Desolvation-Driven 100-Fold Slow-down of Tunneling Relaxation Rate in Co(II)-Dy(III) Single-Molecule Magnets through a Single-Crystal-to-Single-Crystal Process

Single-molecule magnets (SMMs) are regarded as a class of promising materials for spintronic and ultrahigh-density storage devices. Tuning the magnetic dynamics of single-molecule magnets is a crucial challenge for chemists. Lanthanide ions are not only highly magnetically anisotropic but also highly sensitive to the changes in the coordination environments. We developed a feasible approach to understand parts of the magneto-structure correlations and propose to regulate the relaxation behaviors via rational design. A series of Co(II)-Dy(III)-Co(II) complexes were obtained using in situ synthesis; in this system of complexes, the relaxation dynamics can be greatly improved, accompanied with desolvation, via single-crystal to single-crystal transformation. The effective energy barrier can be increased from 293 cm−1 (422 K) to 416 cm−1 (600 K), and the tunneling relaxation time can be grown from 8.5 × 10−4 s to 7.4 × 10−2 s. These remarkable improvements are due to the change in the coordination environments of Dy(III) and Co(II). Ab initio calculations were performed to better understand the magnetic dynamics.

The ground J manifold of the lanthanides could be regarded as the spin S in the case of classical spin magnets, such as Mn 12 Ac 1 . Large zero-field splitting of the latter is difficult to induce, i.e., the zero-field splitting parameter D is typically small, whereas the typical splitting of the ground J manifold of lanthanides in the absence of applied field is as large as several hundreds of wavenumbers (cm −1 ). Furthermore, the advantage of the crystal-field induced magnetic axiality in anisotropic Ln(III) ions compared with that induced by zero-field splitting in polynuclear complexes is that the environment surrounding a single metal (Ln) ion can be rationally designed, modified and adapted by using various terminal groups, solvents, or counterions. In this manner, the non-axial terms of the crystal-field Hamiltonian can be diminished, thus making them unimportant for the magnetic anisotropy in the low-lying states. We have recently found that quasi-D 5h environment of the Dy(III) ion in Zn-Dy-Zn 15 and Fe-Dy-Fe 17 compounds leads to strong magnetization blocking. Herein, we go beyond the previous analysis and attempt to understand the structural reasons for such strong magnetic blocking in a series of Co-Dy-Co complexes having similar quasi-D 5h symmetry of the Dy(III). Moreover, we demonstrate that the non-bonded co-crystallized water molecules influence directly the structural environment of the Dy(III) and Co(II) sites, having crucial consequences on increasing the magnetization-blocking barrier in this series as well as the magnetic relaxation time.
All molecular structures of this [Co II 2 Dy III ] series contain a 7-coordinate (compressed pentagonal bipyramid, D 5h ) Dy(III) ion at the center and two asymmetric 6-coordinate Co(II) at the two sides ( Fig. 1). Upon removing the outer water molecules, the bond between Dy(III) and the terminal water molecule becomes significantly longer, from 2.419(4) to 2.508 (19) Å, as presented in Table 1. The five equatorial atoms are more coplanar, as indicated by the decrease of the standard deviation of the distance to its least-squares plane, from 0.226 to 0.076 Å. Thus, the geometry of Dy(III) for 1 deviates less than that of 1•3H 2 O (see the Continuous Symmetry Measures (CSM) values calculating by program Color Codes: Dy, gold; Co, violet; Br, brown; O, red; N, blue; C, silver. Dashed lines represent the main anisotropy axes g Z on the individual metal sites. Green arrows show the orientation of magnetic moments in the ground exchange state. The deviations of the local moments on Co(II) sites from their local z direction (dashed) is due to relatively strong ferromagnetic Ising-type exchange interaction with the Dy(III) site. The magnetic moment on the Co(II) site is particularly small in the ground exchange state. The reduction of the magnetic moment arises from the Ising-type exchange interaction with the Dy(III), which conserves the moment in the z direction of the latter.
