Relationship between the Coordination Geometry and Spin Dynamics of Dysprosium(III) Heteroleptic Triple-Decker Complexes

Abstract

When using single molecule magnets (SMMs) in spintronics devices, controlling the quantum tunneling of the magnetization (QTM) and spin-lattice interactions is important. To improve the functionality of SMMs, researchers have explored the effects of changing the coordination geometry of SMMs and the magnetic interactions between them. Here, we report on the effects of the octa-coordination geometry on the magnetic relaxation processes of dinuclear dysprosium(III) complexes in the low-temperature region. Mixed ligand dinuclear Dy³⁺ triple-decker complexes [(TPP)Dy(Pc)Dy(TPP)] (1), which have crystallographically equivalent Dy³⁺ ions, and [(Pc)Dy(Pc)Dy(TPP)] (2), which have non-equivalent Dy³⁺ ions, (Pc²⁻ = phthalocyaninato; TPP²⁻ = tetraphenylporphyrinato), undergo dual magnetic relaxation processes. This is due to the differences in the ground states due to the twist angle (φ) between the ligands. The relationship between the off-diagonal terms and the dual magnetic relaxation processes that appears due to a deviation from D_4h symmetry is discussed.

1. Introduction

Rational design and synthesis of single molecular magnets (SMMs) and molecular nanomagnets (MNMs) suitable for quantum information processing (QIP) in quantum computers (QCs) remains difficult [1,2,3,4,5,6,7]. Over the past two decades, a wide range of SMMs with controlled spin relaxation processes and high performance have been reported. The charge density distribution of oblate-type lanthanoid ions, (like terbium(III) and dysprosium(III)), strongly improves axial coordination properties of square antiprism (D_4d), pentagonal bipyramidal (D_5h), and “vent metallocene” type complexes (SMM characteristics have been confirmed for C₁ symmetry) [8,9,10]. In the D_4d ligand field system, the SMM characteristics can be controlled by manipulating the ground state via rotation of the ligands by protonation/deprotonation [11,12], coupling of Tb³⁺-bisphthalocyaninato (Pc²⁻) complex with cadmium ions, etc. [13]. Recently, several groups have shown the relationship between octa-coordination environments and the magnetic relaxation processes of Tb³⁺-Pc²⁻ multiple-decker SMMs along the C₄ rotation axis. From these reports, correlations between the twist angle (φ), ligand field (LF) parameters, and the lowest ground state of Pc²⁻ have been clarified [14]. However, the influence of the coordination environment on the spin relaxation phenomena is not completely understood. In the case of Dy³⁺ ions, the magnetic relaxation mechanism strongly depends on the electronic structure and can sometimes be complicated. In 2003, Ishikawa and coworkers determined that the lowest ground states (J_z) of the DyPc₂ complex to be |J_z| = 13/2 by using magnetic measurements when φ is 45° and |J_z| = 11/2 when φ is 32° [15,16]. In our previous work, we have shown that for some complexes with two crystallographically equivalent Dy³⁺ ions, the ground state is split by the Zeeman effect only if the angle is 45°, resulting in dual relaxation processes. There have been other attempts to elucidate the identities of the dual processes by using theoretical and experimental approaches. Thus, it is important to carefully design the coordination environment around the Dy³⁺ ion in order to investigate the correlation between the magnetic relaxation process and the ground state in detail. In other words, due to the sensitivity toward the coordination environment, Dy³⁺ complexes are easier to control than Tb³⁺ complexes. In this paper, in addition to the dinuclear Dy³⁺ triple-decker complexes we have reported so far, we discuss the relationship between coordination environment and magnetic properties for (TPP)Dy(Pc)Dy(TPP)] (1) and [(Pc)Dy(Pc)Dy(TPP)] (2) (Pc²⁻ = phthalocyaninato and TPP²⁻ = tetraphenylporphyrinato) with C₄ symmetry.

2. Results and Discussion

2.1. Synthesis and Crystal Strucures

We synthesized the compounds following reported procedures [17]. Single crystal X-ray diffraction analyses on triple-decker complexes 1 and 2 were performed to investigate the coordination environment around the Dy³⁺ ions (Table S1). For 1, which crystallized in the tetragonal space group I4/m, the twist angle (φ) between the outer TPP²⁻ ligand and the inner Pc ligand was determined to be 4°. Therefore, the coordination environment around the Dy³⁺ ions has a slightly distorted square-prism (SP) structure. Since the inner Pc²⁻ ligand acts as a mirror plane in the molecule, the two Dy³⁺ ions are equivalent, and the distance between them was determined to be 3.71 Å. This is a relatively long value among the dinuclear Dy³⁺ triple-decker complexes reported so far. Compound 2 crystallized in the monoclinic space group C2₁/c, and the Dy³⁺ ions are inequivalent. φ between the outer and the inner Pc²⁻ ligands was determined to be 39°, meaning that it has a square-antiprism (SAP) structure. φ between the inner Pc²⁻ ligand and the TPP²⁻ ligand was 14°, which is indicative of a highly distorted SAP structure.

