Eufemio Moreno
Pineda
^{a},
Yanhua
Lan
^{b},
Olaf
Fuhr
^{a},
Wolfgang
Wernsdorfer
*^{ab} and
Mario
Ruben
*^{ac}
^{a}Institute of Nanotechnology (INT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany. E-mail: mario.ruben@kit.edu
^{b}Institut Néel, CNRS, Université Grenoble Alpes, 25 rue des Martyrs, F-38000 Grenoble, France
^{c}Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS, Université de Strasbourg, 23 rue du Loess, BP 43, F-67034 Strasbourg Cedex 2, France
First published on the web 22nd September 2016
Carbamate formation in green-plants through the RuBisCO enzyme continuously plays a pivotal role in the conversion of CO_{2} from the atmosphere into biomass. With this in mind, carbamate formation from CO_{2} by a lanthanide source in the presence of a secondary amine is herein explored leading to a lanthanide–carbamate cage with the formula [Dy_{4}(O_{2}CN^{i}Pr_{2})_{12}]. Magnetic studies show slow relaxation leading to the observation of hysteresis loops; the tetranuclear cage being a single molecule magnet. Detailed interpretation of the data reveals: (i) the presence of two different exchange interactions, ferromagnetic and antiferromagnetic and (ii) the observation of exchange-bias quantum tunnelling with two distinct sets of loops, attributable to ferromagnetic interactions between dysprosium ions at longer distances and antiferromagnetic exchange between dysprosium ions at shorter distances. The results clearly demonstrate that the [Dy_{4}(O_{2}CN^{i}Pr_{2})_{12}] cage acts as a quantum magnet which in turn could be at the heart of hybrid spintronic devices after having implemented CO_{2} as a feedstock.
Reminiscent of enzymatic CO_{2} activation, where an oxophilic Mg^{2+} centre is involved, transition metals have demonstrated that they can be versatile catalytic entities to activate and interconvert CO_{2} in organic compounds.^{8,9} Moreover, they have been shown to be successful in coordinating to CO_{2}, forming metal complexes.^{10–13} Recently Long et al. have studied the cooperative insertion of CO_{2} into diamine-appended metal–organic frameworks (MOFs) where the removal of CO_{2} from solution can be directly achieved through the insertion of CO_{2} into amine groups leading to a carbamate-containing MOF.^{14}
In this regard, lanthanide metal ions seem to be promising agents for CO_{2} capture due to their strong oxophilic characteristics which allow the concerted insertion of CO_{2} as a carbamate^{15–18} or as carbonate-containing compounds with high lanthanide/CO_{2} ratios.^{19,20} Several polymetallic carbonate-containing systems have been described, showing not just interesting structural motifs but also bewildering physical properties.^{20} Similarly, lanthanides are milestone entities in terms of their magnetism, and have also shown fascinating physical behaviours such as nuclear spin detection and manipulation^{21,22} blocking of magnetisation at high temperatures^{23–26} magnetic memory in chiral systems with a non-magnetic ground state^{27} and, very recently, blocking magnetisation at the atomic level.^{28} These properties have led researchers to envisage a diverse range of possible applications for lanthanide-based molecules, including their potential to act as qubits for quantum information technologies and prototype quantum spintronic devices such as molecular spin valves and transistors.^{22,29,30} Thus, the quantum correlations observed in lanthanide molecules (e.g. superposition, entanglement, coherence, etc.) are important resources for quantum communication and processing, particularly in quantum computing.^{31}
Based on these two points, i.e. (i) CO_{2} abundance and (ii) the quantum physical properties of lanthanide units, we explore the physical implementation of CO_{2} as a feedstock for the synthesis of lanthanide molecular nanomagnets. Herein, we firstly explore the CO_{2} fixation of an amine in the presence of dysprosium chloride to form a complex with the formula [Dy_{4}(O_{2}CN^{i}Pr_{2})_{12}] (1) (O_{2}CN^{i}Pr_{2} = diisopropylcarbamate) (Fig. 1b and 2). Moreover, we explore the magnetic properties of such a material, which in turn could shed light on its possible applicability in quantum spintronic devices or quantum computing. Herein, through a combination of alternating current SQUID measurements, and μ-SQUID measurements along with a simple electrostatic analysis, we show that the [Dy_{4}(O_{2}CN^{i}Pr_{2})_{12}] cage exhibits both ferro- and antiferromagnetic interactions, that can be associated with the intramolecular interactions between the Ising-like dysprosium ions within the compound, exhibiting exchange-bias quantum tunnelling, where the two different exchange interactions could, in principle, be employed in four-qubit quantum gate operations;^{32} these characteristics highlight the importance of our proposal to employ CO_{2} as a C_{1} building block to form added-value materials.
