Suppression of Magnetic Quantum Tunneling in a Chiral Single

Article Cite This: Inorg. Chem. 2017, 56, 15119−15129

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Suppression of Magnetic Quantum Tunneling in a Chiral SingleMolecule Magnet by Ferromagnetic Interactions Kai-Alexander Lippert,† Chandan Mukherjee,†,§ Jan-Philipp Broschinski,† Yvonne Lippert,† Stephan Walleck,† Anja Stammler,† Hartmut Bögge,† Jürgen Schnack,‡ and Thorsten Glaser*,† †

Lehrstuhl für Anorganische Chemie I, Fakultät für Chemie, Universität Bielefeld, Universitätsstrasse 25, D-33615 Bielefeld, Germany Fakultät für Physik, Universität Bielefeld, Universitätsstrasse 25, D-33615 Bielefeld, Germany

‡

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S Supporting Information *

ABSTRACT: Single-molecule magnets (SMMs) retain a magnetization without applied magnetic field for a decent time due to an energy barrier U for spin-reversal. Despite the success to increase U, the difficult to control magnetic quantum tunneling often leads to a decreased effective barrier Ueff and a fast relaxation. Here, we demonstrate the influence of the exchange coupling on the tunneling probability in two heptanuclear SMMs hosting the same spin-system with the same high spin ground state St = 21/ 2. A chirality-induced symmetry reduction leads to a switch of the MnIII−MnIII exchange from antiferromagnetic in the achiral SMM [MnIII6CrIII]3+ to ferromagnetic in the new chiral SMM RR[MnIII6CrIII]3+. Multispin Hamiltonian analysis by full-matrix diagonalization demonstrates that the ferromagnetic interactions in RR[MnIII6CrIII]3+ enforce a well-defined St = 21/2 ground state with substantially less mixing of MS substates in contrast to [MnIII6CrIII]3+ and no tunneling pathways below the top of the energy barrier. This is experimentally verified as Ueff is smaller than the calculated energy barrier U in [MnIII6CrIII]3+ due to tunneling pathways, whereas Ueff equals U in RR[MnIII6CrIII]3+ demonstrating the absence of quantum tunneling.

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magnetic field at higher temperatures than 3d-SMMs.15,17−21 The origin is the quantum nature of molecules: there is not only a thermal pathway over the top of the energy barrier, but also pathways through the barrier, which are either coherent transitions (also termed quantum tunneling of the magnetization, QTM)24,25 or thermal transition caused by interaction with lattice vibrations. These short cuts result in a lower effective energy barrier Ueff. In the Landau−Zener model, the probability for QTM depends on the tunnel splitting, which is caused by the mixing of the MS substates.2,4,26−28 This mixing is induced by transversal field components,29,30 which may arise from stray fields of neighboring molecules, hyperfine interactions, the noncollinearity of local D tensors, or the rhombicity ESt/DSt of the spin St. The latter results in a term for the QTM probability p ∝ 1 − exp(ESt/DSt)St, that is, the QTM probability decreases for high spin ground states St and small rhombicities ESt/DSt, which vanishes for symmetries containing at least a C3 axis.

INTRODUCTION Single-molecule magnets (SMMs) are individual molecules, which can retain a magnetization without an external magnetic field in analogy to solid-state magnets. This phenomenon does not arise from long-range magnetic order but from a slow relaxation of the magnetization due to an energy barrier U for magnetization reversal.1−4 The energy barrier is given by U = DSt·St2 (U = DSt·St2 −1/4 for half-integer spins) for a molecule of spin ground state St and zero-field splitting DSt. In the archetype SMM, [Mn12O12(O2CCH3)16(H2O)4], the energy barrier is in the order of 65 K and the magnetization relaxes with a half-live of a few months at 2 K and at zero-field.1 Strong research efforts focus on improving the properties of SMMs5−21 especially in order to stabilize the magnetization for longer times at higher temperatures. Fascinating research on lanthanide complexes10−13,20−22 led to an increase of the energy barriers U from values below 100 K for complexes comprised of 3d transition metal ions up to several hundreds K with a current record of 1815 K for a pentagonal-bipyramidally coordinated DyIII complex.23 However, only a few examples exhibit increased relaxation times without an external dc © 2017 American Chemical Society

