Tuning quantum tunnelling of magnetization through 3d–4f magnetic interactions: an alternative approach for manipulating single-molecule magnetism

Abstract

The magnetic relaxation and magnetization blocking barriers of butterfly complexes, [Dy₂Zn₂(L)₄(NO₃)₂(CH₃OH)₂] (1), [Dy₂Mn₂(L)₄(NO₃)₂(DMF)₂] (2) and [Dy₂Co₂(L)₄(NO₃)₂(DMF)₂]·2DMF (3) (H₂L = (E)-2-ethoxy-6-(((2-hydroxyphenyl)imino)methyl)phenol), were systematically investigated. The change of SMM behavior originating from the purposeful replacement of two Zn^II sites in 1 with Mn^II and Co^II was elucidated by a combined experimental and theoretical study. The quantum tunnelling of magnetization (QTM) was observed in 1. Contrarily, it was quenched in 2 and 3 by spin–spin exchange. A detailed comparative study on these closely-related model complexes reveals the remarkable changes of the ligand field splitting, anisotropy of the Dy-coordinated moiety and the total exchange spectrum due to the replacement of Zn^II with Co^II and Mn^II.

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Introduction

As an attractive property of molecular materials, single-molecule magnet¹ (SMM) behaviour displays slow relaxation and quantum tunnelling of magnetization (QTM) because of its molecule-based blocking anisotropy. In 2003, Ishikawa et al.² discovered the first mononuclear lanthanide SMM, [Pc₂Tb]⁻TBA⁺. Since then designing SMMs with lanthanide ions has been applied as a possible strategy in generating large barriers due to the presence of significant magnetic anisotropy arising from the prominent spin–orbital coupling. Over the past few years, lots of mono- and polynuclear complexes with large energy barriers have been synthesized.³ For example, Tong et al.⁴ reported a mononuclear lanthanide SMM with a record energy barrier up to 1000 K, ten times larger than that of the [Mn₁₂] complex (60 K).¹ Song et al. discovered that the idiosyncrasy of inherent anisotropy within the Dy^III ion is the main reason leading to the slow relaxation rather than any other coupling interaction.⁵ Hence, the Dy^III ion has become a good choice for designing and synthesizing SMMs. However, most of the mononuclear Dy^III complexes are field-induced SMMs due to the QTM effect under zero magnetic field, which limits their range of application. Suppressing the QTM effect poses a new challenge to chemists. In the previous reports, it has been believed that spin–spin exchange effects in clusters^6a–h and a special crystal field or/and local symmetry around individual lanthanide ions⁶ⁱ have been the successful strategies to suppress the QTM effect. Nevertheless, there has been no direct and clear evidence reported about the former so far. Several years ago, Powell's group^7a reported a butterfly complex [Co₂Dy₂(L′)₄(NO₃)₂(THF)₂]·4THF (H₂L′ = (E)-2-methoxy-6-(((2-hydroxyphenyl)imino)methyl)phenol) with extraordinary SMM properties. Owing to its magnetization hysteresis loop up to 4 K, this complex can be a good candidate for achieving a thorough understanding on how the spin–spin exchange interaction between 3d–4f ions disturbs the Dy^III ion energy levels and reduces zero-field QTM. Based on this strategy, three complexes, [Dy₂Zn₂(L)₄(NO₃)₂(CH₃OH)₂] (1), [Dy₂Mn₂(L)₄(NO₃)₂(DMF)₂] (2) and [Dy₂Co₂(L)₄(NO₃)₂(DMF)₂]·2DMF (3), were synthesized after the modification of ligands. Quite obviously and surprisingly, different from the typical lanthanide-based SMM behaviour of 1, the 3d–4f magnetic interaction quenches the SMM properties in 2, but enhances the SMM properties in 3. Herein, we report the synthesis, structure and magnetostructural correlation of complexes 1, 2 and 3.

