Comparison of the Magnetic Anisotropy and Spin Relaxation

Feb 5, 2018 - Institute of Inorganic Chemistry, Heidelberg University, ... Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahir...
0 downloads 0 Views 5MB Size
Download PDF
Article Cite This: J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

pubs.acs.org/JACS

Comparison of the Magnetic Anisotropy and Spin Relaxation Phenomenon of Dinuclear Terbium(III) Phthalocyaninato SingleMolecule Magnets Using the Geometric Spin Arrangement Takaumi Morita,† Marko Damjanović,‡,⊥ Keiichi Katoh,*,† Yasutaka Kitagawa,§ Nobuhiro Yasuda,∥ Yanhua Lan,⊥ Wolfgang Wernsdorfer,⊥,# Brian K. Breedlove,† Markus Enders,*,‡ and Masahiro Yamashita*,†,△,¶ †

Department of Chemistry, Graduate School of Science, Tohoku University, 6-3, Aramaki-Aza-Aoba, Aoba-ku, Sendai, Miyagi 980-8578, Japan ‡ Institute of Inorganic Chemistry, Heidelberg University, Im Neuenheimer Feld 270, D-69120 Heidelberg, Germany § Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-8531, Japan ∥ Japan Synchrotron Radiation Research Institute (JASRI), 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan ⊥ Physikalisches Institut and Institute of Nanotechnology, Karlsruhe Institute of Technology, Wolfgang-Gaede-Strasse 1, 76131 Karlsruhe, Germany # CNRS and Université Grenoble Alpes, Institut Néel, 38042 Grenoble, France △ WPI Research Center, Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan ¶ School of Materials Science and Engineering, Nankai University, Tianjin 300350, China S Supporting Information *

ABSTRACT: Herein we report the synthesis and characterization of a dinuclear TbIII single-molecule magnet (SMM) with two [TbPc2]0 units connected via a fused-phthalocyaninato ligand. The stable and robust complex [(obPc)Tb(FusedPc)Tb(obPc)] (1) was characterized by using synchrotron radiation measurements and other spectroscopic techniques (ESI-MS, FT-IR, UV). The magnetic couplings between the TbIII ions and the two π radicals present in 1 were explored by means of density functional theory (DFT). Direct and alternating current magnetic susceptibility measurements were conducted on magnetically diluted and nondiluted samples of 1, indicating this compound to be an SMM with improved properties compared to those of the well-known [TbPc2]−/0/+ and the axially symmetric dinuclear TbIII phthalocyaninato triple-decker complex (Tb2(obPc)3). Assuming that the probability of quantum tunneling of the magnetization (QTM) occurring in one TbPc2 unit is PQTM, the probability of QTM simultaneously occurring in 1 is PQTM2, meaning that QTM is effectively suppressed. Furthermore, nondiluted samples of 1 underwent slow magnetic relaxation times (τ ≈ 1000 s at 0.1 K), and the blocking temperature (TB) was determined to be ca. 16 K with an energy barrier for spin reversal (Ueff) of 588 cm−1 (847 K) due to D4d geometry and weak inter- and intramolecular magnetic interactions as an exchange bias (Hbias), reducing QTM. Four hyperfine steps were observed by micro-SQUID measurement. Furthermore, solution NMR measurements (one-dimensional, two-dimensional, and dynamic) were done on 1, which led to the determination of the high rotation barrier (83 ± 10 kJ/mol) of the obPc ligand. A comparison with previously reported TbIII triple-decker compounds shows that ambient temperature NMR measurements can indicate improvements in the design of coordination environments for SMMs. A large Ueff causes strong uniaxial magnetic anisotropy in 1, leading to a χax value (1.39 × 10−30 m3) that is larger than that for Tb2(obPc)3 (0.86 × 10−30 m3). Controlling the coordination environment and spin arrangement is an effective technique for suppressing QTM in TbPc2-based SMMs.

