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

Since their initial discovery, single molecule magnets (SMMs) have been lauded as candidates for high density data storage devices. A major breakthrough in the field occurred in 2003 with the observation of SMM behavior in a monometallic {TbPc2} complex with an energy barrier, Ueff = 230 cm . The ensuing decade saw rapid growth in lanthanide SMMs with the Ueff 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. The highest blocking temperature TB (i.e. the temperature at which hysteresis is observed) was also increased to 14 K, via an N2 3 radical bridge in a {Tb2N2 3 } complex. Although three of these milestones employ the Tb ion, by far the most utilized lanthanide ion in SMMs is Dy by virtue of its unique electronic structure. Apart from a radical-bridged {Dy2N2 3 } complex, nearly all polymetallic Dy-based SMMs possess negligible interactions between magnetic spin centres, and instead rely on the single ion anisotropy of Dy (i.e. the local crystal field environment) to provide the barrier to the reversal of magnetization. Intraor intermolecular interactions are often detrimental to the performance of Dy SMMs so that doping a small amount of the paramagnetic ion into a diamagnetic host lattice (usually the Y analogue) often results in an increased Ueff. 7

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 field 3 occurred in 2003 with the observation of SMM behavior in a monometallic {TbPc 2 } À complex with an energy barrier, U eff = 230 cm À1 . 4 The ensuing decade saw rapid growth in lanthanide SMMs 5 with the U eff barrier to magnetization reversal increased to 652 cm À1 for another derivative of {TbPc 2 }, 6 and 585 cm À1 for a polymetallic Dy@{Y 4 K 2 } 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 N 2 3À radical bridge in a {Tb 2 N 2 3À } 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 {Dy 2 N 2 3À } 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 multiconfigurational complete active space Self consistent field (CASSCF) ab initio calculations 12 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 {Dy 5 } and {Dy 4 K 2 } alkoxide complexes 7 because of the strongly axially repulsive crystal field potentials along the local z-direction of each Dy III . Other compounds such as [(C 8 H 8 ) 2 Ln] À (ref. 15) or Cloke's bis(arene) lanthanide complexes 16 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(Si i Pr 3 ) 2 was designed, and synthesised from ClSi i Pr 3    Formally each nitrogen atom carries a single negative charge and the Sm II ion is divalent, with an [Xe]4f 6 configuration. The f 6 configuration leads to a formally diamagnetic 7 F 0 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 m 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(Si i Pr 3 ) 2 } 2 I] 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 [( i Pr 3 Si) 2 N-Dy-N(Si i Pr 3 ) 2 ] + 2 are predicted by CASSCF/RASSI/SINGLE_ANISO 22 ab 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 6 H 15/2 ground multiplet, which is split by the crystal field into eight Kramer's doublets with total angular momentum projections m J = AE1/2, AE3/2,. . . AE15/2. The ab initio calculations show that the lowest six Kramers doublets are the almost pure m J states of m J = AE15/2, AE13/2, AE11/2, AE9/2, AE7/2 and AE5/2, 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 N axis. 14 Along the main magnetic axis these two states can be expressed as |c ab i = 64%|AE3/2i + 26%|81/2i and |c cd i = 68%|AE1/2i + 31%|83/2i and (Table S2, ESI †), giving the most energetic Kramers doublet a large g y value of B17.5 perpendicular to the main magnetic axis.
Magnetic relaxation in lanthanides follows three possible routes: (1) QTM within the ground doublet (e.g. |À15/2i -|+15/2i in Fig. 3), (2) thermally assisted QTM (TA-QTM) via excited states (e.g. |À15/2i -|À13/2i -|+13/2i -|+15/2i), or (3) an Orbach process composed of direct and/or Raman mechanisms (e.g. |À15/2i -|À13/2i -|+15/2i). The most probable pathway depends on the composition of the states involved and their interactions with phonons. For example, the slow magnetic relaxation for {Dy 4 K 2 } 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 E 1800 cm À1 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 {Tb 2 N 2 3À }, {Mn 12 } and {Mn 6 } are approximately 1/16, 1/15 and 1/13 cm À1 K À1 , respectively. Calculations for the Tb II analogue 3, which is also a 4f 9 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 AE0.51 and AE0.01 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 1801 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 N 2 (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 f n ions suggest that f 9 is ideal; even for the oblate f 8 Tb III analogue, 4, we find that the pseudo-doublets show strong mixing between the |Àm J i and |+m J i 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. [( i Pr 3 Si) 2 C-Dy-C(Si i Pr 3 ) 2 ] À , 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.