Design Criteria for High-Temperature Single-Molecule Magnets

Substituted fullerenes as a promising capping ligand towards stabilization of exohedral Dy(III) based single-ion magnets: a theoretical study

Organometallic dysprosocenium-based molecular magnets are the forefront runners in offering giant magnetic anisotropy and blocking temperatures close to the boiling point of liquid nitrogen. Attaining linearity in the organometallic dysprosocenium complexes is the key to generating giant magnetic anisotropy and blocking barriers. In the present study, we have unravelled the coordination ability of the substituted fullerene (C55X5)- (where X = CCH3, B, and N) generated by fencing around the five-membered ring of fullerene towards stabilizing a new family of exohedral dysprosium organometallic complexes showcasing giant magnetic anisotropy and blockade barriers. Eight exohedral mononuclear dysprosium organometallic complexes, namely [Dy(η5-C55X5)(η4-C4H4)] (1), [Dy(η5-C55X5)(η5-Cp)]+ (2), [Dy(η5-C55X5)(η5-Cp*)]+ (3), [Dy(η5-C55X5)(η6-C6H6)]2+ (4), [Dy(η5-C55X5)(η8-C8H8)] (5), [Dy(η5-C55X5)2]+ (6) (where X = CCH3), [Dy(η5-C55B5)2]+ (7) and [Dy(η5-C55N5)2]+ (8), were studied using scalar relativistic density functional theory (SR-DFT) and the complete active space self-consistent field (CASSCF) methodology to shed light on the structure, stability, bonding and single-ion magnetic properties. SR-DFT calculations predict complexes 1-8 to be highly stable, with a strictly linear geometry around the Dy(III) ion in complexes 6-8. Energy Decomposition Analysis (EDA) predicts the following order for interaction energy (ΔEint value): 5 > 1 > 2 ≈ 3 > 6 > 7 > 8 > 4, with sizable 4f-ligand covalency in all the complexes. CASSCF calculations on complexes 1-8 predict stabilization of mJ |±15/2〉 as the ground state for all the complexes except for 5, with the following trend in the Ucal values: 6 (1573 cm-1) ≈ 3 (1569 cm-1) > 1 (1538 cm-1) > 8 (1347 cm-1) > 2 (1305 cm-1) > 7 (1284 cm-1) > 4 (1125 cm-1) > 5 (108 cm-1). Ab initio ligand field theory (AILFT) analysis provides a rationale for Ucal ordering, where π-type 4f-ligand interactions in complexes 1-4 and 6-8 offer giant barrier height while the large (C8H8)2- rings generate δ-type interaction in 5, which diminishes the axiality in the ligand field. Our detailed finding suggests that the exohedral organometallic dysprosocenium complexes are more linear compared to bent [DyCp*2]+ cations and display a giant barrier height exceeding 1500 cm-1 with negligible quantum tunnelling of magnetization (QTM) - a new approach to design highly anisotropic dysprosium organometallic complexes.

Construction of intermolecular σ-hole interactions in rare earth metallocene complexes using a 2,3,4,5-tetraiodopyrrolyl anion

The generation of noncovalent intermolecular interactions represents a powerful method to control molecular vibrations and rotations. Combining these with the axial ligand field enforced by the metallocene ligand scaffold provides a dual-pronged approach in controlling the magnetic-relaxation pathways for dysprosium-based single-molecule magnets (SMMs). Here, we present the first implementation of 2,3,4,5-tetraiodopyrrole (TIPH) in its anionic form [TIP]- as a ligand in three isostructural rare-earth metal complexes Cp*2RE(TIP) (1-RE, RE = Y, Gd, and Dy; Cp* = pentamethylcylopentadienyl), where the TIP ligand binds through the nitrogen and one iodine atom κ2(N,I) to the metal centre. The shallow potential energy surface of the intermolecular σ-hole interaction yields distortions of the interatomic distances at elevated temperatures which were investigated by variable-temperature SCXRD. 1-RE constitute the first crystallographically characterized molecules containing TIP as a ligand for any metal ion, and 1-Dy is the first SMM that employs the TIP ligand. The structural dependence on temperature allowed the mechanism of magnetic relaxation to be explored through ab initio calculations at different temperatures. The electronic influence of the coordinated iodine substituent was probed via magnetometry and cw-EPR spectroscopy on 1-Gd. To further scrutinize the impact of the iodine substituents on the physical properties, a second set of new complexes Cp*2RE(DMP) (2-RE, RE = Y, and Dy) where DMP = 2,5-dimethylpyrrolyl were synthesized. Here, the DMP ligand binds similarly to the TIP ligand and represents an all-hydrocarbon analogue to 1-RE. 2-Dy constitutes the first SMM bearing a DMP ligand.