Results and discussion

Through adjusting the reference method,⁷ three complexes 1, 2 and 3 with similar construction were synthesized (Fig. 1). Complex 1 crystallizes in the triclinic space group P1̄ with Z = 1, which is a heterometallic 3d–4f tetranuclear cluster with the metallic core displaying a butterfly-type topology. The asymmetric unit consists of a half component of the cluster, and the whole molecule is grown by an inversion centre. The two Zn^II ions are found at the “body” sites of the butterfly, whereas the Dy^III ions occupy the outer “wing” position. The eight-coordinated Dy^III ion can be seen as a hula-hoop configuration. One of the two L²⁻ ligands chelates Dy1 through its two phenolate O atoms (O1 and O2) and an imine N atom (N1), while the other one chelates through one phenolate and one ether oxygen atom (O5 and O6, respectively). Therefore, five ligand atoms on the equatorial plane construct a distorted hoop with a mean deviation of 0.1731 Å. Two nitrate O atoms (O7 and O8) and phenolate O4ⁱ (symmetry code: i, −x, −y, −z) coordinate to the Dy^III ion and complete the eight-coordinated environment. The Zn^II ion is located in the centre of a slightly distorted octahedron. In the equatorial plane, two phenolate O atoms (O4 and O5) and an imine N one (N2) are all provided by the same ligand, and the residual oxygen atom (O1) is from the other ligand. One MeOH molecule and phenolate O1ⁱ (symmetry code: i, −x, −y, −z) occupy the axial positions, respectively. All the atoms in the two equatorial planes are approximately coplanar with Dy1 and Zn1 bridged by two phenolate O atoms (O1 and O5) from two ligands, respectively. The cluster molecule is further formed via the axial coordination of a μ₃-O (O1, bridging Dy1, Zn1 and Zn1ⁱ, symmetry code: i, −x, −y, −z) and a μ₂-O (O4, bridging Zn1 and Dy1ⁱ, symmetry code: i, −x, −y, −z). Complex 3 also crystallizes in the triclinic space group P1̄ with Z = 1, while complex 2 in the monoclinic space group P2₁/c with Z = 2 (Table S1†). The molecular structures of 2 and 3 are similar to 1 except that the solvent molecule coordinating to Mn or Co is DMF instead of MeOH, and there are two additional DMF molecules found in the lattice of 3. In 2, the Mn^II ion is located in the centre of a more distorted octahedron, which is unusual for a d⁵ ion (Table S2†). A THF coordinating to the Co^II ions of the [Co₂Dy₂] complex reported in ref. 7a is replaced by a DMF molecule in 3. The bond lengths and angles of the fragment surrounded Dy^III ions in two [Co₂Dy₂] complexes are basically consistent, except the Co–O bond linked with THF is 2.197 Å, much longer than that (2.060 Å) with DMF in 3 (Fig. S16 and Table S7†).

Fig. 1 Molecular structures of the coordination clusters in 1 (up, left), 2 (up, right), 3 (down, left) and ligand atoms linked to Dy^III (down, right).

Direct current (dc) magnetic susceptibility measurements of 1, 2 and 3 were performed in the temperature range 1.9–300 K in a field of 100 Oe on a polycrystalline sample. The χ_MT versus T plots for three complexes are shown in Fig. 2. The room-temperature χ_MT value of 28.13 cm³ K mol⁻¹ for 1 is in good agreement with the value of the two isolated Dy^III (S = 5/2, L = 5, ⁶H_15/2, gJ = 4/3, C = 14.17 cm³ K mol⁻¹) ions. The χ_MT value gradually decreases with cooling due to the thermal depopulation of the excited m_J states of the Dy^III ions until reaching a minimum of 23.1 cm³ K mol⁻¹ at ca. 9.5 K, below which it increases to 24.1 cm³ K mol⁻¹ at 2 K. This anomaly can be modelled by using the effective g values (g_x = 0.006, g_y = 0.008 and g_z = 19.05) of the ground Kramers doublet obtained from CASSCF/RASSI calculations, taking into consideration the anisotropic dipole interaction between the two effective spins of S_eff = 1/2 (J = +2.8 cm⁻¹ for a Hamiltonian function S1), which is in agreement with a ferromagnetic dipolar interaction observed for the reported dimeric lanthanide systems.⁸ Complexes 2 and 3 show similar plots of χ_MT–T except a peak was observed at 2.5 K for 3. The room-temperature χ_MT products are 37.01 and 34.71 cm³ K mol⁻¹ for 2 and 3, respectively, corresponding to the value of two non-interacting Mn^II (S = 5/2, g = 2) or Co^II (S = 3/2, g > 2) and Dy^III (C = 14.17 cm³ K mol⁻¹) ions. The higher χ_MT value of 3 is ascribed to the unquenched orbital contribution from the Co^II ions.^7a,9 Upon cooling, χ_MT gradually decreases and reaches the minimum at 70 K for 2 and 60 K for 3, resulting from the thermal depopulation of the Starks levels of the Dy^III ions and the additional orbital contribution of the Co^II ions in 3. As expected, owing to the total contribution of both Dy^III and Co^II ions, complex 3 shows a lower temperature with a minimum χ_MT value than 2, but the latter is only due to the effect of Dy^III ions. And then, χ_MT begins to increase and increases steeply below 18 K (2) and 25 K (3). This behaviour suggests the presence of weak intramolecular ferromagnetic interactions between the metal centres, which, however, is strong enough to overwhelm the contribution of the thermal depopulation of the Starks levels of the Dy^III ions leading to the decrease of χ_MT, even including the unquenched orbital effect of the Co^II ions in 3.