Received: September 25, 2017 Published: November 30, 2017 15119

DOI: 10.1021/acs.inorgchem.7b02453 Inorg. Chem. 2017, 56, 15119−15129

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Inorganic Chemistry

magnetization. [MnIII6MnIII](lactate)3 exhibits a record hysteretic opening up to ±10 T.56 A high molecular and crystal symmetry in [MnIII6CrIII](lactate)3 enforces magnetic hysteresis with almost complete suppression of QTM.49 However, the blocking temperatures of these SMMs do not exceed 2 K.49 (i) To understand why blocking temperatures of our [Mt6Mc]n+ complexes are not higher and then (ii) to be able to rationally improve our SMMs, we have analyzed their molecular, electronic, and magnetic structures in detail.58 Although the coupling is ferromagnetic in extended phloroglucinol complexes of CuII3,38,46,59−61 CoII3,62 NiII3,63 and VIV3,47 it is only weak and even antiferromagnetic in MnIII3 complexes.48−56,64−68 We have attributed this inefficiency of the spin-polarization mechanism to a resonance hybrid of the phloroglucinol backbone consisting not only of a delocalized aromatic system I necessary for spin-polarization but also a nonaromatic heteroradialene contribution II (Scheme 1b) with the latter being the only resonance structure in the free ligands.58,60,69−74 Using the chiral triplesalen ligand H6chandRR (Scheme 1a), which was initially synthesized for enantioselective catalysis,66 the corresponding chiral heptanuclear complexes of the general formula RR[Mt6Mc]n+ (= [{chandRR)Mt3}2{Mc(CN)6}]n+)75 are accessible. Interestingly, in the complexes RR[MnIII6FeII]2+ and RR [FeIII6FeII]2+ the interactions between the MnIII and FeIII ions, respectively, through the phloroglucinol backbone are for the first time ferromagnetic. RR[MnIII6FeII]2+ even shows a slow relaxation of the magnetization although the central metal ion is diamagnetic FeII low-spin. Therefore, we thought to synthesize the complex RR[MnIII6CrIII]3+ as an analogue to the already existing SMM [MnIII6CrIII]3+. Assuming that the MnIII−MnIII coupling in RR[MnIII6CrIII]3+ is also ferromagnetic, this would provide the opportunity to investigate the consequences of a switch from antiferromagnetic to ferromagnetic interactions in a SMM of given spin system and spin ground state. In this respect, we present here the synthesis, structural, spectroscopic, electrochemical, and magnetic characterization of the new enantiopure chiral triplesalen-based SMM RR [MnIII6CrIII](ClO4)3. Enantiopure chiral magnets (ECMs) have been regarded as an archetype of multifunctional materials,76 for example, for magneto-chiral dichroism.76−79 We compare the properties of the new chiral SMM RR [Mn III 6Cr III ] 3+ to that of the parent achiral SMM [MnIII6CrIII]3+.48−50 The analysis by means of a multispin Hamiltonian with full-matrix diagonalization provides the exchange couplings Jij, the local zero-field splitting tensors Di, and the whole magnetic energy spectra and wave functions including the energy barriers U for spin reversal and the tunneling probabilities for this multispin system. As intended, JMn−Mn switches from antiferromagnetic in [MnIII6CrIII]3+ to ferromagnetic in RR[MnIII6CrIII]3+ as a result of a chiralityinduced symmetry reduction. The ferromagnetic coupling in RR [MnIII6CrIII]3+ leads to a spin ground state that (i) is energetically better stabilized, (ii) is better described by a spin quantum number St, (iii) exhibits less MS mixing, (iv) exhibits lower QTM probabilities, and (v) exhibits a larger energy barrier U, which is (vi) matched by the experimental barrier Ueff from AC measurements in contrast to [MnIII6CrIII]3+. Thus, the switch from antiferromagnetic to ferromagnetic results in an effective suppression of QTM and an increase of the magnetic relaxation times, which experimentally underlines the impor-

In this simplified description, only the spin ground state of the SMM is considered and energetically higher spin states are neglected (effective spin or giant-spin approximation),31 which is a crude description for the multitude of spin states in polynuclear SMMs.30,32,33 Importantly, zero-field splitting mixes energetically higher spin states into the ground state which also contributes to the tunnel splitting and thus QTM. This mixing is stronger, the lower the excited spin states are. Thus, the exchange coupling J, which determines the energies of the spin states, also influences the relaxation properties of SMMs. A well separated spin ground state should be important for good SMMs.34 Most SMMs are not in the strong exchange limit so that the giant-spin approximation is not valid and a multispin Hamiltonian must be used. This has been educationally summarized recently for the SMMs Mn3 and Mn6.31 We have followed a supramolecular approach to polynuclear SMMs of transition metals and developed the ligand system triplesalen (see Scheme 1a for the two specific triplesalen Scheme 1. (a) Triplesalen Ligands Used in the Study and (b) Heteroradialene Contribution

ligands used in this study).35,36 Triplesalen ligands contain a central phloroglucinol (= 1,3,5-trihydroxybenzene)37,38 coupling unit in order to enforce a C3 symmetry and high-spin ground states through ferromagnetic interactions by the spinpolarization mechanism.39−42 A salen-like coordination environment was chosen to introduce a strong tetragonal ligand field as source for anisotropy.43,44 The trinuclear complexes [(talent‑Bu2)M3]n+ exhibit a bowl-shaped molecular structure45−47 that allows a supramolecular assembly of two triplesalen complexes [(talent‑Bu2)M3]n+ and one hexacyanometallate to heptanuclear complexes of the general formula [Mt6Mc]n+ (= [{(talent‑Bu2)Mt3}2{Mc(CN)6}]n+): [MnIII6CrIII]3+,48−50 [MnIII 6FeIII]3+,51,52 [MnIII6FeII]2+,51 [Mn III 6 Co III ] 3+ , 53 [Mn III 6 Os III ] 3+ , 54 [Mn III 6 Os II ] 2+ , 54 [MnIII6MnIII]3+,55,56 and [FeIII6CrIII]3+.57 Most of these complexes show out-of-phase components in AC magnetic measurements in agreement with a slow relaxation of the 15120


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RESULTS AND ANALYSIS Synthesis. The reaction of the molecular building block [(chand R R ){Mn I I I (solv) n } 3 ] 3 + formed in situ with [Cr III (CN) 6 ] 3− results in solutions of [{(chand RR )MnIII3}2{CrIII(CN)6}]3+ (≡ RR[MnIII6CrIII]3+), which can be isolated in form of different salts and solvates. These are contaminated by a MnIICrIII−Prussian Blue analogue (evidenced by magnetic ordering around Tc ≈ 60 K and ν(CN) = 2160 cm−1) and HNEt3ClO4 (evidenced by IR). A tedious procedure involving three recrystallization steps was developed in order to obtain reproducible pure crystalline batches for single-crystal X-ray diffraction and magnetic measurements. The single crystals analyzed by X-ray diffraction as [{(chandRR)2MnIII6(THF)5.5(MeOH)0.5{CrIII(CN)6}](ClO4)3· MeOH·1.5THF·1.5Et2O (1b). As in all our heptanuclear triplesalen-based complexes, the solvent molecules coordinated to the metal ions (here THF and MeOH) found in the crystal structure are not detected in ESI mass spectra, indicating weak Mn−OMeOH and Mn−OTHF bonds. The dried sample used for magnetic and other measurements analyzed by elemental analysis as [{(chandRR)MnIII3}2{CrIII(CN)6}](ClO4)3·1THF· 1MeOH·3H2O·2Et2O (1a) indicative for an at least partial loss of coordinating solvent molecules. The specific rotation (see Supporting Information) and the CD spectrum (Figure S2) manifests the chirality of RR[MnIII6CrIII]3+ in the solid and in solution. Structural Characterization. Single-crystals of 1b crystallize in the chiral space group P1 with one whole heptanuclear complex in the asymmetric unit. The molecular structure of RR [MnIII6CrIII]3+ is shown in Figure 1 (thermal ellipsoid plot in Figure S3, plots including the numbering scheme used in Figure S4, selected interatomic distances and angles in Table S1). The heptanuclear complex is supramolecularly formed by two MnIII3 triplesalen building blocks bridged by a central [CrIII(CN)6]3−. The terminal MnIII ions are coordinated by the N2O2 salen-like coordination compartments, a cyanide nitrogen atom, and an oxygen donor from coordinated THF. This is disordered for Mn1 with MeOH (1:1). The crystallization in space group P1 that provides no crystallographic symmetry elements results in only approximate molecular C3 axes (Figure 1b) but in a strict collinear orientation of these approximate molecular C3 axes in the crystal. The molecular structure of RR[MnIII6CrIII]3+ is described in comparison to that of [MnIII6CrIII]3+ as their magnetic properties show significant differences (vide infra). We have already shown, that the ligand (chandRR)6− leads to significant differences in the molecular structures of RR[MnIII6FeII]2+ and RR [FeIII6FeII]2+ compared to the ligand (talent‑Bu2)6− in [MnIII6FeII]2+.75 Mean values of selected structural parameters of RR[MnIII6CrIII]3+ in 1b are summarized and compared to two different salts of [MnIII6CrIII]3+ in Table 1. The main part of their molecular structures are compared in Figure 2. The chirality of the ligand (chandRR)6− has a significant influence on the symmetry of RR[MnIII6CrIII]3+. The ligand (talent‑Bu2)6− is not chiral, but the bowl-shaped molecular building blocks [(talent‑Bu2)MnIII3]3+ of [MnIII6CrIII]3+ are of C3 symmetry and therefore chiral. The heptanuclear complex [MnIII6CrIII]3+ has a center of inversion at the central CrIII ion, so that the two [(talent‑Bu2)MnIII3]3+ building blocks are of