1. INTRODUCTION Single-molecule magnets (SMMs) show slow magnetic relaxation rates and quantum tunneling of the magnetization © XXXX American Chemical Society

Received: December 12, 2017 Published: February 5, 2018 A

DOI: 10.1021/jacs.7b12667 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Article

Journal of the American Chemical Society

Figure 1. (a) A tilted side view of the structure of 1. The Fused-Pc ligand is shown in green. An inversion center is located at the center of the benzene ring of the Fused-Pc ligand. (b) Chemical structure of the Fused-Pc ligands. The orange sphere indicates CHLinker, which corresponds to that in Figure 1a. (c) Crystal structure of complex Tb2(obPc)3 from CCDC-753306 (Cambridge Crystallographic Data Centre) with an inversion center located at the center of the inner phthalocyaninato ring (obPc2).23 Relevant aromatic 1H nuclei in NMR measurements are indicated with orange spheres (labeled as CHari in our previous work21a). (d and e) Schematic illustrations of the relative positions of the TbIII ions and protons in (a) and (c), respectively. The indicated 1H nuclei in both complexes have very similar geometric parameters (G, as mentioned in the NMR measurements). n-Butoxy side chains on the β-positions and crystal solvents were omitted for clarity. Coloring scheme: TbIII, pink; N, light blue; C, gray; H, white.

drastically suppressed, and magnetic hysteresis is observed up to 14 K. Several examples of the suppression of QTM via π−f exchange couplings have since been reported.1g As just described, radical ligands play an indispensable part in upgrading SMMs. Magnetic interactions, which do not cause long-range ordering, acting as a perturbation, affect the ground state of individual SMMs as an internal magnetic field. Therefore, QTM is affected by the quantum numbers and magnetic interactions of adjacent SMMs which deviate from a zero magnetic field by Hbias. In 2002, Wernsdorfer et al. showed this mechanism in a dimerized Mn4 cluster SMMs by van der Waals hydrogen bonding and the bridging chlorine atom.7 On the other hand, the neutral, anionic, and cationic species of TbIII−phthalocyaninato double-decker complex [TbPc2]−/0/+ have been reported to be SMMs having large Ueff.8 The three oxidation states can be easily obtained by using proper oxidants or reductants, and the magnetic properties of each species have been reported. The alternating current (ac) magnetic susceptibilities for each species are frequency (ν) dependent, which is a characteristic property of SMMs. In addition, the twist angle between the two Pc ligands (φ) has been determined to be 45° on the basis of the crystal structures, indicating that the complexes have a square-antiprismatic (SAP) coordination geometry with D4d symmetry. In the case of coordination geometry with D4d symmetry, only the axial terms are relevant for describing the ligand field (LF). However, if φ deviates from 45°, the off-diagonal terms (Bqk; q ≠ 0) also contribute to the LF, and make the probability for quantum tunneling larger.9 It has been shown that Ueff decreases with a decrease in φ because of the fast QTM processes.10 The anionic species [TbPc2]− has a Ueff of 230 cm−1.8a For the neutral species [TbPc2]0, which possesses a π

(QTM) in a single molecule due to the nature of nanosized materials, which is different from bulk magnets.1 These phenomena make them potentially useful in spintronic devices, such as ultrahigh density memory devices and quantum computers.2 In order to design SMMs of practical use, the energy barrier for spin reversal (Ueff) must be increased, and fast QTM processes must be suppressed.3 Recently, significant improvements have been made in the development of 3dcluster based SMMs.4 Many methods to control the magnetic relaxation processes of SMMs have been tried. Depending on the situation, intermolecular magnetic interactions and coupling with nuclear spins generate a transverse internal magnetic field and induce fast QTM.1a,c,5 Therefore, depending on the compound, SMM characteristics can be improved by sufficiently separating individual molecules. To improve the properties, for example, the exchange couplings (J) of SMMs can be increased to suppress fast relaxation pathways, such as QTM, but it remains a challenge.6 In simple terms, in the case of a two-spin system, the energy gap of triplet-singlets increases when J is large. As a result, a strong J suppresses QTM in the ground state via an exchange bias (Hbias).6 Strictly speaking, these phenomena are dependent on the ground-multiplet structure. Depending on the situation, thermally assisted QTM and Orbach processes may occur. In order to study this problem, Long and co-workers have shown that QTM can be suppressed by introducing a large exchange coupling between two lanthanoid(III) (LnIII) ions with π radicals.6 They have synthesized radical dinitrogen unit (N23−•)-bridged dinuclear terbium(III) (TbIII) complexes where two LnIII ions and one π radical on the N23−• unit are strongly antiferromagnetically coupled with each other (i.e., π−f interactions). Due to the large J values, ground state QTM is B

DOI: 10.1021/jacs.7b12667 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Article