Scientific RepoRts | 5:16621 | DOI: 10.1038/srep16621 SHAPE) 26 . Furthermore, the geometries of the two asymmetric Co(II) are transformed from distorted octahedron (O h ) to the intermediate between octahedron and trigonal prism (D 3h ) according to the CSM values, and both of Dy-Co1 and Dy-Co2 distances increase slightly by 0.05-0.08 Å.
Measurements of the ac susceptibilities were performed to probe the magnetic dynamics of [Co II 2 Dy III ] compounds (Fig. 3). Temperature-and frequency-dependent ac signals of these compounds indicate slow magnetic relaxation under zero field. These signals were fitted using a generalized Debye model ( Figure S5) 28 , revealing narrow distributions of the relaxation times (α parameters: 0.05-0.10 for 1•3H 2 O and 0.00-0.13 for 1).
In general, the relaxation rate (τ −1 ) is a combination of the Orbach process (τ Orbach −1 ~ exp(− U eff /k B T)), the direct and Raman process (τ Orbach −1 ~ T n ; n = 1 for direct process, 4 ≤ n ≤ 9 for typical Raman process), and the QTM process (τ QTM  The best fits for all compounds obtained using this model are displayed in Fig. 4 and Table 2. These three different mechanisms of magnetic relaxation are dominant at high-, intermediate-, and low-temperature regimes, respectively, giving rise to three trends: 1. Enhancing anisotropy barriers, 293 cm −1 (422 K) for 1•3H 2 O < 416 cm −1 (600 K) for 1; 2. Weakening direct process, n = 1 for 1•3H 2 O vs. n = 3.2 for 1; 3.   Figure S7 and Table 2). The differences may be caused by tiny structural changes (inherent nature), doping of each other (magnetic dipolar interactions) and measurement/fitting errors (especially the high-temperature regime). As single-crystal X-ray diffraction can only provide an average structure, determining the difference between 1•H 2 O and the other two structures is not guaranteed. However, the discrete relaxation dynamics in 1•H 2 O confirms that the outer environment of the molecules indeed results in distinct magnetic behaviors, which we discuss based on the corresponding solvated (1•3H 2 O) and desolvated (1) analogs.     Ab initio calculations of the CASSCF/RASSI-SO/SINGLE_ANISO type using the MOLCAS program package 18,32 were performed to determine the local electronic and magnetic properties on individual metal sites. We refer to the ESI for the computational details and the complete set of results. Here, we discuss the main findings.
As expected, Dy(III) sites in 1 and 1·3H 2 O were found to have strong uniaxial magnetic anisotropy in their ground doublet states (Fig. 1). Table 3 presents the ab initio calculated low-lying energy spectrum on metal sites in the investigated compounds, and Table 4 provides information related to magnetic anisotropy in the ground and first-excited Kramers doublet (KD) states. The obtained magnetic axiality is comparable with the magnetic anisotropy of the Dy(III) in the Zn(II)-Dy(III)-Zn(II) 15 and Fe(II)-Dy(III)-Fe(II) 17 compounds, where the main anisotropy axes on Dy(III) had similar orientations. We can see from Table 4 that the transversal g-factors for the first excited KD are much smaller in 1 compared to 1·3H 2 O, implying a higher axiality of the excited states in the former compound. Therefore, while the activation barrier corresponds to the first excited KD in 1·3H 2 O, it corresponds to a higher KD in 1, which explains the observed large discrepancy in the relaxation barriers of two compounds ( Table 2).
To understand the obtained strong magnetic axiality of the Dy(III) in this coordination environment, we analyzed the main structural features underlying the strongest axial effect on this metal site. Table 1 presents the main structural differences between the investigated compounds.