Figure 1. Molecular structure of RR[MnIII6Cr III]3+ including coordinated THF ligands in crystals of 1b drawn (a) perpendicular and (b) parallel to the approximate molecular C3 axis; hydrogen atoms have been omitted for clarity.

opposite chirality and the C3 axis is also a S6 axis (Figure 2b bottom) resulting in the point group S6. In contrast, inversion symmetry in RR[MnIII6CrIII]3+ synthesized with the enantiopure chiral ligand (chandRR)6− would require the presence of the other enantiomer (chandSS)6−, which is not present in the reaction solution. Thus, the two molecular building blocks [(chandRR)MnIII3]3+ are of the same chirality and prohibit a center of inversion and a S6 axis a in RR[MnIII6CrIII]3+ (Figure 2a bottom). Instead, there are three C2 axes perpendicular to the main C3 axis resulting in the point group D3. Because of the S6 symmetry, the MnIII-salen subunits in [MnIII6CrIII]3+ (Figure 2b bottom) are in a staggered conformation, whereas they are in an almost eclipsed conformation in RR[MnIII6CrIII]3+ (Figure 2a bottom). These different conformations induce changes in the central {CrIII(CN−MnIII)6} core, which determines the CrIII−MnIII exchange pathway. The unit CN−Mn in RR [MnIII6CrIII]3+ is less linear (∼144° vs ∼160°) and d(Mn− CN ) slightly longer (2.23 Å vs ≈2.18 Å). N This chirality-induced symmetry difference also enforces different wrappings of the triplesalen ligands around the same central {CrIII(CN−MnIII)6} core, which have no significant influence on the metal−ligand distances (Table 1), but on the ligand foldings (Figure 2a and d). We identified parameters to quantify the ligand folding in our triplesalen complexes.45,46,53 The bent angle φ characterizes a bending along an idealized line through neighboring N and O donors (Table 1).80 The heptanuclear complexes [MnIII6CrIII]3+ show only a small bending (φterm ≈ 10°) at the terminal phenolates but a 15121


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Inorganic Chemistry Table 1. Mean Values of Selected Structural Parameters compound cent

d(Mn−O ) (Å) d(Mn−Oterm) (Å) d(Mn−Ncent) (Å) d(Mn−Nterm) (Å) d(Mn−Xsixth) (Å) d(Mn−NCN) (Å) d(Cr−C) (Å) d(CN) (Å) ∠(Cr−CN) (deg) ∠(CN−Mn) (deg) ∠(C−Cr−C) (deg) φcent (deg)a φterm (deg)a θ (deg)b ϑ (deg)c d(C−C)cent HOMAcentd

RR

[MnIII6CrIII](ClO4)3 1.88 1.88 2.02 1.97 2.43 2.23 2.07 1.15 173.3 143.9 93.3 18.3 −22.6 25.9 39.8 1.42 0.77

[MnIII6CrIII](lactate)3e

[MnIII6CrIII](BPh4)3f

1.89 1.88 1.98 1.98 2.31 2.19 2.06 1.15 179.0 159.4 91.4 34.6 10.4 8.5 36.1 1.42 0.69

1.90 1.87 1.96 1.98 2.49 2.18 2.07 1.15 176.1 161.3 88.7 46.7 8.5 1.3 39.0 1.42 0.68

Bent angle φ = 180° − ∠(Mn−XNO−XR) with XNO = midpoint of adjacent N and O donor atoms and XR = midpoint of the six-membered chelate ring containing the N and O donor atoms. bAngle between the benzene plane of the central phloroglucinol and the vector formed by the central phenolate O atom and the central ketimine N atom. cAngle between the local MnIII Jahn−Teller-axes and the molecular C3 axis. dHOMA (harmonic oscillator model of aromaticity) takes a value of 1 for the model aromatic system benzene and of 0 for a model nonaromatic system.81 e [{(talent‑Bu2){MnIII(MeOH} 3}2{Cr(CN)6}](lactate)·9MeOH.48 f[{(talent‑Bu2)MnIII3}2{CrIII(CN)6}(MeOH)3(CH3CN)2](BPh4)3·4CH3CN· 2Et2O.48 a

