Weak exchange coupling effects leading to fast magnetic relaxations in a trinuclear dysprosium single-molecule magnet

Yin-Shan Meng *ab, Yu-Sen Qiao b, Mu-Wen Yang b, Jin Xiong b, Tao Liu a, Yi-Quan Zhang c, Shang-Da Jiang b, Bing-Wu Wang *b and Song Gao *b
aState Key Laboratory of Fine Chemicals, Dalian University of Technology, 2 Linggong Rd., Dalian 116024, P. R. China. E-mail: mengys@dlut.edu.cn
bBeijing National Laboratory for Molecular Sciences, Beijing Key Laboratory for Magnetoelectric Materials and Devices, Peking University, Beijing 100871, P. R. China. E-mail: wangbw@pku.edu.cn; gaosong@pku.edu.cn
cJiangsu Key Laboratory for NSLSCS, School of Physical Science and Technology, Nanjing Normal University, Nanjing 210023, P. R. China

Received 28th September 2019 , Accepted 30th October 2019

First published on 31st October 2019


Investigating the magnetic anisotropy and magnetic interactions of lanthanide complexes is of vital importance for an in-depth understanding of their magnetic properties. Herein, we reported the synthetic, structural and magnetic studies of a triangular type dysprosium complex (1Dy3, [{(Cp)(Tp*)Ln(μ-bta)}3·2(thf)], Cp = C5H5, Tp* = hydrotris(3,5-dimethyl-1-pyrazolyl)borate anion, btaH = 1H-1,2,3-benzotriazole). 2Dy ([(Cp)Dy(Tp)2·C7H8], Tp = hydrotris(1-pyrazolyl)borate) was investigated by single-crystal angular-resolved susceptibility measurements and computational studies to help understand the magnetic anisotropy of 1Dy3. The easy axis of three DyIII ions in 1Dy3 was orientated out of the triangular dysprosium plane. The exchange interactions were small (−0.85 cm−1) but caused remarkable effects on magnetic relaxations at low temperature. In the temperature range from 2 K to 4 K, magnetic relaxation occurred via the exchange-coupled low-lying excited states, inhibiting magnetic hysteresis. Our study showed that weak intramolecular magnetic interactions can significantly affect the dynamic properties in the low temperature regime.


Introduction

In the last twenty years, molecular nanomagnets have attracted a lot of attention due to their potential applications in high-density information storage and spintronic devices.1 Lanthanide ions, benefitting from the large angular momentum and strong spin–orbit coupling, are considered as promising candidates for constructing single-molecule magnets (SMMs). Until now, people have put a lot of effort in understanding their single-ion magnetic anisotropy and magnetic relaxation behaviours.2–6 These include: the rational design of the crystal field from the view of an electrostatic model;2a–e experimental determination of magnetic anisotropy and energy levels;3,4 in-depth analysis of electronic structures and magneto-structural correlations via ab initio calculations.5 In comparison with 3d metal based SMMs, the magnetic interactions between lanthanide ions are usually weak and of several wavenumbers due to the core-like character of 4f electrons. For mononuclear lanthanide-based SMMs, the magnetic interactions are usually dominated by the intermolecular dipole–dipole interactions, which is one of the most important reasons that result in quantum tunnelling in the ground state. For polynuclear lanthanide complexes, the magnetic interactions become more complicated because the anisotropic superexchange interactions via bridging ligands are involved. A previous study indicated that some dinuclear and trinuclear lanthanide SMMs showed both intramolecular superexchange and dipole–dipole interactions.7 They can sometimes exhibit opening hysteresis near the zero magnetic field as a consequence of exchange bias. Particularly, radical-bridged lanthanide-based SMMs can show relatively larger magnetic interactions,8 wherein the quantum tunnelling of magnetization was largely quenched and opening hysteresis can be observed at up to 14 K.8a To obtain high-performance SMMs, on the one hand, one can design new types of mononuclear lanthanide-based SMMs with ultimate uniaxial anisotropy; on the other hand, one can apply a coupling strategy to manipulate the arrangement of spin carriers and therefore the magnetic interactions between them. Recently, cyclopolyene supported SMMs were synthesized and characterized, showing exceptional relaxation properties.2h,6 Inspired by cyclopolyene/β-diketone supported Dy-SMMs and taking the similarity of cyclopentenyl and hydrotrispyrazolylborate anions into account,9 we followed the hybridization strategy by utilizing cyclopolyenes/Tp* to construct 4f polynuclear SMMs. Herein, we report a trinuclear dysprosium compound [{(Cp)(Tp*)Dy(μ-bta)}3·2(thf)] (1Dy3; Cp = C5H5, Tp* = hydrotris(3,5-dimethyl-1-pyrazolyl)borate anion, btaH = 1H-1,2,3-benzotriazole). The magnetic interactions were evaluated based on the ab initio calculated results and the effects on its magnetic relaxation properties were discussed. To help understand the magnetic anisotropy of 1Dy3, the mononuclear analogue [(C5H5)Dy(Tp)2·C7H8] (2Dy; Tp = hydrotris(1-pyrazolyl)borate anion) was also synthesized and investigated.

