In-depth investigation of large axial magnetic anisotropy in monometallic 3d complexes using frequency domain magnetic resonance and ab initio methods: a study of trigonal bipyramidal Co(ii)

Symmetry control using DABCO generates a large easy-plane magnetic anisotropy with zero rhombic anisotropy.


Introduction
The investigation of molecules that retain their magnetisation in the absence of an applied magnetic eld, single-molecule magnets (SMMs), has been driven by the need to nd new materials for high-density data storage and quantum computing. 1 Recent work in this eld has focused on engineering high magnetic anisotropy in complexes containing a single paramagnetic ion, which has led to the rst examples of SMMs showing slow relaxation of their magnetisation above the temperature of liquid nitrogen. 2 This approach requires that we develop an understanding of how molecular geometry can be tailored to achieve large spin-orbit coupling (SOC) contributions to magnetic anisotropy, and how undesired relaxation processes can be controlled. 3 Hence, monometallic 3d complexes have generated signicant interest in this area, with simple modication of the ligands inuencing the zero-eld splitting parameters and, consequently, the observation of slow relaxation of the magnetisation. 4 The majority of monometallic 3d SMMs are based on the half-integer spin Co(II) ion, due to its ability to display slow relaxation of magnetisation in a range of coordination environments. The mechanism for relaxation of magnetisation is governed by the magnetic anisotropy, with the dominant processes contributing to spin reversal being dependent on the magnitudes of both D and E. Slow magnetic relaxation arising from an Orbach process (i.e. relaxation involving transitions to real m s states) can occur for systems with small/moderate D parameters, irrespective of the sign of D. For larger D values, Raman (two-phonon) and direct (single-phonon) spin-lattice relaxation pathways should also be considered. 5 Furthermore, if the rhombic zero-eld splitting (ZFS) parameter E is zero, as is the case in a high symmetry molecule, then the contribution to the relaxation from quantum tunneling transitions mediated by hyperne or dipole elds will be further inhibited, thus isolating spin-lattice relaxation processes. These complexes therefore present ideal model systems to study spin-lattice relaxation, which can oen also be detrimental in other more complex molecules. To achieve a large D value in combination with a zero, or negligible, E term requires geometric control of the coordination environment. Herein, we use the bulky C 3 symmetric ligand 1,4-diazabicyclo[2.2.2]octane (DABCO) to achieve trigonal symmetry around the Co(II) ion in the monometallic complex [Co II Cl 3 (DABCO)(HDABCO)] (1). Strict D 3h symmetry, in the rst coordination sphere, is imposed by the molecules packing in the R32 space group. 6 We use a combination of magnetic susceptibility measurements, ab initio calculations, high eld electron paramagnetic resonance (HF-EPR), and frequency-domain magnetic resonance (FDMR) spectroscopy to elucidate the relaxation mechanisms and the large easy-plane magnetic anisotropy for Co(II) in a strict trigonal bipyramidal (TBP) coordination environment.

Results and discussion
Structure Complex 1 crystallizes in the trigonal R32 space group (see Table  S1 †) and comprises a central Co(II) ion in a trigonal bipyramidal coordination environment (D 3h ) with two axial DABCO ligands and three equatorial chloride ligands (see Fig. 1). Charge balance requires one cationic HDABCO + and one DABCO ligand per molecule and, crystallographically, the proton on N2 is modeled with half-occupancy. The Co-Cl bond distance is 2.3252(8)Å, the Co-N distance is 2.2680(5)Å, and the axial and equatorial bond angles are 180 and 120 , respectively. Continuous shape measures (CShMs) were calculated using the program SHAPE to quantify the degree of distortion around the Co II center from the ideal trigonal bipyramidal coordination geometry, 7 and the value of 0.015 obtained for 1 indicates an almost perfect TBP environment. The shortest intermolecular Co/Co distance is 7.3627(13)Å and propagates along the aand b-axes of the crystal lattice. There is a strong intermolecular hydrogen-bonding interaction between neighbouring molecules of 1 (N2-H/N2 0 with an N2/N2 0 distance of 2.638(10)Å), which pack into a 1D chain along the 3-fold symmetry axis of each molecule (N1-Co1-N1 0 ), which coincides with the crystallographic c-axis (see Fig. 1).