significantly stronger bending (φcent = 35−48°) at the central phloroglucinol.48 The positive sign for both angles indicates folding to the same side with respect to the MnIIIN2O2 coordination plane resulting in the overall bowl-shaped molecular structure of the trinuclear triplesalen building blocks (Figure 2d). In contrast, the central bending is much smaller for RR [MnIII6CrIII]3+ (φcent = 18°), while the terminal bending (φterm = −23°) is larger. The negative sign of φterm indicates bending toward the opposite site, resulting in an overall “soup plate-shaped” molecular structure of the trinuclear triplesalen building blocks (Figure 2a). Furthermore, the angle θ describing a helical distortion 53 is much larger in RR [MnIII6CrIII]3+ (Table 1). These changes in the ligand wrappings quantified by the angles φcent, φterm, and θ vary the bond angles around the MnIII ions and reduces the local symmetry around the MnIII ions (Figure 2c+f). This in turn changes the σ and π contributions of the Mn−O and Mn−N bonds, hence the local electronic structure of all MnIII ions. A consequence of the lower symmetry is a better total overlap of the O p(z) orbitals with the MnIII d orbitals. Thus, more spin-density is delocalized into the O p(z) orbitals. Furthermore, the phloroglucinol backbone is less distorted (Figure 2c and f) and this goes along with a higher aromaticity of the central phloroglucinol backbone. The HOMA index as a quantitative measure for aromaticity81 has a value of ∼0.70 for [MnIII6CrIII]3+48 while it is 0.77 for RR [ M n I I I 6 C r I I I ] 3 + . T h e l a r g e r H O M A va lu e f o r RR [MnIII6CrIII]3+ indicates a higher aromatic character of the central phloroglucinol unit (resonance structure I) strengthening the spin-polarization mechanism in RR[Mn6Cr]3+. This is not a contradiction to the general principle that a decent in symmetry is not good for targeting ferromagnetic couplings. The overall molecular symmetry is reduced due to the absence of inversion symmetry. This enforces a change of the ligand wrapping that reduces the symmetry of the local MnIII coordination environments, whereas the symmetry of the

Mn−Mn exchange pathway is actually increased. These effects of the chirality-induced symmetry reduction on the local electronic structure of the MnIII ions and the aromaticity are independently reflected in the FTIR and UV−vis spectra as well as in the electrochemical and magnetic properties (vide infra). FT-IR Spectroscopy. The FT-IR spectrum of 1a is dominated by four intense absorption bands at 1620, 1552, 1537, and 1490 cm−1 (Figure S5). We identified signatures of the heteroradialene character in the FT-IR spectra of the free ligands72−74 and complexes.54,74 In [MnIII6CrIII]3+, the bands at 1567 and 1491 cm−1 correspond to the exocyclic ν(CC) and ν(CO) stretching modes of the heteroradialene, respectively. The ν(CO) stretch is not shifted in 1a, but the exocyclic ν(CC) stretch is shifted from 1567 cm−1 in [MnIII6CrIII]3+ to 1552 cm−1 in 1a also indicating a lower heteroradialene character II in RR[MnIII 6CrIII]3+ than in [MnIII6CrIII]3+ (Scheme 1b). Moreover, the ν(CN) stretch of the terminal aldimines shifts from 1610 cm−1 in [MnIII6CrIII]3+ to 1620 cm−1 in RR[MnIII6CrIII]3+ reflecting differences in the Mn−N bonds of the terminal aldimines. UV−vis Spectroscopy. The UV−vis spectrum of RR [MnIII6CrIII]3+ is compared to that of [MnIII6CrIII]3+ in Figure S6. The spectrum of RR[MnIII6CrIII]3+ exhibits lower intensity above 20000 cm−1 but more pronounced intensity below 20000 cm−1. These differences are remarkable as the spectra of (i) [MnIII6CrIII]3+ and [MnIII6MnIII]3+ are superimposable56 and (ii) of the ligands H6chandRR and H6talent‑Bu2 are almost superimposable.69 The difference spectrum ([MnIII6CrIII]3+ − RR[MnIII6CrIII]3+) has significant intensity features in the 25000−35000 cm−1 region. In this region, the heteroradialene character of the central phloroglucinol backbone causes two strong absorption features,58 that is, the lower heteroradialene contribution in RR[MnIII6CrIII]3+ indicated by the structural and FT-IR data is also observed in solution. 15122


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Figure 2. Comparison of the molecular structures of (a−c) RR[MnIII6CrIII]3+ in crystals of 1a and (d−f) [MnIII6CrIII]3+ in crystals of [{(talent‑Bu2){MnIII(MeOH}2{CrIII(CN)6}](lactate)·9MeOH.48 Some group of atoms (that is, t-Bu, CH3, (CH2)4, and coordinated solvent molecules) and all hydrogen atoms have been omitted for the sake of clarity in panels a, b, d, and e. Please note that, in panel e, the “O2-openings” of the salen compartments of the top and bottom [(talent‑Bu2)MnIII3]3+ building blocks point in one direction of rotation in accordance to a S6 axis, while in panel b, these “O2-openings” of the top and bottom [(chandRR)MnIII3]3+ building blocks point in opposite direction of rotation in accordance to the three C2 axes perpendicular to the C3 main axis. Panels c and f show sections of the molecular structures to illustrate the variation of the local MnIII coordination environments.

The transitions below 22 000 cm−1 are mainly d−d in nature and have been fitted and compared to [MnIII6CrIII]3+ (Figure S7).48 These strong differences in the d-d transitions reflect significant differences in the electronic structure of the MnIII ions of RR[MnIII6CrIII]3+ and [MnIII6CrIII]3+ in line with the different ligand wrappings. Electrochemistry. The electrochemical properties of RR [MnIII6CrIII]3+ were measured by cyclic (CV) and squarewave (SW) voltammetry (Figure S8). RR[MnIII6CrIII]3+ exhibits irreversible oxidations at Ep,ox = 1.15 V vs Fc+/Fc, and chemically reversible reductions at Ep,red = −0.50 and −0.68 V vs Fc+/Fc. The oxidative features closely resemble those of [MnIII6CrIII]3+,48 which corroborates previous findings that these oxidations are ligand-centered at the terminal phenolates.48,50,51,54 In contrast, the reductive features are strongly shifted relative to [MnIII6CrIII]3+ (Ep,red at −0.80 and −0.96 V vs Fc+/Fc). These reductions are assigned to metal-centered MnIII/MnII reductions and their differences indicate differences in the electronic structures of the MnIII ions. Thus, the variations of the electronic structure of the MnIII ions due to the different wrappings of the triplesalen ligands are reflected by the differences in the d-d transitions, the ν(CN) stretches