The neutral homoleptic tetramer 1 is composed of four Dy(III) ions and twelve carbamate groups resulting from the capture of twelve CO_{2} molecules under mild synthetic conditions. Two Dy(III) ions are found in the asymmetric unit, interrelated by a two-fold axis and both ions, i.e. Dy(1) and Dy(2) are hepta-coordinated featuring a capped trigonal prism geometry^{33} (Table S3†). The Dy(1)⋯Dy(2) and Dy(1)′⋯Dy(2)′ distances are 3.8381(6) Å whilst the Dy(1)⋯Dy(2)′ and Dy(1)′⋯Dy(2) distances are 4.6090(7) Å. The Dy⋯O distances are in the range of 2.238(5) to 2.404(4) Å. The versatility of carbamates as coordinating groups is evidenced with the three distinct coordination modes present in the cage, 1.11, 2.11 and 3.21 (ref. 34) (Fig. S2†). All carbamates are rather regular with C⋯N distances ranging between 1.33(1)–1.372(8) Å and C⋯O in the range of 1.25(1)–1.30(1) Å (Table S2†). The closest intermolecular Dy⋯Dy distance is 12.8530(8) Å.
To probe the dynamic behaviour of compound 1, alternating current (AC) susceptibility measurements under an oscillating field of 3.5 Oe were undertaken. Compound 1 shows clear signatures of a Single Molecule Magnet (SMM) at zero field, i.e. strong frequency dependent magnetic behaviour with a maximum shifting upon frequency change and temperature. At zero field the out-of-phase component is observed in the χ′′_{M}(T) below 12 K, with a broad maximum at about 3.8 K for a frequency of 1.5 kHz. The maximum shifts towards lower temperatures with decreasing frequency. In the χ′′_{M}(ν) a single broad process is observed which can be fitted using a generalised Debye model. The Arrhenius plot is based on AC results and was fitted to data between 7.5 and 10 K yielding an energy barrier of U_{eff} = 25.7(1) K, a τ_{0} = 6.7(1) × 10^{−6} s, with α varying from 0.07 to 0.45 from high to low temperature indicating a wide distribution of relaxation times, which could be associated with the two slightly distinct dysprosium ions in 1 (Fig. 3b–d and S3†).
Given that the U_{eff} at zero field is small, the investigation of an optimal field was carried out to try to reduce the quantum tunnelling rate. An optimal field of 1.5 kOe was obtained and under this condition 1 was reinvestigated (Fig. S4–S6†). Likewise at zero field, upon application of the optimal field, the out-of-phase component in the temperature dependence χ′′_{M}(T) begins from 12 K, with a very broad maximum at 6 K at the highest frequency (1.5 kHz) whilst the χ′′_{M}(ν) shows just a single broad process, which can be fitted to a simple Debye model. Arrhenius treatment of the data above 7.5 K yields U_{eff} = 31.1(1) K, τ_{0} = 2.55(1) × 10^{−6} s, and 0.008 < α < 0.015 showing a narrower distribution of relaxation times but not considerable improvement in the U_{eff}. As evidenced, application of the optimal DC field does not completely slow down the fast tunnelling of 1 highlighting that the quantum tunnelling of the magnetisation (QTM) is not efficiently suppressed. This can be attributed to transverse anisotropy and to dipolar/exchange and/or hyperfine interactions. The linear dependence of ln(τ) at high temperatures indicates an Orbach relaxation mechanism, whilst the data at lower temperatures is markedly nonlinear at zero and under application of the optimal field, suggesting the onset of competing Orbach and/or Raman processes. The anisotropic nature of compound 1 does not allow fitting of the χ_{M}T(T) and M(H) without advanced and costly ab initio calculations.
