Yan
Peng
^{ab},
Mukesh Kumar
Singh
^{c},
Valeriu
Mereacre
^{a},
Christopher E.
Anson
^{a},
Gopalan
Rajaraman
*^{c} and
Annie K.
Powell
*^{ab}
^{a}Institute of Inorganic Chemistry, Karlsruhe Institute of Technology, Engesserstrasse 15, 76131 Karlsruhe, Germany. E-mail: annie.powell@kit.edu
^{b}Institute of Nanotechnology, Karlsruhe Institute of Technology, Postfach 3640, 76021 Karlsruhe, Germany
^{c}IITB-Monash Research Academy, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India. E-mail: rajaraman@chem.iitb.ac.in
First published on 16th April 2019
We describe the synthesis, characterisation and magnetic studies of four tetranuclear, isostructural “butterfly” heterometallic complexes: [M^{III}_{2}Ln^{III}_{2}(μ_{3}-OH)_{2}(p-Me-PhCO_{2})_{6}(L)_{2}] (H_{2}L = 2,2′-((pyridin-2-ylmethyl)azanediyl)bis(ethan-1-ol), M = Cr, Ln = Dy (1), Y (2), M = Mn, Ln = Dy (3), Y (4)), which extend our previous study on the analogous 5 {Fe_{2}Dy_{2}}, 6 {Fe_{2}Y_{2}} and 7 {Al_{2}Dy_{2}} compounds. We also present data on the yttrium diluted 7 {Al_{2}Dy_{2}}: 8 {Al_{2}Dy_{0.18}Y_{1.82}}. Compounds dc and ac magnetic susceptibility data reveal single-molecule magnet (SMM) behaviour for complex 3 {Mn_{2}Dy_{2}}, in the absence of an external magnetic field, with an anisotropy barrier U_{eff} of 19.2 K, while complex 1 {Cr_{2}Dy_{2}}, shows no ac signals even under applied dc field, indicating absence of SMM behaviour. The diluted sample 8 {Al_{2}Dy_{0.18}Y_{1.82}} shows field induced SMM behaviour with an anisotropy barrier U_{eff} of 69.3 K. Furthermore, the theoretical magnetic properties of [M^{III}_{2}Ln^{III}_{2}(μ_{3}-OH)_{2}(p-Me-PhCO_{2})_{6}(L)_{2}] (M = Cr, 1 or Mn, 3) and their isostructural complexes: [M^{III}_{2}Dy^{III}_{2}(μ_{3}-OH)_{2}(p-Me-PhCO_{2})_{6}(L)_{2}] (M = Fe, 5 or Al, 7) are discussed and compared. To understand the experimental observations for this family, DFT and ab initio CASSCF + RASSI-SO calculations were performed. The experimental and theoretical calculations suggest that altering the 3d^{III} ions can affect the single-ion properties and the nature and the magnitude of the 3d^{III}–3d^{III}, 3d^{III}–Dy^{III} and Dy^{III}–Dy^{III} magnetic coupling, thus quenching the quantum tunneling of magnetisation (QTM) significantly, thereby improving the SMM properties within this motif. This is the first systematic study looking at variation and therefore role of trivalent transition metal ions, as well as the diamgnetic Al^{III} ion, on slow relaxation of magnetisation within a series of isostructural 3d–4f butterfly compounds.
The single-ion anisotropy of a metal ion depends mainly on its coordination geometry and ligand field,^{5} while the molecular anisotropy depends on several factors such as ligand field,^{6} relative orientation of the individual single-ion easy axes,^{7} magnetic coupling, and the structural topology of the magnetic core.^{8,9}
It is well-known that the magnetic interactions between the 3d–3d, 3d–4f, and 4f–4f ions in heterometallic clusters are rather complicated to figure out, especially for clusters with high nuclearity. Thus, to better understand the magnetic interactions between 3d and 4f metal ions as well as the effect of magnetic interactions on the SMM behaviour,^{10,11} the construction of simple complexes with a limited number of 3d and 4f ions is required in order to elucidate the magneto-structural correlations. A fruitful test-bed system is provided by the tetranuclear “butterfly” motif. There are two possibilities for 3d/4f butterflies, either the 4f metal ions can be in the body positions and the 3d transition metal M ions are at the wingtips (Type I) or the reverse situation where the 4f metal ions are at the wingtips and the transition metal M ions are in the body positions (Type II). There are relatively few examples of the Type I situation compared with compounds with the Type II motif. The most famous Type I compounds have been reported by the Murray group where the isostructural compounds, {M^{III}_{2}Ln^{III}_{2}}, (M = Co, Cr and Ln = Dy, Tb, Ho) were studied.^{12–14} The corresponding {Cr_{2}Ln_{2}} and {Co_{2}Ln_{2}} compounds have similar U_{eff} values, but open magnetic hysteresis was only observed for the {Cr^{III}_{2}Ln_{2}} compounds where the 3d ion is paramagnetic rather than diamagnetic. It was found using ab initio calculations that this is the direct result of the cooperative 3d–4f coupling between the Cr^{III} and Ln^{III} ions.
