The first near-linear bis(amide) f-block complex: a blueprint for a high temperature single molecule magnet

Abstract

We report the first near-linear bis(amide) 4f-block compound and show that this novel structure, if implemented with dysprosium(III), would have unprecedented single molecule magnet (SMM) properties with an energy barrier, U_eff, for reorientation of magnetization of 1800 cm⁻¹.

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Since their initial discovery,¹ single molecule magnets (SMMs) have been lauded as candidates for high density data storage devices.² A major breakthrough in the field³ occurred in 2003 with the observation of SMM behavior in a monometallic {TbPc₂}⁻ complex with an energy barrier, U_eff = 230 cm⁻¹.⁴ The ensuing decade saw rapid growth in lanthanide SMMs⁵ with the U_eff barrier to magnetization reversal increased to 652 cm⁻¹ for another derivative of {TbPc₂},⁶ and 585 cm⁻¹ for a polymetallic Dy@{Y₄K₂} complex.⁷ The highest blocking temperature T_B (i.e. the temperature at which hysteresis is observed) was also increased to 14 K, via an N₂³⁻˙ radical bridge in a {Tb₂N₂³⁻˙} complex.⁸

Although three of these milestones employ the Tb^III ion, by far the most utilized lanthanide ion in SMMs is Dy^III by virtue of its unique electronic structure.⁹ Apart from a radical-bridged {Dy₂N₂³⁻˙} complex,¹⁰ nearly all polymetallic Dy^III-based SMMs possess negligible interactions between magnetic spin centres, and instead rely on the single ion anisotropy of Dy^III (i.e. the local crystal field environment) to provide the barrier to the reversal of magnetization. Intra- or intermolecular interactions are often detrimental to the performance of Dy^III SMMs so that doping a small amount of the paramagnetic ion into a diamagnetic host lattice (usually the Y^III analogue) often results in an increased U_eff.⁷

An electrostatic model for the design of ideal ligand environments to exploit the maximal anisotropy of Dy^III has been postulated,^11,12 and shown to be in good agreement with multi-configurational complete active space Self consistent field (CASSCF) ab initio calculations¹² that are often employed to examine 4f complexes, pioneered by Chibotaru.^7,13 Electrostatic approaches suggest that the optimal ligand environment to exploit the oblate spheroidal electron density of Dy^III is axial, where rigorously axial systems have the benefit of maintaining a single, unique quantization axis for the total angular momentum m_J states.¹⁴ A set of unadulterated m_J states implies that the probability of quantum tunnelling of the magnetization (QTM) is reduced, therefore increasing magnetic relaxation times.²

The simplest axial ligand environment is a linear two-coordinate complex with donor atoms exclusively on a single Cartesian axis; the U_eff barrier is so large for the {Dy₅} and {Dy₄K₂} alkoxide complexes⁷ because of the strongly axially repulsive crystal field potentials along the local z-direction of each Dy^III. Other compounds such as [(C₈H₈)₂Ln]⁻ (ref. 15) or Cloke's bis(arene) lanthanide complexes¹⁶ are sometimes described as linear, but lack donor atoms directly on the axis. Linear 3d-metal compounds also show remarkable magnetic behaviour with very high U_eff values.¹⁷ A one coordinate lanthanide complex [DyO]⁺ has been considered theoretically with a very large U_eff predicted,¹⁴ however such an entity is not chemically feasible.

Very low coordination numbers for 4f-ions are difficult to achieve as these are large, electropositive ions, which require a sterically demanding ligand. Such a pro-ligand HN(SiⁱPr₃)₂ was designed, and synthesised from ClSiⁱPr₃ and LiHN(SiⁱPr₃), and this was converted to the group 1 transfer agent [KN(SiⁱPr₃)₂] with KH. Reacting two equivalents of [KN(SiⁱPr₃)₂] with samarium(II) diiodide yields the mononuclear homoleptic bis(amide) complex, [(ⁱPr₃Si)₂N–Sm–N(SiⁱPr₃)₂] 1 (Fig. 1, see ESI† for details).

Fig. 1 Synthetic route to 1.