of the aldimines, and the MnIII/MnII reduction potentials of [MnIII6CrIII]3+ and [MnIII6CrIII]3+. Magnetic Properties. The effective magnetic moment, μeff, of 1a is 12.20 μB at 300 K (Figure 3a), which is slightly below the theoretical value of 12.48 μB for six uncoupled MnIII ions and one CrIII ion (gi = 1.98). By decreasing the temperature, μeff decreases to a minimum of 12.03 μB at 165 K and then increases to a maximum of 20.71 μB at 8 K, indicating a ferrimagnetic coupling scheme with a high spin ground state of St = 21/2. The variable temperature-variable field (VTVH) measurements (Figure 3b) exhibit significant nesting indicating a strong anisotropy. The temperature-dependence of μeff and the VTVH data were simulated simultaneously by a full-matrix diagonalization of the multispin Hamiltonian given in eq 1 including isotropic HDvV exchange (eq 2, inset Figure 3a), zero-field splitting, and Zeeman interaction. RR

Ĥ = ĤHDvV +

∑ Di(Ŝi ·ei(ϑi, φi))2 + μB ∑ B·g i·Ŝi i

i

(1) 15123


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as by unit vectors ei, which are parametrized by polar angles ϑi and φi. The unit vectors of the six MnIII ions point along their local Jahn−Teller axes, which were approximated to be along the MnIII−NNC bonds. In both S6 and D3 symmetry, all six local unit vectors ei can be parametrized by the common polar angle ϑ between the Jahn−Teller axis and the C3 symmetry axis, which has been extracted from the crystal structures (Table 1). It should be noted that RR[MnIII6CrIII]3+ has no crystallographically imposed symmetry so that the angles and the spin-Hamiltonian parameters are only mean values. Reducing the symmetry for the simulations would not only result in a highly overparametrized system but also in an enormous increase in computational time, which is already at today’s limits (45 GByte, ≈ 3 days for one parameter set and just one B value). The procedure for the simulation of the magnetic data to extract meaningful spin-Hamiltonian parameters and their error ranges by performing a multitude of simulations with varying parameters follows the published procedures for [M t 6 Mc]n+49−56,68,75 in general and [MnIII6CrIII]3+ in particular.48 The careful evaluation of all simulations performed allows an estimation of the parameters including an error range: JMn−Cr = −5.0 ± 0.5 cm−1, JMn−Mn = +0.8 ± 0.1 cm−1, and DMn = −3.5 ± 0.4 cm−1. The measurements are well reproduced by the simulations (Figure 3) especially by considering that the symmetry in RR[MnIII6CrIII]3+ is lower than represented by the spin-Hamiltonian. Most important, the MnIII−MnIII coupling is ferromagnetic in RR[MnIII6CrIII]3+ while it is antiferromagnetic in [MnIII6CrIII]3+.48−50 AC susceptibility data were measured temperature- and frequency-dependent and analyzed as described previously.48 Both χ′M and χ″M components almost vanish below their maxima indicating an efficient suppression of zero-field tunneling. The temperature-dependence of χ″M (Figure S9) exhibits frequencydependent maxima, providing Ueff = 34.9 K and τ0 = 1.91 × ′ and χM ″ 10−8 s (Figure S10a). The frequency-dependence of χM for selected temperatures and their fits to the generalized Debye model82 is shown in Figure 4a and 4b, respectively. ″ = f(ω), the average magnetization relaxation From the fit of χM

Figure 3. (a) Temperature-dependence of μeff for 1a at 0.01 T and coupling scheme used. (b) VTVH (variable temperature−variable field) magnetization measurements at 1, 4, and 7 T for RR [MnIII6CrIII]3+. Experimental data are given as circles. The solid lines correspond to simulations performed by a full-matrix diagonalization of the multispin Hamiltonian provided by eq 1.

ĤHDvV = −2JCr − Mn (S1̂ Ŝ 7 + Ŝ 2Ŝ 7 + Ŝ3Ŝ 7 + S4̂ Ŝ 7 + S5̂ Ŝ 7 + S6̂ Ŝ 7) − 2JMn − Mn (S1̂ Ŝ 2 + Ŝ 2Ŝ3 + Ŝ3S1̂ + S4̂ S5̂ + S5̂ S6̂ + S6̂ S4̂ )

(2)

It must be noted that the second term in eq 1 reflects the major contribution of the local zero-field splitting tensors Di. These tensors are parametrized by a strength factor Di, as well

Figure 4. Plots of (a) the in-phase (χ′M) and (b) the out-of-phase (χ″M) components of the AC susceptibility vs the angular frequency (ω) for RR [MnIII6CrIII]3+ at zero-DC field with an oscillating AC field of 3 Oe, at fixed temperatures. Solid lines are least-squares fits to the generalized Debye model. (c) Argand plots of the AC susceptibility at zero-DC field. Solid lines are least-squares fit to the function χM ″ = f(χM ′ ).48 15124


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Figure 5. Magnetic energy spectra for RR[MnIII6CrIII]3+ (a and c) and [MnIII6CrIII]3+ ([{(talent‑Bu2)MnIII3}2{CrIII(CN)6}(MeOH)3(CH3CN)2](BPh4)3·4CH3CN·2Et2O48 b and d), obtained from the simulation of the magnetic data. Only low-lying energy levels are shown. The x-axis represents the magnetization of each eigenstate, which corresponds to the expectation value for a tiny magnetic field along the C3 quantization axis. The spectra were calculated by a full-matrix diagonalization of the complete spin-Hamiltonian (1) with the parameters provided in the text. The blue crosses in panels a and b correspond to the MS states of an isolated S = 21/2 spin multiplet of the same barrier as of the respective complexes. The eigenstates are colored with respect to their symmetries (red, symmetric; black, antisymmetric). In panels c and d, selected values of the probabilities of coherent transitions by transversal field components (QTM) are provided. The bold green arrows summarize the “allowed” phonon-assisted thermal direct, Raman, and Orbach processes. The thin red arrows correspond to coherent QTM pathways. E* denotes the excitation energy (above the ground state).