A particularly fruitful test-bed system for Type II is the generic [M^{III}_{2}Ln^{III}_{2}(μ_{3}-OH)_{2}(RCO_{2})_{6}(L)_{2}] coordination cluster. There are many such examples of 3d–4f butterfly compounds in the literature, including an interesting systematic study by Winpenny, McInnes and their co-workers on a family of {M_{2}Ln_{2}} compounds where M = Mg^{II}, Mn^{III}, Co^{II}, Ni^{II}, and Cu^{II}, Ln = Y^{III}, Gd^{III}, Tb^{III}, Dy^{III}, Ho^{III}, and Er^{III}. The results revealed that the SMM behaviour observed in the Dy- and Er-based systems are intrinsic to the lanthanide ion and the strength of the 3d–4f exchange interaction plays a key role in the nature of the SMM properties observed.^{15} For this system, all the metals (M) are bivalent apart from the Mn^{III} analogue. Up to now the equivalent exploration of this type of butterfly system for M = M^{III} has not been available, probably because of the synthetic challenge to vary the M^{III} metal ions. On the other hand, it is straightforward to vary the 4f ion, as shown for (Type II) {Fe_{2}Ln_{2}} butterflies.^{16} We were particularly interested to gauge the effect that changing the electron configuration of the 3d ion has on the magnetic properties, including potential single molecule magnet (SMM) behaviour in a series of compounds incorporating the highly anisotropic Dy^{III} ion. In order to find some clear-cut ground rules, the system should be poised in such a way that the appearance of SMM behaviour allows an easy identification of the “best” choice of 3d configuration to optimise the slow relaxation and therefore SMM properties. With this in mind, and stimulated by our recent work^{17} on {M^{III}_{2}Dy^{III}_{2}}, M = Fe and Al, we extended our study on the high spin 3d^{5} (Fe^{III}) to 3d^{3} (Cr^{III}) and high spin 3d^{4} (Mn^{III}), and also the yttrium diluted {Al_{2}Dy_{2}} analogue, {Al_{2}Dy_{0.18}Y_{1.82}}. This allows us to probe the nature of the 3d^{III}–3d^{III}, 3d^{III}–4f^{III} and 4f^{III}–4f^{III} interactions and the effects on SMM behaviour. We have used a combined experimental and theory approach, using detailed ab initio calculations to elucidate the observations from bulk susceptibility and magnetisation data in order to explore the cooperativity and nature of any magnetisation relaxation for the complexes 1 {Cr_{2}Dy_{2}}, 3 {Mn_{2}Dy_{2}}, 5 {Fe_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}}.
The molecular structures of the complexes are very similar in all cases and always centrosymmetric, which was also the case for the previously reported 5 {Fe_{2}Ln_{2}} (Fig. 1 and S1, ESI†).^{17} The description of 1 {Cr_{2}Dy_{2}} is given as representative for the description of the features of the molecular structures. The neutral cluster is composed of 2 Cr^{III}, 2 Dy^{III}, 2 μ_{3}-OH, and 6p-Me-PhCOOH. All M^{III} ions have an octahedral O6 donor set which was established from the crystal data and through a SHAPE 2.1 analysis.^{18–20} The M^{III} ions have deviation values of 0.42, 1.37, 0.80 and 0.49 (Table 1) for complexes 1 {Cr_{2}Dy_{2}}, 3 {Mn_{2}Dy_{2}}, 5 {Fe_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}}, respectively.
