Gavin A.
Craig
^{a},
Arup
Sarkar
^{b},
Christopher H.
Woodall
^{cd},
Moya A.
Hay
^{a},
Katie E. R.
Marriott
^{a},
Konstantin V.
Kamenev
^{cd},
Stephen A.
Moggach
^{cd},
Euan K.
Brechin
^{cd},
Simon
Parsons
*^{cd},
Gopalan
Rajaraman
*^{b} and
Mark
Murrie
*^{a}
^{a}WestCHEM, School of Chemistry, University of Glasgow, Glasgow, G12 8QQ, UK. E-mail: mark.murrie@glasgow.ac.uk
^{b}Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400 076, India. E-mail: rajaraman@chem.iitb.ac.in
^{c}Centre for Science at Extreme Conditions, University of Edinburgh, Edinburgh, EH9 3FD, UK. E-mail: Simon.Parsons@ed.ac.uk
^{d}EaStCHEM, School of Chemistry, University of Edinburgh, Edinburgh, EH9 3FJ, UK
First published on 19th December 2017
Understanding and controlling magnetic anisotropy at the level of a single metal ion is vital if the miniaturisation of data storage is to continue to evolve into transformative technologies. Magnetic anisotropy is essential for a molecule-based magnetic memory as it pins the magnetic moment of a metal ion along the easy axis. Devices will require deposition of magnetic molecules on surfaces, where changes in molecular structure can significantly alter magnetic properties. Furthermore, if we are to use coordination complexes with high magnetic anisotropy as building blocks for larger systems we need to know how magnetic anisotropy is affected by structural distortions. Here we study a trigonal bipyramidal nickel(II) complex where a giant magnetic anisotropy of several hundred wavenumbers can be engineered. By using high pressure, we show how the magnetic anisotropy is strongly influenced by small structural distortions. Using a combination of high pressure X-ray diffraction, ab initio methods and high pressure magnetic measurements, we find that hydrostatic pressure lowers both the trigonal symmetry and axial anisotropy, while increasing the rhombic anisotropy. The ligand–metal–ligand angles in the equatorial plane are found to play a crucial role in tuning the energy separation between the d_{x2−y2} and d_{xy} orbitals, which is the determining factor that controls the magnitude of the axial anisotropy. These results demonstrate that the combination of high pressure techniques with ab initio studies is a powerful tool that gives a unique insight into the design of systems that show giant magnetic anisotropy.
Giant magnetic anisotropy was predicted on the basis of gas phase calculations for a simulated complex of the type [Ni(MeDABCO)_{2}X_{3}]^{+}, where X^{−} is a halide ion and MeDABCO is the cationic ligand 1-methyl-4-aza-1-azoniabicyclo[2.2.2]octanium.^{10} The bulky MeDABCO ligand was expected to minimise structural distortions that would arise from the Jahn–Teller effect. These distortions would lift the degeneracy of the d_{xy} and d_{x2−y2} orbitals in this d^{8} trigonal bipyramidal complex and quench the first order SOC that would otherwise yield a very large axial magnetic anisotropy.^{11} We experimentally confirmed the presence of giant magnetic anisotropy in the compound [Ni(MeDABCO)_{2}Cl_{3}](ClO_{4}) (1) through magnetic measurements, and high- and low-field electron paramagnetic resonance (EPR) studies performed on both oriented single crystals and powder samples of 1 (the molecular structure of the cation is shown in Fig. 1).^{12} Even so, the axial magnetic anisotropy was found to be so large that it was not possible to directly determine its magnitude on the basis of high-field, high-frequency EPR measurements, for which best fits of the data suggested that the axial zero-field splitting (ZFS) parameter |D| could not be lower than 400 cm^{−1}. Given the dependence of magnetic anisotropy on the coordination environment around the metal ion, we were interested in probing (i) whether we could use hydrostatic pressure as a means of inducing changes to the coordination sphere around Ni(II) in 1 and (ii) the effect this would have on the anisotropy. The application of hydrostatic pressure is becoming a more convenient tool to unveil unusual properties in coordination complexes.^{13} Previously, we have used pressure to increase the magnetic ordering temperatures in mononuclear Re(IV) complexes,^{14} and to control the orientation of Jahn–Teller axes in polymetallic complexes.^{15}