Results and discussion

Structural characterization

The synthesis of [{(Cp)(Tp*)Ln(μ-bta)}3·2(thf)] was previously reported by Zhou and co-workers, wherein the lanthanide ion was erbium instead of dysprosium.10 Different from the reported method, we used halide precursor Cp2DyCl reacting with one equivalent KTp* and one equivalent benzotriazole in THF for 24 h. The colorless crystals of 1Dy3 suitable for X-ray diffraction were obtained by slow diffusion of hexane into THF solution. 1Dy3 crystallizes in a monoclinic space group P21/c. There are two uncoordinated THF molecules co-crystallized within the asymmetric unit. Each Dy3+ ion is coordinated with one η5-Cp ion, one κ3-Tp* ion and two N atoms from bta brigding ligands (Fig. 1a). The bond lengths and angles for each DyIII ion are similar to each other, as shown in Table 1. The deprotonated bta ligand shows the delocalized nature of π electrons, as indicated by the bond lengths of the N[double bond, length as m-dash]N bond and N–N bond (1.33(1) Å vs. 1.349(7) Å). The average Dy–C bond length is 2.669 Å. The average Dy–N bond length (2.491 Å) from Tp* is slightly longer than that from the bta bridges (2.462 Å). The angles formed by the N atoms of bta ligands and DyIII ions are in the range of 94.5–99.2°. The nearest intermolecular Dy⋯Dy distance is 9.110 Å. Considering the distances and bond angles between DyIII ions, the intramolecular superexchange interaction via the bta bridge (Jex) and intramolecular dipole–dipole interaction (Jdip) should mainly account for magnetic interactions. The mononuclear analogue 2Dy was synthesized by mixing [(Cp)2DyCl]x with two equivalents of KTp in toluene and recrystallized at −25 °C. Complex 2Dy crystallizes in an orthogonal space group Pnma with one highly disordered toluene molecule inside the lattice. The crystallinity of 2Dy was kept well at room temperature for several weeks under an inert atmosphere. The co-crystallized toluene molecules can be removed when heating under vacuum, resulting in a solvent-free and amorphous form, named 2Dy′. The structure of 2Dy has a mirror plane through the DyIII ion and 2Dy shows a similar local coordination environment to 1Dy3. The κ2-Tp ion coordinates to the DyIII ion instead of the bta ligands (Fig. 1b). The Dy–N bond length between the DyIII ion and κ3-Tp is slightly shorter than that in 1Dy3 (2.468 Å vs. 2.491 Å). The Dy–N bond length between the DyIII ion and κ2-Tp is also shorter than that in 1Dy3 (2.433 Å for 2Dyvs. 2.462 Å for 1Dy3). The major difference between them is the angle formed by the κ2-Tp and DyIII ion (see Table 1).
image file: c9qi01252d-f1.tif
Fig. 1 Chemical schemes of 1Dy3 (a). Molecular structures of 1Dy3 (b) and 2Dy (c). The co-crystallized THF and toluene and hydrogens are omitted for clarity. Color code: C, grey; N, blue; B, light orange; Dy, yellow.
Table 1 Selected Distances (Å) and Angles (°) for 1Dy3 and 2Dy
Complex 1Dy3 (a) 1Dy3 (b) 1Dy3 (c) 2Dy
a Average value of Dy–N bond lengths from tridentate Tp*/Tp. b Dy–N bond lengths from bidentate Tp for 2Dy. c Intramolecular distances for 1Dy3 and intermolecular distance for 2Dy.
Dy–C(Cp) 2.673(7) 2.668(8) 2.666(8) 2.656(7)
Dy–Centroid(Cp) 2.395(4) 2.389(4) 2.384(3) 2.379(4)
Dy–N(κ3-Tp*/κ3-Tp)a 2.491(7) 2.484(6) 2.499(6) 2.468(6)
Dy–N1(benzotriazole/κ2-Tp)b 2.457(5) 2.475(6) 2.470(6) 2.433(5)
Dy–N2(benzotriazole/κ2-Tp)b 2.454(7) 2.472(6) 2.447(8) 2.433(5)
∠N1–Dy–N2 94.5(2) 99.2(1) 95.1(2) 79.5(1)
Dy⋯Dyc 6.497(6) (a⋯b) 6.577(6) (b⋯c) 6.547(5) (c⋯a) 8.009(4)