Fig. 1 Structure of compound 1 {Cr_{2}Dy_{2}} (left), ligand (right upper) and coordination mode of ligand (right lower) in complexes 1, 3, 5 and 7. |
M^{III} | 1 {Cr_{2}Dy_{2}} | 3 {Mn_{2}Dy_{2}} | 5 {Fe_{2}Dy_{2}} | 7 {Al_{2}Dy_{2}} |
---|---|---|---|---|
Cr | Mn | Fe | Al | |
a HP (D_{6h}) hexagon, PPY (C_{5v}) pentagonal pyramid, OC (C_{4v}) octahedron, TPR (D_{3h}) trigonal prism, JPPY (C_{5v}) Johnson pentagonal pyramid J2, CSAPR (C_{4v}) spherical capped square antiprism, TCTPR (D_{3h}) spherical tricapped trigonal prism, MFF (C_{s}) muffin. | ||||
HP | 30.21 | 32.10 | 31.35 | 30.31 |
PPY | 25.60 | 25.69 | 24.99 | 25.54 |
OC | 0.42 | 1.37 | 0.80 | 0.49 |
TPR | 14.09 | 11.78 | 12.01 | 13.54 |
JPPY | 29.37 | 28.75 | 29.09 | 29.31 |
Ln^{III} | 1 {Cr_{2}Dy_{2}} | 3 {Mn_{2}Dy_{2}} | 5 {Fe_{2}Dy_{2}} | 7 {Al_{2}Dy_{2}} |
---|---|---|---|---|
Dy | Dy | Dy | Dy | |
CSAPR | 0.94 | 1.20 | 1.00 | 1.00 |
TCTPR | 1.43 | 1.25 | 1.22 | 1.90 |
MFF | 1.51 | 1.67 | 1.47 | 1.44 |
The Dy^{III} ions with an O7N2 donor set were also systematically analysed using SHAPE 2.1 software,^{18–20} and are best described as having a distorted spherical capped square anti-prism geometry with deviation values of 0.94, 1.20, 1.00 and 1.00 (Table 1) for complexes 1 {Cr_{2}Dy_{2}}, 3 {Mn_{2}Dy_{2}}, 5 {Fe_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}}, respectively. The high spin Mn^{III} ions in {Mn_{2}Dy_{2}} show an axial Jahn–Teller elongation along O4–M–O1′ with an elongated octahedral environment typical for this d^{4} metal ion (Mn–O_{eq} range = 1.894(16)–1.972(18) Å, Mn–O_{ax} = 2.161(16)–2.206 (16) Å) (Table 2). The Y analogues were established to be isostructural from the single crystal structure analysis or, in the case of 4, from the unit cell parameters.
1 (Cr^{III}) | 3 (Mn^{III}) | 5 (Fe^{III}) | 7 (Al^{III}) | |
---|---|---|---|---|
Dy1–O2 | 2.340 (4) | 2.3183 (18) | 2.3215 (17) | 2.3200 (15) |
Dy1–O3 | 2.326 (4) | 2.3651 (15) | 2.3416 (16) | 2.3308 (16) |
Dy1–O7^{i} | 2.430 (4) | 2.4311 (18) | 2.4332 (17) | 2.4046 (16) |
Dy1–O1 | 2.423 (4) | 2.3742 (17) | 2.3990 (17) | 2.4214 (16) |
Dy1–O9 | 2.430 (4) | 2.5170 (19) | 2.4388 (17) | 2.4538 (16) |
Dy1–O5 | 2.402 (5) | 2.3713 (16) | 2.4434 (17) | 2.4212 (16) |
Dy1–O8 | 2.442 (5) | 2.3943 (18) | 2.4285 (18) | 2.4371 (17) |
Dy1–N2 | 2.567 (5) | 2.584 (2) | 2.566 (2) | 2.5640 (19) |
Dy1–N1 | 2.582 (5) | 2.628 (2) | 2.618 (2) | 2.602 (2) |
M1–M1^{i} | 3.0659 (2) | 3.286 (1) | 3.211 (0) | 3.024 (1) |
Dy1–M1^{i} | 3.4317 (11) | 3.376 (1) | 3.450 (1) | 3.386 (1) |
Dy1–M1 | 3.4404 (11) | 3.467 (1) | 3.444 (1) | 3.383 (1) |
M1–O2 | 1.963 (4) | 1.8963 (16) | 1.9738 (17) | 1.8701 (17) |
M1–O4^{i} | 1.969 (4) | 2.1610 (16) | 1.9944 (17) | 1.8875 (17) |
M1–O6 | 1.976 (4) | 1.9496 (18) | 2.0058 (17) | 1.8977 (17) |
M1–O3 | 1.955 (4) | 1.8944 (16) | 1.9676 (17) | 1.8668 (17) |
M1–O1 | 2.002 (4) | 1.9727 (18) | 2.0584 (17) | 1.9496 (17) |
M1–O1^{i} | 1.996 (4) | 2.2036 (16) | 2.0548 (16) | 1.9346 (17) |
Dy–Dy_{intra} | 6.150 (4) | 6.003 (2) | 6.101 (1) | 6.055 (1) |
Dy–Dy_{inter} | 7.7708 (5) | 10.1349 (2) | 7.951 (1) | 8.093 (2) |
M1–O1–M1^{i} | 100.16 (19) | 103.66 (7) | 102.65 (7) | 102.27 (8) |
M1^{i}–O1–Dy1 | 101.83 (19) | 98.39 (6) | 101.28 (7) | 101.44 (7) |
M1–O1–Dy1 | 101.30 (16) | 101.55 (7) | 100.90 (6) | 100.85 (7) |
M1–O2–Dy1 | 105.47 (17) | 106.03 (7) | 106.32 (7) | 107.29 (7) |
M1^{i}–O3–Dy1 | 106.62 (18) | 108.46 (7) | 106.07 (7) | 106.90 (7) |
In all cases, there are μ_{3}-OH hydrogen bonding interactions to lattice solvent molecules but not to other molecules. Compounds 1 {Cr_{2}Dy_{2}} and the doped 8 {Al_{2}(Y/Dy)_{2}} are isomorphous to the previously reported compounds 7 {Al_{2}Dy_{2}} and 5 {Fe_{2}Dy_{2}}.^{17} There are reasonably strong π–π stacking interactions, with C⋯C distances down to 3.446 Å, linking the molecules into 2-D sheets. For compound 3 {Mn_{2}Dy_{2}}, there are similarly strong π–π interactions (shortest C⋯C 3.411 Å) linking the molecules into 1-D chains. Selected bond lengths and angles for the Dy^{III}-containing complexes are listed in Table 2.