Fig. 1 View of the molecular structure of the [Ni(MeDABCO)_{2}Cl_{3}]^{+} cation in 1. Only heteroatoms are labeled. |
Herein, we use single crystal X-ray diffraction to observe pressure-induced modifications to the symmetry around the Ni(II) ion in 1. These high pressure experimental structural data were used for state averaged complete active space self-consistent field (SA-CASSCF) calculations to predict the effect of the structural modifications on the relative energies of the 3d orbitals in 1 and thus extract the anticipated changes in the magnetic anisotropy. How magnetic anisotropy is influenced by small structural distortions is an important question with wide implications, as deposition of magnetic molecules on surfaces has been shown to lead to structural alterations that induce drastic changes in their magnetic properties.^{16} Finally, we use these results to account for the changes we observe in the DC magnetic properties of 1 upon performing high pressure magnetometry. We find that high pressure drives a loss in trigonal symmetry and axiality around the Ni(II) centre in 1, with a resulting decrease in the magnitude of the axial ZFS and a concomitant increase in the rhombic ZFS, given by the parameter E. These results illustrate the sensitivity of giant magnetic anisotropy to changes in the coordination environment. They also demonstrate the usefulness in applying high pressure techniques to experimentally access structures that cannot be synthesised in the laboratory, allowing their subsequent theoretical study and measurement of their physical properties.
Pressure/GPa | Ambient | 0.58 | 0.90 | 1.40 | 1.65 |
λ/Å | 0.71073 | ||||
T/K | 293 | ||||
Crystal system | Orthorhombic | ||||
Space group | Pca2_{1} | ||||
a/Å | 12.5175(1) | 12.3181(7) | 12.2089(9) | 11.9968(11) | 11.9924(11) |
b/Å | 13.0820(1) | 12.8429(7) | 12.7469(8) | 12.5527(11) | 12.5546(11) |
c/Å | 13.0989(1) | 13.0380(4) | 12.9686(5) | 12.8642(6) | 12.8611(6) |
V/Å^{3} | 2145.0(4) | 2062.61(17) | 2018.2(2) | 1937.2(3) | 1936.4(3) |
Z | 4 | ||||
D _{calc.}/g cm^{−3} | 1.607 | 1.671 | 1.708 | 1.779 | 1.780 |
Reflections | 17781 | 6211 | 6037 | 5214 | 4999 |
Unique data | 4863 | 1738 | 1740 | 1583 | 1596 |
R _{int} | 0.027 | 0.029 | 0.030 | 0.037 | 0.035 |
R | 0.029 | 0.029 | 0.031 | 0.046 | 0.044 |
R _{w} | 0.062 | 0.071 | 0.052 | 0.069 | 0.070 |
S | 0.99 | 1.04 | 1.00 | 1.00 | 0.99 |
Flack param. | 0.012(14) | 0.008(15) | 0.014(15) | −0.01(2) | 0.02(2) |
ρ _{max}, ρ_{min}/eÅ^{−3} | 0.39, −0.36 | 0.22, −0.19 | 0.31, −0.31 | 0.68, −0.92 | 0.58, −0.80 |
Fig. 2 (Top) Contraction of the unit cell lengths in compound 1 with pressure. (Bottom) Pressure dependence of the relative unit cell volume, V/V_{0}, as a function of pressure. The empty circles represent experimental data, and the solid line represents the fit to a second-order Birch–Murnaghan equation of state. The dashed line represents the continuation of the fit, illustrating the change in compressibility of 1 at high pressures (see ESI† for details). |