Magnetic properties

Direct current (DC) susceptibility measurements were performed on polycrystalline samples of 1Dy3 and 2Dy. At room temperature, the χmT value for 1Dy3 is 41.43 cm3 mol−1 K, in accordance with the theoretical values of three DyIII ions (42.51 cm3 mol−1 K). Upon cooling, the χmT value decreased slowly and began to go down rapidly at 20 K. The χmT value at 2 K is 28.38 cm3 mol−1 K. This decrease can be attributed to depopulation of the stark level and/or antiferromagnetic interaction which are expected to operate at low temperature. The χmT values for 2Dy and 2Dy′ are 14.01 and 14.67 cm3 mol−1 K, respectively. Below 10 K, the χmT value for 2Dy showed an unprecedented increase. This increase could be due to: 1. dipole–dipole interaction from adjacent molecules whose easy magnetic axis is nearly along the same direction; 2. the preferred orientation of polycrystals along the magnetic field. The reorientation was excluded by repeated DC susceptibility measurements. The diluted 2Dy in the diamagnetic Y matrix did not show this anomaly, suggesting that this χmT rise at low temperature was induced by the intermolecular dipole–dipole interaction (Fig. 2, pink circles). The temperature-dependent susceptibility measurement was also conducted on solvent-free phase 2Dy′, which lost the crystallinity after removing the lattice toluene molecule. The χmT rise for 2Dy′ became less pronounced.
image file: c9qi01252d-f2.tif
Fig. 2 χ m T vs. T plots. The red line represents the simulation from CASSCF POLY_ANISO calculated results. The χmT value of diluted 1Dy3 was evaluated on account of per dysprosium ion.