Theoretical studies
To predict the likely nature of the ZFS for complex 1, ab initio calculations were performed. Using the NEVTP2 method on top of the CASSCF wave-function, a large positive value of D ¼ +44.2 cm À1 is obtained (vide infra for computational details). 8 This is unusual given the majority of TBP Co(II) complexes reported in the literature have small negative D values (see Table  S4 in ESI †). However, it is consistent with the nature of the coordinated ligands with strong p donating character in the equatorial positions (Cl À ) and weak s donating character in the axial positions ([DABCO] + ). 9 The major anisotropy axis (associated with g zz and D zz ) is collinear with the C 3 rotational axis imposed by the crystallographic space group (Fig. 2). The origin of the easy plane anisotropy in 1, which yields the positive value of D, can be rationalized by using the spin-allowed part of the second-order perturbative equation (see eqn (3) in Computational details). The ground state electronic conguration of the d 7 Co(II) ion corresponds to a non-degenerate 4 A 0 2 term with respect to D 3h point group symmetry. Excitation of a single  Table S3, ESI †). The major contribution to D arises from ground state/excited state mixing of the 4 E 00 states at $4085 cm À1 . The calculations predict that the two 4 E 00 states are almost degenerate, but split by $3 cm À1 (Table S3, ESI †). Hence, eqn (2) yields a nite E/D ratio of 0.000473. However, the computational method should not be considered accurate to four decimal places, and the E/D ratio is expected to be exactly zero (and the 4 E 00 states degenerate) due to the local D 3h point group symmetry found in crystals of 1. There is another smaller, but non-negligible positive contribution to D (+12 cm À1 ) arising from the excited 2 A 0 1 state which lies $19 600 cm À1 above the ground state (Table S3, ESI †). Importantly, it should be noted that the overall/nal D value is obtained directly from the Effective Hamiltonian Approach (EHA) 20 aer diagonalisation of the whole D matrix, including 10 quartets and 40 doublets, and hence the nal obtained D value of 44.2 cm À1 does not reect the sum of individual D values arising from various electronic states. Additionally, ab initio calculations yield g-tensor components for the S ¼ 3/2 manifold of g zz ¼ 1.988 and g xx ¼ g yy ¼ 2.433 or, alternatively, effective values of g eff zz ¼ 1.989 and g eff xx ¼ g eff yy ¼ 4.860 for the lowest Kramers doublet. These estimates are in very good agreement with the values obtained from experiments (see below). The computed identical g xx and g yy values are consistent with the negligible rhombicity present in the complex.