Fig. 2 Comparisons of the experimental (scatters) and calculated (solid line) magnetic susceptibility for 1, 2 and 3. The intermolecular interactions zJ′ were set to −0.01 cm⁻¹, 0 cm⁻¹ and −0.01 cm⁻¹, respectively.

The magnetizations of three complexes from zero dc field to 7 T at different temperatures are shown in Fig. S1.† The field dependence of their magnetization at 1.9 K exhibits an abrupt increase at low fields below 1 T for 1 and 0.5 T for 2 and 3, respectively, providing evidence for the ferromagnetic interaction. At higher fields, the magnetization increases slightly and reaches 10.48 (1), 22.5 (2) and 13.6Nμ_B (3) up to 7 T. These values are lower than the expected saturation value of 20 (1), 30 (2) and 26Nμ_B (3) for two non-interaction Dy^III ions (g_JJ = 4/3 × 15/2 = 10Nμ_B per Dy^III ion), two isolated Mn^II (gS = 2 × 5/2 = 5Nμ_B per Mn ^II ion) or Co^II (gS = 2 × 3/2 = 3Nμ_B per Co^II ion) and two Dy^III ions, respectively. Such a phenomenon arises most likely from magnetic anisotropy,¹⁰ proved by the non-superposition of the M vs. H/T data (Fig. S2†) on a single master curve.¹¹

AC susceptibility measurements in a 2 Oe AC field oscillating at 1–999 Hz were performed on 1, 2 and 3 (Fig. 3 and S3†). For 1, the temperature dependence of both in-phase (χ′_M) and out-of-phase (χ′′_M) susceptibility shows strong frequency dependence under zero dc field. The maximum of χ′′_M is observed at 22 K for 999 Hz, while below 125 Hz no peak is found in the χ′′_Mversus T curve due to the quantum tunnelling effect (Fig. S4(a)†). All of these feature the SMM behaviour. A plot of ln(τ) versus T⁻¹ based on variable-frequency susceptibility data is linear between 17 K and 22 K (Fig. 4). Fitting the data with the Arrhenius law τ = τ₀ exp(ΔE/k_BT) poses a thermal energy barrier to the relaxation of magnetization ΔE = 78 K (54.1 cm⁻¹) with τ₀ = 4.59 × 10⁻⁶ s. At lower temperatures, ln(τ) increases much more slowly with cooling, which shows the onset of a quantum regime, contrary to what is often observed for the majority of Ln-based SMMs where the QTM is fast.^11b,12 The Cole–Cole plots of χ′′_Mversus χ′_M between 10 and 30 K (Fig. S5†) reveal semicircular profiles, and are fitted by the CCFIT program¹³ to a generalized Debye model with α parameters in the range of 0–0.13, indicating a narrow distribution of relaxation times in 1 (Table S3†).^6e,f Given the coexistence of multiple relaxations under zero dc field, the relaxation data can be modelled with QTM, Raman and Orbach relaxation processes. A fit with eqn (1) (where τ_QTM is the quantum tunnelling of the magnetization relaxation time, C is the coefficient of the Raman process, U_eff is the energy barrier to magnetization reversal, and k_B is the Boltzmann constant) is in good agreement with the data over the whole temperature regime (Fig. 4) with parameters of τ_QTM⁻¹ = 108.39 s⁻¹, C = 0.116 s⁻¹ K^−3.26n = 3.26, τ₀ = 2.35 × 10⁻⁶ s, and U_eff = 115 K (79.8 cm⁻¹) (detailed information can be seen in Table S6†). Theoretically, the parameter n in the Raman relaxation pathway is equal to 9 for Kramers ions,¹⁴ and lower values would be allowed due to the optical phonons taken into account.^10b,15 To study the properties of a single Dy^III ion without QTM, we searched dc fields from 200 to 2000 Oe, and found an appropriate dc field of 1000 Oe to hinder the QTM effect (Fig. S6†). The maximum of χ′′_M is observed at 24 K for 999 Hz and it varies at different frequencies (Fig. S7†). The thermal energy barrier for the relaxation of magnetization is 96 K (66.6 cm⁻¹) with τ₀ = 3.79 × 10⁻⁶ s (Fig. 4). The Cole–Cole plots, fitted between 10 and 30 K, give the parameters of 0–0.095, which shows that QTM was hindered by the extra dc field effectively (Fig. S8 and Table S4†).^10a,12a

τ⁻¹ = τ_QTM⁻¹ + CTⁿ + τ₀⁻¹ exp(−U_eff/k_BT) (1)

Fig. 3 Frequency dependence of out-of-phase (χ′′_M) AC susceptibilities under zero dc field (1–999 Hz, by MPMS Squid VSM) at indicated temperatures for 1, 2 and 3.