Fig. 4 μ-SQUID measurements and Zeeman diagram for 1. Hysteresis loop measurements performed on a single crystal of 1; red and blue arrows represent the direction of the applied field with respect to the molecule’s orientation within the crystal lattice. Temperature dependence at a fixed sweep rate of 0.14 T s^{−1} with the field applied transverse (a) and parallel (b) to the average direction. Field sweep rate studies at a fixed temperature of 0.03 K with the fields transverse (c) and parallel (d) to the average direction. Panels (a) and (c) show the antiferromagnetic behaviour with a typical double S-shape whilst panels (b) and (d) show the ferromagnetic behaviour. Zeeman diagrams simulated using eqn (1) along the antiferromagnetic projection (e) and the ferromagnetic projection (f). Insets of the panels show the avoided level crossings observed alongside the antiferromagnetic projection at ±0.35 T and along the ferromagnetic projection at ±0.22 T. The spin structure in panels (e) and (f) (green arrows) represent the ground and excited states involved in the quantum tunnelling events (see text). |
In order to understand these two distinct behaviours at the first stage, we invoke spin effective formalism^{38} (S_{eff} = 1/2) employing pure axial g-tensors e.g. g_{xx} = g_{yy} = 0; g_{zz} = 20 and the projection angles of the m_{J} = ±15/2 state for each Dy(III) ion obtained from the electrostatic analysis. Unfortunately, S_{eff} = 1/2 can be, at first order, mixed very quickly by transverse fields leading to huge tunnelling splitting, not representative of the system. This would not be the case with a Dy(III) spin given that the m_{J} = ±15/2 levels only weakly mix by a transverse field (mixing in 15th order only). Unfortunately, due to the huge Hilbert space of the four Dy(III) ions (2S + 1)^{n} = 65536 and all the parameters involved i.e. ligand field splittings (LFS), g-values, Euler angles and exchange interaction(s), we cannot employ a J = 15/2 to understand the μ-SQUID data. To circumvent this problem, we therefore employ a fictitious S = 3/2 with an arbitrarily big LFS (D) of −100 cm^{−1}, given that this spin value is less prone to mixing by transverse field. g-Values were kept isotropic (g_{xx} = g_{yy} = g_{zz} = 20/3) and while the LFS were rotated employing the Euler angles obtained from the electrostatic analysis.^{39} The Hamiltonian describing our system is then given in eqn (1):
(1) |
As observed in Fig. 4e, when the field is applied perpendicular to the a-crystallographic axis the ground state is a singlet. Upon sweeping the field only one quantum tunnelling event is present, in the experimental field range, at ±0.35 T, consistent with the observation in the μ-SQUID data (Fig. 4a, c and e). This event is associated with tunnelling between the ground state and nearest excited state which, at zero field, lies at ca. 1.6 K and involves a single spin flip. Conversely, when the field is applied parallel to the a-axis the situation leads to a well-defined ferromagnetic ground state with three close excited states lying at 3.3 K, 3.8 K and 3.9 K. Application of a negative magnetic field leads to a ground state characterised by ψ_{1} = c_{i}|↓↓↓↓〉 (Fig. 4b, d and f). Upon field sweeping the first crossing point occurs at 0 T, where the possibility of tunnelling from ψ_{1} to ψ_{2} = c_{j}|↑↑↑↑〉 is negligible since it would require all the spins to tunnel simultaneously. At +0.25 T and +0.27 T two crossovers are observed, involving ψ_{1} and the first and second excited states with ψ_{3} = c_{k}|↑↑↑↓〉 and ψ_{4} = c_{l}|↑↑↑↓〉. At these crossovers a tunnelling event occurs, due to the admixture of wavefunctions, which leads to a single spin flip. The third crossover is then observed at +0.42 T, occurring due to quantum tunnelling of ψ_{1} with a diamagnetic excited state with wavefunctions ψ_{5} = c_{m}|↓↑↓↑〉, involving a double spin flip. These events are in good agreement with the crossings observed in the μ-SQUID loops, i.e. ±0.22, ±0.32 and ±0.42 T. Our model does not account for the crossings at ±0.62 T, which occur twice during the field sweep from −1 T to +1 T, which are not present in our simulation even after inclusion of off-diagonal dipolar terms, highlighting the weakness of our assumptions. Despite this, however, the simulations reproduce the ferromagnetic and antiferromagnetic behaviours and most of the tunnelling events observed in the μ-SQUID loops quite well. Several other crossing points at higher field occur, however due to the temperature of the characterisation and the applied field, the population of the ψ_{1f} state at these crossing points is expected to be negligible.