EPR and FDMR measurements
Multi-high-frequency EPR measurements were performed on a microcrystalline powder sample of 1 in order to provide spectroscopic insights into its magnetic anisotropy (Fig. 3a). The spectra reveal two sharp features that can be attributed to parallel and perpendicular excitations within the lowest   3 (a) Multi-frequency powder EPR spectra for 1, recorded at T ¼ 5 K in field derivative, dI/dB, mode (where I represents the absorption intensity and B the magnetic field strength); the frequencies are given in the legend. Features attributed to the perpendicular and parallel components of the spectra are marked with * and #, respectively. The parallel portions of the spectra have been expanded for three of the frequencies (101.6, 201.6 and 319.2 GHz) in order to ease viewing (see ESI † for explanation of the sharp features just below the parallel components of the spectra). (b) Frequency versus resonance position plot corresponding to the perpendicular and parallel mode excitations seen in (a). The solid lines are linear fits to the data (with the zero-field offsets constrained to the origin) from which the effective g-values are obtained (see ESI † for further details).
Kramers doublet, with effective Landé factors g eff k ¼ 2.03(1) & g eff t ¼ 4.80(2) (Fig. 3b). In the limit hf ( D K , where D K [¼ 2(D 2 + 3E 2 ) 1/2 ] is the zero-eld gap between Kramers doublets, f is the microwave frequency and h the Planck constant, g eff k & g eff t are insensitive to the absolute values of the ZFS parameters D and E. However, a nite E parameter is expected to give rise to a splitting of the perpendicular component of the spectrum, with a magnitude that depends on the ratio of E/D. The absence of such a splitting gives an upper bound of E/D # 0.006 (see ESI †), consistent with the theoretical studies. Setting E/D ¼ 0, which is a very good approximation in this case, allows us to directly relate the effective g-factors associated with the lowest Kramers doublet to those of the full S ¼ 3/2 state, giving g zz ¼ 2.03(1) and g xx ¼ g yy ¼ 2.40(1), in good agreement with the theoretical studies, and again conrming the easy-plane anisotropy (see ESI † for detailed explanation). We note that there is no physically realistic scenario under which the obtained effective gfactors can be rationalized on the basis of an easy-axis anisotropy.
A direct measure of D K and, hence, D requires magnetooptical measurements at far higher frequencies. Fig. 4 displays normalized frequency-domain magnetic resonance (FDMR) spectra recorded at a temperature of 4.2 K for a powder sample of 1, spanning the range from 10 to 140 cm À1 (see also Fig. S5 and ESI † for further details of the data analysis). As can clearly be seen, resonances are apparent in two regions of the gure: a low frequency branch below 40 cm À1 , which extrapolates to zero energy at zero eld; and a high-frequency branch centered at z89 cm À1 at zero eld. The former corresponds simply to the perpendicular (g eff t ) resonance associated with the lowest Kramers doublet, and is observed in the low-frequency EPR experiments (Fig. 3a). Meanwhile, the high frequency branch corresponds to an allowed inter-Kramers transition. Consequently, the zero-eld transition frequency (see also Fig. S6 †) corresponds exactly to D K ¼ 2D (assuming negligible E). Superimposed on the FDMR spectra in Fig. 4 are optimum simulations that assume D ¼ +44.5 cm À1 , and exactly the same g-values deduced on the basis of the EPR measurements. The obtained D value, which is the only adjustable parameter in the simulations (apart from a normalization factor needed to reproduce the strengths of the FDMR signals), is in excellent agreement with the ab initio calculations and magnetic measurements (vide infra).

Magnetic properties
Variable eld magnetisation data (M vs. H) of 1 are shown in Fig. 5, with the temperature dependence of the molar magnetic susceptibility product (c m T vs. T) presented in Fig. S7 in the ESI. † The c m T vs. T and M vs. H data were tted simultaneously using the program Phi (the Hamiltonian used and details of the t are presented in the SI †). 10 Considering the results of the FDMR measurements (vide supra), the axial ZFS parameter was xed at D ¼ +44.5 cm À1 . Additionally, the approximation that E ¼ 0 for an axial system was applied in the case of 1, consistent with the HF-EPR measurements and ab initio calculations. Although the calculations and HF-EPR measurements indicated an anisotropic Landé tensor, the magnetic data can be tted using an isotropic g-factor: g ¼ 2.55 was obtained from the t, very close to the value estimated from the experimental c m T value at 290 K (cf. 2.58 cm 3 mol À1 K). In comparison to previously reported TBP Co(II) complexes which employ polydentate ligands, |D| is much larger for 1 (see Table S4 †). 4c, 9,11 In only one case has a higher |D| value been reported for a Co(II) TBP coordination polymer, with the parameters D ¼ +59 cm À1 , E ¼ 7 cm À1 and g ¼ 2.36. 12 However, these parameters were obtained only from a t of the magnetic data, and have not been conrmed by spectroscopic measurements or theoretical studies. The key point for 1 is that not only is D very large for TBP Co(II), but that the rhombicity is zero due to the strict axial symmetry imposed by the combination of the three-fold symmetric DABCO ligands and the R32 space group. Fig. 4 Normalized experimental FDMR spectra (black) with simulations (red) superimposed; see main text and ESI † for parameters and explanation of the analysis. The data were recorded at a temperature of 4.2 K, and the baseline of each spectrum is positioned according to the applied field strength on the ordinate. The gray shading provides a measure of the energy-dependent standard deviation of the FDMR signal from four separately recorded spectra. Alternating current (ac) susceptibility measurements were carried out to investigate the relaxation dynamics of 1. In zero applied dc eld, no out-of-phase (c 00 ) response was observed, but on applying a dc eld, a c 00 is observed (see Fig. S8-S11 †). The eld dependence of this slow relaxation of magnetisation in 1 showed an optimum response under an applied dc eld of 2500 Oe (Fig. S10 †), and so the frequency dependence of the out-of-phase component to the ac susceptibility, c 00 , was measured over the temperature range 2.4 to 7.0 K under this eld (see Fig. 6 and S11 †). The maxima in c 00 move out of the accessible frequency range of the SQUID above 6.6 K. For 1, a t of the relaxation data to an Arrhenius law, corresponding to a two-phonon Orbach process, should yield a value for the activation energy of $|2D|. Attempts to t the data in this way failed in two respects: rstly, they did not t at all well to an Arrhenius behavior; second, the t yielded an activation energy that is much smaller than |2D| (21.5 cm À1 vs. 89 cm À1 , see Fig. S13 in the ESI †). Subsequently, a t of 1/s vs. T (see Fig. 7) was performed using the extended Debye model shown in eqn (1), which takes into account the Raman (s f T n ) and direct (s f T) spin-lattice relaxation processes and Quantum Tunnelling of the Magnetisation (QTM), given as the 1st, 2nd and 3rd terms, respectively. 13 The Raman process does dominate, although inclusion of a direct process is necessary to t the data below 3 K. To avoid over-parameterisation, the terms relating to the direct process (A) and QTM (B 1 and B 2 ) were xed based on ts of the eld-dependence of s at 2 K between 200 and 4000 Oe (see Fig. S12 and eqn (S6) †) yielding A ¼ 277.9 (20.9) s À1 Oe À2 K À1 ; B 1 ¼ 302.4 (9.5) s À1 and B 2 ¼ 181.2 (17.2) Oe À2 . For the Raman process we then obtain C ¼ 0.20(0.04) s À1 K Àn with n ¼ 5.70(0.09), where n ¼ 9 is expected for a Kramers ion, although this value may be lower if optical and acoustic phonons are taken in to account. 5,14