Fig. 4 (a) Magnetization relaxation time, ln τ, versus T⁻¹ for 1: the black solid line (under zero dc field) and the red line (under 1000 Oe dc field) are fitted with the Arrhenius law; (b) ln(τ) versus T⁻¹ for 3 under zero dc field: the red solid line is fitted in the temperature range 16–20 K with the Arrhenius law (see the text). The blue lines in both plots are fitted with eqn (1) over the whole temperature regime.

For 2, the temperature dependence of susceptibility also shows the frequency dependence under zero dc field but without a peak in both χ′_M and χ′′_M (Fig. S4(b)†). Fitting to ln(χ′′_M/χ′_M) = ln(ωτ₀) + E_a/k_BT (ref. 16) allows us to evaluate roughly E_a and τ₀, giving the energy barrier ca. E_a = 11 K (7.6 cm⁻¹) and τ₀ = 1 × 10⁻⁸ s (Fig. S9†). Under H_dc = 1000 Oe (Fig. S10†), the curves of χ′_M and χ′′_Mversus T show a slight change compared with those under H_dc = 0. The result indicates that there is no QTM influence on the magnetic properties, and the signal under zero fields is an intrinsic character of 2.^7b,17

For 3, the strong temperature and frequency dependence of AC susceptibility under H_dc = 0 illustrate the characteristic of SMM (Fig. 3, S3 and S4(c)†). Compared with 1, the maximum of χ′′_M even can be observed at 2.6 K at the lowest 1 Hz, indicating that the magnetic interaction between Co^II and Dy^III has suppressed QTM effectively. The deduced plots of ln(τ ) − T⁻¹ (Fig. 4) can be fitted with ΔE = 88.8 K (61.6 cm⁻¹) and τ₀ = 2.29 × 10⁻⁶ s in the range of 16–20 K through the Arrhenius law. A fit employing eqn (1) obtained τ_QTM⁻¹ = 0.001 s⁻¹, C = 0.301 s⁻¹ K^−3.16, n = 3.16, τ₀ = 2.67 × 10⁻⁶ s, and U_eff = 125.1 K (86.8 cm⁻¹) (detailed information can be seen in Table S6†). The Cole–Cole plots were fitted with the generalized Debye model (Fig. S11 and Table S5†). The α values are in the range of 0–0.18(2), suggesting the coexistence of multiple relaxation pathways, which is discovered in several examples.^7a,12a The AC susceptibilities were also measured under 1000 Oe external dc field (Fig. S12†). A plot of ln(τ) versus T⁻¹ based on variable-frequency susceptibility data shows a slight change compared with those under H_dc = 0 (Fig. S13 and Table S6†), indicating that the magnetic interaction between Co^II and Dy^III dominates the Zeeman effect.

To confirm the SMM behaviour, hysteresis loops were recorded at low temperatures. Below 4 K, butterfly-like hysteresis can be clearly observed for 1 (Fig. S14†). However, for 2 and 3, no hysteresis loop was observed even at 1.8 K (Fig. S15†). Interestingly, Powell et al.^7a reported a [Co₂Dy₂] complex with a THF coordinating to Co^II ions, showing large hysteresis loops below 4 K. However, the difference of the environment between Co^II ions (Fig. S16 and Table S7†) directly influences the molecular magnetic properties. Compared with the calculating results, the g values of Dy^III ions in two complexes are almost equal (g_x = 0.005 (0.004), g_y = 0.008 (0.006), g_z = 19.53 (19.68) for reported [Co₂Dy₂] (and 3)), while the g values of Co^II are much different (g_x = 1.89 (1.60), g_y = 3.24 (2.333), g_z = 6.74 (7.599), respectively). The magnetic axes on all magnetic central ions for 3 are parallel to each other, while those on the reported [Co₂Dy₂] complex are interlaced. The difference of the uniaxial magnetic anisotropy of Co^II influences the magnetic interaction between Co^II and Dy^III, and further impacts on the magnetic properties of the whole complexes. As a result, complex 3 shows a stronger interaction between ions (J_Dy–Co = 11.7 cm⁻¹ and J_Co–Co = 6.8 cm⁻¹) than the reported [Co₂Dy₂] complex^7a (J_Dy–Co = 1.6 cm⁻¹ and J_Co–Co = 2.0 cm⁻¹). In the reference complex, it is believed that the properties of single ion Dy^III were retained due to the weak interaction, and some single ion Dy^III complexes show large hysteresis loops.^6d Nevertheless, the stronger interaction in complex 3 destroyed the properties of the single ion Dy^III, which yielded the properties of the entire molecule [Dy₂Co₂]. For clarifying the effect of 3d–4f magnetic interactions on the difference between complex 3 and the reference complex in hysteresis loops, perhaps, more examples are necessary for obtaining more information in regularity.