Dynamic magnetic properties

Alternating current (AC) susceptibility measurements were performed to investigate their magnetic relaxation properties. For 2Dy, Fig. 3a shows the temperature-independent quantum tunnelling of magnetization (QTM) in the absence of external field below 10 K. Above 10 K, the out-of-phase signals exhibited temperature- and frequency-dependent behaviour. 2Dy′ also exhibited similar behaviour. The QTM relaxation time τQTM of 2Dy is slightly longer than that of amorphous 2Dy′ (0.075 ms vs. 0.049 ms) (Fig. 3(a), (b), (d) and (e)), possibly due to the different local coordination environments and/or different intermolecular interactions. The frequency-dependent AC susceptibilities were plotted as the Argand diagram and fitted with a generalized Debye model (Fig. S1). The distribution of relaxation times α is relatively large below 10 K (0.11–0.21 for 2Dy and 0.08–0.16 for 2Dy′, respectively). The ln[thin space (1/6-em)]τ versus T−1 plots showed nonlinearity even in the high temperature regime. Therefore, we could not apply Arrhenius fitting to obtain the thermal energy barriers in the absence of the DC field. We subsequently applied an optimized 1 kOe DC field in the AC measurement, which was sufficient to suppress the QTM (Fig. S2). The fitted Ueff for 2Dy and 2Dy′ is 55 and 68 cm−1, respectively (Fig. S3,Fig. 3d and e). In comparison with the calculated energy differences between the ground and first excited Kramers doublets (187 cm−1, Fig. 4a), the obtained effective energy barriers are much smaller, suggesting that the reversal of magnetic moment was not via the first excited state. Other relaxation mechanisms such as the Raman process may take a part instead of the Orbach process. We then used the power law τ−1 = CTn to fit the ln[thin space (1/6-em)]τ versus T−1 plots. The obtained n value is 4.61 and C value is 0.064 s−1 Kn for 2Dy, suggesting that the Raman process should be responsible for the magnetic relaxation.11
image file: c9qi01252d-f3.tif
Fig. 3 Out-of-phase signals (χ′′m) versus frequency (υ) plots for 2Dy (a), 2Dy′ (b) and 1Dy3 (c); relaxation times (τ) versus T−1 plots for 2Dy (d), 2Dy′ (e) and 1Dy3 (f), respectively. The blank circles from 2 K to 6 K in (f) represented the fast magnetic relaxation process, as can been seen in (c). The red lines represented the Arrhenius fitting. The green lines represented the power law fitting.

image file: c9qi01252d-f4.tif
Fig. 4 The magnetization blocking barriers for 2Dy and each DyIII ion in 1Dy3, represented by (a)–(d). 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 the off-diagonal relaxation process. The numbers at each arrow stand for the mean absolute value of the corresponding matrix element of transition magnetic moment.

Dynamic magnetization studies on 1Dy3 revealed that 1Dy3 showed typical thermally activated relaxation between 4 K and 19 K in the absence of DC field (Fig. 3c). The fitted Ueff is 74 cm−1 with a pre-exponential factor τ0 of 6.6 × 10−8 s (Fig. 3f and Fig. S4). Compared with the previously reported bta-bridged dysprosium dimer ([{Cp2Dy(μ-bta)}2]) (Ueff = 32 cm−1),12 the blocking barrier is increased, possibly because: 1. the utilization of Tp* instead of Cp is beneficial to the enhancement of single-ion magnetic anisotropy; the DyIII ions in 1Dy3 feel a relatively weaker equatorial ligand field from the bta bridges than that in [{Cp2Dy(μ-bta)}2]. The fast QTM relaxation process which almost dominated the overall magnetic relaxation in 2Dy and 2Dy′ was not so remarkable in 1Dy3. The suppression of QTM can be attributed to the intramolecular exchange interactions via the bta ligands, which were also observed in other exchange bias mediated SMMs.7,8 One can also note that there was another fast magnetic relaxation process observable below 4 K. The relaxation time distribution of this fast relaxation process is rather large as indicated by the very broad resonant peaks below 4 K (Fig. 3c). We then performed field-dependent AC measurement and found that this fast magnetic relaxation process disappeared below 4 K under an optimized 3 kOe DC field (Fig. S5 and S6). This applied field is three times larger than the applied field in the AC measurements for 2Dy and 2Dy′. We further performed a magnetic dilution experiment on 1Dy3 in an yttrium matrix with a Dy[thin space (1/6-em)]:[thin space (1/6-em)]Y ratio of 6.6[thin space (1/6-em)]:[thin space (1/6-em)]93.7. The AC measurement in the absence of DC field clearly showed the frequency-dependent thermal relaxation behaviour between 10 K and 20 K (Fig. S7), in agreement with that of pure 1Dy3. The QTM in diluted 1Dy3 can be fully suppressed by applying only 1 kOe DC field (Fig. S8), indicating that the magnetic relaxation in high temperature region (10 K–20 K) in 1Dy3 is of single-ion origin. For diluted 1Dy3, the fitted effective energy barrier is 83 cm−1 with a pre-exponential factor τ0 of 6.1 × 10−8 s (Fig. S9 and S10). The large difference between the fitted energy barrier and calculated one excluded the Orbach mechanism for the magnetic relaxation. The power law fitting gave a n value of 5.52, similar to the fitting results of 2Dy and 2Dy′. The similar dynamic magnetic properties of diluted 1Dy3 and 2Dy are reasonable since the DyIII ions share similar coordination environments. In comparison with the diluted 1Dy3 and 2Dy, a larger external DC field is needed to suppress fast magnetic relaxation below 4 K for pure 1Dy3. Another difference is that the fast relaxation process is well separated with the thermal relaxation process (Fig. 3c and f). All of these results suggest that this fast relaxation process from 2 K to 4 K in 1Dy3 was associated with intramolecular exchange interactions.