Simulation of the M(H) data utilising parameters from the simulations of the Zeeman diagram is also possible by employing eqn (1) and the J_{1} and J_{2} (see the inset of Fig. 3a). The simulation is slightly higher than the experimental data, which could account for smaller g-values and some rhombicity on the Dy(III) ions. In order to compare our results with a similar structure, we obtained the isotropic analogue i.e. [Gd_{4}(O_{2}CN^{i}Pr_{2})_{12}]^{18} (2) and interestingly simultaneous fitting of the χ_{M}T and M(H) data yields both ferromagnetic and antiferromagnetic interactions, as also observed in 1, highlighting the possible coexistence of two exchange pathways (see Fig. S7 and explanation therein†).
The average interactions projected onto the m_{J} = 15/2 states are found to be J_{1} = −0.022 K and J_{2} = +0.030 K, and are very weak as expected for lanthanide ions. To compare the magnitude of the exchange interaction obtained from our analysis, the exchange and g-values for compound 1 were re-scaled to the most commonly used spin effective (S_{eff} = 1/2) formalism: leading to J_{1} = −4.95 K and J_{2x} = +6.75 K, thus scaled to the magnitude of the exchange within the range of exchange observed in other reported Dy(III)-based SMMs.^{24,40,41}
At this stage, we can understand why the application of an optimal field during the AC data collection had very little effect on the U_{eff} of compound 1. As observed in Fig. 4, due to the two exchange pathways in 1, the application of DC fields also induces many other level crossings, where the magnetisation can tunnel. Many other steps can be present upon application of the applied field in different directions of the molecule, therefore leading to the diminished SMM behaviour observed in the AC measurements of the powdered sample. Moreover, compound 1 shows clear exchange-biased quantum tunnelling,^{42} resulting from the magnetic exchange between neighbouring Dy(III)-ions and non-collinear arrangement of the anisotropic axes. Interestingly, two very different magnetic behaviours, ferro- vs. antiferromagnetic, can be clearly addressed by controlling the direction of the applied magnetic field along the crystal.
Footnotes |
† Electronic supplementary information (ESI) available: Synthesis, crystallographic and magnetic measurements and shape analysis details and figures. CCDC 1483884. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c6sc03184f |
‡ Crystal data for 1 [Dy_{4}N_{12}O_{24}C_{105}H_{192}]: M_{r} = 2656.69, monoclinic, T = 180.15(1) K, a = 28.1117(11), b = 20.1279(6), c = 22.8674(10) Å, β = 105.985(3)°, V = 12438.7(8) Å^{3}, Z = 4, r = 1.419 g cm^{−3}, total data = 41630, independent reflections 11718 (R_{int} = 0.0723), μ = 2.442 mm^{−1}, 699 parameters, R_{1} = 0.0723 for I ≥ 2σ(I) and wR_{2} = 0.1870. The data was collected employing a STOE StadiVari 25 diffractometer with a Pilatus 300 K detector using GeniX 3D HF micro focus with MoK_{α} radiation (λ = 0.71073 Å). |
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