In order to understand how the paramagnetic 3d^{III}-metal affects the magnetic behaviour of the Dy^{III} in the {M^{III}_{2}Dy_{2}} clusters, we also describe the yttrium diluted {Al_{2}Dy_{2}} compound, {Al_{2}Dy_{0.18}Y_{1.82}} and the {M_{2}Y_{2}} examples, as we did in the previous study on {Fe_{2}Dy_{2}}.^{17} This enables us to indirectly assess the 3d–4f interactions in these examples through comparison of the χT vs. T behaviour of {M_{2}Dy_{2}} with the sum of the contributions for the appropriate {M_{2}Y_{2}} and {Al_{2}Dy_{2}} systems. The dc susceptibility data for all the compounds are summarised in Table S2, ESI.†
For {Mn_{2}Y_{2}} (4), the χT value at room temperature is 5.38 cm^{3} K mol^{−1} which is lower than what is expected for two uncoupled S = 2 Mn^{III} ions with g = 2.0 (see Table S2† and Fig. 3). The χT value decreases slowly down to about 30 K below which it decreases rapidly to reach 1.10 cm^{3} K mol^{−1} at 2 K (Fig. 3). This could be due to antiferromagnetic coupling or significant single ion anisotropy. The χT plot of 4 {Mn_{2}Y_{2}} was also fitted using the PHI software^{21} and an antiferromagnetic coupling with J_{Mn–Mn} = −1.00 cm^{−1} and g = 1.92 was found – i.e. about twice as strong as for the Cr^{III} compound and in line with the fact that Mn^{III} has four rather than three unpaired electrons. The stronger Mn–Mn AF coupling is more likely to reflect the single electron now in the 3d_{z2} Mn^{III} orbital, this orbital being empty for Cr^{III}. The Jahn–Teller axis of Mn (and thus this orbital) points towards one of the bridging OH groups, so for each Mn–OH–Mn bridge, one of the two Mn–O interactions involves a 3d orbital with an unpaired electron in it, while for Cr both the 3d orbitals are empty. The reduced magnetisation M–H plots of 4 {Mn_{2}Y_{2}} show a crossover feature at about 2 T (Fig. S2†), which is likely to be the result of significant anisotropy, as previously observed in a {Co^{II}_{2}Y_{2}} compound.^{15}
As shown in the inset of Fig. 2, the χT value at low temperature for {Cr_{2}Dy_{2}} is lower than the corresponding values for [{Cr_{2}Y_{2}} + {Al_{2}Dy_{2}}], indicating a contribution from antiferromagnetic coupling between the Cr^{III} and Dy^{III} ions.
For complex 3 {Mn_{2}Dy_{2}}, the room temperature χT value of 33.16 cm^{3} K mol^{−1} is in good agreement with the expected value of 33.17 cm^{3} K mol^{−1} for two uncoupled Mn^{III} ions (S = 2, g = 2.0, C = 2.50 cm^{3} K mol^{−1}) and two uncoupled Dy^{III} ions (S = 5/2, L = 5, ^{6}H_{15/2}, g = 4/3, C = 14.17 cm^{3} K mol^{−1}). As the temperature is lowered, the χT product gradually decreases until 15 K, below which it increases to 28.03 cm^{3} K mol^{−1} at 2 K. The decrease in χT at higher temperatures can be attributed to the depopulation of the excited states of the Dy^{III} ions, whereas the increase at lower temperature suggests significant ferromagnetic interactions between the Mn^{III} and Dy^{III} ions. Modelling the 3 {Mn_{2}Dy_{2}} data by addition of the curves for 4 {Mn_{2}Y_{2}} and 7 {Al_{2}Dy_{2}}, as shown in the inset of Fig. 3, reveals that the interactions between Mn^{III} and Dy^{III} ions are ferromagnetic.
The field dependence of the magnetisation of 1 {Cr_{2}Dy_{2}} and 3 {Mn_{2}Dy_{2}} were performed at fields ranging from 0 to 7 T at 2 and 5 K. At higher fields, M increases linearly without clear saturation to ultimately reach 16.85 μ_{B} (H = 7 T, at 2 K) for 1 {Cr_{2}Dy_{2}} and 11.90 μ_{B} (H = 7 T, at 2 K) for 3 {Mn_{2}Dy_{2}}. The lack of saturation on a single master curve of M vs. H data for both complexes suggests the presence of magnetic anisotropy (Fig. S2†).
