The first Haldane gap compound with S = 1 was [Ni(en)₂(NO₂)]ClO₄ (hereafter abbreviated as NENP). In 1981, Meyer et al. synthesized this compound,¹³ and in 1987, Renard et al. first recognized it as a Haldane gap compound.¹⁴

We reported a series of one-dimensional N₃⁻-bridged Ni(II) compounds (S = 1) with the chemical formula of [Ni(AA)₂N₃]Y ((AA)₂ = (diamines)₂, linear-tetramines, N₄-macrocycles; Y = ClO₄⁻, PF₆⁻, and BF₄⁻) (Figure 3). The crystal structure of [Ni(dmpn)₂N₃]ClO₄ (hereafter abbreviated as NDMAZ) is shown in Figure 4, where two dmpn in-plane ligands coordinate to Ni(II) ion in the equatorial positions and each planar [Ni(dmpn)₂]²⁺ unit are bridged by N₃⁻ to form a linear chain structure.¹⁵ All Ni(II) sites in NDMAZ are crystallographycally equivalent, which is clearly different from that of NENP.

Figure 3. In-plane ligands (AA) and their abbreviations (ref. 18).

Figure 4. Crystal structure of NDMAZ (ref. 18).

The magnetic susceptibility of NDMAZ shows a broad peak at around 90 K which exponentially decreases with decreasing temperature as shown in Figure 5. The magnetic data were fitted to theoretical calculated values with the parameters g = 2.12 and J = −70.6 K. From the low-temperature components, the Haldane gap is estimated to be 22 K. We also carried out a high-field magnetization process under a magnetic field up to 30 T. The field dependence of the magnetization shows that the critical field H_c is around 14 T (Figure 6).¹⁶

Figure 5. Magnetic susceptibilities of NDMAZ (ref. 18).

Figure 6. Field-induced magnetization curve of NDMAZ (ref. 18).

The main difference between NENP and NDMAZ is the direction of the magnetic g-tensor, that is, alternatively tilted and parallel arrangements, respectively as shown in Figure 7. Accordingly, since 3D-LRO is anticipated in NDMAZ at low temperature and under high magnetic field, we carried out a heat capacity (C_p) measurement on a single crystal of NDMAZ as shown in Figure 8. A C_p anomaly was observed at around 9 K and 12 T. We interpreted this anomaly as an indication of the field-induced long-range magnetic ordering (LRO), which is the first observation in all Haldane gap systems so far reported.¹⁷

Figure 7. Direction of the principle axes of g-tensors of NENP (left) and NDMAZ (right) (ref. 18).

Figure 8. Heat capacities of single crystal of NDMAZ (ref. 18).

The relationship between the parameters |J| and E_g is shown in Figure 9.¹⁸ The straight line is the theoretical relationship between E_g and |J| obtained by the Monte Carlo calculation method, E_g ∼ 0.41|J|. Most experimental data are consistent with the theoretical line. The effects of the bridging ligands, the in-plane ligands, and the counter anions on Haldane gaps (E_g) are as follows; X = N₃⁻ > NO₂⁻; (AA)₂ = (en)₂ ≥ (tn)₂ > linear-tetramine > (dmpn)₂ > Me₆[14]aneN₄ ≧ [15]aneN₄; Y = ClO₄⁻ > PF₆⁻. The effect of the bridging ligands on Haldane gaps is due to the different coordination abilities. The in-plane ligands and counter anions are considered to affect Haldane gaps by their differences of the bulkiness or steric hindrance. As a result, we can manipulate the magnitudes of Haldane gaps (E_g) by substituting the bridging ligands, the in-plane ligands, and the counter anions as will.

Figure 9. Relationship between E_g and |J|. 1; [Ni(tn)₂N₃]ClO₄, 2; [Ni(3,2,3-tet)N₃]ClO₄, 3; [Ni(dmpn)₂N₃]ClO₄, 4; [Ni([15]aneN₄)N₃]ClO₄, 5; [Ni(Me₆[14]aneN₄)N₃]ClO₄, 6; [Ni(en)₂(NO₂)]ClO₄, 7; [Ni(tn)₂(NO₂)]ClO₄, 8; (CH₃)₄N[Ni(NO₂)₃], 9; [Ni(dmpn)₂(NO₂)]PF₆·H₂O (ref. 18).

The physical pressure effect on Haldane gap compounds is very interesting as well. The temperature-dependent magnetic susceptibilities of NDMAZ were measured under pressure up to 10 Kbar.¹⁹ With increasing pressure, the absolute values of the magnetic susceptibilities decrease. At the same time, the peaks gradually shift to higher temperature. Then, the experimental data were fitted to Meyer’s equations. Thus, the |J| values under pressure are shown in Figure 10. With increasing pressure, the |J| values increase by 50%. This is due to an increase in the orbital overlap between Ni(II) ion and N₃⁻ bridging ligand under pressure. As a result, we have realized manipulation of Haldane gaps both chemically and physically.

Figure 10. J (K) values of NDMAZ under pressure up to 10 kbar (ref. 18).

From numerical calculation, Haldane gap (E_g) is predicted to be very small for the spin quantum number S = 2. Therefore, it was considered very difficult to find Haldane gap compounds with S = 2.

Granroth et al. discovered the first Haldane gap compound with S = 2, [Mn(bipy)Cl₃] (bipy = 2,2′-bipyridine).¹⁸ Goodwin and Sylva firstly carried out magnetic measurements of the compound down to 118 K in 1967.¹⁸ In 1991, Perlepes et al. reported the crystal structure.¹⁸ The compound is composed of quasi-linear chain Mn³⁺ (S = 2) ions in Mn(bipy)Cl₂ units, which are asymmetrically connected by bridging Cl⁻ ions. The Mn³⁺ coordination is formed with a distorted octahedron where the Mn-Cl bonds along the chain axis (Mn-Cl(1) = 2.5 Å and Mn-Cl(1′) = 2.71 Å) are longer than those of the equatorial plane (2.24 Å). Axial elongation results in singly occupied \(\text{d}_{z^{2}}\) orbital with a value of D < 0. The Mn-Mn intrachain distance is estimated to be 4.83 Å, and the strongest Mn-Mn interaction is through overlap of the metal \(\text{d}_{z^{2}}\) orbitals with the Cl⁻ bridges. The Mn-Cl-Mn angle of 135° is consistent with the antiferromagnetic exchange interaction.

The magnetic susceptibility measurements of single-crystals of compound were carried out from 1.8 to 300 K with magnetic field parallel and perpendicular to the chains, which yielded g = 2 and J = −35 K. The magnetization M was measured at 30 mK and 1.4 K in a magnetic field up to 16 T. No evidence of magnetic long-range order (LRO) was observed. Depending on the crystal orientation, M = 0 at 30 mK until a critical field is achieved (H || c = 1.2 ± 0.2 T and H ⊥ c = 1.8 ± 0.2 T), where M increases continuously as H is increased. These results were interpreted as evidence of the first Haldane gap compound with S = 2.¹⁸

As described above, about 40 years ago Haldane predicted this theoretically before the first Haldane gap compound was discovered. Therefore, Haldane’s conjecture was quite prescient, and thus he received the Nobel Prize in Physics in 2016.

The double-decker phthalocyaninato Tb(III) complex, TbPc₂ (Pc = phthalocyanine) shows the redox-active to produce [TbPc₂]^0,±1. The [TbPc₂]^0,±1 shows SMM behavior,⁴² and their QTM and magnetic relaxation behaviors have been utilized in spintronics devices. In [TbPc₂]^0,±1, the Tb(III) ions have significant large axial magnetic anisotropies (strong Ising-type anisotropy), and these SMMs have long τ, which means that they can hold spin information for a long time. In other words, [TbPc₂]^0,±1 can store “bits” of ±1 information, and thus, can be used to prepare high-density memory storage devices by taking advantages of the small molecule with a nano-size. Moreover, the spins of multiple-decker SMMs with Tb_nPc_n+1 configuration can have 2ⁿ combinations of spin directions.

In this part, we describe the relationship between the molecular structures and the SMM properties of phthalocyaninato Tb(III) double-decker, triple-decker, quadruple-decker, and quintuple-decker complexes.

2.3.1a Double-Decker Type SMMs;

In 2003, Ishikawa et al. reported that sandwich-type phthalocyaninato Tb(III) double-decker complex (TBA)⁺[TbPc₂]⁻ (The Tb^III ion has a ground state of ⁷F₆ with S = 3, L = 3, and g = 3/2; TBA⁺ = tetrabutylammonium cation) behaves as SMM with a long magnetization relaxation time (τ), originating from the ligand field (Figure 18). Magnetic properties of rare earth metal ions (f electron-based) Ln(III) are strongly related to the charge density distribution. The Tb(III) ions exhibit uniaxial magnetic anisotropy of the easy axis, and the division of ground-state multiples is caused by the LF at the axial position. In this case, the energy gaps between the ground and first excited states are associated with the energy barrier for the reversal of the magnetization (ΔE), thereby causing slow magnetic relaxations, which occur through a different mechanism than those for well-known d metal-based SMMs. The LF energy potential around the Tb(III) ion (4f⁸), with a total angular momentum (J) of 6, splits the ground multiple so that the lower sublevel has the larger J_Z value. For TbPc₂, the ground multiple of the Tb(III) ions ⁷F₆ splits seven energy levels with angular momenta expressed as |J_Z〉 of |0〉, |±1〉, |±2〉, |±3〉, |±4〉, |±5〉, and |±6〉 due to the LF splitting from Pc ligands. As a consequence, there is an energy gap between the |±5〉 and |±6〉 level of ∼400 cm⁻¹, which is attributed to ΔE. Furthermore, the J of |±6〉 couples with the nuclear spins of the Tb(III) ions (I = ±3/2〉, ±1/2〉), and the ground state splits into eight states (I-J coupling), which effects QTM (Figure 18).⁴² Additionally, contractions of the square-antiprismatic (SAP) coordination environment have an influence on the LF of the Ln(III) ions, affecting the SMM properties (Figure 19). It was reported that when considering the LF potential (V), a V_SAP for an ideal SAP coordination geometry with D_4d symmetry is different from the V_SP for SP (square-prismatic) coordination geometry with D_4h symmetry.⁴³ The differences in the characteristics of SMMs are considered to be due to the presence or absence of particularly off-diagonal terms (B₄⁴, B₆⁴) of LF in SAP and SP. Therefore, SAP coordination geometry can suppress QTM, inducing the better SMMs behaviors. Moreover, the intermolecular dipole interactions can suppress QTM by exchange bias as well. Such effects are modified by the substituents of Pc ligands, crystal packings, Tb(III)-Tb(III) distances in multiple-decker SMMs, dipole interactions, crystal solvents, synthetic conditions, etc.

Figure 18. Scheme of the electronic structures of the Tb^III ion (4f⁸) and TbPc₂ complexes. Magnetic dipole-dipole interactions are important for Tb^III dinuclear systems (ref. 40b).

Figure 19. (a) Scheme of the square-antiprismatic (SAP) coordination environment of Ln^IIIPc₂ (b) Twist angle, ϕ, in an SAP in multiple-decker Ln^IIIPc₂ complexes (ref. 40b).

The starting Tb(III) double-decker SMM complex ([TbPc₂]⁻) consists of a Tb(III) ion with 4f⁸ and two Pc ligands having a formal charge of −2 with a closed-shell π electron system. It is well known that one-electron oxidation of the anion radical occurs at the Pc ligand in the open air, resulting in a neutral complex with an open-shell π electron system of Pc ligand (TbPc₂). Therefore, TbPc₂ has two spin systems such as one delocalized unpaired π electron over the top and bottom sandwiched Pc ligands, and central Tb(III) ions with 4f⁸ electrons.