Magnetic anisotropy analysis

The in-depth investigation of the magnetic interactions in 1Dy3 lies on the understanding of single-ion magnetic properties, which can be referred to as the 2Dy, whose local environment is similar to that of 1Dy3. We firstly applied ab initio calculations on 2Dy and each DyIII ion in 1Dy3 based on their X-ray diffraction determined structures. The calculated results indicated that the ground Kramers doublet is approximately Ising type, showing some mixing with the components of MJ = ±|13/2〉and ±|11/2〉 (less than 5%). The non-negligible transversal components (gx,y = 0.32 × 10−2–0.62 × 10−2) should be responsible for the observed fast QTM in 2Dy and diluted 1Dy3 (Fig. 4, Table S2). The calculated easy axis of 2Dy is oriented near to the Dy–N(κ3-Tp) direction, as shown in Fig. 5a. We then further performed the angular-resolved susceptibility measurement on a single crystal of 2Dy (Fig. S11 and S12). As shown in Fig. 4a, the obtained easy axis of the single crystal framework is right orientated to the c axis with a small deviation (6.2°). The eigen value of the g tensor in the single crystal framework also agrees well with the ab initio calculated results (18.09 vs. 18.52 for the easy axis direction). Previously, Sessoli and co-workers have performed an angular-solved magnetization study on a [(Cp*)Er(COT)] single-ion magnet.13 In that case the molecule also crystallized in space group Pnma. The single crystal of [(Cp*)Er(COT)] showed the easy plane anisotropy due to the highly tilted orientation of the molecular easy axis in one unit cell. Therefore, it is not possible to determine the molecular easy axis experimentally. Compared with [(Cp*)Er(COT)], the single crystal of 2Dy exhibited uniaxial magnetic anisotropy. We note that the calculated easy axis of the molecule is close to the crystallographic c axis with an angle of 20.4° (Fig. 5a and b). Therefore, the single crystal showing uniaxial magnetic anisotropy is reasonable and supports the theoretically predicted easy axis orientation of 2Dy. However, one should note that the small geometric structural differences in their DyIII coordination spheres should be responsible for their different electronic structures.
image file: c9qi01252d-f5.tif
Fig. 5 (a) Experimental (red) and ab initio calculated (green) magnetic main axis for the crystal framework and molecular one, respectively. The pale blue plane represented the mirror. The black line represented the direction of the c axis; (b) ab initio calculated (green) magnetic main axis represented within the ac plane; (c) ab initio calculated (green) magnetic main axis for 1Dy3; (d) schematic diagrams of the orientations of the main magnetic axis of each DyIII ion. θ is defined as the angle between the easy axis and tangential direction and φ is the angle between the easy axis and Dy3 plane.