The main anisotropy axis is oriented along the two shortest bonds of the Dy(III) -along the axis connecting oxygen atoms O1 and O4. The short chemical bond means the strong covalent effect arising from these two oxygen atoms. Moreover, oxygen atoms O1 and O4 hold the largest negative electronic charge. The calculated LoProp charges 33 are listed in Tables S7 and S8. This result demonstrates that the total axial crystal-field effect on Dy(III), comprising both covalent effect (short chemical bond) and electrostatic (largest negative charge) from the oxygen atoms O1 and O4, is dominant, defining the orientation of the magnetic axis in these compounds. Indeed, because the axial crystal-field effect of any other ligand atoms cannot overcome the effect of the O1 and O4 atoms (if that was the case, the anisotropy     Table S6 contains the full set of ab initio extracted crystal-field parameters. Analyzing the splitting induced by individual parameters of each rank, the second-rank terms induce the largest crystal-field splitting, although the fourth-order ones are also important. In particular, the B 4 0 axial parameter imposes the high axiality of the ground doublet state and the large energy separation between the ground and the first-excited doublet states. The first coordination environment of Co(II) in 1 and 1·3H 2 O is far from any point group symmetry. However, Table 3 illustrates the tendency that the zero-field splitting of the ground spin state S = 3 / 2 of both Co(II) sites in 1 is significantly smaller than the zero-field splittings of these sites in 1·3H 2 O. Because the size of the zero-field splitting is directly proportional to the effect of spin-orbit coupling, we may assume that the unquenched orbital momentum on the Co(II) sites in 1 is smaller than that in 1·3H 2 O. Indeed, these assumptions are found to be qualitatively correct from Table 4.
The origin of stronger quenching of angular momentum in 1 can be understood by the larger "D 3h " character according to calculated CSM values, which would ideally stabilize a non-degenerate 4 A 1 electronic ground state, implying that the spin-orbit coupling effect arises only in the second order of the perturbation theory. By contrast, both Co(II) sites in 1·3H 2 O exhibit a larger "O h " character according to calculated CSM values, which means that the ground state is ideally triply degenerate 4 T 1g , involving the spin-orbit coupling already in the first order of perturbation theory.
The obtained ab initio results for individual metal sites were further used for the computation of the exchange spectrum and the magnetic properties of the trinuclear complexes using the POLY_ANISO program 18,34 . The exchange interactions of Dy(III)-Co(II) and Co(II)-Co(II) are considered within the Lines model 35 (see ESI for more details), whereas the contribution of the intramolecular dipole-dipole magnetic coupling is precisely accounted for because all of the necessary data are available from the ab initio calculations. The best fitting parameters of the Lines model for the investigated compounds are presented in Table 5. All of the macroscopic magnetic properties were computed based on the resulting exchange spectrum of the complex. The estimation of the exchange couplings via broken-symmetry density functional theory (BS-DFT) calculations used within the ORCA 3.0.0 program 36 (see ESI for more details) on isostructural CoGdCo (using the experimental structures of 1 and 1·3H 2 O) provided slightly overestimated values.
The total magnetic interaction (exchange + dipolar) between the lowest Kramers doublets on the sites can be cast in a good approximation by the non-collinear Ising Hamiltonian: Co is the spin corresponding to the Co(II) sites.
The low-lying exchange doublets arising from the magnetic interactions of the ground manifold of two Co(II) sites (S = 3 / 2 , split by ZFS) and the ground doublet ( = / ) S 1 2 Dy on the Dy(III) ((2 × 3 / 2 + 1) 2 × ( 1 / 2 × 2 + 1) = 32, 16 doublets) are quite axial (g X , Y < 10 −2 , see the ESI), implying a partially suppressed QTM in the tunneling regime, which is established at very low temperature, when only the ground exchange doublet (with zero energy in Table 5) is effectively populated. This regime was not achieved in the present work because of measuring temperature exceeding 2 K.