The effect of applying pressure on the bond lengths around the Ni(II) ion in 1 is negligible. The Ni–Cl bonds in the equatorial plane are found to be insensitive to pressure, while there is a very slight compression in the axial Ni–N bonds, which decrease in length from 2.222(3) to 2.194(6) Å at 1.65 GPa (see ESI, Fig. S3†). In stark contrast, there is a significant deformation of the equatorial bond angles around the Ni(II) ion (Fig. 3). As pressure is applied, the angles formed by Cl1–Ni1–Cl2 and Cl2–Ni1–Cl3 increase, reaching values of 124.3(1) and 123.4(1)°, respectively, at 1.65 GPa, while at the same time the Cl1–Ni1–Cl3 angle decreases to 112.3(1)°, along with a slight decrease in the trans-N–Ni–N angle, from 177.1(1) to 176.2(2)° (Fig. S4†). The result of the pressure-induced angular deformations is a lowering of the symmetry around the Ni(II) ion. Continuous shape measures, which compare the symmetry of the environment around an atom to ideal reference polyhedra,^{20} can be used to quantify the observed symmetry lowering: for compound 1, S(D_{3h}) = 0.09 at ambient pressure, while at 1.65 GPa, S(D_{3h}) = 0.23, where larger values indicate lower symmetry and S(D_{3h}) = 0 would signify ideal D_{3h} symmetry. In an earlier theoretical study regarding the magnetic anisotropy of this type of trigonal bipyramidal Ni(II) complex at ambient pressure, the importance of controlling these angular distortions to avoid the quenching of first order spin–orbit coupling was highlighted for a series of simulated complexes.^{10} We used these new high pressure structural data to perform ab initio calculations on 1 to extract the ZFS parameters D and E associated with the distinct symmetry observed at each pressure point.
(1) |
(2) |
The components of D (say, D_{ij} in general) are themselves negative from the equation derived from second-order perturbation theory,^{22}
(3) |
Therefore, D is negative when the D_{ZZ} term becomes greater than the average of the D_{XX} and D_{YY} terms. The D_{ZZ} term in turn becomes dominant when some M_{L} level electronic transitions take place as shown in eqn (3). In eqn (3), ζ is the effective spin–orbit coupling constant of the molecule, whereas ε_{p}, ε_{r} and ε_{q}, ε_{s} are the energies of the ground and corresponding excited states, respectively. The first term of eqn (3) corresponds to spin allowed β → β electronic transitions from the ψ_{p} MO to the ψ_{q} MO and the second term corresponds to spin-allowed α → α electronic transitions from the ψ_{r} MO to the ψ_{s} MO. Furthermore, l_{i} and l_{j} are the x, y or z components of the total orbital angular momentum operator L, which connects the corresponding ground state wavefunction with the excited state.
Here we have employed the CASSCF/NEVPT2 method along with the effective Hamiltonian approach to extract the ZFS parameters. This approach has been found to yield good numerical estimates for several examples studied by us^{23} and others.^{21} We begin our discussion with calculations based on the crystal structure of complex 1 collected at ambient pressure.^{12} CASSCF calculations yield a D value of −409 cm^{−1} with E/D estimated to be 0.0004, while the inclusion of a dynamic correlation yields very similar parameters (D = −399 cm^{−1} and E/D = 0.0003, Tables S2 and S3†). The very large D parameter obtained from the calculation is consistent with that estimated previously from broadband high-field EPR studies, where the application of a large magnetic field transverse to the easy-axis enabled an indirect estimation of D, with a lower bound set at |D| ∼ 400 cm^{−1}. The computed anisotropy axes (D tensor directions) are shown in Fig. 4. The D_{ZZ} axis is found to lie along the pseudo-C_{3} axis (in the N–Ni–N direction) and the computed g_{zz} is found to coincide with this axis. From symmetry considerations, a Ni(II) complex with a d^{8} electronic configuration possessing perfect D_{3h} symmetry should have degenerate d_{xy} and d_{x2−y2} orbitals and hence, a large first-order spin–orbit contribution to the magnetic anisotropy. However, despite the presence of the bulky ligands in the axial positions of the Ni(II) ion in compound 1, the symmetry is lowered slightly and a Jahn–Teller distortion breaks this orbital degeneracy. Hence, the use of ZFS to describe the magnetic anisotropy is appropriate, although as we noted previously this description does push the limits of the spin-only model.