The temperature dependence of susceptibility for 2 and 3 shows similar intramolecular ferromagnetic interactions between the metal centres. Interestingly, in complex 1, two Dy^III ions separated by two diamagnetic Zn^II ions also show weak ferromagnetic dipole–dipole interactions at a low temperature. But in the AC susceptibility aspect, the three complexes represent much different behaviours. In order to understand the strikingly different properties of 3d–4f mixed complexes with different 3d metal ions and the origin of their magnetic properties, we performed ab initio calculations on 1–3, which are very appropriate for the interpretation of lanthanide complexes.^{6b–d,7a,12a,18}

Complete-active-space self-consistent field (CASSCF) calculations on individual Dy^III, Mn^II and Co^II fragments of 1, 2 and 3 on the basis of X-ray determined geometries have been carried out with MOLCAS 7.8¹⁸ⁱ and SINGLE_ANISO^18d,g,m programs. The lowest Kramers doublets and the g tensors of Dy^III, Mn^II and Co^II ions of three complexes are shown in Table S8,† where the energy separations between the ground and the first-excited doublets for the Dy^III fragments¹⁹ of 1, 2 and 3 are 229.1, 202.4 and 206.6 cm⁻¹, respectively, which indicates that the Dy–Dy, Dy–Mn and Dy–Co exchange interactions can be approximately regarded as the Ising type. Moreover, the Mn^II in 2 from Table S8† is almost isotropic, but the Co^II in 3 is strongly anisotropic. The magnetic susceptibilities of 1, 2 and 3 were simulated with the program POLY_ANISO¹⁸ (Fig. 2) using the exchange parameters shown in Table 1. All parameters from Table 1 were calculated with respect to the pseudospin = 1/2 of the Dy ions. For Co^II with strong anisotropy in 3, we also approximately regard the pseudospin as 1/2. For the three complexes, the total coupling parameters J (dipolar and exchange) were included when fitting the magnetic susceptibilities. The calculated and experimental χ_MT versus T plots of the three complexes are shown in Fig. 2, where a slight discrepancy of the fit to the experimental data for 1 is found above 100 K.^6h From Table 1, the fitted Dy^III–Mn^II, Dy^III–Dy^III, Dy^III–Co^II and Co^II–Co^II couplings in three complexes within the Lines model²⁰ are all ferromagnetic. The main magnetic axes on the magnetic ions of the three complexes are indicated in Fig. S17† where the magnetic axes on all magnetic centre ions for each complex are parallel to each other.

Table 1 Fitted coupling parameters (J = J_exch + J_dip) (cm⁻¹) within the Lines model of complexes 1, 2 and 3

	J (1)	J (2)	J (3)
Dy–Dy	2.8	5.5	2.0
Dy–Mn		4.8
Mn–Mn		0.2
Co–Dy			11.7
Co–Co			6.8

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The calculated exchange spectrum and the corresponding tunnelling gaps and g_z values are given in Table S9.† Considering that those three complexes are not isostructural, we therefore demonstrate the magnetization blocking barriers and the corresponding tunnelling gaps of individual Dy^III ions with the electrostatics generated by the ligands as shown in Fig. 5 (top), which was very important for the discussion between QTM and the magnetic exchange interaction. According to a recent proposal by Ungur and co-workers,²¹ the relaxation path can be related to the tunnelling gaps. Then, the blocking barrier may be defined by the shortest paths, where these quantities are the largest. For 1, the energy barrier cannot be associated with the exchange states since the highest of four exchange states (0.4 cm⁻¹) lies much lower than the experimental barrier (79.8 cm⁻¹), and the order of magnitude of the magnetic moment matrix element connecting the four exchange states is 10⁻⁶ cm⁻¹, so that the corresponding tunnelling transition between these states are efficient. Thus, the energy barrier of 1 should be associated with relaxation through the excited KDs of individual Dy ions. This phenomenon is also observed in the reference complex [Co₂Dy₂].^7a

Fig. 5 Top: The magnetization blocking barrier of individual Dy in [Zn₂Dy₂] (1), [Mn₂Dy₂] (2) and [Co₂Dy₂] (3). Bottom: The low-lying exchange spectrum arising from the exchange interaction of the lowest Kramers doublets on the magnetic centre. The thick black lines represent the Kramers doublets as a function of their magnetic moment along the magnetic axis. The green lines correspond to diagonal quantum tunnelling of magnetization (QTM); the blue lines represent Orbach relaxation processes; the red arrows show the most probable path for magnetic relaxation. The numbers at each arrow stand for the mean absolute value of the corresponding matrix element of the transition magnetic moment.