Fig. 4 Temperature (left) and frequency (right) dependence under zero dc field of the out-of-phase (χ′′) for compound 3 {Mn_{2}Dy_{2}}. |
Fig. 5 Cole–Cole plots at indicated temperature (left) and τ vs. T^{−1} plot in zero dc field (right) for 3 {Mn_{2}Dy_{2}}. |
Temperature and frequency dependent in phase (χ′) and out of phase (χ′′) ac measurements were performed using an applied dc field of 1000 Oe (Fig. 6 and S8, ESI†). This field was chosen to allow for comparisons with previously reported systems. A fitting of the data extracted from the frequency dependent out of phase (χ′′) signals using the Arrhenius equation (τ = τ_{0}exp(U_{eff}/k_{B}T)) gives an energy barrier of U_{eff} = 69.26 K and pre-exponential factor of τ_{0} = 1.18 × 10^{−7} s (Fig. S9, ESI†). Cole–Cole plots (χ′′ vs. χ′) for the temperature range 3.5–9.0 K (Fig. S9, ESI†) can be fitted for a single relaxation process using the Debye model to give α parameters in the range 0.14–0.28, indicating a wider distribution of relaxation times than seen for the non-diluted compound 7 {Al_{2}Dy_{2}}. This result indicates that the dipolar interaction between the two distant wingtip Dy^{III} ions plays a key role in suppressing the QTM.^{30} The comparison data are summarized in Table 3.
Fig. 6 Temperature (left) and frequency (right) dependence under 1000 Oe dc field of the out-of-phase (χ′′) for compound 8 {Al_{2}Dy_{0.18}Y_{1.82}}. |
3d–3d | 3d–Dy | Dy–Dy | SMMs (field/Oe) | |
---|---|---|---|---|
1 {Cr_{2}Dy_{2}} | AF | AF | F | No |
3 {Mn_{2}Dy_{2}} | AF | F | F | Yes (0) |
5 {Fe_{2}Dy_{2}} | AF | AF | F | Yes (1000) |
7 {Al_{2}Dy_{2}} | — | — | F | Yes (0) |
8 {Al_{2}Dy_{0.18}Y_{1.82}} | — | — | F | Yes (1000) |
The energy gap between the ground to first-excited state KDs is found to be 27.0 cm^{−1} (33.9 cm^{−1}), 50.2 cm^{−1} (50.2 cm^{−1}), 39.9 cm^{−1} (44.0 cm^{−1}), 47.0 cm^{−1} (43.5 cm^{−1}), for Dy1 (Dy2) in complexes 1 {Cr_{2}Dy_{2}}, 3 {Mn_{2}Dy_{2}}, 5 {Fe_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}} respectively (see Table 4). For complex 3 {Mn_{2}Dy_{2}}, both Dy1 and Dy2 are equivalent and therefore the ground to first excited state gap and the g-anisotropies are the same while in other cases, both the anisotropy and the gaps are different for the Dy1 and Dy2 ions. In particular, the ground to first excited state energy gaps are significantly larger for complexes 3 {Mn_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}}, while it is computed to be slightly smaller for complex 5 {Fe_{2}Dy_{2}} (Dy1) and much smaller for complex 1 {Cr_{2}Dy_{2}}. Since the energy gap is correlated to the crystal-field splitting energy, this suggests relatively weaker splitting of the m_{J} levels in 1 {Cr_{2}Dy_{2}} compared to complexes 3 {Mn_{2}Dy_{2}}, 5 {Fe_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}}.
Dy1 | E _{KD1} − E_{KD2} (cm^{−1}) | Angle | Dy2 | E _{KD1} − E_{KD2} (cm^{−1}) | Angle | ||
---|---|---|---|---|---|---|---|
1 {Cr_{2}Dy_{2}} | g _{ x1/} g _{ x2} | 0.28/0.22 | 27.0 | 21.8 | 0.18/0.10 | 33.9 | 20.4 |
g _{ y1/} g _{ y2} | 0.47/0.45 | 0.30/0.26 | |||||
g _{ z1/} g _{ z2} | 18.13/18.10 | 18.67/17.90 | |||||
3 {Mn_{2}Dy_{2}} | g _{ x1/} g _{ x2} | 0.13/1.78 | 50.2 | 52.1 | 0.13/1.78 | 50.2 | 52.2 |
g _{ y1/} g _{ y2} | 0.36/5.93 | 0.36/5.92 | |||||
g _{ z1/} g _{ z2} | 19.35/12.16 | 19.34/12.16 | |||||
5 {Fe_{2}Dy_{2}} | g _{ x1/} g _{ x2} | 0.25/1.26 | 39.9 | 25.4 | 0.18/0.88 | 44.0 | 17.3 |
g _{ y1/} g _{ y2} | 0.47/1.40 | 0.35/0.97 | |||||
g _{ z1/} g _{ z2} | 18.01/15.18 | 18.09/15.79 | |||||
7 {Al_{2}Dy_{2}} | g _{ x1/} g _{ x2} | 0.00/1.02 | 47.0 | 35.9 | 0.00/0.70 | 43.5 | 28.3 |
g _{ y1/} g _{ y2} | 0.00/1.62 | 0.00/0.98 | |||||
g _{ z1/} g _{ z2} | 19.05/16.56 | 19.00/16.98 |
SHAPE 2.1 analysis^{18–20} yields a Dy_{Mn} > Dy_{Fe} ∼ Dy_{Al} > Dy_{Cr} trend for the distortion of Dy^{III} ions with respect to the idealised spherical-capped square anti-prismatic geometry and this trend matches with the computed energy gap between ground to first excited state.