Conclusions
We have demonstrated a strategy for generating a large easyplane magnetic anisotropy in trigonal bipyramidal Co(II). The enhanced magnetic anisotropy is conrmed by high eld EPR, frequency-domain magnetic resonance (D ¼ +44.5 cm À1 ) studies and ab initio methods. Compared to other trigonal bipyramidal complexes, such as those using tetradentate ligands, we show that a substantial increase in the axial magnetic anisotropy results from using a blend of axial/ equatorial monodentate ligands. Importantly, the rhombicity in this large positive D system, 1, is zero due to the strict axial symmetry imposed by the combination of C 3 -symmetric axial DABCO ligands and crystallisation in a trigonal space group. Complex 1 displays slow relaxation of magnetisation under an applied dc eld and the relaxation data can be accounted for by considering Raman and direct processes along with Quantum Tunnelling of the Magnetisation. Future work will focus on related systems that will allow us to probe further the role of spin-phonon interactions and, subsequently, how these can be controlled through external stimuli such as high pressure. We will also consider 1 and related species as monometallic building blocks to design larger spin systems with signicant axial magnetic anisotropy, while keeping the rhombic anisotropy to zero. Such building blocks could be linked into chains or networks, whilst maintaining their symmetry and rigidity. Of particular interest is targeting DABCO radical ligands to link together such moieties to promote strong superexchange  interactions, which could be switched on or off in a controlled way using optical or redox probes. Overall, this study contributes to the design criteria for high axial anisotropy 3d monometallic species, to the identication of model systems for the investigation of spin-phonon interactions, and for targets for incorporation into larger functional materials, that can inuence the design of future molecular magnetic materials.

Synthesis
All reagents and solvents were obtained commercially and used without any further purication. Complex 1 was synthesized following a modication of the previously reported procedure. 6 [CoCl 3 (DABCO)(HDABCO)] (1): to a dark purple solution of CoCl 2 (1.30 g, 4 mmol) in methanol (20 ml) a colorless solution of DABCO (1.12 g, 4 mmol) in methanol (20 ml) was added and stirred for 2 hours at 60 C. The resultant blue suspension was allowed to cool to room temperature before ltering to yield a pink solution and blue precipitate (the precipitate was discarded as we were unable to obtain a pure crystalline sample from it on re-dissolving  H 6.32, N 13.88; calc: C 36.90, H 6.45, N 14.34.