Journal of the American Chemical Society radical, the χM″ peak is at a higher temperature, and Ueff is 410 cm−1.8b In contrast to these two, the cationic species [Tb(oePc)2]+ (oePc2− = 2,3,9,10,16,17,23,24-octaethoxyphthalocyaninato) has a much larger Ueff (550 cm−1).8c Ishikawa et al. have reported that cationic species have a shorter interligand distance than those of neutral and anionic ones because electrons are removed from antibonding molecular orbitals.8c,11 Thus, LF contractions cause stronger LF splitting, which directly affects the Ueff value. In this case, it is shown that controlling QTM via the LF effects on the LnIII ions is possible. TbPc2 based materials are suitable for application in molecular spintronics due to their SMM characteristics and physical and chemical stabilities.8a,12 In addition, investigating the influence of the direction of the magnetic dipole interactions acting among TbPc2 SMMs on the magnetic relaxation behavior is important for controlling the magnetic properties which depend on the molecular arrangement in the bulk.13 Recently, we have shown that the [TbPc2]0 SMM arrangement in the crystal affects the ground state and that QTM is suppressed at low temperature.14 Furthermore, QTM is suppressed in the TbPc2 dimer (abbreviated as [Tb2]) in which the TbPc2 units are connected via spacer causing space magnetic dipole interactions, which act as an Hbias.15 Moreover, it is possible to eliminate the influence of the transverse field by arranging the spin in the C4 axis direction.16 Thus, if the QTM probability occurring in one TbPc2 unit is PQTM, then the probability of QTM simultaneously occurring in [Tb2] is PQTM,2 which means QTM is effectively suppressed. Herein we report the relationship between molecular design and the magnetic properties of [(obPc)Tb(Fused-Pc)Tb(obPc)] (1) (Fused-Pc2− = bis{72,82,122,132,172,182-hexabutoxytribenzo[g,l,q]-5,10,15,20-tetraazaporphirino}[b,e]benzenato, obPc2− = 2,3,9,10,16,17,23,24-octabutoxyphthalocyaninato; Figure 1a) using single-crystal X-ray diffractometry, direct current (dc)/alternate current (ac) magnetic measurements, micro-SQUID measurements for SMM properties, and density functional theory (DFT) calculations, which give insights into the magnetic interactions between the radical centers in 1. In addition, dynamic and two-dimensional solution NMR spectroscopy was used to analyze this complex. To date, several methods, such as magnetic susceptibility measurements, electron spin resonance (ESR)17 and muon spin rotation and relaxation (μSR)18 spectroscopies, solid-state 1H NMR spectroscopy using T1 relaxations,19 and polarized neutron diffractometry,20 have been used to characterize SMM properties. Although these methods provide extensive information, they often require special facilities and equipment and long data acquisition times. On the other hand, NMR spectroscopy in solution is a widely available, routine method for characterizing organic molecules because structural information is easily and quickly obtained. Moreover, NMR spectroscopy can be used for studying coordination compounds, such as SMMs, which behave as paramagnets at room temperature. In the NMR of paramagnetic compounds (pNMR), besides the diamagnetic term, signals contain hyperfine contributions, including Fermi contact and pseudocontact terms, which reflect the magnetic nature of the compounds. Combined with DFT calculations, we have previously used pNMR spectroscopy to study different types of Ln SMMs and have obtained not only structural but also magnetic information, such as magnetic susceptibility anisotropies, the orientation of the magnetic easy axis, and spin density distributions.11,21 Furthermore, solution

NMR spectroscopy can be used to derive the LF parameters for LnIII−Pc SMMs.22 For these reasons, we used pNMR to study 1 in detail to find a correlation between common magnetic measurements and the magnetic susceptibility anisotropy obtained from NMR measurements in solution and near room temperature. In NMR spectra, the C2h symmetry of 1 leads to many more NMR signals than the D4d symmetry of the double-decker complex does.11 Thus, the determination of the obPc ligand rotation barrier was possible. In addition, 1H−1H COSY, exchange spectroscopy (EXSY), and variable-temperature NMR (VT-NMR) spectroscopy were used to fully assign the 1H NMR signals of 1. By comparing the NMR data for 1 with those for the previously reported Tb2(obPc)321a,23 (Figure 1c), we show that solution NMR spectroscopic methods provide a means for quick identification of potential SMMs. Compounds 1 and Tb2(obPc)3 have aromatic hydrogen atoms at positions that make the extraction and comparison of the axial component of the magnetic susceptibility tensor (χax) values straightforward (Figure 1d and 1e, respectively), and we show that NMR spectra near room temperature reflect the SMM properties. As will be shown in this work, magnetic susceptibility anisotropies obtained from NMR measurements at ambient conditions reflect the potential quality of SMMs, which is quantified at very low temperatures. Solution NMR can also distinguish between easy plane24 and easy axis21a anisotropies.