The LoProp computed charges^{38} obtained from CASSCF calculations for complexes 1 {Cr_{2}Dy_{2}}, 3 {Mn_{2}Dy_{2}}, 5 {Fe_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}} are shown in Fig. 8. For the Dy^{III} ion, the oblate anisotropy ellipsoid means that the density is expected to lie along the plane with the least repulsion. The charge on the μ-alkoxo and μ_{3}-OH are found to be very large in all four cases as they are connected to the trication which tend to polarise the oxygen atom charges significantly. Thus the oblate density lies perpendicular to this direction and the g_{zz} axis lies along the O–Dy–O direction where the oxygen atoms possess the largest negative charges^{39,40} In complex 1 {Cr_{2}Dy_{2}}, the g_{zz} axis lies in the direction defined by the oxygen atom of one of the carboxylates and the μ-alkoxo oxygen connected to the Cr^{III} ion. While this is found to be similar for complexes 1 {Cr_{2}Dy_{2}}, 3 {Mn_{2}Dy_{2}}, 5 {Fe_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}}, clearly there are structural variations. For example, the Cr–O (alkoxo) bridging distance is 1.963(4) Å, while in complex 3 {Mn_{2}Dy_{2}}, the Mn–O distance is much shorter (1.896(16) Å) in line with the Jahn–Teller distortion. A shorter bond distance is expected to lead to a greater polarisability of the oxygen and resulting the g_{zz} aligning closest to the μ-alkoxo oxygen with a deviation of only 18°.This is much smaller compared to the case in complex 1 {Cr_{2}Dy_{2}} (25°). This significant variation in the orientation of the g_{zz} axis caused by the electronic structure of the trication at the body of the butterfly apparently leads to the variation in the ground-state to excited-state gaps. A similar scenario is noted also for complexes 5 {Fe_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}}, where the ground state g_{zz} axis is found to align along the μ-alkoxo oxygen atom (with deviations of 18.5° for 5 {Fe_{2}Dy_{2}} and 15.4° for complex 7 {Al_{2}Dy_{2}}). Another important result from the analysis of the charges concerns the charge found at the equatorial position of the Dy^{III} ion, as this is reflected in the transverse anisotropy. For complex 7 {Al_{2}Dy_{2}}, significant reduction of charge on the μ_{3}-OH group lying in the equatorial plane is noted and this leads to a drastic reduction of transverse anisotropy at −0.84 in 7 {Al_{2}Dy_{2}} rather than −0.93 in 1 {Cr_{2}Dy_{2}} or −0.96 in 3 {Mn_{2}Dy_{2}} and 5 {Fe_{2}Dy_{2}}.
In all the complexes, m_{J} = ±15/2 is found to be stabilized as the ground state (see Fig. S10, ESI†). This can be attributed to the stronger axial interactions compared to transverse interactions. However, significant transverse anisotropy is present for the ground state KD of complexes 1 {Cr_{2}Dy_{2}} and 5 {Fe_{2}Dy_{2}} g_{xx} = 0.28/0.18, g_{yy} = 0.47/0.30, g_{zz} = 18.13/18.67 for Dy1/Dy2 of complex 1 {Cr_{2}Dy_{2}} and g_{xx} = 0.25/0.18, g_{yy} = 0.47/0.35, g_{zz} = 18.01/18.09 for Dy1/Dy2 of complex 5 {Fe_{2}Dy_{2}} (Table 4), as a result of the strong mixing of the m_{J} = ±15/2, ±13/2, ±11/2 and ±9/2 states (see Fig. S10, ESI†). The transverse components for both the complexes are found to be larger for Dy1, and the effect on the measured χT values for both compounds, and in particular for the {Cr_{2}Dy_{2}} one, is a substantial decrease in the value expected considering the summation of the Y and Al analogues with the deleted 4f/3d contributions respectively. This at first sight surprising reduction in the χT value has also been observed for a recently reported {Cr_{2}Dy_{3}} system^{41} where this was attributed to the changes in the anisotropies of the Dy(III) ions. It should also be noted that the magnetisation plots for the {Cr_{2}Y_{2}} compound indicate that the contribution of the coupled Cr(III) ions is far from isotropic in nature.