The energy barrier of 2 is very small given the fact that the energy separations between the exchange states split by the weak Dy–Mn exchange coupling are quite small (the highest exchange state is only 12.3 cm⁻¹). According to the relaxation path indicated in Fig. 5, we deduced that the blocking barrier of 2 corresponding to the magnetic relaxation from −31 to +35 is 6.5 cm⁻¹, which is very close to the experimental fitting value (Fig. S9†). For 3, the high excited state (15 cm⁻¹, see Table S9†) is much smaller than the energy barrier (86.8 cm⁻¹), which is associated with the relaxation through the excited KDs of the magnetic centre ions rather with the exchange states. Although the height of this barrier matches well with that in the complex 1 (79.8 cm⁻¹), we note that these two quantities are not directly related. For the difference between complexes 2 and 3 in the magnetic behaviours, we try giving some possible reasons here. In our opinion, the main difference of their energy barriers is originated from the tunnelling gaps between the low-lying exchange states and the temperature disturbing. From Table S9,† complex 2 has 72 low-lying exchange states and there are a lot of magnetic relaxation pathways. Although higher energy states would be populated at higher temperatures, the large tunnelling gaps between the 72 low-lying non-Kramers doublet exchange states will destroy the probable magnetic relaxation of 2 to a higher energy state. Compared to complex 2, complex 3 only has 8 low-lying non-Kramers doublet exchange states, and the magnetic relaxation will not happen between 8 exchange states. The thermally assisted QTM is another choice for 3 under this situation. At higher temperatures, higher energy states will be populated for 3.

From the relaxation path indicated in Fig. 5 top, a conclusion can be made is that their low-lying state energies are close. Particularly, the energy gaps are 229.1, 202.4 and 206.6 cm⁻¹ for complexes 1, 2 and 3, respectively (Table S8†). Additionally, the ground state in individual Dy ions without magnetic interaction displays much larger tunnelling splitting (of 10⁻² cm⁻¹, Fig. 5 top), indicating that the slight difference in the structure and space group did not influence the tunnelling splitting gaps of individual Dy ions obviously, and the discussion between the three complexes based on the isostructure is acceptable. For 1, the Dy–Dy anisotropic dipole interaction changed the ground state tunnelling splitting (from 10⁻² cm⁻¹ to 10⁻⁶ cm⁻¹), and should have hindered the QTM. However, the highest one of the four exchange states (0.4 cm⁻¹) is still small when confronting with thermal disturbance. As a result, the dipole interaction between Dy ions can be ignored in the relaxation process which is in good agreement with the experimental data (Fig. 3 and 4). For 2 and 3, after bringing in the 3d–4f magnetic exchange coupling interaction, the tunnelling gaps in the ground state become very small (on the order of 10⁻⁷ to 10⁻⁹ cm⁻¹), indicating that QTM is quenched largely in the process.

The calculated energy gaps between the ground and the first excited states for the individual Dy ions of complexes 1 and 3 are much larger than the experimental one, while the latter is much larger than the energy gaps of the exchange splitting state. Considering the large error of the fitted parameters with eqn (1), we infer that the above-mentioned phenomenon could result from the Raman process instead of the Orbach one. The effective energy barriers extracted from the experiment may not be the “real barrier”. As a result, we fit the relaxation times with two processes (Raman + QTM) (Fig. 6):

τ⁻¹ = τ_QTM⁻¹ + CTⁿ (2)

Fig. 6 Magnetization relaxation time, τ⁻¹, versus T for 1 (a) and 3 (b), respectively. The black solid line (under zero dc field) and the red line (under 1 kOe dc field) are fitted with eqn (2).