2. RESULTS AND DISCUSSION 2.1. Molecular Design Principle for Improved SMM Properties. The first SMMs discovered were multinuclear 3d metal complexes with high ground spin states and ferromagnetic and/or ferrimagnetic intramolecular interactions.25 However, molecular design has become conceptually simpler with the discovery of mononuclear lanthanide-based SMMs.8a In general, it is possible to control LF for LnIII type mononuclear SMMs. On the other hand, this becomes more complicated for multinuclear complexes, such as transition metal clusters. Thus, it is necessary to create the optimum LF for each LnIII ion. The uniaxial magnetic anisotropies of LnIII ions are affected by changes in the LF of the axial or the equatorial position relative to the charge density distributions of the complexes.1e There have been many attempts to elucidate the relationship between the coordination geometry and the LF parameters both experimentally and theoretically.1c,8a,c,10,22a,26 The LF parameters have been shown to have a significant influence on the ground state multiplet structure and magnetic anisotropy. Contractions of the SAP coordination environments affect the LF of the LnIII ions, which affects the SMM properties. It has been reported that the LF parameters (Bqk, where q accounts for the proportionality between the electrostatic potential, and k is the order of spherical harmonicity) of an ideal SAP coordination geometry with D4d symmetry are different from Bqk of an SP coordination geometry with D4h symmetry. Differences in the SMM properties are thought to be due to the presence or absence of particular offdiagonal LF terms (Bqk; q ≠ 0). Thus, SAP geometry only occurs in the terms B02, B04, and B06, which are LF parameters for the axial anisotropy (in an f electron system, k is limited to 0, 2, 4, 6.). 9a,c,27 The LF Hamiltonian can be written as ̂ = ∑ ∑k HLF B q O q where Oqk are Stevens’ operators.9a,c,27 q =−k k k The off-diagonal LF terms have an effect on the uniaxial magnetic anisotropies and the ground state multiplet structure. C

DOI: 10.1021/jacs.7b12667 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Article

Journal of the American Chemical Society The differences in the characteristics of SMMs, such as [TbPc2]−/0/+ with axial coordination geometry (Jz = ± 6), are thought to be due to the presence or absence of particular offdiagonal LF terms. The relationship between LF and point charge location must be considered very carefully because the twist angle (φ) and the angles (α) between the C4 axis and the direction of the Ln−Niso coordination bond strongly influence the LF parameters (An ideal D4d SAP symmetry show φ = 45°, α = 54.74°).9 In addition, the distortion of the structure must be considered. Since the SP geometry has a contribution from the off-diagonal term, the probability for QTM is larger.9 In fact, we have shown in a previous report that the barrier energy (Ueff) and magnetic anisotropy changes upon changing LF of TbIII multiple-decker complexes.10 In contrast, a prolate ion is stabilized with an equatorial coordination geometry.28 The reported Er(NHPhiPr2)3(THF)2 complex exhibits SMM properties because the prolate-shaped ground states of the ErIII ion (Jz = ± 15/2, which is responsible for the SMM properties) is stabilized by the equatorial coordination of the ligands. In addition, the effects of the internal magnetic field (Hbias), as a perturbation, on QTM is a problem. Hbias in SMMs, which change their magnetization reversal field via QTM through weak interactions between SMMs, have been reported.7 The weak magnetic interactions acting on the SMM dimer affects Hbias, and so QTM shifts. Previously, we have reported that Ueff changes in relation to QTM in dinuclear TbIII−Pc multipledecker SMMs, in which weak TbIII−TbIII interactions are more effective in suppressing QTM.23,29 Thus, it is possible to change the SMM properties by controlling not only the intarmolecular but also the intermolecular magnetic interactions, which are a source of perturbation.30 Here we used molecular design to improve the SMM properties on the basis of the previously reported works. We prepared, structurally characterized, and studied the magnetic properties of a very stable TbIII−Fused-Pc triple-decker complex (1) (Figures 1a, 2). By using a Fused-Pc ligand, which is like a dimer of phthalocyanine and has two coordination sites, and by controlling the number of stacking obPc ligands, a dinuclear complex with two π radicals was prepared by modifying a previously reported procedure (Supporting Information).31 We believed that connecting two TbPc2 units would induce several magnetic effects. First, two TbIII ions and two π radicals are in close proximity of each other. Therefore, there are magnetic couplings, including f−f, π−π, and π−f interactions, among four spin centers. These interactions help to suppress QTM and increase Ueff. Second, Hbias are present in 1 due to the close location of two TbPc2 units, meaning the QTM was also suppressed by Hbias. Hence, 1, which was designed to have a large Ueff, synergistic effect, causes an increase in Ueff and a high magnetic hysteresis temperature (see magnetic properties section). In addition, the robustness of the structure of 1 makes it an excellent candidate for a solution NMR study. Moreover, due to the C2h symmetry of 1, more peaks were observed in the 1H NMR spectra than they were for the double-decker complex with D4d symmetry, making it possible to experimentally determine the rotation barrier of the obPc ligand. 2.2. Crystal Structure and Coordination Geometry. Complex 1 crystallized with CHCl3 and MeOH molecules in the crystal lattice in the triclinic space group P1̅ (Figures 3, S1− S3). The crystallographic parameters are summarized in Table S1. An inversion center is located at the center of the benzene ring on the bridging part of Fused-Pc. Therefore, the two TbIII