We investigated the relationship between the crystal structures and magnetic properties of TbPc₂ (1) and TbPc₂.CH₂Cl₂ (2), which are influenced by the crystal solvent of CH₂Cl₂. Their crystal structures and their crystal packings are shown in Figure 20. The compounds (1) and (2) crystallize in the orthorhombic space group P2₁2₁2₁ and Pnma, respectively. The average distance between Tb(III) ion and a coordinated isoindole N atom (N_iso) was estimated to be 2.408 Å in (1) and 2.418 Å in (2). The twist angle (ϕ) between the two sandwiched Pc rings was estimated to be 41.37° in (1) and 44.93° in (2), which form SAP coordination geometry and a pseudo four-fold axis (C₄) perpendicular to the Pc rings in both crystal structures. TbPc₂ has a magnetic easy axis in the same orientation with the C₄ axis, as shown in Figure 21 with the red arrow. Additionally, the angle (α) between C₄ axis and the direction of the Ln(III)-N_iso coordination bond is known to have a strong influence on the LF parameter. It is 54.56° in (1) and 54.60° in (2). When the coordination geometry is distorted from D_4d, the off-diagonal terms (B₄⁴, B₆⁴) with the parameters for the transverse anisotropy, appear in the Hamiltonian. They cause a mixing between the ground states of the up spin and down spin, and induce QTM. As mentioned above, ϕ strongly affects the SMM properties via the LF parameters since the structure deviates from D_4d symmetry. In these compounds, the deviation from D_4d symmetry is smaller for (2) than (1). Therefore, QTM in (2) is effectively suppressed, compared with that in (1) from the viewpoint of their crystal structures.⁴⁴ To eliminate the effects of intermolecular interaction, magnetically diluted crystalline samples were prepared (1′) by doping TbPc₂ into YPc₂ (diamagnetic complex). Both TbPc₂ and YPc₂ have an unpaired electron delocalized on sandwiched Pc ligands.

Figure 20. (a) Twist angle in square antiprism (SAP) in LnPc₂; (b) Schematic illustration of the SAP coordination environment of LnPc₂. Crystal structures of 1 (c) and 2 (d). Top views (upper) and side views (lower). (Tb, pink; N, blue; C, gray) (ref. 40b).

Figure 21. Molecular packings of TbPc₂ (a) for 1 viewed from the c axis, and (b) for 2 viewed from the b axis. The values in the figures are the intermolecular Tb^III–Tb^III distances. (ref. 44).

As shown in Figure 22a, the χ_MT values for (1) and (2) increased with a decrease in T below 10 K, due to the ferromagnetic dipole interactions between Tb(III) ions. The increase of them is larger for (2) than (1). This result indicates that the dipole interaction in (2) is stronger than (1), which is consistent with the conclusions from the crystal structure. In the magnetization (M) versus field (H) for (1), (2), and (1′) at 1.82 K, magnetic hysteresis was observed. The loop widths increased in the order of (1) < (1′) < (2). This result shows that the dipole interactions affect the magnetic hysteresis. To investigate the magnetic relaxation process, AC magnetic susceptibilities were measured on (1) and (2) with and without an applied external magnetic field (H_dc). The peaks in χ_M′′ plot for (2) were observed in a lower frequency (ν) region than (1), meaning that τ was slower for (2). As shown in Figure 23b, the plot is divided into two parts. In the high-T region, where τ depends on T, the Orbach process is dominant. U_eff and frequency factor (τ₀) were estimated by fitting the data in the high-T region using the Arrhenius equation ((1) U_eff = 523 cm⁻¹, τ₀ = 7.7 × 10⁻¹² s; (2) U_eff = 556 cm⁻¹, τ₀ = 2.2 × 10⁻¹⁰ s). These results mean that the molecular packing in (2) effectively suppresses QTM via the small contribution of the off-diagonal terms of the LF Hamiltonian and the relatively strong dipole interactions. Similar phenomena were observed as well in comparison of TbPc₂ and Tb(obPc)₂ (obPc = 2,3,9,19,16,17,23,24-octabutoxy-phthalocyanato), because Tb(obPc)₂ has a SAP coordination environment with a Pc stacking angle (ϕ) of 45°, while TbPc₂ has ϕ of 41° due to the steric hindrance of the n-butoxy moieties.⁴⁰

Figure 22. (a) dc magnetic susceptibilities for 1, 2, and 1′. Magnetization (M) versus field (H) and dM/dH versus H for (b) 1; (c) 2; and (d) 1′ at 1.82 K. (ref. 44).

Figure 23. (a) χ_M′′ vs. ν plot for 1 and 2 in a zero field. The solid lines were fitted by using the generalized Debye model; (b) Arrhenius plots for 1 and 2. The solid lines were fitted by using the Arrhenius equation. (ref. 40b).

In 2002, Wernsdorfer et al. reported that the exchange bis can suppress QTM in dimerized Mn₄ SMM formed by the hydrogen bonds.⁴⁵ If QTM probability occurring in one SMM is defined as P_QTM, the probability of QTM simultaneously occurring in an SMM dimer is P_QTM², which means that QTM is effectively suppressed in the dimer SMMs. As an extension of their proposal of exchange bias, we reported sandwich-type hetero double-decker phthalocyaninato naphthalocyaninato Tb(III) [TbNcPc]^0/+1 SMMs.⁴⁶ [TbNcPc]PF₆ was obtained by using the electrochemical method in a CH₂Cl₂ solution of [TbNcPc] containing the electrolyte TBA.PF₆ (TBA = tetrabutylammonium). As shown in Figure 24, [TbNcPc]PF₆ has 1D stacking structure. The Tb(III) ion is sandwiched between Nc²⁻ and Pc²⁻ ligands with a twist angle (ϕ) of 43.4°, causing the coordination environment to be slightly offset from the ideal square antiprism (SAP) structure. Therefore, the LFs are expected to be almost the same as those for [TbPc₂]⁺. There are ferromagnetic dipole interactions among Tb(III) ions in 1D structure. Furthermore, there are π–π interactions (3.410 Å) between the benzene moieties of Nc²⁻ ligands of adjacent columns. As a result, the distance between the adjacent 1D Tb(III) ions are sufficiently long enough (15.994 Å), and the magnetic interactions along the a- and b-axes should be weaker than those along the c-axis (1D direction). The PF₆⁻ counter ion and crystal solvent CH₂Cl₂ are incorporated in the pores created by the four columns, creating a robust crystal structure.

Figure 24. a) ORTEP diagram of [TbNcPc]PF₆. b) Side view of 1D structure of [TbNcPc]PF₆ along the c-axis. The ferromagnetic interactions between Tb³⁺ ions are represented by arrows. c) Top view of the 2D structure of [TbNcPc]PF₆ on the ab plane. Tb³⁺, light pink; N, cyan; C, gray (ref. 46).

Since the ferromagnetic dipole interaction occurs among Tb(III) ions below 20 K, the χ_MT increased to 12.6 cm³ K mol⁻¹. The magnetic behavior is consistent with the results from crystal structures. The field cooled (FC) and zero-field cooled (ZFC) measurements of [TbNcPc]PF₆ diverged from 20 K which is the spin blocking temperature (T_B). Butterfly-type magnetic hysteresis was observed at 1.8 K for single crystal and powder samples as shown in Figure 25. Magnetic hysteresis showed clear DC magnetic field (H_dc) sweep rate dependence of 20 mTs⁻¹ (100 Oe s⁻¹). The butterfly hysteresis loops above 25 K, which were associated with spin-phonon interactions and not due to spin blocking, were observed up to 31 K. To estimate τ, magnetization decay curves were acquired because the magnetic relaxations were extremely slow and fitted by using a stretched exponential function to obtain mean values. The τ values (65 s at 1.8 K, 37 s at 3 K and 10 s at 5 K) became faster with an increase of the temperature. To clarify the influence of the ferromagnetic dipole interactions, AC magnetic measurements were performed. Without an applied H_dc, the real (χ′) and the imaginary component (χ′′) of AC magnetic susceptibilities exhibited clear frequency (ν) dependence. To investigate the ν dependence in detail, we prepared χ′ and χ′′ vs ν plots and analyzed the data by using the Debye model to estimate τ. The τ value became slow with a decrease in the temperature and reached a value of about 22 s at 1.8 K. An Arrhenius plot was prepared for the temperature dependence of τ, and the magnetic relaxation mechanism was studied. Above 30 K, an Orbach process based on spin-lattice relaxation was observed. On the other hand, below 30 K, the ground state is complicated by magnetic dipole interaction among [TbNcPc] units. Considering optical-acoustic phonons for a Raman process (CTⁿ), it was reported that n can take values from 1 to 6.⁴⁷ Therefore, the numerical simulation of τ was carried out by using a combination of Orbach and Raman processes (τ⁻¹ = τ₀⁻¹exp(−U_eff/T) + CTⁿ). The data could be fitted when U_eff = 584 cm⁻¹ (840 K) with τ₀ = 5.5 × 10⁻¹² s, C = 0.0257 s⁻¹K⁻ⁿ and n = 2.35. Additionally, when considering the thermally activated relaxation process, U_eff was about 8.9 cm⁻¹ (12.9 K) between the ground state and excited state below 30 K. This value is on the same order as the energy gap for the Schottky type heat capacity (ΔE/k_B) estimated from the magnetic heat capacity (C_mag). As described above, [TbNcPc]PF₆ shows high hysteresis temperature ∼30 K by using the exchange bias. From these results, the ASP configuration and the exchange bias in double-decker type Tb(III) SMMs efficiently suppress QTM to produce better SMMs behavior with the higher hysteresis temperature and longer magnetic relaxation time.

Figure 25. Magnetization curves for [TbNcPc]PF₆ (2, single crystal, H || c-axis) and the diluted sample (3) at 1.8 K between ±1.5 T. (ref. 46).

2.3.1b Triple-Decker Type SMMs;

Although TbPc₂ type double-decker SMMs were studied in detail, little is known about triple-decker type Tb₂Pc₃ SMMs. Ishikawa et al. reported a series of studies on the magnetic properties of phthalocyaninato Ln(III) triple-decker complexes [(Pc)Ln(Pc)Ln(obPc)], which were the first reports on the dynamic magnetism of a coupled 4f system.⁴⁸

To evaluate the effects of the coordination geometry around the Tb(III) ions in the triple-decker SMMs, the relationship between the f-f interactions in the complexes with the same coordination environment and SMM properties should be discussed.⁴⁹ Therefore, we reported triple-decker Tb₂(obPc)₃, which is easily soluble in most organic solvents, crystallized with ethanol in the crystal lattice in the triclinic space group P-1 as shown in Figure 26. Triple-decker Tb₂(obPc)₃ has two Tb(III) ions sandwiched between three obPc ligands with eight isoindole-nitrogen donor atoms (N_iso) and a center of symmetry. The center of the square formed by the four pyrrolic nitrogen atoms of the inner obPc ligand is a crystallographically imposed inversion center, which makes the two Tb(III) ions and outer obPc ligands equivalent, and both outer obPc ligands of Tb₂(obPc)₃ are equally distorted from planarity, adopting a biconcave shape. The Tb(III) ions are unevenly spaced between the two obPc ligands by 2.58–2.63 Å from the mean plane of the four N_iso of the inner obPc ligands and 2.34–2.37 Å from the mean plane of the four N_iso of the outer ones. The displacements are different from those in double-decker TbPc₂ (2.40–2.43 Å). The intramolecular Tb^III-Tb^III distance was estimated to be 3.52 Å, and the twist angle between the outer rings and the center one was determined to be 32°, causing a SAP arrangement. The intermolecular Tb^III-Tb^III distance along the a axis was estimated to be 10.98 Å. Hence, each molecule of Tb₂(obPc)₃ is rather well separated from neighboring molecules due to the n-butoxy chains. The size and height of Tb₂(obPc)₃ were determined to be ∼24 and 7 Å, respectively (Tb(obPc)₂: ∼24 × 4 Å).

Figure 26. (a) Crystal structure of Tb₂(obPc)₃. (b) Hysteresis loops for a single crystal of Tb₂(obPc)₃ (ref. 40b).