Magnetic interaction analysis

As the DyIII ions in 1Dy3 share a similar coordination environment to those in 2Dy, we then used the ab initio calculated results of 1Dy3 in the next step of magnetic interaction analysis. The gz values for dysprosium fragments in 1Dy3 are 19.72, 19.73 and 19.74, respectively, all close to 20 (Table S2). Thus, the DyIII ion can be treated as the Ising type. The calculated main magnetic axis of each DyIII ion is near to the Dy–N (κ3-Tp*) direction (Fig. 5c and d, Table 2), similar to that for 2Dy. The easy axis of three DyIII ions is orientated out of the triangular dysprosium plane and forms an average angle of 73.5° with the Dy3 triangle plane (Fig. 5c and d). We note that the calculated results demonstrated the similarity of three DyIII ions, as indicated by the energy splitting and magnetic anisotropies of low-lying states (Table S2). Therefore, we assumed that the superexchange interactions Jexch were equal between three DyIII ions. By utilizing the Lines model,14 the spin Hamiltonian was written as: Hexch = −JtotalS1zS2zJtotalS2zS3zJtotalS3zS1z (Jtotal = Jexch + Jdip), where the S was treated as pseudospin 1/2. Jdip parameters were calculated on account of the X-ray determined molecular structures using the following eqn (1):
 
image file: c9qi01252d-t1.tif(1)
where |r| was the distance between two DyIII ions and θ was the angle between the r vector and easy axis. The susceptibilities of 1Dy3 were simulated with the above Hamiltonian considering all calculated eight energy levels of ground multiplets of three DyIII ions using the POLY_ANISO program.15 As shown in Fig. 2, the simulated χmT plots agreed well with the experimental ones. The fitted Jtotal is −0.87, −0.85 and −0.86 cm−1, respectively. Compared with the previously reported toroidal magnetic trinuclear compound [Dy33-OH)2L3Cl(H2O5)]Cl3 (the exchange interaction was about 7.3 cm−1),4c the magnitudes are rather small. This is reasonable since exchange interactions for 1Dy3 go through a longer pathway via three-membered bta-bridges exceeding 6.5 Å. The three DyIII ions formed four exchange-coupled low-lying Kramers doublets. The exchange-coupled low-lying states are depicted in Fig. 6. The ground states consist of three quasi-degenerate states (0 cm−1, 0.004 cm−1 and 0.011 cm−1), wherein two spins are up and one spin is down. The excited exchange states with all spin up and/or down are only 0.84 cm−1 higher. As a consequence, the fast magnetic relaxation process shown in Fig. 3c may occur via the excited exchange states even at low temperatures. The ratio values of Boltzmann distributions for the low-lying state (0.84 cm−1) and ground state (0 cm−1) were found to be 1.02, 2.27 and 5.68 at 1.8, 4 and 10 K, respectively. It means that when the temperature was increased, the excited exchange states were already thermally populated, responsible for the disappearance of fast magnetic relaxation.

image file: c9qi01252d-f6.tif
Fig. 6 Exchange-coupled low-lying states for 1Dy3. The thick black lines represent the exchange Kramers doublets as a function of their magnetic moment along the magnetic axis. The green lines correspond to diagonal quantum tunneling of magnetization (QTM), the blue lines represent the off-diagonal relaxation process. The numbers at each arrow stand for the mean absolute value of the corresponding matrix element of the transition magnetic moment.
Table 2 Angles between the easy axis and Dy–N (κ3-Tp*) direction (α), between the easy axis and tangential direction (θ), and between the easy axis and Dy3 plane (φ). Fitted exchange interactions from χmT vs. T plots
1Dy3 Dy(1) Dy(2) Dy(3)
α 4.76 5.10 4.27
θ 74.04 73.38 73.45
φ 73.96 73.32 73.36

  Dy(1)–Dy(2) Dy(2)–Dy(3) Dy(3)–Dy(1)
J ex −0.22 −0.22 −0.22
J dip −0.65 −0.63 −0.64
J tol −0.87 −0.85 −0.86