Figure 2. (a) Synthetic route for 1. The detailed procedure is described in the Methods section. (b) Top view and (c) side view of the natural orbitals of the two π radicals in 1. The natural orbital (NO) of one π radical with an α spin is distributed over one double-decker moiety, whereas the NO of the other π radical with a β spin is localized on the other double-decker moiety. The α- and β-orbitals overlap on the benzene ring. Hence, strong antiferromagnetic interactions between the π radicals (large negative value of J4) were predicted from theory. The calculations were based on the crystal structure of 1. Hydrogen atoms were omitted for clarity. More details are provided in the Supporting Information. Color scheme: TbIII, pink; N, light blue; C, gray; O, red.

ions are crystallographically equivalent. The intramolecular TbIII−TbIII distance was determined to be 11.31 Å (3.52 Å in Tb2(obPc)3). The twist angle (φ) between the obPc and the Fused-Pc ligands was found to be 45° with an average α value of 54.44°, which corresponds to a square antiprismatic (SAP) coordination environment and local D4d symmetry. On the other hand, the TbIII ions in Tb2(obPc)3 are unevenly spaced between the outer Pc2− and inner Pc2− ligands with α values of 57.1° from the mean plane of the four Niso of the outer Pc2− ligands and 47.9° from the mean plane of the four Niso of the inner Pc2− ligand with φ = 32°. For the TbIII ions in 1, the SAP coordination geometry, which does not have off-diagonal LF terms (Bqk; q ≠ 0), contributes to the SMM behavior by suppressing QTM.1e,10 The distance between the TbIII ions and the mean plane of the four isoindole nitrogen atoms (Niso) in the Fused-Pc ligand was determined to be 1.44 Å, and the Tb−Niso bond lengths D

DOI: 10.1021/jacs.7b12667 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Article

Journal of the American Chemical Society

interactions of the surrounding molecules act as Hbias, which is reflected on the bulk magnetic properties (vide infra). 2.3. Exchange Couplings from Computational Chemistry. In order to investigate the biradical nature of 1, density functional theory (DFT) calculations were performed by using the crystal structure without geometry optimization. For estimating the strengths of the magnetic couplings, an Ising Hamiltonian (/Ising = −2 ∑a > b Jabz SazSbz , where Jijz is the z component of J between spins i and j and Siz is the z component of a spin operator for spin i) was used. The interactions of the four spin sites were assigned on the basis of the symmetry of the molecule, as shown in Figure S8. The coupling constants were calculated to be 2.0 cm−1 for Tb1−π radical(1) and Tb2−π radical(2), −0.7 cm−1 for Tb1−Tb2, −2.7 cm−1 for Tb1−π radical(2) and Tb2−π radical(1), and −174.3 cm−1 for π radical(1)−π radical(2) (Supporting Information). Natural orbital (NO) analysis showed that the organic radical containing orbitals were distributed on separate double-decker moieties and overlap at the bridging benzene ring fragment of Fused-Pc (Figures 2b and c). Although magnetic interactions were weak, Fused-Pc ligands induced four magnetic interactions, including indirect TbIII−TbIII interactions through π radicals. Strong antiferromagnetic coupling between the π radicals results in a lower than expected χMT value at room temperature, as described below. Calculations on the yttrium (YIII) analogue of 1 gave a similar radical(1)−radical(2) coupling constant as that for the TbIII complex (Figure S7). In other words, the TbIII ions do not affect the magnetic coupling between the π radicals. The antiferromagnetic coupling of the π radicals was also confirmed by using NMR spectroscopy, as discussed below. 2.4. Static and Dynamic Magnetic Properties. Direct current (dc) magnetic susceptibilities for a randomly oriented