In complexes 3 {Mn_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}}, the mixing of KD1 with KD2 is relatively smaller compared to the two complexes 1 {Cr_{2}Dy_{2}} and 5 {Fe_{2}Dy_{2}} because of the larger energy separation between them. Significant axial anisotropy is present for the ground state KD of complex 3 {Mn_{2}Dy_{2}}. A clear Ising nature is observed for the Dy^{III} ions in complex 3 {Mn_{2}Dy_{2}} (g_{xx} = 0.13/0.13, g_{yy} = 0.36/0.36, g_{zz} = 19.35/19.34 for Dy1/Dy2) and even more markedly in complex 7 {Al_{2}Dy_{2}} (g_{xx} = 0.00/0.00, g_{yy} = 0.00/0.00, g_{zz} = 19.05/19.00 for Dy1/Dy2) see Table 4.
To analyse the various possible relaxation processes associated with the single-ion Dy^{III} anisotropy, the mechanisms of the magnetic relaxation were computed and these are shown in Fig. S10, ESI.†
In complexes 1 {Cr_{2}Dy_{2}} and 5 {Fe_{2}Dy_{2}}, the ground state tunnelling probability is large for the Dy1 ion (1.2 × 10^{−1}μ_{B}). For the Dy ions in the other compounds, the ground state tunnelling probability is found to be smaller (5.0 × 10^{−2} to 8.8 × 10^{−2}μ_{B}). In complexes 1 {Cr_{2}Dy_{2}} and 5 {Fe_{2}Dy_{2}}, the tunnelling probability at the single ion level in the ground state is larger than in 3 {Mn_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}} and the calculations predict the absence of SMM behaviour. This is in accord with the experimental measurements. If we consider relaxation processes beyond those of the single-ion, then factors such as Dy^{III}–Dy^{III} exchange coupling may play a role in quenching the observed QTM. Therefore, the Dy^{III}–Dy^{III}, Dy^{III}–3d^{III} and 3d^{III}–3d^{III} exchange couplings were taken into account using the POLY_ANISO suite. These gave the 3d^{III} single ion isotropic g-tensors (see Table S3 in ESI†) which have values too small to significantly influence the magnetic anisotropy of the Dy^{III} centres apart from for complex 3 {Mn_{2}Dy_{2}} where the single-ion zero-field splitting, D, values of the Mn^{III} ions are relatively large at −3.35 cm^{−1}, see Table S3 in ESI.†
(1) |
Complex | J values (Lines model) | J _{1} (DFT) | ||||
---|---|---|---|---|---|---|
J _{1} | J _{2} | J _{3} | zJ | |||
1 {Cr_{2}Dy_{2}} | J _{Tot} | −0.65 | −1.15 | 0.405 | −0.045 | −0.81 |
J _{Exc} | −0.50 | −0.80 | 0.370 | |||
J _{Dip} | −0.15 | −0.35 | 0.035 | |||
3 {Mn_{2}Dy_{2}} | J _{Tot} | −3.20 | 0.15 | 0.035 | — | −2.10 |
J _{Exc} | −2.10 | 0.09 | −0.001 | |||
J _{Dip} | −1.10 | 0.06 | 0.036 | |||
5 {Fe_{2}Dy_{2}} | J _{Tot} | −4.20 | −0.12 | 0.060 | — | −4.92 |
J _{Exc} | −3.00 | −0.05 | 0.025 | |||
J _{Dip} | −1.20 | −0.07 | 0.035 | |||
7 {Al_{2}Dy_{2}} | J _{Tot} | — | — | 0.049 | — | — |
J _{Exc} | — | — | 0.025 | |||
J _{Dip} | — | — | 0.024 |
For complexes 1 {Cr_{2}Dy_{2}}, 3 {Mn_{2}Dy_{2}} and 5 {Fe_{2}Dy_{2}}, magnetic interactions between the transition metals (J_{1}) are found to be antiferromagnetic in nature with complex 5 {Fe_{2}Dy_{2}} having the largest magnitude of J_{1} followed by complex 3 {Mn_{2}Dy_{2}} and complex 1 {Cr_{2}Dy_{2}}. To ascertain the J_{1} values independently, DFT calculations were performed on {Cr_{2}La_{2}} and {Mn_{2}La_{2}} models and these values reproduce the sign as well as the magnitude trend for the J_{1} interaction. For complexes 1 {Cr_{2}Dy_{2}} and 5 {Fe_{2}Dy_{2}}, the magnetic interaction between Dy–3d^{III} (J_{2}) is found to be antiferromagnetic whereas for complex 3 {Mn_{2}Dy_{2}}, it is found to be ferromagnetic in nature. All these values are in accord with the earlier literature reports.^{40,42} The weak Cr^{III}–Cr^{III} (J_{1}) interaction in complex 1 {Cr_{2}Dy_{2}} causes the relaxation to occur via the ground state with very high QTM probability.