times τav (Table S2) were obtained, providing Ueff = 34.7 K and τ0 = 2.19 × 10−8 s (Figure S10b). Figure 4c shows the fitting of ″ as a function of χM ′ for selected the Argand plot χM temperatures.

tremendous influence on the wave functions and their linear combinations (vide infra). This rigorous approach allows to quantify the switching of JMn−Mn from antiferromagnetic in [MnIII6CrIII]3+ (JMn−Mn = −0.7 cm−1) to ferromagnetic in RR[MnIII6CrIII]3+ (JMn−Mn = +0.8 cm−1). In both [MnIII6CrIII]3+ and RR[MnIII6CrIII]3+, JMn−Cr (≈ −5 cm−1) is stronger than JMn−Mn. Thus, the antiferromagnetic coupling JMn−Cr orients all the MnIII spins in a parallel alignment. In [MnIII6CrIII]3+, the antiferromagnetic coupling J Mn−Mn competes with this alignment (spin frustration), while the ferromagnetic coupling JMn−Mn in RR [MnIII6CrIII]3+ enforces this parallel alignment and stabilizes the spin ground state of St = 21/2. Moreover, our full-matrix diagonalization provides the energies and wave functions of the magnetic eigenstates which give insight in and understanding of the SMM properties. The low-lying magnetic eigenstates are plotted as a function of their magnetizations in Figure 5a+b. In RR[MnIII6CrIII]3+, a relatively well developed St = 21/2 spin ground state is formed that is separated from a St = 19/2 multiplet, which is still relatively well-defined (Figure 5a). For an isolated St = 21/2, the energy difference between MS = ± 21/2 and MS = ± 19/2 equals to 20 DSt. For RR[MnIII6CrIII]3+, this provides DSt = 0.32 cm−1 and an estimate for the energy barrier of U = DSt·(St2 − 1/ 4) = 50.3 K. However, the calculated magnetic energy spectrum provides the best estimate for the energy barrier U by the energy difference between MS = ± 21/2 and MS = ± 1/2 which is 35.2 K for RR[MnIII6CrIII]3+. The discrepancy between these two values demonstrates that the strong exchange limit (|J| ≫ |D|) is still not valid, i. e. the use of a giant-spin approximation is not justified. For [MnIII6CrIII]3+, the calculated energy barrier U = 31.5 K (Figure 4b) is lower due to the competition of JMn−Cr and JMn−Mn. Moreover, the magnetic energy spectrum can hardly be described by spin quantum numbers St. The

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DISCUSSION The switch of the JMn−Mn exchange from antiferromagnetic in [MnIII6CrIII]3+ to ferromagnetic in RR[MnIII6CrIII]3+ allows to evaluate the influence of the exchange coupling on a given SMM. As we have synthesized and characterized several different salts and solvates of [MnIII6CrIII]3+, we had to choose one specific example for comparison to RR[MnIII6CrIII]3+. Our choice was based to match JMn−Cr and DMn as close as possible to RR [Mn III 6 Cr III ] 3+ . We have chosen [{(talen t‑Bu 2 )MnIII3}2{CrIII(CN)6}(MeOH)3(CH3CN)2](BPh4)3·4CH3CN· 2Et2O with JMn−Cr = −5.0 ± 0.5 cm−1, JMn−Mn = −0.7 ± 0.3 cm−1, and D = −3.0 ± 0.5 cm−1.48 Although the two SMMs presented here possess individually no “record-like” SMM properties, they provide access to a real system constituted of the same metal ions, the same spin system, and the same spin ground state St with a switch from antiferromagnetic to ferromagnetic interactions. This allows to study the effect of exchange coupling on QTM and its quantification by a multispin Hamiltonian. Therefore, we have analyzed the magnetic properties of both RR [MnIII6CrIII]3+ and [MnIII6CrIII]3+48−50 by full-matrix diagonalization of the multispin Hamiltonian (eq 1), which is a formidable task due to the large Hilbert-space of dimension 62500. The high symmetry of the complexes (either S6 or D3) reduces the number of parameters to three (JMn−Mn, JCr−Cr, and DMn), which allows its determination from the DC magnetic data without overparametrization. Moreover, instead of using the common approximation of collinear zero-field splitting tensors, we included their relative orientations, which have 15125


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thermal direct, Raman, and Orbach processes over the top of the anisotropy barrier. Another effect to mention is that the symmetry of the spin system classifies the eigenstates as symmetric and antisymmetric, which cannot mix.84 For RR[MnIII6CrIII]3+, all 22 states of the St = 21/2 ground state are symmetric, while the 20 states of the St = 19/2 state are antisymmetric. This energetic separation of symmetric and antisymmetric states is removed in [MnIII6CrIII]3+, which opens additional thermal relaxation pathways. Selected probabilities for R R [Mn I I I 6 Cr I I I ] 3 + and [MnIII6CrIII]3+ are provided in Figures 5c and 5d, respectively (a complete set is provided in Table S3). We would like to emphasize that the two ground states are degenerate at total zero-field (external and internal) and tunneling is forbidden. Nevertheless, even at an applied external field, which is nominally zero, transversal field fluctuations of internal or external origin can give rise to a nonzero transition probability. Importantly, this “zero-field tunneling” from “MS = −21/2” → “MS = +21/2” and vice versa is forbidden for both complexes. This was already experimentally proven for [MnIII6CrIII]3+.49 The main pathways are as expected the thermal “ΔM = ± 1” transitions (simplified by the bold green arrows in Figure 5c and d), which have values the smaller the larger the mixing of MS eigenstates is. The main importance is the difference in the short-cuts below the top of the barrier, that is, the thermally assisted QTM which results in Ueff being smaller than U. The first efficient short-cut for RR[MnIII6CrIII]3+ is for the “MS = ± 7/2” levels at 32.2 K. In contrast, in [MnIII6CrIII]3+ are QTM pathways at a band of levels around 22−23 K, which are severe mixtures of MS states. This correlates nicely with the experimental results that for RR[MnIII6CrIII]3+ Ueff = 35 K matches perfectly with U = 35.2 K, while for [MnIII6CrIII]3+ Ueff = 25 K is smaller than U = 31.5 K. Thus, the switch of JMn−Mn from antiferromagnetic in [MnIII6CrIII]3+ to ferromagnetic in RR [MnIII6CrIII]3+, which is only small in absolute numbers (ΔJMn−Mn = 1.5 cm−1), is very efficient in suppressing QTM pathways.