Magnetic relaxation in the high temperature regime, i.e., at temperatures much higher than the exchange splitting, occurs via intraionic Orbach mechanism involving local excited Kramers doublets of the Dy(III) only. Due to high activation energy for this relaxation, its rate decreases quickly with lowering the temperature, so that at T < 20 K another relaxation mechanism becomes dominant, as can be seen in Fig. 4. The weak temperature dependence of ln(τ) in this domain suggests a relaxation of QTM type, which involves again intraionic transitions on Dy(III) sites only. The reason why the relaxation remains of intraionic character is the still relatively high temperature, exceeding much the exchange splitting in both compounds ( Table 5). Given that Dy(III) is a Kramers ion, it requires the presence of a transversal magnetic field (directed in one of the two perpendicular directions to its main magnetic axis, see Fig. 1) to induce tunneling splitting and QTM relaxation. This is provided by the neighbor Dy(III) and Co(II) ions, which are sources of oscillating magnetic field 37 . It is natural to assume that the cobalt ions within the same complex will produce a stronger splitting of the ground KD of Dy(III) due to its small distance to the latter, giving rise also to the exchange interaction (see Table 5). However, the close resemblance of the relaxation curves for 1 in Fig. 4 and for the isostructural ZnDyZn complex 15 (cf. Fig. 4 in the latter reference) points at a more significant role played by the neighbor Dy(III) ions in this relaxation process. This could be due to the fact that the magnetic moment on Co(II) flips much faster than on Dy(III) thus diminishing the effect from the cobalt ions.
The main challenge is to understand the large difference in the relaxation times of 1 and 1·3H 2 O in the QTM regime (Fig. 4). The ab initio results in Tables 4 and 5 show close anisotropic properties of the ground Kramers doublets of Dy(III) in the two compounds and similar interaction constants with neighbor ions, which cannot explain the difference of two orders of magnitude of the respective τ QTM (Table 2). Moreover, the spectra of excited Kramers doublets in Table 3 look also quite similarly for both complexes, implying close strengths of spin-phonon coupling. The only visible difference between the two compounds that could affect significantly their relaxation properties is the presence of additional three water molecules in 1·3H 2 O. These enhance the vibrational coupling between different CoDyCo units in the crystal thus providing a better relaxation of magnetization. On the contrary, the absence of the lattice water molecules in 1 causes a phonon bottleneck effect thus suppressing the relaxation.
We now provide some paths along which further enhancement of magnetic behavior can occur. First, the magnetic axiality in the low-lying doublet states of the Dy(III) can be increased together with the axial components of the crystal field by shortening the two axial Dy-O1 and Dy-O4 chemical bonds and by increasing the O1-Dy-O4 angle up to 180°. Furthermore, the non-axial crystal field components can be reduced if weaker equatorial ligands are used, with nearly neutral bonding atoms. Minimization of the equatorial field can be achieved by eliminating all equatorial ligands, thus achieving a D ∞h local symmetry, albeit this is not that easy to achieve.
Another path to achieve performant molecular magnets is to couple strongly one Ising ion, such as Dy(III) in the present system, with two purely isotropic paramagnetic sites, such as a radical, Mn(II), or Fe(III). Such trinuclear compound would behave as a performant molecular magnet because of a multistep character of the blocking barrier. Tunneling will be suppressed at temperatures below the blocking barrier due to large number of intermediate steps required to connect states with opposite magnetization, whereas above this exchange barrier, the large spins on neighboring metal sites will be again a destructive factor for the magnetization blocking.
Finally, a particularly important conclusion emerging from the present work is that special care should be taken in order to diminish the contacts between the complexes in the crystal. Such contacts are promoted by species like water and probably other solvent molecules capable to bind the magnetic units via hydrogen bonds, thus contributing to more efficient heat transfer in the crystal and a faster magnetic relaxation.  In summary, we reported a series of linear Co(II)-Dy(III)-Co(II) single-molecule magnets with a Dy(III) in pentagonal-bipyramid geometry. The loss of the uncoordinated water molecules alters the effective energy barrier (> 100 cm −1 increase) and the tunneling relaxation time (> 100-fold growth) significantly, giving rise to a desolvated molecule with the highest known effective energy barrier for d-f molecules. These pronounced change of relaxation dynamics can contribute to the change in the coordination environments of Dy(III) and Co(II). These factors were understood qualitatively/quantitatively with the aid of ab initio calculations.

X-ray Crystallographic Study. Diffraction intensities were collected using an Oxford Diffraction
Gemini R CCD diffractometer with CuK α radiation (λ = 1.54178 Å) for 1•3H 2 O, 1•H 2 O and 1 at 150 K. The structures were solved by direct methods, and then refined using the SHELXTL program 38 . CCDC 1058028 (1•3H 2 O) 1058029 (1•H 2 O) and 1058030 (1) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.