The χ_MT versus T plots for Tb₂(obPc)₃ increased with a decrease in T and reached a maximum of 36 cm³ K Mol⁻¹ at 1.8 K, which suggests the existence of ferromagnetic dipole interactions between Tb(III) ions. The magnetic dipolar term, not the exchange term, is dominant. There was a sharp drop in the χ_M′ and χ_M′′ values in different T ranges dependent on ν, which indicate that Tb₂(obPc)₃ is an SMM. Moreover, in a χ_M′′T versus T plot at ν = 997 Hz, only a single peak at 24 K was observed. These results clearly show that two Tb(III) ion sites are equivalent and are in agreement with the structure of Tb₂(obPc)₃. Argand plots (i.e. a χ_M′′ versus χ_M′ plot) in the T range of 4–21 K and ν range of 1–1500 Hz in an H_dc of zero and 1000 Oe were made by using the generalized Debye model.⁵⁰ Over the entire T range investigated, the α parameter, which quantifies the width of the τ distribution, was in the range of 0.07–0.17 in both H_dc^s and was T-dependent. The α is equal to 0 for an ideal Debye model with a single τ. This behavior was reported for SMMs and is due to the slow magnetic relaxation. In the case of Argand plots in an H_dc of 3000 Oe, the magnetic relaxation splits from a one-component system into a two-component system (τ₁: high-frequency part and τ₂: low-frequency part), with a decrease in T in the range of 5–10 K. To investigate the different relaxation mechanism corresponding to two observed peaks, an extended Debye model was used to fit τ₁ and τ₂.⁵¹ In other words, there are two different T regions: Above ∼10 K, the relaxation follows a thermally activated mechanism, whereas at lower T, a gradual crossover to a T-independent regime for τ₁ and to a T-dependent regime for τ₂ occurs. The τ₁ behavior is consistent with the appearance of quantum effects acting on the relaxation process. In the case of the τ₂ behavior, the ground-state energy gap and a thermally activated magnetic relaxation mechanism should be considered below 10 K. From Argand plots for several H_dc at 5 K, the magnetic relaxation splits from a one-component system into a two-component system with an increase in the strength of the H_dc in the range of 1000–7000 Oc as shown in Figure 27a. τ₁ did not change in the range of 1000–7000 Oe. On the other hand, τ₂ fluctuated between 0 and 7000 Oe. In addition, the τ₁ and τ₂ processes combine to form a one-component system in an H_dc of ∼10 kOe. Similar behavior was observed for a diluted sample of Tb₂(obPc)₃. This is clear evidence that the τ of Tb₂(obPc)₃ depends heavily on T and H_dc. To estimate the effect of H_dc on the ground state of Tb₂(obPc)₃, the T dependence of the magnetic heat capacity (C_m) was measured in H_dc^s of 0, 1000, 3000, 7000, 10,000, and 30,000 Oe.⁴⁹ The peak width was broadened drastically, and the peak shifted to a higher T with an increase in the strength of the H_dc. The broadening of the C_m peak with an increase in the external H_dc shows that the J_z = ±12 (|−6, −6〉, |+6, +6〉 and J_z = 0 energy levels (|−6, +6〉, |+6, −6〉) of the SMM units are split by the Zeeman energy as shown in Figure 27b. The degenerate J_z = |−6, −6〉, |+6, +6〉 level is split into J_z = |−6, −6〉 and J_z = |+6, +6〉 levels in an H_dc (Zeeman splitting), and the crossing around ±4000 Oe is due to level crossing of the J_z = |−6, +6〉, |+6, −6〉 and J_z = |+6, +6〉 states. The dependence of C_m of Tb₂(obPc)₃ on the H_dc could be reproduced theoretically. There was Schottky contribution, which is commonly observed with SMMs, in the H_dc dependence on C_m. Integration of C_mT⁻¹ with respect to T gives the T dependence of the total magnetic entropy (ΔS) gain of a single crystal of Tb₂(obPc)₃ in a zero field. The saturation value of ΔS for Tb₂(obPc)₃ was determined to be 5.7 J K⁻¹ mol⁻¹. This value is comparable with the maximum S for free J_z = ±12 Ising spin, Rln(2) = 5.76 J K⁻¹ mol⁻¹. We confirmed the SMM behavior by using a micro-SQUID on a single crystal of Tb₂(obPc)₃ with an H_dc along the easy magnetization axis at low T as shown in Figure 26b. Below 1.5 K, hysteresis loops, which were strongly dependent on T (down to ∼0.4 K) and field sweep rate (even at 0.04 K), were observed. This behavior is typical for an SMM with a crossover T of ∼0.4 K. In other words, below ∼0.4 K, the relaxation is due to the pure ground-state tunneling. The large step at about zero field is due to resonant tunneling between the spin ground states. It is slightly broad because of the hyperfine coupling of the Tb(III) ions and small magnetic dipolar interactions among adjacent molecules. In the upsweep, the magnetization jump around ±3500 Oe, for which no counterpart was observed in the level-crossing diagram, depended strongly on both the field sweep rate and T. This behavior is very typical of ions with strong spin-orbit interactions and is attributed to a direct relaxation process between the spin ground states of the dimer. We thought that the step at ±3500 Oe, which is supported by the dip at around 3000 Oe in a τ versus H plot, is a measure of the ferromagnetic coupling strength of the Tb(III) ions. In other words, at this field strength, one of the two Tb(III) ions tunnels, and the other follows a direct relaxation process. Our results show that the dual magnetic relaxation processes observed for dinuclear phthalocyaninato Tb(III) complexes can be explained on the basis of their Zeeman diagrams.

Figure 27. (a) Relaxation time (s) versus magnetic field (H) plot for Tb₂(obPc)₃ by using parameters obtained from Argand plots. (b) Zeeman diagrams of the doublet ground-state for Tb₂(obPc)₃, which were obtained from magnetic heat capacity (C_m) in an H_dc (ref. 40b).

2.3.1c Quadruple-Decker Type SMMs;

Quadruple-decker complex {[(Pc)Tb(Pc)]Cd[(Pc)Tb(Pc)]}, which has two [TbPc₂]⁻ double-decker units linked by a Cd(II) ion was reported.⁵² Then, we synthesized {[(obPc)Tb(obPc)]Cd[(obPc)Tb(obPc)]} (hereafter abbreviated as TbCdTb) by one step method, in which the two Tb(III) ions are arranged along the anisotropic axis. The compound is neutral with a closed shell π electron of obPc ligands. By introducing the octa-butyl moieties at Pc ligand, the compound is soluble in organic solvents. This Tb^III-Cd^II-Tb^III quadruple-decker system is ideal for elucidating the distance dependence of the f-f interactions between two f-electron systems with a longer f-f distance (6.6 Å) than those of the Tb₂(obPc)₃ triple-decker system (3.5 Å).⁵³ The TbCdTb crystallized in the triclinic space group \(P\overline{1}\) (Figure 28). The four obPc ligands of TbCdTb are stacked in regular intervals to reduce steric hindrance, which cause pseudo 16-fold rotational symmetry. The twist angle between the rings of obPc(1) and obPc(2) and it of obPc(3) and obPc(4) in TbCdTb were estimated to be 22.3° and 23.6°, respectively, which cause a pseudo 4-fold axis perpendicular to the obPc rings, with the direction of the uniaxial magnetic anisotropy. The Pc(2)-Cd-Pc(3) angle was estimated to be 24.5°. These twist angles are different from those to Tb₂(obPc)₃ (32°) and Tb(obPc)₂ (45°). The three metal ions are almost linearly aligned with a Tb(1)-Cd-Tb(2) angle of 179.43°. The intramolecular Tb(1) and Tb(2) distance was estimated to be 6.63 Å and is twice that in Tb₂(obPc)₃. The coordination environments of two Tb(III) ions in TbCdTb are similar, which mean that they have the same LF potentials.

Figure 28. Crystal structure of TbCdCTb: (a) top view; and (b) side view. (ref. 40b).

In micro-SQUID measurements, TbCdTb clearly exhibited SMM behavior (Figure 29a). Below 1.3 K, butterfly shaped hysteresis loops were observed which were strongly T-dependent down to ∼0.3 K and field sweep-rate dependent even at 0.03 K. This behavior is typical for an SMM with a crossover T of about 0.3 K. The large step near zero field is due to resonant tunneling between the spin ground states (QTM). The step is slightly broadened because of the hyperfine coupling of the Tb(III) ions and small magnetic dipolar interaction among adjacent molecules. The steps for TbCdTb at around 1500 Oe and Tb₂(obPc)₃ at around 3000 Oc are considered to be a measure of the ferromagnetic coupling strength of the f-f interactions. There was a decrease in the χ_M′ and χ_M′′ peaks in different T range dependent on ν, which indicates that TbCdTb is an SMM. In a χ_M′′T versus T plot at ν = 1488 Hz, only a single peak at 29 K was observed in an H_dc of zero, which is similar to Tb₂(obPc)₃ (24 K) with symmetric Tb(III) sites. These results clearly show that the two Tb(III) ion sites are equivalent and are in agreement with the structure of TbCdTb. ΔE was estimated to be 147 cm⁻¹ with τ₀ = 4.7 × 10⁻⁸ s from an Arrhenius plot in an H_dc of 2000 Oe in the T range of 25.5–32.2 K from a χ_M′′T versus T plot. Below 10 K, χ_M′′ versus χ_M′ plots (Argand plots) for TbCdTb showed two irregular semi-circle Cole-Cole shapes for the two magnetic relaxation processes in an H_dc of zero as shown in Figure 29b. In plots of the obtained τ values versus T⁻¹, a T-independent regime for τ₁ (QTM) and a T-dependent regime for τ₂ appeared as shown in Figure 29b. From an Argand plot in several H_dc at 3 K, it was clear that the magnetic relaxation changes from a two-component system to a one-component system, with an increase in H_dc in the range of 250–2000 Oe. From Argand plots in a field of 2000 Oe, the magnetic relaxation of TbCdTb occurs via a single component system. It is attributed to the magnitude of the f-f interaction between the Tb(III) ions, because the ferromagnetic dipole interaction between the Tb(III) ions in TbCdTb are 1/7 those in Tb₂(obPc)₃ due to the longer Tb-Tb distance. Thus each half of the Tb(III) dimer acts as a field bias on its neighbor, shifting the tunnel resonance to new positions relative to the magnitude of the f-f interactions between the Tb(III) ions. In other words, the dual magnetic relaxation phenomena due to the Zeeman splitting are extremely sensitive to the Tb^III-Tb^III interactions.

Figure 29. (a) Magnetic hysteresis for a single crystal of TbCdTb. (b) Arrhenius plots of TbCdTb in a zero H_dc (ref. 40b).

The TbCdTb compound showed that the connection of Tb(obPc)₂ units through Cd(II) ions causes a distortion in the coordination geometry around Tb(III) ions from SAP, decreasing the intrinsic SMM properties of Tb(Pc)₂ units. Therefore, two TbPc₂ units without Cd(II) ions must be connected to suppress the possibility of QTM and increase ΔE. Thus, we reported the synthesis of a clamshell-type Tb(III) quadruple-decker complex abbreviated as [Tb₂] (Figure 30), where two TbPc₂ units are connected by an ether bond.⁵⁴ In this structure, the magnetic easy axes of TbPc₂ units are longitudinally aligned. From the magnetic measurements on [Tb₂], there are ferromagnetic Tb-Tb interactions occurring in the complex. Additionally, the magnetization of [Tb₂] exhibited butterfly-shaped hysteresis up to 20 K with a normal magnetic sweep rate (15 Oe s⁻¹) and up to 30 K with a fast sweep rate (200 Oe s⁻¹). Reacting [Tb₂] with Cd(II) ion generated the Cd(II) ion inserted complex abbreviated as [Tb₂Cd] in a relatively high yield (60%). To estimate the effect of the Cd(II) ion, we compared the magnetic properties of [Tb₂] and [Tb₂Cd]. The χ_MT values for both [Tb₂] and [Tb₂Cd] at 300 K are estimated to be 23.52 and 23.44 cm³ K mol⁻¹, respectively. These values are close to the value expected for two free Tb(III) ions (23.63 cm³ K mol⁻¹). The χ_MT values for both [Tb₂] and [Tb₂Cd] decreased with a decrease in T down to 20 K, which indicates thermal depopulation of the Stark sub-levels. However, the χ_MT values for [Tb₂] and [Tb₂Cd] increased below 20 K to 25.75 and 24.02 cm³ K mol⁻¹, respectively. These behaviors indicate that the ferromagnetic dipole Tb-Tb interactions occur. In other words, an exchange bias exists in both compounds. Figure 31b shows MH curve for [Tb₂] and [Tb₂Cd] at 2 K. In both cases, magnetic hysteresis was observed, but the hysteresis for [Tb₂] is larger than that of [Tb₂Cd]. This is due to the different coordination environments of TbPc₂ component units in these compounds. Moreover, the τ for [Tb₂] at 2 K is 81 ms, which is more than 100 times longer than that for [Tb₂Cd]. From these results, the exchange bias for [Tb₂] works more efficiently than that for [Tb₂Cd], indicating [Tb₂] is the better SMM.