higher eigenstates have only small magnetizations and form almost a continuum compared to RR[MnIII6CrIII]3+. Another advantage of the multispin Hamiltonian approach is to provide the wave functions of the magnetic eigenstates. Each eigenstate is described by linear combinations of the basis functions |mS1; mS2; mS3; mS4; mS5; mS6; mS7⟩ with S1 − S6 = 2 and S7 = 3/2. It is important to note that under the approximation of collinear zero-field splitting tensors, only linear combinations of the same MS are allowed, that is, the wave functions are eigenfunctions of ŜZ. The noncollinear local zero-field splitting tensors result in linear combinations of basis functions of different MS, that is, the wave functions are no eigenfunctions of ŜZ. As we are in the regime DMn ≈ Ji, there is no separation into effects of DMn and Jj. The wave functions mix severely and deviate strongly from those of a St = 21/2 giant spin. A pure MS = −21/2 state would be described by 100% |−2; −2; −2; −2; −2; −2; +3/2⟩ but the ground state of RR[MnIII6CrIII]3+ contains only 73.9% of this basis function. It also contains 13.2% of the MS = −19/2 wave function |−1; −2; −2; −2; −2; −2; +3/2⟩ (please note that this is a short notation including all symmetry adapted linear combinations, see Supporting Information for details and a complete listing), 13.2% MS = −21/2 |−1; −2; −2; −2; −2; −2; +1/2⟩, 0.8% MS = −17/2 |0; −2; −2; −2; −2; −2; +3/2⟩ as the next main contributions. This linear combination of wave functions results in a magnetization of −20.4 μB instead of −20.8 μB for a pure MS = −21/2 with g = 1.98. The mixing of basis functions is much more pronounced for [MnIII6CrIII]3+. The ground state contains only 42.3% MS = −21/2 |−2; −2; −2; −2; −2; −2; +3/2⟩ but 31.8% MS = −19/2 |−1; −2; −2; −2; −2; −2; +3/ 2⟩, 4.8% MS = −21/2 |−1; −2; −2; −2; −2; −2; +1/2⟩, 4.1% MS = −17/2 |−1; −2; −2; −2; −2; −1; +3/2⟩, etc. This reduces the magnetization of the ground state of [MnIII6CrIII]3+ to only M = −19.3 μB. The mixing of |mS1; mS2; mS3; mS4; mS5; mS6; mS7⟩ basis functions is even more pronounced for the higher states in [MnIII6CrIII]3+, which explains their lower magnetization. Thus, the deviation from a St = 21/2 giant spin is even stronger in [MnIII6CrIII]3+ due to the spin-frustration as in RR[MnIII6CrIII]3+ that is free of spin-frustration. This resembles the results obtained on Mn3 and Mn6.31 The better energy separation of St = 21/2 and the less mixing in RR[MnIII6CrIII]3+ has important consequences for the relaxation behavior. The effective energy barrier Ueff = 35 K obtained from AC data matches perfectly with U = 35.2 K from the magnetic energy spectrum. This means, the relaxation pathway goes over the top of the energy barrier of the St = 21/2 spin ground state without significant short cuts due to QTM. In contrast, the effective energy barrier Ueff = 25 K of [MnIII6CrIII]3+ obtained from AC data48 is lower than U = 31.5 K from the magnetic energy spectrum. This reduction of Ueff arises from efficient QTM pathways below the energy barrier due to transversal fields, which connect eigenfunctions of Ĥ in longitudinal field. It is important to clarify that the term “mixing” is used in two meanings: (i) Eigenstates of Ĥ are superpositions of |mS1; mS2; mS3; mS4; mS5; mS6; mS7⟩ basis functions (this meaning of mixing was used above) and (ii) a transversal field B⃗ ⊥ mixes eigenstates of the original Hamiltonian Ĥ . To obtain relative probabilities of these transitions, we have calculated ⌈⟨Ψk|Ŝxtot/ℏ|Ψl⟩⌉2.83 For a pure zero-field split S = 21/2 state, these values are of order 10 for ΔMS = ± 1 and characterize the pathways for phonon-assisted

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CONCLUSIONS This study demonstrates for a real system of given spin structure and spin ground state the influence of the exchange coupling on the magnetic quantum tunneling and on the anisotropy barrier in SMMs. This anisotropy barrier is regarded as the key property to control and optimize single-molecule magnets. While numerous studies aim at increasing this anisotropy barrier by variation of the single-ion anisotropy or the spin state, the effect of the exchange coupling on the anisotropy barrier is widely underexplored as SMMs varying only in the exchange coupling constants are rare.32,34 An advantage of our triplesalen-based SMM family is its supramolecular assembly by molecular recognition. This provides the opportunity for changes in the molecular building blocks without changing the overall molecular structure of the SMMs. The comparison of the two SMMs RR[MnIII6CrIII]3+ and [Mn III 6 Cr III ] 3+ both with a S t = 21/2 ground state demonstrates that the stronger the exchange coupling, the less quantum tunneling occurs. This demonstration should impact the rational design of SMMs, as the strength of the exchange interactions was usually not considered. QTM pathways of SMMs have been evaluated in the past by analysis of eigenfunctions and transition probabilities based on sophisticated molecular orbital calculations.83 To the best of 15126