Complex 1 is the first near-linear f-element complex, with an N–Sm–N angle of 175.52(18)° in the solid state (Fig. 2, see ESI† for details); this near-linearity contrasts with the bent C–Ln–C angles of [Ln^II{C(SiMe₃)₃}₂] complexes (Ln = Sm, Yb, Eu).^18–20 The bulky ⁱPr groups are vital for the isolation of a homoleptic complex, as [Sm{N(SiMe₃)₂}₂(THF)₂] exhibits additional O-donors.²¹ The Sm–N distances in 1 [2.483(6) Å] are longer than those observed in [Sm{N(SiMe₃)₂}₂(THF)₂] [mean Sm–N 2.433(9) Å] but this is compensated by 1 exhibiting four short Sm⋯C_methine distances [Sm⋯C 3.082(7)–3.224(7) Å] that are closer than the analogous Sm⋯C_methyl contacts observed in [Sm{N(SiMe₃)₂}₂(THF)₂] [Sm⋯C 3.32(1)–3.46(1) Å].²¹ The approximately planar SmNSi₂ fragments in 1 are staggered with respect to each other (twist angle of 44.42°), with the deviation from 90° attributed to agostic Sm⋯C_methine interactions.

Fig. 2 Molecular structure of 1. Hydrogen atoms omitted for clarity. Selected bond lengths (Å) and angles (°): Sm1–N1 2.483(6), Sm1–N2 2.483(6), Sm1⋯C7 3.180(8), Sm1⋯C16 3.169(8), Sm1⋯C19 3.082(8), Sm1⋯C34 3.224(8), N1–Sm1–N2 175.52(18), Sm1–N1–Si1 109.9(3), Sm1–N1–Si2 111.6(3), Si1–N1–Si2 138.5(4), Sm1–N2–Si3 109.8(4), Sm1–N2–Si4 110.8(3), Si3–N2–Si4 138.8(4).

Formally each nitrogen atom carries a single negative charge and the Sm^II ion is divalent, with an [Xe]4f⁶ configuration. The f⁶ configuration leads to a formally diamagnetic ⁷F₀ ground state, with close lying excited states that provide a non-zero magnetic moment at room temperature. Magnetic measurements on 1 give a room temperature magnetic moment of 3.62 μ_B that falls towards zero at low temperature (Fig. S2 and S3, ESI†). This is clearly incompatible with interesting low temperature magnetic behaviour. However, the structure of 1 is close to the ideal linear arrangement to stabilize the large angular momentum states of Dy^III and produce monstrous uniaxial magnetic anisotropy.

Such a Dy^III compound is challenging to make; we believe a route via the heteroleptic [Dy{N(SiⁱPr₃)₂}₂I] treated with the potassium salt of a large anion might work through precipitation of a potassium iodide. Other routes can be imagined, and here we present predictions of the magnetic properties of such a complex, intending to inspire synthetic work towards the linear Dy^III complex, and, more ambitiously, the isoelectronic Tb^II analogue.

The properties of [(ⁱPr₃Si)₂N–Dy–N(SiⁱPr₃)₂]⁺2 are predicted by CASSCF/RASSI/SINGLE_ANISO²²ab initio calculations (see ESI† for details) employing the structure of 1, where Sm^II has been replaced by Dy^III. The validity of the method was tested by calculating the variable temperature magnetic behavior of 1, where the agreement is excellent (Fig. S2 and S3, ESI†). Dy^III has a ⁶H_15/2 ground multiplet, which is split by the crystal field into eight Kramer's doublets with total angular momentum projections m_J = ±1/2, ±3/2,… ±15/2. The ab initio calculations show that the lowest six Kramers doublets are the almost pure m_J states of m_J = ±15/2, ±13/2, ±11/2, ±9/2, ±7/2 and ±5/2, sharing a common quantization axis (Fig. 3 and Tables S1 and S2, ESI†). The two most energetic doublets are strongly mixed; a characteristic of low symmetry complexes due to the lack of a rigorous molecular C_∞ axis.¹⁴ Along the main magnetic axis these two states can be expressed as |ψ_ab〉 = 64%|±3/2〉 + 26%|∓1/2〉 and |ψ_cd〉 = 68%|±1/2〉 + 31%|∓3/2〉 and (Table S2, ESI†), giving the most energetic Kramers doublet a large g_y value of ∼17.5 perpendicular to the main magnetic axis.

Fig. 3 Electronic states and magnetic transition probabilities for the ground ⁶H_15/2 multiplet of 2 in zero field. The x-axis shows the magnetic moment of each state along the main magnetic axis of the molecule. Relaxation commences from the |−15/2〉 state and only includes pathways which reverse the magnetization. Relaxation probabilities are calculated based on a magnetic perturbation and are normalized from each departing state (see ESI† for details).