In complex 1, the very large D value stems from the closely lying d_{x2−y2} and d_{xy} orbitals (their separation is estimated to be 239 cm^{−1}) which contribute −488 cm^{−1} to the total D parameter (see Fig. 4 and Table S4†). We find that there are very small positive contributions from the other excited states which diminish the negative D value. Among these transitions, excitations from the d_{xz} and d_{yz} to the d_{xy} orbital are the most important contributions, as shown in Fig. 4. The energy of the first six spin–orbit states with their contribution from the ground state and first excited state are provided in Table S5.† Since D is negative, M_{S} = ±1 is the ground state followed by the M_{S} = 0 state. The first two spin–orbit states consist mostly of the ground triplet state (64%). Most importantly, the tunnel splitting between the M_{S} = ±1 states is estimated to be 0.21 cm^{−1}, suggesting very fast ground state relaxation. This is consistent with our previous study, where no out-of-phase ac susceptibility signals for 1 were observed in the absence of an applied dc field.^{12} Strong tunnelling for the M_{S} = ±1 state is essentially due to the rhombic E term as noted in Table 2 (E = 0.10 cm^{−1}). The main contributions to E stem from electronic transitions between different M_{L} levels but due to the presence of relatively high symmetry, these cancel each other out leading to a moderately small contribution to E. In addition to the E term, both the Cl and the N atoms cause hyperfine interactions, which offer an additional pathway for resonant tunnelling and lower the effective barrier to reorientation of the magnetisation, even in the presence of an applied dc field.^{12}
Pressure | D (cm^{−1}) | E (cm^{−1}) | Contribution from 1^{st} excited state (NEVPT2) (cm^{−1}) | Tunnel splitting (cm^{−1}) | Sum of Cl–Ni–Cl angle deviation, δ (°) |
---|---|---|---|---|---|
Ambient | −399 | 0.104 | −488 | 0.21 | 6.49 |
0.58 GPa | −347 | 0.208 | −435 | 0.42 | 7.64 |
0.90 GPa | −317 | 0.419 | −403 | 0.84 | 10.44 |
1.40 GPa | −264 | 0.861 | −346 | 1.72 | 15.19 |
1.65 GPa | −264 | 0.871 | −346 | 1.75 | 15.4 |
The decrease in D as the pressure increases is essentially due to the deviation in the α angles around the equatorial plane, with larger deviations away from 120° leading to a larger separation between the d_{xy} and d_{x2−y2} orbitals (vide supra). As the gap between these two orbitals increases, the associated major contribution to D drops significantly, leading to much lower D values (Fig. 5 and Table S2 in the ESI†). As the structural changes induced by pressure lead to negligible variations in the contributions to D from other excited states, the major change in D thus arises from the shift in the relative energies of the d_{xy} and d_{x2−y2} orbitals. The decrease in the magnitude of D with pressure is accompanied by an increase in the rhombic anisotropy E, from 0.10 cm^{−1} at ambient pressure to 0.86 cm^{−1} at 1.4 GPa (Table 2). The most significant contribution to the increasing E parameter arises from the increasing separation of the d_{xz} and d_{yz} orbitals with pressure (Fig. 5 and Tables S6–S14 in the ESI†). As E increases, the tunnel splitting between the M_{S} = ±1 states increases from 0.42 cm^{−1} to 1.72 cm^{−1} at 1.4 GPa. This suggests that as the applied pressure increases, not only does the axial anisotropy decrease, but the increased tunnel splitting will also lead to faster quantum tunnelling of the magnetisation.
Fig. 5 NEVPT2 computed ligand field d-orbital splitting for the 3d orbitals in 1 at the pressure points corresponding to the single crystal X-ray structures. |
To see clearly how the α angles influence the calculated magnitude of D, we define the parameter δ as the sum of the deviations of each angle α from the ideal value of 120° associated with trigonal symmetry (Fig. 6). There is an approximately linear relationship between the size of this structural deviation δ and the axial zero-field splitting parameter. To further illustrate the importance of the parameter δ in determining the magnetic anisotropy in 1, and to exclude the possibility that the small changes in other structural features (such as the Ni–N and Ni–Cl bond lengths) have any significant impact on D, we calculated D for a series of simulated structures of 1 where δ was varied while all of the other structural parameters were kept constant. We computed eight points with various δ values and their associated D values (shown as white squares in Fig. 6). The computed values of D for the simulated complexes are close to those calculated for the HP structural data (shown as black circles in Fig. 6), and lie very close to the linear relationship observed between D and δ, suggesting that the observed variation in D is essentially due to δ and independent of other structural features.