Figure 30. Structures and syntheses of [Tb₂] and [Tb₂Cd]. [Tb₂] can capture Cd(II) ions to form [Tb₂Cd], meaning that TbPc₂ units in [Tb₂] align in a linear fashion (ref. 54).

Figure 31. (a) χ_MT vs. T plots and (b) MH curves for solid [Tb₂], [Tb₂] in frozen CH₂Cl₂ and [Tb₂Cd]. Widths of magnetic hysteresis for [Tb₂] in solution and solid [Tb₂Cd] are smaller than that for solid [Tb₂], meaning fast QTM occurs in the former complexes (ref. 54).

As the other trial for using exchange bias, we reported the Tb(III)-phthalocyaninato double-decker SMM having four 15-crown-5 moieties in one of the Pc ligand (PC) abbreviated as [TbPcPC]⁰. Then, its dimerization and magnetic properties were investigated for an attempt to utilize the supramolecular aggregation for enhancing the SMM properties as shown in Figure 32.⁵⁵ Aggregation of two [TbPcPC]⁰ units to form quadruple-decker type [(TbPcPC)₂K₄]⁴⁺ in the presence of K⁺ ions was investigated by using UV/Vis-NIR absorption and paramagnetic solution NMR spectroscopies. DC magnetic susceptibility measurements revealed that there were Tb-Tb dipole ferromagnetic interactions in [(TbPcPC)₂K₄]⁴⁺, whereas there was no indication of ferromagnetic dipole interactions in monomer [TbPcPC]⁰ unit. Upon the formation of quadruple-decker [(TbPcPC)₂K₄]⁴⁺ from two [TbPcPC]⁰ and four K⁺ ions, the temperature at which the magnetic hysteresis occurred increased from 7 to 15 K. Additionally, the width of magnetic hysteresis became larger for [(TbPcPC)₂K₄]⁴⁺, which means that SMM properties of [(TbPcPC)₂K₄]⁴⁺ are superior to those of [TbPcPC]⁰. AC magnetic measurements were used to confirm this observation. Magnetic relaxation times at 2 K increased 1000-fold upon dimerization of [TbPcPC]⁰ to quadruple-decker [(TbPcPC)₂K₄]⁴⁺, which demonstrate the effectiveness of using K⁺ ions to induce dimer formation for the improvement of SMM behavior by using exchange bias.

Figure 32. K⁺-induced dimer formation (ref. 55).

As another trial for using exchange bias, we synthesized a new system in which two TbPc₂ units are connected via fused phthalocyaninato ligand named [(obPc)Tb(Fused-Pc)Tb(obPc)] as shown in Figure 33.⁵⁶ The magnetic couplings between the Tb(III) ions and two π radicals in this compound were explored by means of density functional theory (DFT). DC and AC magnetic susceptibility measurements were performed on magnetically diluted and undiluted samples of this compound, indicating this compound to be an SMM with improved properties compared to those of the well-known [TbPc₂]^0,±1 and the axially symmetric Tb₂(obPc)₃. By assuming that the probability of QTM occurring in one TbPc₂ unit is P_QTM, the probability of QTM in this compound is P²_QTM, which means that QTM is effectively suppressed. Moreover, non-diluted sample of this compound underwent slow magnetic relaxation time (τ = 1000 s at 0.1 K), and the blocking temperature (T_B) was determined to be ca. 16 K with an energy barrier for spin reversal (U_eff) of 588 cm⁻¹ (847 K) due to the D_4d geometry and weak inter- and intramolecular magnetic interactions as an exchange bias (H_bias), reducing QTM. Four hyperfine steps were observed by micro-SQUID measurement. Furthermore, solution NMR measurements (one-dimensional, two-dimensional, and dynamics) were performed on this compound, which led to the determination of the high rotation barrier (83 ± 10 kJ mol⁻¹) of obPc ligand. A comparison with previously reported Tb₂(obPc)₃ shows that ambient temperature NMR measurements can indicate improvements in the design of coordination environments for SMMs. A large U_eff causes strong uniaxial magnetic anisotropy in this compound, leading to a χ_ax value (1.39 × 10⁻³⁰ m³) that is larger than that for Tb₂(obPc)₃ (0.86 × 10⁻³⁰ m³). To control both the coordination environment and spin arrangement is an effective technique for suppressing QTM in multiple-decker-type phthalocyaninato Tb SMMs.

Figure 33. (a) The tilted side view of the structure of [(obPc)Tb(Fused-Pc)Tb(obPc)]. 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 CH_Linker, which corresponds to that in Figure (a). (c) Crystal structure of complex Tb₂(obPc)₃. (d and e) Schematic illustrations (ref. 56).

2.3.1d Quintuple-Decker Type SMMs;

As an extension, Ln^III-Cd^II-Cd^II-Ln^III quintuple decker Pc complexes (Ln = Nd^III, Sm^III and Eu^III) were reported.⁵⁷ However, until our reports, the crystal structure and magnetic properties were not reported. Hence, we reported the crystal structure and magnetic properties of the quintuple-decker complex [(obPc)Tb(obPc)Cd(ObPc)Cd(ObPc)Tb(obPc)] (hereafter abbreviated as TbCdCdTb).⁵⁸

TbCdCdTb crystallized in the monoclinic space group C2/c and has two Tb(ob)₂ units linked by one obPc and two Cd(II) ions (Figure 34). The Tb(ob)₂ units are crystallographycally equivalent, and the intramolecular Tb^III-Tb^III distance was estimated to be 9.88 Å. The stacking angle between obPc ligands coordinated to the Tb^III ion was estimated to be 21.8°, and the Tb^III ion is located closer to obPc(1) than obPc(2) due to electron repulsion between the Tb^III and Cd^II ions coordinated by obPc(2). Similar behavior can be observed for TbCdTb and Tb₂(obPc)₃, but not for mononuclear Tb(obPc)₂. In other words, the coordination environments around Tb^III ions in TbCdCdTb are distorted square antiprism (SAP), and the overall symmetry of the complex is low in comparison with that of Tb(obPc)₂. The intramolecular Tb^III-Tb^III distance in TbCdCdTb is clearly longer than those in the other multiple-decker phthalocyaninato-Tb(III) complexes. The stacking angle involving the Tb^III ions (ϕ) becomes narrower with an increase in the number of stacks. TbCdCdTb complex in the ab plane are well separated from each other because the n-butoxy chains of obPc extend out in the ab plane, which prevent the molecule from approaching closely to each other. On the other hand, along the c axis, TbCdCdTb molecules are arranged in slipped columns due to π–π interactions between obPc(1) ligands, and the nearest Tb^III-Tb^III distance was estimated to be 11.99 Å.

Figure 34. Crystal structure of TbCdCdTb: a) top view; and b) side view (ref. 40b).

With a decrease in T, the χ_MT value slightly increased and reached 23 cm³ K mol⁻¹ at 1.8 K. The maximum values of χ_MT at 2 K increases in the order of TbCdCdTb < TbCdTb < TbTb, because the ferromagnetic dipole interactions become stronger with a decrease in the intramolecular Tb^III-Tb^III distance as shown in Figure 35a. There was a sharp decrease in the χ_M′ and χ_M′′ peaks in different T ranges dependent on ν, which indicate that TbCdCdTb is an SMM. In a χ_M′′T versus T plot at ν = 997 Hz, only a single peak at 27 K was observed. These results clearly show that two Tb^III ion sites are equivalent and in agreement with the molecular structure. Additionally, the χ_M values of a diluted TbCdCdTb exhibited similar T and ν dependence. ΔE was estimated to be 237 cm⁻¹, with a τ₀ of 5.2 × 10⁻⁹ in an H_dc of 2000 Oe. As H_dc increased, the χ_M′′T peaks became sharper and shifted to the higher T region due to the suppression of QTM. In the high-T region, the τ for TbCdCdTb strongly depended on T because an Orbach process, where the spin reversal occurs through first excited Stark sublevels, is dominant. When H_dc was zero or weak, the weak dependence of τ at low T is due to the mixing of the Orbach process and QTM. In an H_dc strong enough to completely suppress QTM, the weak dependence of τ was attributed to a direct relaxation process. Argand plots for TbCdCdTb showed some irregular semi-circular Cole-Cole shapes due to dual magnetic relaxation processes with τ₁ and τ₂ in an H_dc of zero as shown in Figure 35b. The magnetic relaxation changed from a dual magnetic relaxation process to a single magnetic relaxation process with an increase in the strength of H_dc, which is similar with the behavior of TbCdTb.

Figure 35. a) Comparison of χ_MT versus T plots for the dinuclear Tb^III-obPc multiple-decker complexes. b) Arrhenius plots for TbCdCdTb in a zero H_dc (ref. 40b).

More recently, a Dy(III) phthalocyaninato sextuple-decker complex DyCdCdCdDy as well as a TbCdCdCdTb have been also synthesized and characterized in their crystal structures and magnetic properties.⁵⁹

2.3.1e High Oxidation States of Multiple-Decker Type Tb(III) SMMs;

We investigated the relationship between the highly oxidized multiple-decker phthalocyaninato SMMs and their magnetic properties.⁶⁰ The SMMs are hereafter abbreviated according to the number of obPc ligands as follows; [2] for Tb(obPc)₂, [3] for Tb₂(ob)Pc₃, [4] for [(obPc)Tb(obPc)Cd(obPc)Tb(obPc)], and [5] for [(obPc)Tb(obPc)Cd(obPc)Cd(obPc)Tb(obPc)] as shown in Figure 36. Therefore, the charges of the complexes (m) are expressed as [n]^m+. All multiple-decker SMMs are stepwise oxidized electrochemically using cyclic voltammetry and chemical methods with phenoxathiine hexachloroantimonate (Ox.SbCl₆). The UV-Vis-NIR spectroelectrochemistry method was performed to follow the oxidation states. In the spectra of the oxidized species presented here, isosbestic points were observed as shown in Figure 37d, which indicates that the oxidized complexes are stable in open air. The redox potentials became narrower (Figure 37b), and number of stable oxidized species increased when the number of obPc ligands was increased because the π-system extension decreased the electronic repulsion between the positively charged holes in obPc ligands. Since Tb(III) and Cd(II) ions do not participate in the redox reactions, the oxidation reactions occurred only in the extended Pc ligand π-systems. The delocalization of holes is expected due to the highly delocalized molecular orbitals (Figure 37c). The agreement between the calculated oscillator strengths and absorption spectra support the validity of our calculations. The HOMO of the neutral species (Figure 37c) has nodes between the obPc ligands, which indicates that the ligand oxidation (i.e., removal of electron from the HOMO) results in a decrease in the inter-ligand distances.

Figure 36. Scheme of structures and abbreviations of the phthalocyaninato multiple-decker complexes. obPc ligands can be distinguished as either inner (obPcⁱ and, for the central ligand in compound [5], obPcⁱⁱ) and outer (obPc⁰) (ref. 60).