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(5) Frost, J. M.; Harriman, K. L. M.; Murugesu, M. The rise of 3-d single-ion magnets in molecular magnetism: towards materials from molecules? Chem. Sci. 2016, 7, 2470−2491. (6) Pedersen, K. S.; Bendix, J.; Clérac, R. Single-molecule magnet engineering: building-block approaches. Chem. Commun. 2014, 50, 4396−4415. (7) Ungur, L.; Le Roy, J. J.; Korobkov, I.; Murugesu, M.; Chibotaru, L. F. Fine-tuning the local symmetry to attain record blocking temperature and magnetic remanence in a single-ion magnet. Angew. Chem., Int. Ed. 2014, 53, 4413−4417. (8) Pinkowicz, D.; Southerland, H. I.; Avendaño, C.; Prosvirin, A.; Sanders, C.; Wernsdorfer, W.; Pedersen, K. S.; Dreiser, J.; Clérac, R.; Nehrkorn, J.; Simeoni, G. G.; Schnegg, A.; Holldack, K.; Dunbar, K. R. Cyanide single-molecule magnets exhibiting solvent dependent reversible “on” and “off” exchange bias behavior. J. Am. Chem. Soc. 2015, 137, 14406−14422. (9) Milios, C. J.; Vinslava, A.; Wernsdorfer, W.; Moggach, S.; Parsons, S.; Perlepes, S. P.; Christou, G.; Brechin, E. K. A record anisotropy barrier for a single-molecule magnet. J. Am. Chem. Soc. 2007, 129, 2754−2755. (10) Ishikawa, N.; Sugita, M.; Ishikawa, T.; Koshihara, S.; Kaizu, Y. Lanthanide double-decker complexes functioning as magnets at the single-molecular level. J. Am. Chem. Soc. 2003, 125, 8694−8695. (11) Ishikawa, N.; Sugita, M.; Tanaka, N.; Ishikawa, T.; Koshihara, S.y.; Kaizu, Y. Upward temperature shift of the intrinsic phase lag of the magnetization of bis(phthalocyaninato)terbium by ligand oxidation creating an S = 1/2 spin. Inorg. Chem. 2004, 43, 5498−5500. (12) Liu, J.-L.; Wu, J.-Y.; Chen, Y.-C.; Mereacre, V.; Powell, A. K.; Ungur, L.; Chibotaru, L. F.; Chen, X.-M.; Tong, M.-L. A heterometallic FeII-DyIII single-molecule magnet with a record anisotropy barrier. Angew. Chem., Int. Ed. 2014, 53, 12966−12970. (13) Woodruff, D. N.; Winpenny, R. E. P.; Layfield, R. A. Lanthanide single-molecule magnets. Chem. Rev. 2013, 113, 5110−5148. (14) Feltham, H. L.C.; Brooker, S. Review of purely 4f and mixedmetal nd-4f single-molecule magnets containing only one lanthanide ion. Coord. Chem. Rev. 2014, 276, 1−33. (15) Blagg, R. J.; Ungur, L.; Tuna, F.; Speak, J.; Comar, P.; Collison, D.; Wernsdorfer, W.; McInnes, E. J. L.; Chibotaru, L. F.; Winpenny, R. E. P. Magnetic relaxation pathways in lanthanide single-molecule magnets. Nat. Chem. 2013, 5, 673−678. (16) Liu, J.; Chen, Y.-C.; Liu, J.-L.; Vieru, V.; Ungur, L.; Jia, J.-H.; Chibotaru, L. F.; Lan, Y.; Wernsdorfer, W.; Gao, S.; Chen, X.-M.; Tong, M.-L. A stable pentagonal bipyramidal DyIII single-ion magnet with a record magnetization reversal barrier over 1000 K. J. Am. Chem. Soc. 2016, 138, 5441−5450. (17) Rinehart, J. D.; Fang, M.; Evans, W. J.; Long, J. R. A N23− radical-bridged terbium complex exhibiting magnetic hysteresis at 14 K. J. Am. Chem. Soc. 2011, 133, 14236−14239. (18) Rinehart, J. D.; Fang, M.; Evans, W. J.; Long, J. R. Strong exchange and magnetic blocking in N23−-radical-bridged lanthanide complexes. Nat. Chem. 2011, 3, 538−542. (19) Meihaus, K. R.; Long, J. R. Magnetic blocking at 10 K and a dipolar-mediated avalanche in salts of the bis(η8-cyclooctatetraenide) complex Er(COT)2‑. J. Am. Chem. Soc. 2013, 135, 17952−17957. (20) Goodwin, C. A. P.; Ortu, F.; Reta, D.; Chilton, N. F.; Mills, D. P. Molecular magnetic hysteresis at 60 K in dysprosocenium. Nature 2017, 548, 439−442. (21) Guo, F.-S.; Day, B. M.; Chen, Y.-C.; Tong, M.-L.; Mansikkamäki, A.; Layfield, R. A. A dysprosium metallocene singlemolecule magnet functioning at the axial limit. Angew. Chem., Int. Ed. 2017, 56, 11445−11449. (22) Demir, S.; Zadrozny, J. M.; Nippe, M.; Long, J. R. Exchange Coupling and Magnetic Blocking in Bipyrimidyl Radical-Bridged Dilanthanide Complexes. J. Am. Chem. Soc. 2012, 134, 18546−18549. (23) Ding, Y.-S.; Chilton, N. F.; Winpenny, R. E. P.; Zheng, Y.-Z. On approaching the limit of molecular magnetic anisotropy: A near-perfect pentagonal bipyramidal dysprosium(III) single-molecule magnet. Angew. Chem., Int. Ed. 2016, 55, 16071−16074.

our knowledge, analysis of the QTM pathways based on the simulation of the magnetic properties of a polynuclear SMM by the appropriate multispin Hamiltonian has not been described yet. We have shown experimentally on a real system that the better the spin ground state is separated from higher spin states, the lower is the mixing of states, the lower is the QTM probability, the higher is the effective energy barrier Ueff, and the slower is the magnetic relaxation. Thus, the main conclusion of this study is in order to increase the magnetic relaxation times of SMMs, that is, to slow down the thermal and the QTM mechanism simultaneously, a rational design for SMMs must consider strong exchange interactions to separate the spin ground state from excited states.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02453. Experimental details of synthesis, X-ray crystallography, and computations; thermal ellipsoid plots; CD, IR, and UV−vis spectra; electrochemistry; AC measurements (PDF) Accession Codes

CCDC 1501638 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_ [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +49-521-1066003. ORCID

Chandan Mukherjee: 0000-0002-2771-2468 Thorsten Glaser: 0000-0003-2056-7701 Present Address §

Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the DFG (FOR945 “Nanomagnets”) and Bielefeld University.

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REFERENCES

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