a phenolate/pyrazolyl fragment, thus completing a double

Figure 2 .
Figure 2. Plot of χMT vs T for complex 1. Inset: plots of AC χ' (full symbols) and χ" (open symbols) vs T per mol of 1.The solid line is a Curie-Weiss fit of the

Figure 3 .
Figure 3. Plot of τ vs 1/T for complex 1 extracted from the maxima of χ" vs T at different frequencies (black circles), from χ' vs T data at ν = 3330 Hz using the

Figure 4 .
Figure 4. Heat capacity of 1 in zero-field (black full circles) and under 0.5 and 1 T (open blue and orange circles, respectively).Full lines are the computed heat capacity considering the ZFS of two S = 11/2 spins with D/kB = 0.6 K (full thin line), plus Debye (dotted line) and Einstein (dashed line) contributions to the lattice heat capacity.The inset shows the minimum exhibited at 0.7 K by the thermal coupling parameter of the PPMS, and indicative of the blocking temperature TB of the slow relaxing species in 1.