The best fit parameters obtained were n ≥ 4 for both complexes under different fields which is in accordance with the expected values for Kramers ion SMMs.¹⁵ All parameters and standard error can be seen in Table S10.†

Conclusions

A series of butterfly [M₂Dy₂] complexes have been successfully developed to probe into the magnetic relaxation mechanism of 3d–4f complexes systematically. Single-crystal X-ray diffraction shows that the molecular structures of 1, 2 and 3 are comparable. Complex 1 with two diamagnetic Zn^II ions shows typical SMM behaviour with a blocking energy (ΔE) of 54.1 cm⁻¹ under zero dc field with an obvious QTM effect in the low temperature region. However, with two Co^II ions instead of Zn^II ions, complex 3 undergoes a relaxation process with ΔE = 61.6 cm⁻¹ without the QTM effect, and complex 2, with two Mn^II ions, shows the same magnetic behaviour under both H_dc = 0 and 1000 Oe, indicating that the 3d–4f spin–spin exchange effects can reduce the zero-field QTM. Unexpectedly, complexes 2 and 3 undergo two totally different relaxation processes. Through a detailed comparative study of these closely-related model complexes, the structure and magnetic properties, especially the total exchange spectrum due to the replacement of Zn^II with Co^II and Mn^II, were investigated. Finally, the blocking barriers in these two complexes were rationalized, which explains their different blocking behaviours.

This analysis was made possible through a deliberate design of butterfly model complexes with purposeful metal replacement. Our study gives direct and clear evidence that spin–spin exchange effects can reduce the zero-field QTM and enhance our understanding of magnetic interactions in elucidating the relaxation dynamics of the 3d–4f mixed metal system. However, the results indicate that the spin–spin interaction can improve the SMM properties in some lanthanide-based systems, but also weakens the magnetic properties in another system. Thus, the selected 3d ions play a key role in designing 3d–4f SMM. Accordingly, 3d ions, not all, with strong spin–orbital coupling contribution, might provide an alternative pathway for the rational design of new 3d–4f SMMs with high performance.

Experimental

General methods

All the reagents and solvents were purchased from commercial sources without any purification. The compound (E)-2-ethoxy-6-(((2-hydroxyphenyl)imino)methyl)phenol (H₂L) was prepared by reported procedures.^7b

Preparation of [Dy₂Zn₂(L)₄(NO₃)₂(CH₃OH)₂] (1). A mixture of Dy(NO₃)₃·5H₂O (0.1 mmol, 45 mg), Zn(NO₃)₂·6H₂O (0.1 mmol, 29 mg), and H₂L (0.2 mmol, 52 mg) was stirred in 2 mL DMF. After the solution is clear, NEt₃ (0.4 mmol, 42 mg) was added. 5 minutes later, 20 mL MeOH was added, then filtered and left undisturbed. After keeping overnight, yellow colour block shaped crystals of 1 were produced in 80% yield. Elemental analysis (%): Calcd for C₆₂H₆₀Dy₂N₆O₂₀Zn₂: C 44.72, H 3.63, N 5.04; found: C 44.55, H 3.67, N 4.92. IR (KBr, cm⁻¹): 3414(b), 3066(w), 2950(w), 2914(w), 2360(m), 2324(m), 1618(m), 1601(s), 1586(m), 1478(s), 1450(s), 1390(s), 1223(s), 1291(m), 1183(m), 1175(m), 816(m), 729(m), 521(w).

Preparation of [Dy₂Mn₂(L)₄(NO₃)₂(DMF)₂] (2). The same synthetic procedure for 1 was followed, but using Mn(NO₃)₂ solution in place of Zn(NO₃)₂·6H₂O and under N₂ protection, giving 2 in 55% yield. Elemental analysis (%): Calcd for C₆₆H₆₆Dy₂Mn₂N₈O₂₀: C 45.92, H 3.85, N 6.49; found: C 45.78, H 3.87, N 6.52. IR (KBr, cm⁻¹): 3409(b), 3058(w), 2982(w), 2907(w), 2869(w), 2357(m), 2330(m), 1640(m), 1603(s), 1586(m), 1542(m), 1479(s), 1450(s), 1388(s), 1287(s), 1243(m), 1220(m), 1178(m), 1112(m), 815(m), 741(m), 510(w).

Preparation of [Dy₂Co₂(L)₄(NO₃)₂(DMF)₂]·2DMF (3). A mixture of Dy(NO₃)₃·5H₂O (0.1 mmol, 45 mg), Co(NO₃)₂·6H₂O (0.1 mmol, 29 mg), and H₂L (0.2 mmol, 52 mg) was stirred in 4 mL DMF. After the solution is clear, NEt₃ (0.4 mmol, 42 mg) was added. 5 to 7 minutes later, the solution was filtered and left undisturbed. After keeping overnight, yellow colour block shaped crystals of 3 were produced in 62% yield. Note: the crystals decompose after a long time in air, might be due to the solvent molecules in crystal lattice released. Anal. Calc. (%) for C₇₂H₈₀Dy₂Co₂N₁₀O₂₂ (C 45.99, H 4.29, N 7.45) corresponding to solvent DMF released and absorbed water from air leading to [Dy₂Co₂(L)₄(NO₃)₂(DMF)₂]·DMF·2H₂O, namely C₆₉H₇₇N₉Co₂Dy₂O₂₃: C 44.96, H 4.21, N 6.84; found: C 44.94, H 4.02, N 6.84 IR (KBr, cm⁻¹): 3410(b), 2987(w), 2367(m), 2340(m), 1491(s), 1386(s), 1347(s), 1234(m), 1220(w), 1100(m), 960(w), 870(w), 820(w), 741(m), 728(w), 684(w), 511(w).