Besides the φ between the ligands in the multi-decker type SMM [18], the distance between the coordination isoindole nitrogen atom (N_iso) and the metal ions (d), and the angles between the C₄ axis and the direction of Dy³⁺–N_iso (α) affect the properties of these type of SMMs [19]. From a comparison of 1 and 2 with previously studied Dy³⁺ triple-decker complexes 1–6 (

Table 1. Selected crystallographic data for Dy³⁺-Pc triple-decker complexes.

Complex	α1 [°]	α2 [°]	α3 [°]	α4 [°]	d1 [Å]	d2 [Å]	d3 [Å]	d4 [Å]	φA [°]	φB [°]
[(TPP)Dy(Pc)Dy(TPP)] 1	59	46	46	59	2.39	2.67	2.67	2.39	4	4
[(Pc)Dy(Pc)Dy(TPP)] 2	57	49	45	60	2.35	2.57	2.72	2.37	39	14
[(Pc)Dy(ooPc)Dy(Pc)] 3 a	57	48	48	57	2.35	2.59	2.59	2.35	45	45
[(ohPc)Dy(ohPc)Dy(ohPc)] 4 b	57	47	47	57	2.35	2.60	2.60	2.35	27	27
[(obPc)Dy(obPc)Dy(obPc)] 5 c	57	48	48	57	2.35	2.60	2.60	2.35	32	32
[Dy4] 6 d	57	46	49	57	2.33	2.65	2.53	2.37	23	45

^a ooPc = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato; ^b ohPc²⁻ = 2,3,9,10,16,17,23,24-octakis(hexyloxy) phthalocyaninato; ^c obPc²⁻ = 2,3,9,10,16,17,23,24-octakis(butoxy)phthalocyaninato; ^d [Dy(obPc)₂]Dy(Fused-Pc)Dy[Dy(obPc)₂] (Fused-Pc⁴⁻ = bis{72,82,122,132,172,182-hexabutoxytribenzo[g, l, q]-5, 10, 15, 20-tetraazaporphirino}[b, e]benzenato).

) [20,21], site A of 1 and 2 involving a TPP²⁻ ligand has a small φ. Moreover, distances d₂ and d₃ between the N_iso of the Pc²⁻ ligand and the metal ions, as indicated in Figure 1, are greater than those in other complexes. 6 has a large d₂ at the small φ site, and φ decreases with increases in d₂ and d₃. In other words, the TPP²⁻ ligands strongly push the Dy³⁺ ions to the outside of the complex.

The ground states of the Dy³⁺ ions can be estimated from the structure, and theoretical calculations of electrostatic potentials distributed over α for the 4f-shells indicate that the ground state |J_Z| is highly dependent on α and d [22]. The ground states of 1 and 2 were estimated from the data in Table 1, and |J_Z| = 11/2 and 13/2 are the lowest ground states, respectively. However, the |J_Z| levels of these dinuclear Dy³⁺ triple-decker complexes are known to mix [19], and intermediate |J_Z| levels have the lowest basal order since α is near the magic angle of 54.7° [20,21]. Therefore, φ determines the ground states of the Dy³⁺ ions.

Crystal packing diagrams for 1 and 2 are shown in Figure 2. The intermolecular Dy³⁺-Dy³⁺ distances along the c axis in 1 and 2 were determined to be 13.61 Å and 11.63 Å, respectively. The molecules of 1 and 2 are rather well-separated from neighboring molecules due to the tetraphenyl groups of the TPP²⁻ ligands and chloroform molecules as crystal solvents (Table S2). Furthermore, PXRD patterns for 1 and 2 at 293 K are slightly different from those simulated from X-ray single crystallographic data for 1 at 120 K because of partial elimination of crystal solvents (Figure S7). From elemental analysis, some of the crystal solvent desorbed. However, the magnetic properties of the same sample remained unchanged after several months, meaning that solvent desorption has little effect on the magnetic properties. The crystal system is the same regardless of whether a solvent is present or absent, meaning that it does not affect the magnetic measurements.