Figure 37. (a) Cyclic voltammograms, (b) redox potentials, (c) HOMO (isovalue = 0.01) of neutral species and (d) electrochemical UV/Vis/NIR spectra and oscillator strength (black bars) for multiple-decker complexes (ref. 60).

We determined crystal structures of [3]²⁺, [4]²⁺, [4]⁴⁺, and [5]⁴⁺, the crystals of which were grown by using chemical oxidations and solvent diffusion methods. The X-ray structures, including the structures of the neutral species reported previously, [3]⁰, [4]⁰, and [5]⁰ are shown in Figure 38a–c. The molecular length (d), stacking angle between the obPc ligands (θ) sandwiching the Tb(III) ions, and the Tb(III) to neighboring metal ion distance (R_Tb-M; M = Tb and Cd) from X-ray and DFT optimized structures are shown in Figure 38d. In both [3]⁰ and [3]²⁺, the two Tb(III) ions are crystallographically equivalent and are connected by an inversion center (Figure 38a). In [3]⁰, d, R_Tb-Tb and θ were estimated to be 6.095 Å, 3.517 Å, and 31.77°, respectively. Oxidation to [3]²⁺, which corresponds to the removal of electrons from the antibonding HOMO of [3]⁰ (Figure 38d), causes d and R_Tb-Tb (5.959 Å and 3.435 Å, respectively) to shorten, which results in a square antiprism (SAP) geometry with a wide θ (42.21°) in order to avoid steric repulsion between the phenyl rings of obPc ligands. Due to the large inter-ligand steric effects induced by longitudinal compression, the outer obPccs (obPc^o) of [3]²⁺ have bowl-shaped distortion. The distortions and changes in the geometrical parameters (θ, d, R_Tb-Tb) are similar with those predicted from geometry optimization, as is shown in Figure 38d.

Figure 38. Crystal structures of (a) [3], (b) [4] and (c) [5]. (d) Charge dependence of the molecular length d, Tb-metal ion (Tb or Cd) distances R_Tb-M and stacking angle around metal ions θ_obPc. (e) Packing structures of multiple-decker complexes. Red, green and blue parts represent multiple-decker units, counter anions (SbCl₆) and solvent molecules, respectively (ref. 60).

In the case of [4], the space groups of [4]²⁺ and [4]⁴⁺ were determined to be P4/ncc and P4/n, respectively, and there are four-fold axes along the Tb-Cd-Tb axes (c-axes). Similarly to the other multiple-decker series, in [4], the obPc^o ligands have bowl-shaped distortions induced by oxidation. In series [4], although the two Tb(III) ions are crystallographically inequivalent, the θ values of Tb₁ and Tb₂ (left side of Figure 38b) of [4]⁰ are similar to each other (22.32° and 23.65°). In [4]²⁺, the θ of Tb₁ and Tb₂ are 42.28° and 38.72°, respectively. In [4]⁴⁺, the θ of Tb₁ and Tb₂ are 44.94° and 16.43°, respectively. Thus, in [4]⁴⁺, SAP and SP geometries are co-existing. The asymmetric structure of [4]⁴⁺ seems to be induced by steric effects from the solvent molecule and SbCl₆⁻ counterion incorporated into the crystal. The SP conformations are stabilized by toluene molecules incorporated into the grooves of the obPc ligands.

In the case of the structure of [5]⁴⁺, the obPc^o ligands of [5]⁴⁺ have bowl-shaped distortions due to longitudinal compression effects induced by the oxidation in contrast to the wave-like distortions in [5]⁰. Although the Tb(III) ions in [5]⁰ are crystallographically equivalent with each other, those in [5]⁴⁺ had different geometries, one of which was SAP and the other was SP. Moreover, the solvent molecules (benzene) located in the grooves formed by the ligands stabilize the SP geometry. Stacking of alternating [5]⁴⁺ and a disordered SbCl₆⁻ counterion generates 1D column packing along the c-axis as shown in Figure 38e. The θ values increase when the complexes are oxidized from neutral (θ ∼ 22°–32°) to +2 (θ ∼ 38°–44°) because the wider θ decreases the steric hindrance between the cofacial ligands. In the cases of [4]⁴⁺ and [5]⁴⁺, there are two different Tb(III) ions per molecular unit with θ ∼ 45° (SAP) and 0° (SP). Although the SP arrangement is unfavorable from the view point of steric hindrance, the aromatic solvent (benzene) molecules in the crystal packing of [5]⁴⁺ stabilize it. The structure of [4]⁴⁺ with a narrow θ crystallized from toluene was also stabilized, which indicates that both SAP and SP geometries generally occur in the crystal packing of highly oxidized species.

From the paramagnetic NMR analyses of [4]²⁺ and [5]²⁺, the π-radicals are on the ligands, especially on obPc^o. To investigate the presence of π-radicals, we measured electron spin resonance (ESR) spectroscopy on Y(III) analogues of the oxidized complexes, which are synthesized by bulk electrolysis in CH₂Cl₂ and characterized by comparing their absorption spectra with those of Tb(III) complexes. Although Y(III) analogues of [4]²⁺ and [5]²⁺ have even charges, theses complexes are ESR active at room temperature, and their g-values are close to 2.0, which is common for organic radicals. After cooling down to 80 K, in the ESR spectra of [4]²⁺ and [5]²⁺, the complicated signals, which were characteristic of a triplet biradical with an axial zero-field splitting parameter D, were observed as shown in Figure 39b. The simulated |D| value for [4]²⁺ (0.0032 cm⁻¹) is slightly larger than that for [5]²⁺ (0.0029 cm⁻¹), which indicates that [4]²⁺ has stronger dipole interactions between unpaired electrons than [5]⁴⁺ due to the smaller π-extended system in the former compound. Focusing on the shape and energy of the molecular orbitals in the even-charged complexes, HOMO-LUMO gaps (ΔE_LUMO-HOMO as shown in Figure 39c) for [4]²⁺ and [5]²⁺ (0.20 and 0.14 eV, respectively) are considerably smaller than those for others (0.47 to 1.21 eV), because the HOMO and LUMO of [4]²⁺ and [5]²⁺ are non-bonding orbitals whose shapes are similar with each other. The smaller ΔE_LUMO-HOMO for [4]²⁺ and [5]²⁺ allows the electrons to occupy the LUMO with low energy, which results in the formation of biradical states.

Figure 39. (a) Spin densities (isovalue = 0.004) of triplet biradical species. (b) EPR spectra of Y(III) analogues at RT (experimental) and at 80 K (experimental and simulated). (c) Molecular orbital energies and HOMO–LUMO gaps of singlet species. (d) Comparison of J_ex values between the dimer of double-decker complexes connected by a phenyl linker and the double-decker complexes connected by π–π stacking (ref. 60).

DC and AC magnetic measurements revealed that the series of highly oxidized multiple-decker complexes show SMMs behaviors, which are controlled by the multi-step redox induced structural changes. However, the systematic changes according to the stepwise redox of multiple-decker phthalocyaninato Tb(III) SMMs have not been observed yet.

More recently, we have synthesized a sextuple-decker [6] and carried out the electrochemistry of [6]. The oxidation states of [6] with +1, +2, +3, +4, and +5 are realized in the solutions, however, [6]⁺⁶ is not realized. Furthermore, their isolations as single-crystals are difficult.

Molecular spintronics is an emerging research field that combines spintronics and molecular electronics.⁶¹ Using molecules is advantageous because their electronic and magnetic properties can be controlled under specific conditions. However, we should control the spin switching and the electric-conductance variation for the realization of molecular spintronics.⁶² The SMMs are attractive target compounds, because their spin relaxation is slow and they can hold the spin information for a long time.⁶³ Therefore, SMMs are considered to work as high density memory devices. From the beginning, researchers have considered that SMMs will show the Kondo effect, because SMMs have spins. The Kondo effect attracts much attention as a conductance control mechanism, which is observed in single atoms,⁶⁴ single molecules,⁶⁵ and quantum dots.⁶⁶ The Kondo effect occurs by the interaction between conducting electrons and a localized spin, and causes a change in conductance.⁶⁷ The ability to tune the Kondo effect of SMMs would be useful for the conductance control with the use of the spin. Scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) are powerful methods for detecting the Kondo effect of SMMs. In our study, we used double-decker bis-phthalocyaninato TbPc₂ SMM, which has two spin systems of 4f⁸ in Tb(III) ion and π-radical on Pc ligand.

TbPc₂ SMM was deposited on a clean Au(111) surface kept at room temperature by using a sublimation method in ultra-high vacuum. The sample was then transferred to the STM head, which was cooled to ∼4.7 K. An STM image of an isolated TbPc₂ molecule adsorbed on Au(111) is shown in Figure 40a. The height of the molecule was determined to be ∼0.40 nm, and eight bright lobes were visible at the perimeter of the molecule. Figure 40b shows a top view of the molecule, in which the upper and lower Pc ligands are colored in blue and silver, respectively, with an azimuthal rotation angle (θ) between two Pc ligands of 45°. The two Pc ligands adopted a bent configuration with respect to each other as shown in Figure 40c. An STM image of a monolayer film of TbPc₂ molecules obtained with a sample bias (V_sample) of ∼0.8 V is shown in Figure 40e. Nine full molecules, which make a pseudo-square lattice, are visible in the image. The image shows a checkerboard contrast pattern, which is depicted to the right-hand side of Figure 40e. The bright molecule (b) and the dark molecule (d) are shown in yellow and brown, respectively. Magnified images of two neighboring molecules are shown in Figure 40f, in which the top and bottom molecules correspond to (b) and (d), respectively. Eight lobes are clearly observed for (b), which are marked as 1–8. However, in the image of (d), we observe four tiny lobes (marked as 2, 4, 6, and 8), and the four other lobes (1, 3, 5, and 7) are either shadowed or shared by the bright lobes of the neighboring (b). As a result, the azimuthal rotation angle (θ) between the upper and lower Pc ligands in (b) is 45°, while in (d) is 30° as shown in Figure 40g. Figure 41 shows the analysis of tunneling conductance (dI/dV) on TbPc₂ molecule. The zero-bias peak (ZBP) was assigned to a Kondo resonance. We observed clear Kondo features for the molecules with θ = 45° when the tip was positioned over one of the lobes of (b) (labeled I in Figures 41a and 41b), while no Kondo features at the center of TbPc₂ were observed (labeled II in Figures 41a and 41b). This result clearly indicates that the magnetic spin for Kondo resonance is not Tb(III) 4f⁸ but π-radical on Pc ligand. To prove the Kondo resonance in the origin of ZBP, we examined the changes in the peak width and height in relation to both the sample temperature and the presence of a magnetic field as shown in Figure 42. The ZBP broadened, and the height decreased as the temperature increased as shown in Figures 42b and 42c. By using Nagaoka’s equation on Kondo temperature (T_K), T_K was estimated to be ∼31 K, which is higher than those of metals and lower than CoPc and FePc molecules reported previously.⁶⁸ To further investigate the mechanism of the appearance of the Kondo feature, we acquired dI/dV spectra of double-decker YPc₂ and triple-decker Y₂Pc₃, as shown in Figure 43. Neither double-decker YPc₂ with π-radical on Pc ligand nor triple-decker Y₂Pc₃ without π-radical on Pc ligand are SMMs, because Y(III) ions have no f electrons. Figure 43 shows that Kondo resonance on YPc₂ was observed, while no Kondo resonance on Y₂Pc₃ was observed. From these results, the π-radical on Pc ligand is clearly the origin of Kondo resonance.

Figure 40. (a) STM image of an isolated molecule of TbPc₂ on Au(111). (b) A schematic model of the double-decker TbPc₂ molecule. The upper (lower) Pc is colored in blue (silver). (c) Side view of the TbPc₂ molecule after structural optimization using DFT calculations. (d) A simulated STM image of the TbPc₂ molecule by DFT calculations. (e) Film of TbPc₂. An alternating contrast pattern of nine molecules is shown on the right-hand side with brighter molecules in yellow and darker molecules in brown. (f) A magnified image of bright (upper) and dark (lower) molecules. The black (green) line connects lobes 2 and 6 of bright and dark molecules. The two lines are rotated 15° with respect to each other. (g) A tentative model of the adsorption configuration of TbPc₂ film, corresponding to the image in e. Bright (θ = 45°) and dark (θ = 30°) molecules form a pseudo-square lattice, and the red and blue Pc ligands correspond to vacuum- and substrate-side Pc ligands, respectively (ref. 69a).