Physical measurement

Elemental analyses of C, H, and N were performed on a PerkinElmer 240C elemental analyser. IR spectra were obtained with a Nexus 870 FT-IR spectrometer using KBr pellets in the range from 400 to 4000 cm⁻¹. Magnetic data were collected on a Quantum Design VSM SQUID magnetometer. Static magnetic measurements were performed in the temperature range 1.9–300 K in a field of 100 Oe on a polycrystalline sample. The alternating-current (AC) susceptibility measurements were performed under an oscillating field of 2 Oe with the frequency ranging from 1 to 999 Hz. Due to the air-sensitivity of complex 3, the magnetic data were obtained under paraffin oil protection. Experimental susceptibilities were corrected for the diamagnetism estimated Pascal's tables²² and for the sample holder by previous calibration.

Ab initio calculations for complexes 1, 2 and 3

Complete-active-space self-consistent field (CASSCF) calculations on individual lanthanide Dy^III, Mn^II (S = 5/2) and Co^II (S = 3/2) fragments of complexes 1, 2 and 3 on the basis of the X-ray determined geometry have been carried out with the MOLCAS 7.8 program package.¹⁸ⁱ During the calculations, the other Dy^III, Mn^II and Co^II ions were replaced by diamagnetic Lu^III, Zn^II and Zn^II, respectively. The basis sets for all atoms are atomic natural orbitals from the MOLCAS ANO-RCC library: ANO-RCC-VTZP for Dy^III, Mn^II and Co^II ions; VTZ for close O and N; VDZ for distant atoms. The calculations employed the second order Douglas–Kroll–Hess Hamiltonian, where scalar relativistic contractions were taken into account in the basis set and the spin–orbit couplings were handled separately in the restricted active space state interaction (RASSI-SO) procedure. For the fragment of Dy^III, active electrons in 7 active spaces include all f electrons CAS (9 in 7) in the CASSCF calculation. For Mn^II, CAS (5 in 5) was used. For Co^II, CAS (7 in 10) was used. To exclude all the doubts, we calculated all the roots in the active space. We have mixed the maximum number of spin-free states which was possible with our hardware (all from 21 sextets, 128 from 224 quadruplets, 130 from 490 doublets for the Dy^III fragment; all from 1 sextet, 24 quadruplets and 75 doublets for the Mn^II fragment; all from 10 quadruplets, all from 40 doublets for the Co^II fragment).

Crystallographic data collection and refinement

The crystallographic data of complexes 1 and 2 were collected on a Bruker Smart CCD area-detector diffractometer with Mo-Kα radiation (λ = 0.71073 Å) by using an ω scan mode at 296 K, and of complex 3 were collected on a PHOTON100 CMOS detector with Mo-Kα radiation (λ = 0.71073 Å) by using the ω scan mode at 173 K. The diffraction data were treated using SAINT,^23a and all absorption corrections were applied by using SADABS.^23b All non-hydrogen atoms were located by the Patterson method^23c using the SHELXS programs of the SHELXTL package and subsequent difference Fourier syntheses. Hydrogen atoms bonded to carbon were determined theoretically and refined with isotropic thermal parameters riding on their parents. The H-atoms of methanol were first located by difference Fourier E-maps and then treated isotropically as riding. All non-hydrogen atoms were refined by full-matrix least-squares on F². All calculations were performed by using SHELXTL-97.^23d Complex 3 is a non-merohedral twin, which has two R_int values (0.0519 and 0.0551) corresponding to two crystal domains. The value of 0.0000 in the CIF was automatically generated during refinement. CCDC 1430222–1430224 contain the supplementary crystallographic data for this paper.

Acknowledgements

This work was supported by the Major State Basic Research Development Program (2013CB922102), the National Natural Science Foundation of China (21571097 and 21171089), the Natural Science Foundation of Jiangsu Province of China (BK20130054 and BK20151542), the Specialized Research Fund for the Doctoral Program of Higher Education and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Auxiliary magnetic data and the methods for ab initio calculation. CCDC 1430222–1430224. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c6qi00407e

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