Conclusions

In summary, we have investigated the weak exchange coupling effects on the magnetic relaxations in [{(Cp)(Tp*)Ln(μ-bta)}3·(thf)2] (1Dy3). Its mononuclear analogue [(Cp)Dy(Tp)2·C7H8] (2Dy) was also investigated by a combination of magnetic measurements, angular-resolved magnetization measurements and ab initio calculations to elucidated the magnetic anisotropy. The main magnetic axes are orientated near to the Dy–N(κ3-Tp/Tp*) direction for both 1Dy3 and 2Dy. The thermally activated magnetic relaxation of 1Dy3 at high temperature is of single-ion origin. The fast magnetic relaxation at low temperature can occur via the excited exchange-coupled low-lying states. Although intramolecular magnetic interactions are comparably small, it can significantly affect the dynamic properties in the low temperature regime. To further design new high-performance SMMs featuring high blocking temperature, one should avoid the low-temperature fast relaxation process caused by the QTM and/or weak intramolecular exchange interactions. One can refer to radical bridges to link high-performance single-ion magnets and take advantage of strong exchange coupling and Ising type anisotropy together. On the other hand, if the Ising type DyIII ions were in a head-to-head mode and the magnetic easy axis were colinear, the magnetic interactions would prefer the ferromagnetic one. And the uniaxiality of the low-lying exchange-based levels would be enhanced and the fast tunneling will be suppressed, resulting in an opening hysteresis at higher temperatures. This work is under way.

Experimental section

Materials and methods

The synthesis of air and/or moisture sensitive compounds was carried out under an atmosphere of argon using Schlenk techniques or in an argon filled glovebox. THF and hexane were dried in a solvent purification system, transferred under vacuum, and stored in the glovebox. Precursor [Cp2LnCl]x (Ln = Dy and Y) was prepared according to literature procedures with some modifications.16 Unless otherwise noted, all starting materials were commercially available and were used without further purification. Elemental analysis was performed by using an Elementar Vario MICRO CUBE (Germany). The ICP analysis was performed by using an Inductively Coupled Plasma-Atomic Emission Spectrometer designed by Leeman company.
1Dy3 . A THF solution (10 mL) of Tp*K (555.1 mg, 1.65 mmol) and btaH (182.5 mg, 1.65 mmol) was slowly added to the solution of [Cp2DyCl]x (541.2 mg, 1.65 mmol) in THF and stirred overnight. The precipitates were filtered and the solvent was removed under vacuum and dissolved in 3 mL THF. The colorless single crystals were obtained by slow diffusion of hexane into THF solution for several days. Yield: 378 mg. Anal. Calcd (%) for C86H109B3Dy3N27O2: C, 49.82; H, 5.30; N, 18.24. Found: C, 50.05; H, 5.71; N, 17.75.
2Dy . A toluene solution (10 mL) of TpK (615.2 mg, 2.44 mmol) was added into the slurry of [Cp2DyCl]x (400 mg, 1.22 mmol) in toluene and stirred for 24 h. The precipitates were filtered and the solution was concentrated to 5 mL. The large single crystals were obtained at −25 °C. Yield: 452 mg. Anal. Calcd (%) for C23H25B2DyN12(C7H8): C, 48.31; H, 4.46; N, 22.53. Found: C, 48.27; H, 4.54; N, 22.40.
2Dy′ . The co-crystallized toluene molecule was removed by grinding the crystals into powders and was heated under vacuum. Anal. Calcd (%) for C23H25B2DyN12: C, 42.26; H, 3.85; N, 25.71. Found: C, 42.56; H, 3.97; N, 25.87.
Diluted 2Dy. 2Dy and its Y analog [(Cp)Y(Tp)2·C7H8] were co-crystallized with a molar ratio of 5[thin space (1/6-em)]:[thin space (1/6-em)]95 in toluene under −25 °C.
Diluted 1Dy3. [Cp2DyCl]x and [Cp2YCl]x were mixed in 5[thin space (1/6-em)]:[thin space (1/6-em)]95 molar ratio, and subjected to the same procedure as 1Dy3. The obtained crystals are isostructural to the pure 1Dy3. The unit cell parameter is a = 14.6667(8) Å, b = 22.3993(7) Å, c = 14.6667(8) Å, α = 90°, β = 101.426(4)°, γ = 90°, V = 9222.3(7) Å3. The final ratio is determined by ICP with a Dy[thin space (1/6-em)]:[thin space (1/6-em)]Y molar ratio of 6.6[thin space (1/6-em)]:[thin space (1/6-em)]93.7.