Figure 41. STS measurements of TbPc₂ near Fermi level. (a) STS detection positions on the film together with a model of the upper Pc plane. (b) dI/dV spectra at I and II in a. (c) Change in the Kondo peak height when the tip position was moved along the blue line in the STM topography panel. The different colors correspond to the dI/dV intensity (ref. 69a).

Figure 42. Proving the assignment of the ZBP to the Kondo feature. (a) Temperature dependence of the peaks measured in the temperature of 4.7–66 K. (b, c) Peak width (b) and peak height (c) changes versus temperature for the peak near the Fermi level. The error bars correspond to the distribution of the measured data of more than ten samplings. (d, e) Peak changes in the presence of a magnetic field of 8 T; d is experimental (exp.) data and e is a simulation (simul.) of two convoluted peaks separated by two times the Zeeman splitting for the Kondo effect (ref. 69a).

Figure 43. Kondo peaks in related molecules. Comparison of the dI/dV curves for YPc₂ (I) and Y₂Pc₃ (II). Corresponding STM images are shown in the right-hand side (V_sample = 0.8 V and I_tunnel = 0.3 nA). A side view of Y₂Pc₃ is superimposed (ref. 69a).

The configuration of the π-radical on Pc ligand has an important role in the appearance of Kondo peaks, and its manipulation should make it possible control of the Kondo states. To determine if this is possible, we tried to rotate the upper Pc ligand by injection of enough current via the STM tip to overcome the activation barrier for the conformation change. Figures 44a and 44b show an STM image, in which the center molecule was converted from (b) in Figure 44a to (d) in Figure 44b by applying a pulse V_sample to the TbPc₂ molecule. Rotation of the upper Pc ligand in the molecule can be monitored by the tunneling current change, helping to understand the mechanism of the rotation. Figure 44c shows changes in the current during injection of a current pulse with V_sample = −2.0 V. The high and low states of the tunneling current correspond to (b) and (d), respectively. The sharp changes in the current indicate that the rotation occurs. We rotated the upper Pc ligand of more than 50 molecules and obtained an average rate of rotation (R) from (b) to (d) as a function of the current (I). The results are summarized in Figure 44d for V_sample = ∼2.0 V. The least squares analysis of a plot of log(R) versus log(I) yielded a slope of ∼1.09. Thus, the rotation order n in the rotation R ∝ Iⁿ should be close to 1. This indicates that the current induced rotation is a one electron phenomenon. To understand the mechanism, the theoretical calculation is very important. In the TbPc₂ SMM in the bulk state, π-radical is delocalized on both upper and lower Pc ligands, moreover, the interaction between the delocalized π-radical and 4f⁸ on Tb(III) ions is very weak. On the other hand, in the TbPc₂ on Au(111), π-radical is localized on the upper Pc ligand. Figure 45 shows the energy level of SOMO and HOMO of TbPc₂ on Au(111), where SOMO means the π-radical on the upper Pc ligand. In the (b) with θ = 45°, the SOMO level is high, thus the Kondo peak was observed. By pulse injection, θ was reduced to 30° in (d), resulting in lowering the SOMO level. Then the electron transfer occurred from Au substrate to the π-radical on the upper Pc ligand to combine with each other to make a singlet state. Therefore, Kondo peak was not observed in (d) with θ = 30°. The switching between (b) with a Kondo peak and (d) with no Kondo peak reversibly occurred by the pulse injection. This indicates that we have realized a single memory device on one TbPc₂ molecule with appearance and disappearance of Kondo peak reversibly.⁶⁹

Figure 44. Molecular manipulation and control of Kondo feature. (a, b) Conversion of the center molecule from b (θ = 45°) to d (θ = 30°) by applying a current pulse. The target molecule is marked by an arrow, and magnified images are shown in the bottom panel. Changes in the contrast and the top view of the center molecule are schematically illustrated. (c) Current during a −2.0 V voltage pulse over a TbPc₂ molecule initially in the b state; the tip remained fixed over a lobe position with the feedback loop open. Each jump in the current indicates the moment of rotation of the molecule and the low state corresponds to the d state. (d) Rotations per electron as a function of tunneling current for V = −2.0 V. Both axes are in log scale. More than 50 molecules similar to the one in a were sampled. Data indicate the rotation from b to d. The red line corresponds to a least-squares fit. (e) Comparison of the Kondo peaks before I and after II with the application of the pulse (ref. 69a).

Figure 45. Energy level and level crossing of SOMO and HOMO. (a) Change in the peak positions of the SOMO and HOMO levels versus θ determined by using DFT calculations. (b) Molecular orbitals for SOMO and HOMO for θ = 0° Top view shows eight lobes both for outer circles and inner circles of the molecule. In the side view, a bonding between the two Pc can be seen in HOMO. Note the phase difference of the upper and lower Pc of SOMO and HOMO (ref. 69a).

The substrates are very important for influencing Kondo resonance, hence we compare Au, Ag and Cu. As mentioned above, the Kondo resonance on Au(111) is observed. However, no Kondo resonance was observed on Cu(111) because the interaction between TbPc₂ and Cu(111) substrate is strong, and electron transfer from Cu(111) substrate to π-radical of Pc ligand in TbPc₂ occurs to combine and make a singlet state. Next we used Ag(111) as a substrate to compare with Cu(111). We can hardly find Kondo resonance originating from the π-radical of Pc ligand on the first layer of TbPc₂ due to the interaction between Ag(111) substrate and the first layer of TbPc₂ similar to Cu(111) system. Instead, TbPc₂ on the second layer shows the Kondo resonance at the Fermi level as shown in Figure 46. This means that the first layer interrupts the interaction between Ag(111) substrate and π-radical of Pc ligand on the second layer of TbPc₂. Thus, the π-radical of Pc ligand on the second layer could exist. In addition, when a magnetic field of 2 T normal to the surface is applied, the second layer molecule of TbPc₂ shows a sharp dip at the Fermi level. We attributed this to the inelastic tunneling feature caused by the spin flipping. This feature was not observed for TbPc₂/Au(111) system. As a result, the strength of the interaction between the substrates and TbPc₂ is in the order; Au < Ag < Cu.⁷⁰

Figure 46. dI/dV spectra obtained at the lobe position of TbPc₂/Ag(111). dI/dV of the molecules in the first layer (a) and the second layer (b) are compared. When the outer magnetic field normal to the surface of 2 T is applied, the peak in (b) changes into the dip in (c) (ref. 70).

In the next step, we carried out Cs atom doping to double-decker YPc₂ monolayer film on Au(111). The Cs atom has 6s¹ electron and YPc₂ molecule has π-radical of Pc ligand like TbPc₂. The molecules became brighter when a Cs atom was adsorbed because alkali atoms, like Cs, donate an electron to the YPc₂ molecules, increasing the density of state (DOS) of the occupied states. Evidence for charge transfer can be obtained from STS on the molecular layer, as shown in Figure 47, because the tunneling conductance above a given molecule is measured. In Figure 47a, an STS spectrum of a molecule without a Cs atom (marked by a square) is plotted together with that of a molecule with one in a small bias window of 80 mV. Figure 47b shows the two locations at which STS were taken. In the STS spectrum, a zero-bias anomaly due to a Kondo effect was observed, whereas no Kondo peak was observed for the doped molecule. In other words, a spin from the Cs atom is transferred to the SOMO (π-radical of Pc ligand) of the YPc₂ molecules, which quench the molecular magnetic moment. Moreover, we could manipulate the Cs at the atomic level with the STM tip by applying a pulse voltage (2.8 V, 10 ms duration, feedback-loop open) to the sample bias. Figure 47c shows an STM image of the controlled desorption of a Cs atom, which is marked with a blue arrow, and Figure 47d shows STS spectra taken before (marked with I) and after (marked with II) removal of the Cs atoms. The Kondo peak reappeared when the Cs atom was removed from a YPc₂ molecule. The phenomena are reversible, indicating that the single-molecule memory by using Kondo resonance is realized. We further demonstrate that the STM tip could arrange Cs atoms into the initials (T and U) of Tohoku University, as shown in Figures 47e and 47f.⁷¹

Figure 47. (a) STS spectra acquired over the locations shown in (b). The square corresponds to a location close to the π-orbital of a θ = 45° molecule, where a zero-bias anomaly corresponding to a Kondo peak was observed, and the circle corresponds to a π-orbital of a θ = 45° molecule with an adsorbed Cs atom. No Kondo peak was observed. θ = 30° molecules do not present Kondo peaks. (c) Before (I) and after (II) removal of a Cs atom from a molecule with θ = 45° using an STM tip. (d) Recovery of the Kondo peak after the removal of the Cs atom shown in (c). (e, f) Initials of Tohoku University prepared by manipulating Cs atoms with the STM tip (ref. 71).

As described above, the Kondo peak is considered as a bit of the single molecular memory device.

In order to use SMMs as memory storage devices, an information pathway is needed to allow read-and-write processes. Thus, electrons would be the best messenger because they can deliver information by using their spin orientation of up and down. Molecule-based materials are good candidates for such a pathway, because they mainly consist of light elements and can maintain their spin currents longer than metals due to weak hyperfine coupling. Moreover, nanocarbon materials are interesting, because 98.9% of naturally occurring carbon, ¹²C, has no nuclear spin. Therefore, SMMs have been combined with nanocarbon materials such as carbon nanotube (CNTs)⁷² and graphene,⁷³ by attaching SMMs onto their surfaces. When SMMs interact with nanocarbon materials, their electronic structures are affected, and spintronics properties such as GMR are observed. Another example involves the encapsulation of SMMs into 1D pores of multi-walled CNTs (MWCNTs).⁷⁴ Encapsulation of SMMs into MWCNTs can cause them to orient with respect to their easy axes, and their magnetic properties can be controlled, as in the case of Mn₁₂ SMM encapsulated in MWCNT so far reported. However, little has been reported on SMMs to encapsulate into single-walled carbon nanotubes (SWCNTs), which should be more interesting because they can show metallic or semiconducting properties depending on their structures.⁷⁵ Furthermore, their narrow inner space can cause the SMMs to stack, forming a quasi 1D arrangement, wherein their properties will be enhanced by the dipole interaction and exchange bias.⁴⁶ Thus, we focused on an endohedral metallofullerene, DySc₂N@C80, having a cage with I_h symmetry, as an SMM. The SMM properties of DySc₂N@C80 were reported in 2012,⁷⁶ as part of a pioneering work on metallofullerene-SMMs. It shows high SMMs properties due to the Dy(III) ion having ⁶H_15/2 multiple structures with J_z = ±15/2 states in the ground doublet,⁷⁷ and its discovery has led to the development of other metallofullerene-SMMs and further applied research.⁷⁸ One important feature of the fullerene species is that they can be easily encapsulated into SWCNTs with high filling yields due to strong π–π interactions between them. Hence, they are commonly called “peapods” since the spherical fullerenes are regularly stacked one-dimensionally inside the SWCNTs. These peapods exhibit interesting properties such as the modulation of electrical properties.⁷⁹

The DySc₂N@C₈₀ SMM has been encapsulated into SWCNT under high vacuum and high temperature conditions for a few days. The obtained hybrids were observed by transmission electron microscopy (TEM). Spherical structures were confirmed in the SWCNTs, as shown in Figure 48. In addition, signals for the Dy and Sc ions were observed in the same regions in energy dispersive X-ray (EDX) spectra. Moreover, from high-angle annular dark field (HAADF) scanning TEM (STEM), white dots due to the heavy Dy(III) ions were clearly observed at the same positions as those of the fullerenes in the TEM image. These results showed that the DySc₂N@C₈₀ were encapsulated into the SWCNTs to afford [DySc₂N@C₈₀]@SWCNT in the presence of air.