Overall, the structural data collected point to a lowering of symmetry around the Ni(II) ion in 1 as high pressures induce a change in the Cl–Ni–Cl equatorial bond angles. The ab initio calculations indicate that these structural changes lead to a loss of the axial nature of the ligand field in 1, with a resulting decrease in the axial ZFS parameter D. To determine whether the anticipated changes to the magnetic properties of 1 were accurately described by theory, we performed high pressure magnetic measurements on the compound.
Fig. 7 (Top) The temperature dependence of the molar magnetic susceptibility, χ_{M}T, for 1, measured at ambient pressure and 1.08 GPa. (Bottom) Field dependence of the magnetisation for 1 measured at 2 and 5 K, at ambient pressure and 1.08 GPa. The solid lines represent simulations of the data (red – ambient; blue – 1.08 GPa) using the parameters given in Table 3. |
Fitting the magnetic data for compound 1 was found previously to be non-trivial because of the large magnetic anisotropy it displays, which requires a highly anisotropic g-factor and consequently many parameters.^{12} This leads to a large number of local minima in the fitting process, and thus, it is difficult to reach a unique solution for each pressure point. Therefore, the previously described high field EPR study together with the results of the ab initio calculations described here were used as guides to simulate the magnetic data at ambient pressure. As the level of theory employed for the calculations is more suitable for the determination of zero-field splitting parameters than for accurate calculation of g-factors, the results yielded by the ab initio calculations for D and E were used directly in the simulation of the magnetic data. The g-factors were taken from the previous study,^{12} in which HF-EPR was used to experimentally determine g_{z} (Table 3). The χ_{M}T data at 1 T and the magnetisation data collected at 2, 3, 4 and 5 K were then simulated using the program PHI (v3.0.6),^{24} following the Hamiltonian:
Ĥ = DŜ_{z}^{2} + E(Ŝ_{x}^{2} − Ŝ_{y}^{2}) + μ_{B}·g·Ŝ |
g _{ z } | g _{ x } | g _{ y } | D/cm^{−1} | E/cm^{−1} | |
---|---|---|---|---|---|
Ambient pressure | 3.36 | 2.05 | 2.05 | −399 | 0.10 |
0.52 GPa | 3.28 | 2.12 | 2.13 | −349 | 0.22 |
0.79 GPa | 3.24 | 2.16 | 2.18 | −323 | 0.33 |
1.08 GPa | 3.20 | 2.20 | 2.22 | −295 | 0.52 |
To determine the values of the various parameters for the simulations at high pressure, the pressure dependence of the ab initio-calculated parameters was fitted, and used to derive the values for each pressure point used in the magnetic study (the graphs and fits for this process are included in the ESI†). Although the estimations of D and E are known to be accurate within the reference space chosen for the calculations, reliable estimation of the g-tensors requires ligand orbitals to be incorporated in the reference space to fully capture the effect of covalency.^{25} For this reason, the g-factors obtained from the ab initio calculations were normalised to the g-factors found at ambient pressure. The results of this approach are plotted in Fig. 7 at 1.08 GPa (for clarity, the plots for the pressure points at 0.52 and 0.79 GPa are given in the ESI†). Given the giant magnetic anisotropy presented by 1, and the limitations of the level of theory used in the calculations with respect to the g parameters, the results of the ab initio study are shown to reasonably describe the effect of applying pressure on the magnetic properties of 1 and show very good agreement with the experimental data.
Footnote |
† Electronic supplementary information (ESI) available. CCDC 1579468–1579472. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c7sc04460g |
This journal is © The Royal Society of Chemistry 2018 |