Figure 3. Packing diagram of the crystal of 1 along c axis. Crystal solvents, n-butoxy chains, and hydrogen atoms were omitted for clarity. Relevant TbIII−TbIII distances are shown in the figure. Coloring scheme: TbIII, pink; N, light blue; C, gray.

were in the range 2.43−2.45 Å, which are similar to those in Tb2(obPc)3. The corresponding values for the obPc ligands are 1.38 Å and 2.40−2.42 Å, respectively. These values are shorter than those for the Fused-Pc ligands. The angle centroid−TbIII− centroid (Fused-Pc), where the centroid is the center point between the four Niso atoms of each ligand, was 178° because the Fused-Pc ligands were slightly bent due to the steric hindrance of the obPc ligands. 1 is arranged in a dimer chain structure along the a axis, and the intermetallic TbIII···TbIII distance was determined to be 7.35 Å, which suggests the existence of weak magnetic interactions between the TbIII ions (Figure S3). At low temperatures, the magnetic dipole

Figure 4. Micro-SQUID measurements on a single crystal of 1, (a) recorded at 0.5 K with various sweep rates, (b) magnification of the region around 0 T of the micro-SQUID data recorded at 0.5 K with various sweep rates, (c) differential curves of (b), (d) 0.140 T/s at various T, and (e) at 5 K with various sweep rates. Below 1 K, thermally induced relaxations were suppressed, and so, pure QTM processes were observed. The abrupt decreases in the magnetizations at 0 T were attributed to QTM processes in the ground states. Small steps at 0 T are attributed to the hyperfine couplings (I−J coupling, where I is the nuclear spin of TbIII ion (I = ± 3/2) and J is the total angular momentum of TbIII). E

DOI: 10.1021/jacs.7b12667 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Article

Journal of the American Chemical Society

Figure 5. (a) ν-dependent ac magnetic susceptibility measurements in the absence of a dc field in the temperature range of 1.8−50 K. Black solid lines were fitted by using a generalized Debye model. (b) Magnetization decay curves for 1, measured by using micro-SQUID at the temperature shown in the figure. (c) Arrhenius plot made by using the data from (a), (b) and temperature dependent measurements (Figure S20). Open red circles: values obtained from (a). Closed red circles: values obtained from temperature dependent measurements (Figure S20). Blue triangles: reproduced by using reported data for Tb2(obPc)3.23 In the main graph, three points having longer τ, forming the plateau, were deleted for clarity. All data are shown in the inset. The solid lines (red and green) are guides for eye. The inset is an Arrhenius plot made by using the data from (a). Black solid lines are least-square fits of the data, which afforded the following parameters: Ueff = 588 cm−1 (847 K), τ0 = 3.1 × 10−12 s for 1, 230 cm−1 (331 K) and 1.1 × 10−10 s for Tb2(obPc)3. Fitting the plots (c) by using the equation in which Orbach, direct, and QTM processes were considered was unsuccessful due to a large deviation in τ in the low-T region.

χMT value slightly decreased below 10 K, meaning that intermolecular dipole−dipole interactions are weakly ferromagnetic (nearest neighbor intermolecular Tb···Tb distance is 7.35 Å in Figure 3). In addition, field-cooled (FC) and zero-field cooled (ZFC) magnetizations of 1 were measured (Figure S9b). The magnetization increased with a decrease in the temperature. Below 18 K, FC and ZFC curves diverge from each other, which means that magnetic blocking starts at this temperature. This behavior is a common characteristic of nanomagnets and SMMs, and magnetic blocking to SMMs is discussed below with the ac magnetic susceptibility. To elucidate the quantum nature of 1 in the low temperature region, micro-SQUID measurements on oriented single crystals were carried out on a micro-SQUID array.32 The SMM properties of 1 differ from those of Tb2(obPc)3, which has the same number of metal ions as 1, but a different coordination environment.23 A hysteresis loop for Tb2(obPc)3 remained open up to 1.5 K, whereas for 1 it appeared up to 5 K (Figure 4e), with a sweep rate of 0.002 T/s. The presence of such a large coercivity (Hc) is in agreement with the high Ueff and slow τ observed for 1, which will be discussed in the following section on the ac magnetic susceptibility measurements. As shown in Figures 4a, d, and e, the width of the hysteresis loops exhibited both temperature and sweep rate dependences, which are characteristic features of SMM behavior. Below 1 K, thermally induced spin reversals (Orbach process) are negligible, meaning that pure ground state QTM processes are observed at 0 T. In fact, a large step was observed around 0 T and was attributed to QTM processes in the ground state. Hyperfine steps (I−J coupling) were visible in a zero field (Figure 4c) due to the four possible nuclear spin states of the