Figure 48. (a) Schemes of DySc₂N@C₈₀ (left) and DySc₂N@C₈₀ encapsulated in SWCNT (right). (b, c) TEM images of [DySc₂N@C₈₀]@SWCNT. (d) Scheme of (c) (ref. 79b).

To determine the effect of encapsulation of the DySc₂N@C₈₀ SMM into SWCNTs on the magnetic properties, the static magnetic measurement on [DySc₂N@C₈₀]@SWCNT were carried out, and the results were compared with those for free DySc₂N@C₈₀ SMM. DC measurements were carried out to obtain the magnetization (M), which depend on T and the magnetic field (H). Figure 49a shows M vs H/T plots for [DySc₂N@C₈₀]@SWCNT in an applied H in the range of 10–70 KOe. The saturated M values depended on the applied H, which is the same for DySc₂N@C₈₀, indicating that the Dy(III) ion in DySc₂N@C₈₀ still has uniaxial magnetic anisotropy and/or a low-lying excited state. In M vs H plots, as is shown in Figure 49c, the clear M loops were detected when T ≤ 5 K, which is the same for DySc₂N@C₈₀. This result strongly indicates that DySc₂N@C₈₀ maintains the SMM properties even inside the SWCNTs. Moreover, when the M loops for DySc₂N@C₈₀ before and after the encapsulation into SWCNTs were compared, the coercivity was increased from 0.5 to 4 KOe as shown in Figures 49c and d. The enhancement of the SMM property in [DySc₂N@C₈₀]@SWCNT is due to the suppression of QTM by the exchange bias induced by dipole interactions among [DySc₂N@C₈₀]@SWCNTs.^79b

Figure 49. (a) M vs H/T plots for [DySc₂N@C₈₀]@SWCNT. (b) M vs H plots for [DySc₂N@C₈₀]@SWCNT. (c) M vs H plots for DySc₂N@C₈₀ (open circles) and [DySc₂N@C₈₀]@SWCNT (filled circles) at 1.8 K. Arrows indicate the direction of the measurements. (d) Magnification of (c) (ref. 79b).

More recently, we have tried to measure the magnetoresistance of the singly isolated [DySc₂N@C₈₀]@SWCNT with Ni electrodes. It showed the very weak negative magnetoresistance.

As one of the methods to realize high density memory devices, photo-switchable memory devices composed of SMMs are very promising, due to the high speed of light. We incorporated photochromic diarylethene derivatives with two edging carboxylate groups (dae), which reversibly isomerizes between open (dae-o) and closed forms (dae-c) when irradiated with UV or visible light, respectively. We introduced dae photochromic ligands into SMMs to control the magnetic properties by irradiation.⁸⁰ In the open type (dae-o), the π-conjugated system of photochromic dae is cut off, resulting in no interactions between two terminal carboxylate-coordinated SMMs, while in the closed type (dae-c), the π-conjugated system of photochromic dae is created, resulting in the interactions between two terminal carboxylate-coordinated SMMs.

In this study, the SMM behavior of a complex composed of [Mn₂(salen)₂(H₂O)₂](ClO₄)₂ units bridged by dae-c (1c) could be controlled by irradiation with visible light, which affords a complex containing dae-o in the (1c-Vis). Crystal structure analyses of Ic and Ic-Vis showed that dae-c could be converted to dae-o in the solid states. Additionally, UV-vis spectroscopy was used to confirm that the photo-conversion was reversible and repeatable.

1c crystallized in the orthorhombic space group P2₁/cn as shown in Figure 50. The Mn^III ions are hexa-coordinated with an N₂O₂ atom set from 2,2′-ethlenebis(nitrilomethylidene)phenol (salen²⁻), one oxygen atom from carboxylate group of dae-c²⁻, and one oxygen atom from a coordinated methanol molecule. The two Mn^III ions showed Jahn-Teller distortion with elongation of the oxygen-metal distance perpendicular to the N₂O₂ atom set of salen²⁻. The dae-c²⁻ ligand acts as a monodentate ligand, bridging Mn(salen) monomers via the carboxylate groups. In the packing diagrams of 1c, Mn(salen) and dae-c²⁻ units are not organized in organic and inorganic sub networks. Two non-coordinated methanol solvent molecules are present in the asymmetric unit. No π–π interactions are observed in the crystal. However, hydrogen bonds between the non-coordinated and coordinated oxygen atoms of the dae-c²⁻ ligand and non-coordinated methanol molecules were observed. Additionally, there are hydrogen bonds between the fluorine atoms of dac-c²⁻ and the hydrogen atoms of the solvent methanol molecules. The intramolecular Mn^III⋯Mn^III distance across the dac-c²⁻ ligand was estimated to be 13.943 Å, whereas the nearest intermolecular distance was estimated to be 6.533 Å.⁸¹

Figure 50. ORTEP diagrams of 1c (ref. 81a).

Crystals of 1c-Vis were obtained by irradiating those of 1c with sunlight (UV light), and it crystallized in the P2₁/cn space group. The coordination modes of the Mn^III ions are similar to those of 1c. Packing diagrams for 1c-Vis are also similar to those for 1c. The intramolecular Mn^III⋯Mn^III distance across the dae-o²⁻ ligand was estimated to be 15. 147 Å, and the nearest inter-unit Mn^III⋯Mn^III distance was estimated to be 8.168 Å. These distances are longer than those in 1c.

Since the photochromic dae ligand undergoes reversible isomerization between closed and opened ring forms upon visible light (opening process) and UV irradiation (closing process) in both the solution and the solid state,⁸² we investigated the photo-isomerization processes in the solid state using KBr pellets of 1c before and after visible irradiation. In the absorption spectra, there are two bands around 380 and 580 nm, which were assigned to π–π* transitions of dae²⁻ ligand. Irradiation of KBr pellets of 1c with visible right (λ > 480 nm) showed a pronounced color change from black to pale brown, which is characteristic of dae²⁻-c and dae²⁻-o, respectively. After visible light irradiation, the two absorption bands disappeared due to ring opening. After UV light irradiation (λ < 480 nm) of 1c-Vis, the initial spectrum was recovered, which means that the photocyclization reaction was reversible. In other words, isomerization between the closed and opened forms occurs reversibly in the solid state.

The temperature dependence of the magnetic susceptibilities (χ_mT) of polycrystalline samples of 1c and 1c-Vis was performed in the T range of 2–300 K as shown in Figure 51. The χ_mT values at room temperature were determined to be 5.97 and 5.88 cm³mol⁻¹K for 1c and 1c-Vis, respectively. These values are comparable with the expected values of 6.0 cm³mol⁻¹ K for two non-interacting high-spin Mn^III ions (S = 2). The χ_mT values decreased monotonically from 300 to 30 K and sharply between 30 K to 2 K, indicating the presence of antiferromagnetic interactions. AC magnetic susceptibilities were obtained for polycrystalline samples of 1c and 1c-Vis as a function of T, H and frequency. No out-of-phase signal was observed for 1c, however the weak frequency dependence was observed for 1c-Vis. Detailed H-dependence ac measurements at 1.9 K showed that an H of 5000 Oe was needed to observe slow magnetic relaxation for 1c-Vis. In-phase (χ′) and out-of-phase magnetic susceptibilities (χ′′) for 1c-Vis were measured in an H of 5000 Oe at various T. The relaxation time τ was estimated by using a generalized Debye model for a distributed single relaxation process of M. The Δ_eff/K_B and τ₀ were estimated to be 13.13 K and 1.008 × 10⁻⁷ s at 5000 Oe, respectively. These values are comparable to those determined for other [Mn₂] SMMs.⁸³

Figure 51. Magnetic properties of 1c and 1c-Vis. (a) Comparison of the magnetic properties of 1c and 1c-Vis. Temperature dependence of χ_mT. Insets: M vs. H at 1.82 K. Slow magnetic relaxation of 1c-Vis. (b) Cole-Cole plots at several T in an H of 5000 Oe. (c) Arrhenius plots (ref. 81a).

As described above, the magnetic properties significantly changed upon photo-isomerization of the dae ligand. The closed form did not show the slow magnetic relaxation, whereas the open form showed clear frequency dependent magnetic relaxation. To observe the reversibility and repeatability of this activation, the sample was successively irradiated with visible and UV light over one day at room temperature, and magnetic measurements were performed at 1.9 K at each wavelength as shown in Figure 52. After visible irradiation, a clear peak appeared, whereas no peak appeared after irradiation with UV light, which demonstrate that the SMM behavior could be switched on/off reversibly and repeatedly.

Figure 52. Switching on/off of the SMM behavior. Frequency dependences of out-of-phase susceptibility for the complex after opening and closing process at 1.9 K (ref. 81a).

To the best of our knowledge, this is the first example of a coordination assembly where the magnetic properties are activated upon irradiation with visible light, and it is a significant advance in the area of molecular memory devices by using SMMs.

Conducting single-molecule magnets have been attracting much attention from the viewpoints of SMMs-based spintronics by the interactions between the delocalized electron in the conducting molecules and localized SMMs to show negative or giant magnetoresistance (GMR) (Figure 53). One of the strategies for synthesizing conducting SMMs is simply to combine SMMs and partially oxidized donor or accepter conducting molecules as shown in Figure 54.⁸⁴ However, the best way for the syntheses are electrochemical methods of solutions of donor molecules (or SMMs) and accepter molecules (or SMMs). We synthesized the first conducting SMM composed of [{Mn^II₂Mn^III₂(hmp)₆(MeCN)₂}{Pt(mnt)₂}₄][Pt(mnt)]₂ (hmp⁻ = 2-hydroxymethylpyridinate, mnt²⁻ = maleonitriledithiolate) by electrochemical methods.⁸⁵ The SMM cation units [Mn₄(hmp)₆(MeCN)₂]⁴⁺ and conducting anion units [Pt(mnt)₂]ⁿ⁻ are segregated and stacked with each other. The [Pt(mnt)₂]ⁿ⁻ unit has a non-integer or partial oxidation state, however, [Pt(mnt)₂]ⁿ⁻ units stack not evenly but irregularly. Considering the charge balance, the conducting [Pt(mnt)₂]ⁿ⁻ system was expected to behave as 1/3 filled band for the ordered packing, however the irregular stacking led to band gaps at the Fermi level. Indeed, the electrical conductivity measured in the single crystals showed the semiconducting behavior around room temperature and activation energy with 0.22 S cm⁻¹ and 136 meV, respectively. The magnetic properties of this compound were dominated by a contribution to the corresponding [Mn₄(hmp)₆(MeCN)₂]⁴⁺ units with a ground state S_T = 9/2. At the low temperature, AC susceptibility measurement as a function of frequency and temperature revealed an effective energy barrier of Δ_eff/k_B = 20 K. This behavior was confirmed by isothermal magnetization curve (2 Oe s⁻¹) at 470 mK, indicating hysteresis with coercive fields of 900 Oe. However, the compound is almost insulating below 10 K, while it shows SMM behavior below 10 K. As a result, there is no interaction between [Mn₄(hmp)₆(MeCN)₂]⁴⁺ SMMs and insulating acceptor [Pt(mnt)₂]ⁿ⁻ units, showing no negative magnetoresistance.

Figure 53. Scheme of hybrid conducting SMM materials with indication of relevant interactions, either between SMM units and delocalized conduction electrons (J) or inter-SMM (J′) (ref. 84).

Figure 54. Electroactive molecules and SMM components used in hybrid conducting SMM materials (ref. 84).