For complexes 1 {Cr_{2}Dy_{2}} and 5 {Fe_{2}Dy_{2}}, the tunnelling (Δ_{tun}) parameters of the exchange coupled ground state are computed to be large (≤4.3 × 10^{−3} and ≤2.1 × 10^{−4} respectively, see Fig. 10a and c respectively, see Fig. S11 in ESI† for low lying exchange spectra for complexes 1 {Cr_{2}Dy_{2}}, 3 {Mn_{2}Dy_{2}}, 5 {Fe_{2}Dy_{2}} and 7 {Al_{2}Dy_{2}}), whereas for complexes 3 {Mn_{2}Dy_{2}} (6.0 × 10^{−6}, see Fig. 10b) and 7 {Al_{2}Dy_{2}} (3.6 × 10^{−6}, see Fig. 10d) the same is computed to be very small. Thus in complex 1 {Cr_{2}Dy_{2}}, the magnetic relaxation occurs via the ground state. In complex 3 {Mn_{2}Dy_{2}}, the first excited state possesses relatively high tunnel splitting (Δ_{tun} = 1.0 × 10^{−5} cm^{−1}) suggesting relaxation via the first excited state with U_{cal} value of 16.4 cm^{−1} (see Fig. 10b). This picture is consistent with the experimental data where a relaxation process is observed with a barrier height of 13.5 cm^{−1} (U_{eff}). For complex 5 {Fe_{2}Dy_{2}}, the tunnelling probability of the exchange coupled ground state is found to be large which suggests a possible relaxation pathway via the ground state.
Other excited states are found to be below 1.3 cm^{−1} so applying an external magnetic field can overcome this energy barrier and relaxation can occur through the next higher excited state with a barrier height of 40.2 cm^{−1}. This picture is consistent with the experimental data, where in the presence of an external magnetic field relaxation occurs through an excited state with a barrier height of 11.3 cm^{−1} (U_{eff}). Since the tunnelling probability is high, one can expect a reduction in the U_{eff} value compare to the U_{cal} value, where this probability is not taken in to consideration.
For complex 7 {Al_{2}Dy_{2}}, the tunnelling probability of the exchange coupled ground state is almost negligible (Δ_{tun} = 3.6 × 10^{−6}). This places the estimate of U_{cal} for this molecule as 43.5 cm^{−1} and relaxation via the exchange coupled first excited state (Δ_{tun} = 6.3 × 10^{−5}, see Fig. 10d). This picture is consistent with the experimental data where in absence of an external field relaxation occurs with a barrier height of 26.9 cm^{−1}.
It is important to note here that there are some deviations in the experimental and theoretically estimated barrier heights. This is essentially due to the fact that our relaxation mechanism has not factored other possibilities such as intermolecular interaction, hyperfine coupling of the metal ions/nitrogen atoms etc., that are likely to contribute the overall relaxation process and thus this difference between U_{eff} and U_{cal} is inevitable.
Ac susceptibility measurements indicate no SMM behaviour was observed for any of the analogues using diamagnetic yttrium at the wingtips instead of Dy. This reveals that the SMM behaviour is intrinsic to the presence of the Dy^{III} ions. Furthermore, for the {Al_{2}Dy_{2}} analogue, the weak (+0.049 cm^{−1}) dipolar interaction between the two far away Dy^{III} ions plays a key role in suppressing the zero-field QTM of the individual Dy^{III} ions as revealed by this compound showing SMM behaviour under zero dc field. Thus the weak but key cooperative interaction plays a significant role for the performance of the system in terms of the dynamic and thus SMM behaviour. Changing from Cr to Mn in the {M^{III}_{2}Ln^{III}_{2}} motif, the anisotropy of the Dy^{III} ion can be utilised to improve the performance of the SMM through tuning the suppression (quenching) of the QTM processes of the Dy^{III} ions. The SMM behaviour for the four complexes follows the trend, {Al_{2}Dy_{2}} > {Mn_{2}Dy_{2}} > {Fe_{2}Dy_{2}} > {Cr_{2}Dy_{2}}. Ab initio calculations performed on all Dy^{III}-containing molecules reveal similar results. It is clear that the strength and maybe the sign of the 3d–4f exchange interaction plays a key role in directing the nature of the SMM properties observed.
Footnote |
† Electronic supplementary information (ESI) available. CCDC 1880458, 1880459, 1880460 and 1902469. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c8sc05362f |
This journal is © The Royal Society of Chemistry 2019 |