powder sample of 1 were acquired in the temperature (T) range 1.8−300 K in a dc magnetic field of 0.1 T. As shown in Figure S9a, the χMT value at 300 K was 23.40 cm3 K mol−1, which is lower than the theoretical value of 24.37 cm3 K mol−1 for two free TbIII ions (7F6, S = 3, L = 3, g = 3/2) and two radicals (S = 1/2 × 2). Curie−Weiss fitting was performed in the temperature range 300−200 K to afford a Curie constant of 24.50 cm3 K mol−1 and a negative Weiss constant of −14.73 K. The strong antiferromagnetic coupling of two π radicals, predicted from DFT calculations, explains the lower than expected χMT value and the decrease in χMT with a decrease in temperature. The behavior of χMT clearly shows that the magnetic behavior depends heavily on the magnetic dipole− dipole interactions between the TbIII ions in the molecule.10 At 10 K, χMT reached a minimum and then increased with a decrease in temperature to 20.93 cm3 K mol−1 at 1.82 K. This increase in the χMT value was attributed to inter- and/or intramolecular ferromagnetic dipole−dipole ( f−f) interactions. The intra- and intermolecular TbIII distances in 1 were determined to be 11.31 and 7.35 Å, respectively, which means that there are weak magnetic interactions between the TbIII ions in the molecules (Figure 3). In addition, it has been reported that the intramolecular antiferromagnetic interactions occur in sandwich-type YIII complexes with two fused bis(phthalocyaninato) units isostructural with 1.31 We did not observe any ferromagnetic interactions between the radicals in the YIII complex. Thus, we think that the increase in χMT in the low temperature region observed for 1 indicates weak ferromagnetic interactions between the TbIII ions. In other words, the χMT of dinuclear TbIII complexes depend on the f−f interactions between the metal ions within a single molecule. For a magnetically diluted sample 1′ in a THF solution, the F

DOI: 10.1021/jacs.7b12667 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Article

Journal of the American Chemical Society TbIII ions (IZ = ± 3/2). Such an observation has often been reported for TbIII−Pc complexes.1c,33 Observations of hyperfine steps for an oriented crystal of 1 mean that inter- and intramolecular interactions were considerably weak. Normally, magnetic dipole−dipole interactions make the magnetization curve broaden. All four steps corresponding to the four nuclear spin states were detected when the system was warmed to 0.5 K in order to populate all nuclear spin energy levels. The four steps were equally spaced in a field of 0.032 T. The hyperfine coupling constant was calculated to be 0.015 cm−1, which is slightly smaller than that for [TbPc2]− (0.017 cm−1).1c However, these steps were broad due to the hyperfine couplings of the TbIII ions and inter- and intramolecular f−f interactions. In a field of ca. 0.7 T, a broad step, which is strongly field sweep rate dependent, was observed, and it was concluded to be due to a direct relaxation process between the spin ground states of the two TbIII ions. In addition, magnetization decay was investigated in detail (Figure 5b). The measurements were performed in the temperature range 0.1−4.9 K. In this temperature range, magnetization decay curves were observed due to extremely slow magnetic relaxations and fitted by using a stretched exponential function to obtain mean lifetime (τ) values. The τ values were plotted in an Arrhenius plot with those obtained from ac magnetic susceptibility measurements (Figure 5c). Figure 5c shows that the τ value is temperature independent in the low temperature region, meaning that pure QTM processes are suppressed in this temperature region. At 0.1 K, τ was more than 1000 s, meaning that the spin reversal was strongly frozen and gradually relaxed by pure QTM and possible direct processes. It is indicated that the splitting for tunneling (Δtunnel) in the ground state is small, which is responsible for quenching QTM at 0.1 K by the high symmetry around the TbIII ions. In this case, the magnetic interactions between the TbIII ions in 1 are weak because the hyperfine structure of 1 can be clearly observed in the M−H curve (Figure 4c). It has been shown that intermolecular interactions, which act as perturbations, are important for suppressing QTM.7 If we discuss the effect of inhibition of QTM in terms of Hc, the interactions between the TbIII ions effectively work as an Hbias. As in the case a permanent (hard) magnet, Hc should be large. The Hc values for 1 at 0.5 K (Hc = −0.06 T at a sweep rate 0.280 T/s) and 5 K (Hc = −0.03 T at a sweep rate 0.280 T/s) are shown in Figure 4e. In the case of diluted [TbPc2]−TBA+, the Hc value is −0.01 T at 30 mK and a sweep rate of 0.280 T/s.1c In order to compare the SMM characteristics, we estimated Hc for powders (1) and isolated molecules (1′) at 1.8 K under the same conditions (Figures S13 and S16). The Hc values of 1 and 1′ are −0.086 T (0.04 cm−1) and −0.018 T (0.008 cm−1), respectively. Considering the relationship between the molecular form and Hc, the weak intermolecular interactions in 1 are more effective at suppressing QTM. In addition, M−H curves for 1′ showed an open hysteresis loop at 5 K, indicating that SMM properties of 1′ are better than those of diluted samples of [TbPc2]−/0/+ (Figure S16). Our results show that the τ is slow at low temperature, and it becomes faster due to thermal fluctuations when the temperature is above 5 K. Thus, the magnetic hysteresis curve is closed at higher temperatures. The hysteresis loop in the M−H curves is influenced significantly by the measurement method and the field sweep rate. In order to determine the temperature at which the hysteresis loop opens, the magnetization of 1 was measured in a continuous sweep mode (sweep rate: 0.0195 T s−1) on a PPMS