2.2. Static Magnetic Properties

The static magnetic susceptibility of 1 and 2 were measured in the T range of 1.8–300 K using a superconducting quantum interference device (SQUID) magnetometer. The χ_MT value at 300 K is consistent with the value expected for the two Dy³⁺ ions (⁶H_15/2, S = 5/2, L = 5, g = 4/3). Curie–Weiss plots for 1 and 2 are shown in Figure 3. Linear approximation was performed over the entire T range to obtain values of the Curie (C) (28.50 cm³ K mol⁻¹ (1) and 28.20 cm³ K mol⁻¹ (2)) and Weiss constants (θ) (–2.33 K (1) and –1.97 K (2)) (Figures S8 and S9). In χ_MT versus T plots, the values for 1 decreased with a decrease in T, reaching a minimum of 19.9 cm³ K mol⁻¹ at 1.8 K, which indicates that magnetic properties of the Dy³⁺ complexes mainly originate from LF effects, such as thermal depopulation of the Stark sublevels [23,24,25]. As for 2, there was a slight increase in the χ_MT values when T < 4 K. Since the intermolecular metal distance is sufficiently long [26], the increase is thought to be due to the magnetic dipole interactions between the Dy³⁺ ions in the molecule. All Dy³⁺-Pc complexes so far reported exhibit similar ferromagnetic behavior. However, the behavior of the χ_MT values for 1 is different from the other Dy³⁺ triple-decker complexes, and an increase in the χ_MT values was not observed in the low T region. Although the fact that the intermolecular distance is similar for each complex, the difference in LF parameters of the Dy³⁺ ions has a dramatic effect. In other words, the increase in the off-diagonal terms and the change in the LF splitting energy along with the change in symmetry are important factors affecting the magnetic behavior. Fitting of the data was performed using the PHI program with reported LF parameters [27]. However, we could not obtain consistent results for 1 and 2 because their ground states are complicated due to mixing of the off-diagonal terms.

In order to confirm the magnetic anisotropy of the molecule, T dependence of MH were performed (Figure 4). For both complexes, the magnetization did not saturate up to 70 kOe. However, splitting of the M versus HT⁻¹ plot occurred, indicating that not only depopulation occurred but also both complexes had large magnetic anisotropies. In addition, butterfly-type hysteresis was not observed during the MH measurements at 1.8 K. When uniaxial anisotropy is strong, the saturation magnetization value (M_s) is expressed as M_s = 1/2 × g*(z) × $\tilde{S}$ where $\tilde{S}$ = 1/2 [28]. So, the M_s values of 1 and 2 were M_s = 8.6 μ_B and M_s = 7.4 μ_B, calculated using |J_z| = 13/2 (g*(x) = g*(y) = 0, g*(z) = 17.3) and 11/2 (g*(x) = g*(y) = 0, g*(z) = 14.7), respectively. Although the measured values are larger than the calculated values (1: 13.6 μ_B, 2: 13.7 μ_B), they are smaller than the effective magnetic moments (μ_eff) of two Dy³⁺ ions (μ_eff = 21 μ_B).

2.3. Dynamic Magnetic Properties

In order to investigate the magnetic relaxation processes, alternating current (ac) magnetic susceptibility measurements were performed on powder samples of 1 and 2. For 2, the χ_M″ values were frequency (ν) dependent in the range of 0.1–1000 Hz in a zero magnetic field (Figures S10–S13), whereas for 1, they were not. To clarify these differences, ac magnetic susceptibility measurements were performed in different magnetic fields at 1.8 K. When H was in the range of 0–5 kOe, the magnetization of both complexes underwent dual relaxation processes (Figure 5). As shown in Figure 6, the magnetic relaxation times (τ) calculated from the χ_M″ versus ν plot on the low ν side increased monotonically with an increase in H, and the τ values calculated from the high ν side reached a local maximum in specific applied H_dc. These results indicate that the maximum H_dc suppresses QTM and promotes a direct process [29], and the results can be reproduced using a mixture of QTM, direct and Raman processes with Equation (1) (Table S3):

$${\tau }^{-1}=A{H}^{n}T+\frac{B_1}{1+B_2{H}^2}+D.$$

(1)

In previous work, we have reported that compound 3 exhibited dual magnetic relaxation processes when H_dc was larger than 2.5 kOe [14]. To understand the details of the dual magnetic relaxation dynamics of 1 and 2, we analyzed the ratio of relaxation time ρ (= τ₂/τ₁). The ρ values of 1 correspond to the occurrence of a single relaxation process in the Dy³⁺ SMM system. If the value is large enough (>1000), dual magnetic relaxation processes are observed separately [30]. Since the splitting of relaxation is observed at 0.25 kOe for 1 and 2, it can be said that it responds more sensitively to H_dc. This is another indication that the ground states of Dy³⁺ ions are more complicated.