Physical methods
Elemental analysis was performed in-house by the microanalysis services at the School of Chemistry, University of Glasgow. IR spectra were collected using a Shimadzu FTIR spectrometer in the range 4000-600 cm À1 . Crystallographic data were collected for 1 at 100 K using a Bruker APEXII CCD diffractometer with an Oxford Cryosystems n-Helix low-temperature device mounted on a sealed tube generator. Structures were solved using SHELXT and rened using full-matrix leastsquares renement using Olex 2 soware. 15 The powder X-ray pattern was collected on a PANalytical XPert MPD, with Cu Ka1 radiation at ambient temperature over a range of 5 < 2q < 50 using a step size of 0.0167 . The calculated pattern was generated from Mercury using the CIF of the crystal structure at 100 K. 16 All magnetic measurements were carried out on powdered crystalline samples restrained in eicosane using a Quantum Design MPMS-XL SQUID magnetometer. Data were corrected for the diamagnetic contribution of the sample holder and eicosane by measurements, and for the diamagnetism of the compound (c m (dia) ¼ À216 Â 10 À6 cm 3 mol À1 ). High-eld/ frequency EPR spectra were collected on a microcrystalline powder sample of 1, which was immobilized in a polyethylene cup with a Teon® stopper. The transmission-type spectrometer used in this study employed a 17 T superconducting magnet. 17 Microwave frequencies were generated in the 50 to 635 GHz range using a phase-locked Virginia Diodes source combined with a series of frequency multipliers. The eld modulated EPR signal was obtained via lock-in detection using an InSb hot-electron bolometer (QMC Ltd., Cardiff, U.K.). Temperature control was achieved using an Oxford Instruments (Oxford, U.K.) continuous-ow cryostat. FDMR spectra were obtained by recording far-infrared (FIR) spectra under various external magnetic elds. 18 For this purpose a Bruker Vertex 80v vacuum Fourier transform infrared (FTIR) spectrometer with a resolution of 0.12 cm À1 was used. The sample was mounted in a 17 T superconducting magnet with optical access, such that the applied eld was parallel to the direction of light propagation (Faraday geometry). The sample was in thermal equilibrium with the liquid helium bath of the magnet and, therefore, at a temperature of 4.2 K. The transmitted FIR radiation was detected using a composite Si bolometer placed directly beneath the sample.

Computational details
First principle calculations have been carried out using the ORCA 4.0.0. program. 19 To determine the zero-eld splitting (ZFS) Hamiltonian parameters we have employed a multi-congurational ab initio (CASSCF/NEVPT2) approach, which is one of the best methods to determine these properties. For the complete active space self-consistent eld (CASSCF), all of the 10 quartets and 40 doublets have been considered with an active space consisting of CAS (7,5). During this calculation, the ZORA-def2-TZVP basis set for all elements were considered, which are relativistic contracted versions of def2 basis sets available in ORCA. Also the ZORA (zeroth-order regular approximation) Hamiltonian was employed to account for the scalar relativistic effect. NEVPT2 (N-electron valence perturbation theory second order) was also performed on top of the CASSCF wavefunction to add the dynamic electron correlation effect into the results. Final spin-Hamiltonian parameters and spin-orbit properties have been derived from the QDPT-EHA (quasi-degenerate perturbation theory-effective Hamiltonian approach) method. 20 This methodology has been successfully used to estimate zero-eld splitting in many transition metal complexes. 21 The zero-eld splitting (ZFS) parameters were determined in accordance with the Hamiltonian shown in eqn (2) where the rst and second terms describe the axial and rhombic ZFS interactions parameterized through D and E respectively. The third term takes into account the Zeeman interaction with the spin operatorŜ, applied eldB, and Landé tensor g ! : For this complex, the spin-allowed part of the second-order perturbative treatment for the D ! tensor components are given by eqn (3): are the matrix indices and z is the effective spin-orbit coupling constant of the molecule.

Conflicts of interest
There are no conicts to declare.