X-ray crystallography and magnetic measurement

All crystals were manipulated under a nitrogen atmosphere and covered in grease. Data collections were performed at 180 K on an Agilent technologies Super Nova Atlas Dual System, with a (Mo Kα = 0.71073 Å) microfocus source and focusing multilayer mirror optics. The structures were solved by direct methods and refined by the full-matrix least-squares technique based on F2 using the Olex2 program.17 All non-hydrogen atoms were refined anisotropically. All hydrogen atoms were placed at the calculation positions.

Samples were fixed by N-grease to avoid moving during measurement. A direct current susceptibility experiment was performed on a Quantum Design MPMS XL-5 SQUID magnetometer on a polycrystalline sample. Alternative current susceptibility measurement with frequencies ranging from 100 to 10[thin space (1/6-em)]000 Hz was performed on a Quantum Design PPMS and ranging from 1 to 1000 Hz was performed on a Quantum Design MPMS-XL5 SQUID magnetometer on a polycrystalline sample. All dc susceptibilities were corrected for diamagnetic contribution from the sample holder, N-grease and diamagnetic contributions from the molecule using Pascal's constants.

Angular-resolved magnetometry measurement was performed using a Quantum Design horizontal rotator. The faces of suitable single crystals of 2Dy were indexed on an Aglient technologies Super Nova Atlas Dual System. The experimental Cartesian coordinates XYZ were defined as follows. We define the crystallographic cb direction parallel to the X axis, and the -a direction parallel to the Z axis. The crystal was fixed using N-grease on the plate of the rotator. Then we performed the rotation measurement along defined XYZ axes under applied 1 kOe dc field (Fig. S11). The obtained g values along the main magnetic axes were derived by applying the equation: g = (32χmT/3)1/2 (Fig. S12). As the mass of the sample cannot be obtained with required accuracy, we compared the mass from electronic balance and the product of density and volume. All data were corrected for the diamagnetic contribution from the grease and rotator.

Ab initio calculations

Complete-active-space self-consistent field (CASSCF) calculations on the complete structures of complexes 1Dy3 and 2Dy on the basis of X-ray determined geometry have been carried out with a MOLCAS 8.0 program package.18 For CASSCF calculations, the basis sets for all atoms are atomic natural orbitals from the MOLCAS ANO-RCC library: ANO-RCC-VTZP for the DyIII ion; VTZ for close C 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 coupling was handled separately in the restricted active space state interaction (RASSI-SO) procedure. The active electrons in 7 active spaces included all f electrons (CAS(9 in 7)) in the CASSCF calculation. To exclude all the doubts we calculated all the roots in the active space. We have mixed all of the possible spin-free states. The information about the magnetic anisotropy was obtained by applying the SINGLE_ANISO program. And the susceptibility simulation and exchange coupled low lying states were obtained by applying the POLY_ANISO program, where the eight Kramers doublets of the ground multiplet (6H15/2) were all considered.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (21801037, 21621061, 21290171, 21571008 and 91422302), the National Key R&D Program of China (2017YFA0206301 and 2017YFA0204903), the Natural Science Foundation of Jiangsu Province of China (BK20151542) and the Fundamental Research Funds for the Central Universities, China.

Notes and references

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Footnote

Electronic supplementary information (ESI) available: Additional structures, IR spectra, thermal stability analysis, DSC and magnetic data. CCDC 1521818 and 1521819. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c9qi01252d

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