ν dependences of the χ_M″ values of 1 and 2 were measured in the range of 1–1000 Hz in various H_dc, and a split in the χ_M″ values was observed below 8 and 20 K, respectively. In a χ_M″ versus T plot, a peak top was observed in the T range below 2 K, indicating that the magnetic moment was not frozen or that a different relaxation processes, like QTM, was dominate. We used the Kramers–Kronig equation [31,32,33,34,35], which infers the pre-exponential factor τ₀ and the activation barrier U_eff from the χ_M″/χ_M’ versus T (2.5–4 K) plot, to fit the data:

χ_M″/χ_M′ = ωτ,

(2)

χ_M″/χ_M′ = ωτ₀ + exp (U_eff/T),

(3)

ln (χ_M″/χ_M′) = ln (ωτ₀) + U_eff/T.

(4)

From a χ_M″/χ_M′ plot for 1, U_eff was determined to be about 8.1 cm⁻¹, and τ₀ ≈ 10⁻⁷ s. For 2, U_eff was determined to be about 2.7 cm⁻¹, and τ₀ ≈ 10⁻⁶ s (Figures S14 and S15). The small τ₀ indicates, that the contribution from an Orbach process becomes small. Figure 7 shows the relationship between U_eff and φ [15,16]. From this figure, as φ decreases from 45°, the activation energy tends to decrease. This is because a contribution from the off-diagonal LF terms promotes QTM, and during the conversion from SAP to SP geometries. Thus, $B_2^0$ becomes smaller, and off-diagonal terms $B_4^4$ and $B_6^4$ become larger, resulting in a narrower U_eff. It is thought that a small φ has a negative effect on the activation barrier. In other words, the small φ of 1 and 2 cause a decrease in the activation barrier.

To investigate the magnetic relaxation properties of 1 and 2 at low T, ν dependence measurements were performed in an applied H_dc in the T range of 1.8–4.5 K. An Argand plot for both complexes showed that a dual magnetic relaxation process occurred. τ for each component was calculated by fitting the imaginary component of the ac magnetic susceptibility with the extended Debye model (Equations S2 and S3, Figure 8), and using those values, an Arrhenius plot was obtained (Figure 9). From a fitting with Equation (5) on the values for 1, τ obtained from the low ν side indicates that a QTM process independent of T occurs, and that obtained from the high ν side is proportional to T⁻⁹, meaning that it is a Raman process (Table S4). However, the fitting of the data for 1 is not accurate due to large deviation in the τ values. In particular, when τ values at T > 2.5 K, the spin dynamics of 1 could not be determined. On the other hand, for 2, τ obtained from the low ν side is proportional to T^−1.7, and that obtained from the high ν side indicates that a direct process occurs. For both complexes, the lowest ground state estimated from the crystal structure is expected to contain a large amount of mixing. Therefore, even when a complex has crystallographically equivalent Dy³⁺ ions, dual relaxation processes occur between mixed states in an applied magnetic field. In the case of 1, the D_4h symmetry around the Dy³⁺ ion has a large effect on the off-diagonal term, causing QTM to be dominant. In addition, T is proportional to n ≈ −2 which could be reproduced using a PB process to fit the data. However, since Raman processes can involve acoustic-optical phonons (n = 1–6) [18], it is difficult to separate each contribution due to the complicated ground state of 2.

$${\tau }^{-1}=A{H}^{n}T+C{T}^m+{\tau }_{\mathrm{QTM}}^{-1}.$$

(5)

3. Materials and Methods

3.1. Synthesis

Solvents were used without further purification. Dy(acac)₃·4H₂O and the free ligand were purchased from TCI Tokyo Chemical Industry Co., LTD, Tokyo, Japan. Dy(acac)₃·4H₂O (180 mg, 0.40 mmol) and H₂TTP (tetraphenylporphyrin) (150 mg, 0.25 mmol) were added to dry 1,2,4-trichlorobenzene (40 mL). The solution was refluxed under nitrogen for 4 h. After cooling, Li₂Pc (158 mg, 0.60 mmol) was added to the mixture. Then, the solution was refluxed for 12 h. After cooling, the reaction mixture was added to n-hexane (500 mL). The obtained solid was purified by using column chromatography on silica gel with chloroform as the eluent. [(TTP)Dy(Pc)Dy(TTP)] (1) was obtained from a deep brownish red fraction, which was the first fraction, by removing the solvent (16%), and [(Pc)Dy(Pc)Dy(TTP)] (2) was obtained from the dark green second fraction (34%). Spectroscopic data used for characterization are described in the SI (Figures S5 and S6). Column chromatography (C-200 silica gel, Wako and Sephadex G-10, Pharmacia Biotech) was used to remove the remaining impurities. Dark red block crystals of 1 were obtained from chloroform/n-hexane (27 mg). ESI-MS: m/z (%): 2062.47242 (100) [M−1⁺] (Figures S1 and S2); elemental analysis calcd (%) for C₁₂₀H₇₂N₁₆Dy₂·4CHCl₃: C 58.62, H 3.02, N 8.82; found: C 60.03, H 3.21, N 8.89. Black fine needle crystals of 2 were obtained from chloroform/n-hexane (83 mg). ESI-MS: m/z (%): 1962.38956 (100) [M⁺] (Figure S3 and S4); elemental analysis calcd (%) for C₁₀₈H₆₀N₂₀Dy₂·CHCl₃: C 60.01, H 2.84, N 12.72; found: C 62.91, H 3.28, N 13.36. The results of the elemental analysis for 2 indicates desorption of some of the CHCl₃ molecules compared with the number of CHCl₃ molecules calculated from the crystal structure.