VSM system (Figures S17 and S18). We detected the Hc of 1 at 10 K by using PPMS (Hc = −0.008 T), but no Hc was observed for 1 at 16 K (Figure S18). On the other hand, the hysteresis loop of 1 was observed at temperatures as high as 27 K. For temperatures above 20 K, it is quite difficult to distinguish between a direct process and phonon bottleneck (PB). PB is a phenomenon that occurs when a process moves to the heat bath where phonons are generated via a direct process.34 It is a phenomenon that induces spin-phonon interactions by increasing the time that a phonon stays in the sample. Next, ac magnetic susceptibility measurements on a randomly oriented powdered sample were performed in a 3 Oe oscillating ac magnetic field in the ν range 1−1500 Hz to elucidate dynamic magnetic properties. As shown in Figures 5a and S19, sharp ν-dependent drops in the in-phase (χM’) and out-of-phase (χM″) peaks in different temperature ranges were observed, indicating that 1 undergoes slow magnetic relaxation processes, confirming this compound to be an SMM. The Arrhenius plot, shown in Figure 5c, was made by using the ac magnetic susceptibility data. Since τ obeys the Arrhenius law in the high temperature range, the data in the higher temperature range could be fitted. The Ueff value was extracted from the χM″ values and was estimated to be 588 cm−1 (847 K) with a preexponential factor (τ0) of 3.1 × 10−12 s from the Arrhenius equation of τ = τ0 exp(ΔE/kBT), where τ = 1/(2πν), kB is the Boltzmann constant, and ΔE/kB is the energy barrier for spin reversal (Ueff). In a dc magnetic field of 0.3 T, ground state QTM processes were suppressed, and the peaks of χM″ in the low ν region were at higher temperature (Figure S19d). Measurements on a magnetically diluted THF solution of 1 (1′) were also performed (Figure S20). As in the case of the powder sample of 1, ac χ values were ν dependent. Ueff and τ0 were determined to be 428 cm−1 (616 K) and 3.9 × 10−12 s, respectively (Figures S22 and S24), which are slightly smaller than those of the powdered sample. In solution, since the influence of intermolecular interactions became negligible, it was thought that the effects of the Hbias decreased and QTM was enhanced. As a result, it seems that the Ueff of 1′ is lowered by about 100 cm−1 compared with 1.29 From the ac magnetic susceptibility of 1 and 1′ at 1.8 K without a dc magnetic field, the τ for 1 was 13 s which is more than 18 times slower than that for 1′ (τ = 0.7 s). It means that the weak intermolecular ferromagnetic interactions in 1 lead to a further suppression of QTM. In comparison to TbIII−Pc multiple-decker complexes as a single molecule, the temperature for magnetic hysteresis of the magnetically diluted sample of 1′ is higher (∼5 K) than that of Tb2(obPc)3 (