Magnetic relaxation in lanthanides follows three possible routes: (1) QTM within the ground doublet (e.g. |−15/2〉 → |+15/2〉 in Fig. 3), (2) thermally assisted QTM (TA-QTM) via excited states (e.g. |−15/2〉 → |−13/2〉 → |+13/2〉 → |+15/2〉), or (3) an Orbach process composed of direct and/or Raman mechanisms (e.g. |−15/2〉 → |−13/2〉 → |+15/2〉). The most probable pathway depends on the composition of the states involved and their interactions with phonons. For example, the slow magnetic relaxation for {Dy₄K₂} was shown to occur via the first or second excited states (TA-QTM), depending on the number and location of neighboring Dy^III ions providing a source of transverse magnetic field.⁷ The states with opposing magnetic projections are mixed proportionally to the product of the transverse field and the transverse g-factors and therefore TA-QTM will occur via the excited state which has transverse g-factors above a certain threshold or where its main magnetic axis is non-collinear with that of the ground state. All non-QTM transitions are induced by the vibrational modes of the lattice (phonons) which create local oscillating magnetic fields through modulation of dipolar fields as well as an oscillating crystal field potential.²³ To a first approximation, we can associate the probability of a phonon induced transition with the average magnetic^13,14,24 and crystal field perturbation matrix elements (see ESI† for details).

Compared to all known Dy^III complexes the calculated properties for 2 are unique with very small transverse g-factors and a common principal axis for the lowest six Kramers doublets. This suggests that both the probability of QTM within the ground doublet and TA-QTM is vanishingly small until the two most energetic doublets. Orbach relaxation is also strongly disfavoured in the low lying states as magnetic transition probabilities due to phonons are miniscule (Fig. 3). Efficient magnetic relaxation will only occur via the highest energy doublets (Fig. 3, Fig. S4 and Tables S4 and S5, ESI†). Therefore the ab initio calculation predicts U_eff ≈ 1800 cm⁻¹ for 2 – far greater than any complex to date. Whilst such calculations may over-estimate the energies of the crystal field states,^25,26 we can predict a T_B in excess of 77 K as such temperatures are often around 1/20th of the U_eff value if QTM within the ground doublet is disfavored, e.g. the T_B/U_eff ratios for {Tb₂N₂³⁻˙}, {Mn₁₂} and {Mn₆} are approximately 1/16, 1/15 and 1/13 cm⁻¹ K⁻¹, respectively. Calculations for the Tb^II analogue 3, which is also a 4f⁹ ion, predict analogous behavior to 2 (Table S6, ESI†). The high local symmetry at the Dy^III site implies that the nuclear quadrupole and hyperfine interactions will be axially symmetric, preventing efficient QTM within the lower energy doublets.

To examine the stability of 2, we have performed ab initio calculations for modified geometries where the N–Dy–N angle and the Dy–N bond lengths have been altered by ±0.5° and ±0.01 Å, respectively (Fig. S5, ESI†). The results show that 2 is stabilized when the Dy–N bond length is shortened and the N–Dy–N angle is closer to 180° compared to 1, yielding more favorable electronic properties. These calculations do not take into account the inclusion of a counter-ion in the structure, which may have consequences for crystal packing and the local structure of 2.

Compound 1 is the first near-linear bis(amide) 4f-block complex. It allows us to propose a blueprint for the first generation of ‘high-temperature’ SMMs, with blocking temperatures exceeding that of liquid N₂ (77 K). The synthesis of the proposed archetypes, viz. the Dy^III and Tb^II analogues of 1, is currently underway in our laboratory, however we believe this is a target many other groups should be pursuing. Calculations on other fⁿ ions suggest that f⁹ is ideal; even for the oblate f⁸ Tb^III analogue, 4, we find that the pseudo-doublets show strong mixing between the |−m_J〉 and |+m_J〉 projections, (Tables S7 and S8, ESI†), which would lead to strong zero-field QTM.

While 2 would have a huge U_eff, an even higher U_eff barrier might be possible if dianionic monodentate ligands could be incorporated, e.g. [(ⁱPr₃Si)₂C–Dy–C(SiⁱPr₃)₂]⁻, containing dianionic methanediides. Our preliminary results suggest this could raise U_eff by a factor of 1.2 to 1.3. The incredible advances made in low coordination number metal–organic compounds in the last decade suggest that such hypothetical complexes are now chemically feasible. These metal–organic compounds are becoming of great importance in molecular magnetism.^8,10,27,28

This work was supported by the EPSRC (grant number EP/K039547/1) (UK). N.F.C. thanks The University of Manchester for a President's Doctoral Scholarship. R.E.P.W. thanks The Royal Society for a Wolfson research merit award. We would like to thank J. P. S. Walsh for assistance with graphics.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Full synthetic details, crystallography, NMR spectroscopy, magnetism, and ab initio and magnetic relaxation methodologies. CCDC 1017031. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c4cc08312a

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