3.2. Physical Measurements

Elemental analyses were conducted on a PerkinElmer 240C elemental analyzer (PerkinElmer, Waltham, MA, USA) at the Research and Analytical Centre for Giant Molecules, Tohoku University. UV-Vis-NIR spectra were acquired using CHCl₃ solution on a Shimadzu UV-3100pc (Shimadzu, Kyoto, Japan). IR spectroscopy was performed on ATR method on FT/IR-4200 spectrometer at 298 K. Magnetic susceptibility measurements were conducted on a Quantum Design SQUID magnetometer MPMS-XL and MPMS-3 (Quantum Design, San Diego, CA, USA) in the T and dc field ranges of 1.8–300 K and ±50 kOe, respectively. AC measurements were performed in the frequency range of 0.1–1000 Hz with an ac field amplitude of 3 Oe. A polycrystalline sample suspended in n-eicosane was used for the measurements. Crystallographic data for 1 and 2 were collected at 120 K on a Rigaku Saturn724+ CCD Diffractometer (Rigaku, Tokyo, Japan) with graphite-monochromated Mo Kα radiation (λ = 0.71075 Å) produced using a VariMax microfocus X-ray rotating anode source. Single crystals with dimensions of 0.10 × 0.07 × 0.01 mm³ (1) and 0.15 × 0.20 × 0.04 mm³ (2) were used. Data processing was conducted using the Crystal Clear crystallographic software package [36]. The structures were solved by using direct methods using SIR-92 [37]. Refinement was carried out using the Yadokari-XG package [38] and SHELXT. The non-Hydrogen atoms were refined anisotropically using weighted full-matrix least squares on F. Hydrogen atoms attached to the carbon atoms were fixed using idealized geometries and refined using a riding model. CCDC 1940003 for 1 and 1940004 for 2. Powder X-ray diffraction was conducted on a Bruker AXS D2 phaser (Bruker Corporation Billerica, MA, USA).

4. Conclusions

Complexes 1 and 2 were synthesized similar to previously reported Dy³⁺-Pc complexes with a TPP²⁻ ligand. The TPP²⁻ ligands induce a smaller twist angle (φ) between the ligands than those in the previous complexes due to the effects of steric repulsion from the phenyl group. Although 1 has D_4h symmetry due to the two TPP²⁻ ligands, 2 has lower symmetry due to having only one TPP²⁻. From dc magnetic measurements on both complexes, the χ_MT values decreased due to depopulation. Measurement of M-HT⁻¹ indicated uniaxial anisotropy, but it is smaller than the expected values for a pseudospin model. No hysteresis opening at 1.8 K was observed, suggesting a mixture of ground states, which is consistent with the estimation of the ground state using the value of α obtained from the crystal structure data. In addition, dual slow magnetization relaxation was observed for both complexes from ac magnetic susceptibility measurements in an applied H_dc. U_eff calculated by using the Kramers–Kronig equation is very small and corresponded to the tendency of previous triple-decker compounds to decrease with decrease of φ. From above the results, 1 and 2 are field-induced SMMs. For 1, QTM and Raman processes occur due to the symmetry of D_4h, whereas for 2, mixed relaxation (Raman, PB) and QTM processes occur. The contributions of the Raman and PB processes must be clarified. The magnetic processes involve spin relaxation in mixed ground states, and the off-diagonal term is dominant. This is different from conventional dinuclear Dy³⁺ complexes. Multiple relaxation processes could be turned on by adjusting φ to 4° (1) and 14° (2), and this can be used to prepare functional SMMs whose characteristics can be switched on and off by changing φ.