In Table 1, the conducting SMMs with the electrical conductivities so far reported are listed, where some compounds are composed of the donor SMMs and the conducting acceptor molecules, while the others are composed of the conducting donor molecules and the acceptor SMMs. As the next strategy, we used BEDO-TTF donors (BO), because many BEDO-TTF charge transfer (CT) complexes show superconductivities and/or metallic conductivities with the shorter S⋯S interactions between the neighboring molecules, forming stable 2D metallic electronic structures. Then, we used [Co^II(pdms)₂]²⁻ as an acceptor SMMs, because it shows redox active and large negative uniaxial anisotropy (D = −115 cm⁻¹).⁸⁶ We obtained β′′-(BEDO-TTF)₄[Co(pdms)₂]·3H₂O (hereafter abbreviated as BO4) (BEDO-TTF = bis(ethlenedioxy)tetrathiafulvalene; pdms = 1,2-bis(methanesulfonamido)) by electrochemical methods. BO4 crystallized in the centro-symmetric triclinic P-1 space group with four crystallographically independent BO molecules, one Co(pdms)₂ unit and three water molecules as shown in Figure 55. Figure 55b shows the molecular packing structure in the bc plane. The SMM layer alternates with the metallic BO layer along the c-axis, where the thickness of the layers are 7.2 Å and 11.0 Å, respectively, which indicate that both of them are 2D nanosheets. Many hydrogen-bonds (C-H⋯O) are observed between BO and SMM layers in addition to those within the BO layer, both of which stabilize the crystal structures. As shown in Figure 55c, the Co ions are arranged to form an infinite arrangement of parallelograms in the ab plane, where the shortest distance between Co ions is estimated to be 8.6 Å. The magnetic easy axes of all Co(pdms)₂ units are aligned along the b-axis to show 1D magnetic anisotropy. Figure 55d shows the packing of the BO molecules. While intermolecular S⋯S and S⋯O atomic contacts shorter than the sum of van-der-Waals radii are observed along the a-b direction, significant magnitudes of intermolecular orbital overlap (transfer integral) are manifested along the a-axis and along the 3a + 2b direction. In the EPR spectrum, a single peak with g = 2.004 was observed at room temperature, confirming the presence of a BO radical. Raman spectroscopy was performed to determine the charge on the BO molecules to estimate the degree of CT in the BO layer. The room-temperature Raman band at around 1480 cm⁻¹ observed to be a superposition of two bands (∼1477 cm⁻¹ and ∼1483 cm⁻¹) was attributed to the total symmetry C=C vibration of the BO, of which charges are +0.44 and +0.38 by using the equation, respectively.⁸⁷

Figure 55. Crystal structure of BO4 at 120 K. a) A unit cell projected along the b-axis (black: C, blue: Co, pale blue: N, red: O and yellow: S). b) Packing structure in the bc plane. The SMM layer (green background) alternates with the conducting layer (violet background) via short contacts, and the thickness of the SMM and conducting layers are 7.2 Å and 11.0 Å, respectively. c) The arrangement of the Co ions in the SMM layer in the ab plane. The arrows represent the direction of the easy axis of the Co ions in the Co(pdms)₂ molecules. The angle (φ) between three Co ions in one parallelogram is 42°, and the distances between two adjacent Co ions are 8.6 Å and 13.7 Å. d) The BO molecules arranged side-by-side along the a-axis and face-to-face in the a-b direction. The black dotted lines represent the short contacts (S⋯S and S⋯O) between BO molecules along the a-axis and a-b direction. All hydrogen atoms are omitted for clarity (ref. 86b).

Table 1. SMMs and their electrical conductivity properties so far reported: Δ/kB = magnetization relaxation barriers (K); σRT = room-temperature electrical conductivities (S cm−1); Ea = activation energies (meV) (ref. 84).

Table 1. SMMs and their electrical conductivity properties so far reported: Δ/k_B = magnetization relaxation barriers (K); σ_RT = room-temperature electrical conductivities (S cm⁻¹); E_a = activation energies (meV) (ref. 84).

The magnetic properties and electrical conductivity properties are shown in Figure 56 and Figure 57, respectively. The most striking physical property of BO4 is the simultaneous manifestations of SMM behavior and metallic conductivity in a similar temperature range. While BO4 shows semiconducting behavior from 62 to 32 K and below 6.5 K, the temperature region for the metallic conduction of BO4 includes the one for SMM behavior (T_B = 11 K) of Co(pdms)₂ molecules. The Co(pdms)₂ molecules are arranged in an ordered 2D narrow sheet (d = 7.2 Å), which causes the magnetic anisotropy of each Co(pdms)₂ unit to be nearly aligned with the b-axis, causing a strong magnetic anisotropy. The ferromagnetic ordering observed between 10.2 K and 6.5 K is caused by weak intermolecular interactions between the Co(pdms)₂ molecules due to the small rhombic angle in the magnetic layer. Subsequently, the antiferromagnetic ordering was observed below 6.5 K assigned to the weak interactions between Co(pdms)₂ SMMs and conducting BO layers. Thus, the weak inter- and intralayer interactions and the strong magnetic anisotropy maintain the SMM behavior in a region of antiferromagnetic ordering. In other words, the Co(pdms)₂ molecules are not significantly influenced by the surrounding Co ions, which essentially protects the SMM behavior. On the other hand, we observed that T_B of the Co(pdms)₂ units significantly increased and that QTM was suppressed at low frequency below T_N, which are caused by both intra- and interlayer interactions in the appropriate geometry of the lattice. For the electron transport, the first decrease in electrical conductivity at 62 K was suppressed by applying very low pressure (P = 0.03 GPa), as is reported for several low dimensional organic metals with a metal-insulator transition into a charge density wave (CDW) state at low temperature. The second decrease in electrical conductivity below 6.5 K is insensitive to pressure. In this temperature range, a negative MR was observed for both perpendicular and parallel field with respect to the conducting layer. Thus, the π-d interactions between the SMM and BO layer are important in BO4. Negative MRs were observed in fields perpendicular and parallel to the conducting layer up to ∼0.5 T, which is consistent with the characteristic spin-flop field (H₂) in the MH curve.

Figure 56. Magnetic properties. a) Temperature dependence χT (black circles) in a 0.1 T field in field cooling (FC) and zero field cooling (ZFC) modes, respectively. b) Magnetic hysteresis of the magnetization at a sweep rate of 200 Oe·s⁻¹ at 2.5 K and the first differential curve of dM/dH (dash curves) in the range of −0.8–+0.8 T. c) A comparison of frequency dependences of out-of-phase ac magnetic susceptibilities χ′′ of BO4 and (HNEt₃)₂[Co(pdms)₂] in a field of 0 Oe. d) τ as a function of T in fields of 0 and 1500 Oe for BO4 and (HNEt₃)₂[Co(pdms)₂]. The black, pink circles and the red curve represent the experimental data and best fit, respectively (ref. 86b).

Figure 57. Electrical conductivity and magnetoresistance effects. a) Temperature dependence of σ of two single-crystals. b) Magnetic field dependence of MR at different temperatures with magnetic field perpendicular to the 2D plane, θ = 0°, B // c-axis. c) MR-B plot in the range of 0–1.5 T at 2 K, 5 K and 7.5 K at θ = 0°. d) Magnetic field dependence of MR at different temperatures with magnetic field parallel to 2D plane, θ = 90°, B // b-axis. e) MR-B plot in the range of 0–1.5 T at 2, 5 and 7.5 K with θ = 90°. f) The MR-B plot in the range of 0–1.5 T at 2 K with θ = 0° and 90° (ref. 86b).

As mentioned above, for the first time, we observed π–d interaction in metallic conducting SMM with negative magnetoresistance. As the next step, we must realize GMR as well as superconducting SMMs.

Quantum bits, or qubits, represent the elementary units for the realization of quantum computers.⁸⁸ For this purpose, the quantum superposition of 0〉 and 1〉 that characterizes qubits is exploited. In quantum computation, a highly coherent superposition state allows for the retention of the quantum information on the qubits for a time longer than that required to perform a quantum operation (quantum gate). Nowadays, finding suitable, robust, and scalable systems as potential qubits represents one of the main challenges in chemistry, physics, IT, and materials science for the development of these technological applications.

Many physical and chemical systems such as photons,⁸⁹ trapped ions,⁹⁰ quantum dots,⁹¹ and coherent coupled systems of superconducting qubits with nitrogen-vacancy centers in diamond⁹² are investigated as qubit candidates, each of them showing both merits and deficits. Among these qubit realizations, molecular spin qubits have been studied only recently and have shown remarkably advantages such as the capacity of facilely addressing via pulsed EPR techniques,⁹³ a high processability through surface deposition, and a high degree of chemical tunability.⁹⁴ On the other hand, molecular spin qubits often suffer from a relatively short lifetime of the quantum superposition states, compared to other potential qubit systems so far reported. This loss of information is related to the spin-spin relaxation time (T₂), which is usually determined by measuring the phase memory time (T_m), which is a lower limit of T₂. Interactions with the environment cause the collapse of the already fragile superposition state of electronic spins in a process known as decoherence. Another important point is the potential spatial control over qubit-qubit distance achievable through coordination chemistry approaches such as 3D metal-organic frameworks (MOFs). For realization of molecular spin qubits with viable coherent times, oxidovanadium(IV) complexes with S = 1/2 constitute one of the most promising choices, due to the weak orbital contribution to the magnetism and an inefficient spin-phonon coupling interaction, which provides slow spin-lattice relaxation even at room temperature.⁹⁵ The characterization of the spin-lattice relaxation time (T₁) is then crucial in realization of high performing molecular spin qubits, since this process provides an upper limit for the coherence time (T₂ ≤ 2T₁). Furthermore, the investigation of spin-lattice and coherence times of vanadyl-based potential qubits embedded into 3D MOFs materials has not been reported yet. Motivated by the need to acquire additional insights into the role of the crystal lattice properties in determining electronic spin qubit performance, we synthesized a porous vanadyl-based 3D MOF of formula [VO(TCPP-Zn₂-bpy)] (1) (TCPP = tetracarboxylphenylporphyrinate; bpy = 4,4′-bipyridyl). The spin-lattice relaxation times of (1) were studied by AC susceptibility measurements, and the coherence times of an isostructural magnetically diluted sample [VO_0.05TiO_0.95(TCPP-Zn₂-bpy)] (1′) were studied by pulse EPR spectroscopy. The results have been compared to those obtained on a representative mononuclear molecular building block (0D) of formula [VO(TPP)] (TPP = tetraphenylporphyrinate) (2) and its isostructual magnetically diluted sample [VO_0.02TiO_0.98(TCPP)] (2′). The analysis of the temperature dependence of the spin-lattice relaxation time (T₁), which plays a crucial role in determining the coherence at room temperature for two materials, is discussed by considering the different structural and spectroscopic features in the terahertz regime shown by the 3D network and 0D mononuclear analogue.

The reaction between preformed vanadyl and/or titanyl tetracarboxylphenylporphyrinates with Zn²⁺ and bpy has been carried out to obtain the 3D MOF structure shown in Figure 58. Compound (1) crystallizes in the tetragonal P4 space group with one anion complex, two Zn²⁺ ions, and one bpy molecule in the unit cell, where the asymmetric unit is one-fourth of the molecule. The peripheral carboxyl substituents of the porphyrin macrocycle (Figure 58b) interact with Zn²⁺ to form a 2D layer where the porphyrin units are connected in a 4-fold symmetry through [Zn₂(COO)₄] subunits. The pillar bpy ligands allow connection between the 2D layers to form 3D channels with a pore dimension of 1.66 × 1.38 nm² along the a and b axes. The component structure of [VO(TCPP)]⁴⁻ in (1) shows a vanadium(IV) ion in a square pyramidal coordination geometry with the metal ion slightly above the basal plane (ca. 0.59 Å) formed by the four nitrogen donor atoms of the porphyrin macrocycle as shown in Figure 59a. The V=O moiety sits on the 4-fold symmetry axis and is disordered on two positions, symmetric with respect to the macrocycle ligand, with 50:50 occupancy factors, leading a nonpolar crystal structure. The V-O and V-N distances, 1.60 and 2.09 Å, respectively, are in agreement with those of similar vanadyl complexes. The V⋯V distance in (1) is estimated to be 13.9 Å.

Figure 58. Scheme of the two-step self-assembly process responsible for the formation of the 3D MOFs 1 and 1′. Color codes: green, vanadium; orange, zinc; red, oxygen; light blue, nitrogen; gray, carbon (ref. 96).