A highly anisotropic family of hexagonal bipyramidal Dy(III) unsaturated 18-crown-6 complexes exceeding the blockade barrier over 2700 K: a computational exploration

In the present work, we have explored a series of unsaturated hexa-18-crown-6 (U18C6) ligands towards designing highly anisotropic Dy(III) based single-ion magnets (SIMs) with the general formula [Dy(U18C6)X2]+ (where U18C6 = [C12H12O6] (1), [C12H12S6] (2), [C12H12Se6] (3), [C12H12O4S2] (4), [C12H12O4Se2] (5) and X = F, Cl, Br, I, OtBu and OSiPh3). By analysing the electronic structure, bonding and magnetic properties, we find that the U18C6 ligands prefer stabilising the highly symmetric eight-coordinated hexagonal bipyramidal geometry (HBPY-8), which is the source of the near-Ising type anisotropy in all the [Dy(U18C6)X2]+ complexes. Moreover, the ability of sulfur/selenium substituted U18C6 ligands to stabilize the highly anisotropic HBPY-8 geometry makes them more promising towards engineering the equatorial ligand field compared to substituted saturated 18C6 ligands where the exodentate arrangement of the S lone pairs results in low symmetry. Magnetic relaxation analysis predicts a record barrier height over 2700 K for [Dy(C12H12O6)F2]+ and [Dy(C12H12S6)X2]+ (where X = F, OtBu and OSiPh3) complexes, nearly 23% higher than those of the top performing Dy(III) based SIMs in the literature.

Auxiliary Rather Than Dominant. The Role of Direct Dy-S Coordination in Single-Molecule Magnet Unveiled via ab initio Study

The role of Dy-S coordination in a single-molecule magnet (SMM) is investigated via an ab initio study in a group of mononuclear structures. The SMM performance of this group is well interpreted via a concise criterion consisting of long quantum tunneling of magnetization (QTM) time τQTM and high effective barrier for magnetic reversal Ueff. The best SMMs in the selected group, i.e., 1Dy (CCDC refcode: PUKFAF) and 2Dy (CCDC refcode: NIKSEJ), are just those holding the longest τQTM and the highest Ueff simultaneously. Further analysis based on the crystal field model and ab initio magneto-structural exploration indicates that the influence of Dy-S coordination on the SMM performance of 1Dy is weaker than that of axial Dy-O coordination. Thus, Dy-S coordination is more likely to play an auxiliary role rather than a dominant one. However, if placed at the suitable equatorial position, Dy-S coordination could provide important support for good SMM performance. Consequently, starting from 1Dy, we built two new structures where Dy-S coordination only exists at the equatorial position and two axial positions are occupied by strong Dy-O/Dy-F coordination. Compared to 1Dy and 2Dy, these new ones are predicted to have significantly longer τQTM and higher Ueff, as well as a nearly doubled blocking temperature TB. Thus, they are probable candidates of SMM having clearly improved performance.

Constructing high axiality mononuclear dysprosium molecular magnets via a regulation-of-co-ligands strategy

Two lanthanide complexes with formulae [DyIII(LN5)(pentafluoro-PhO)3] (1) and [DyIII(LN5)(2,6-difluoro-PhO)2](BPh4) (2) (LN5 = 2,14-dimethyl-3,6,10,13,19-pentaazabicyclo[13.3.1]nonadecal (19),2,13,15,17-pentaene) were structurally and magnetically characterized. DyIII ions lie in the cavity of a five coordinate nitrogen macrocycle, and in combination with the introduction of multi-fluorinated monodentate phenoxyl coligands a high axiality coordination symmetry is built. Using the pentafluorophenol co-ligand, complex 1 with a D2d coordination environment, is obtained and displays moderate single-molecule magnets (SMMs) behavior. When difluorophenol co-ligands were used, a higher local axisymmetric pentagonal bipyramidal coordination geometry was observed in complex 2, which displays apparent slow magnetic relaxation behavior with a hysteresis temperature of up to 5 K. Further magnetic studies of diluted samples combined with ab initio calculations indicate that the high axiality plays a crucial role in suppressing quantum tunneling of magnetization (QTM) and consequently results in good slow magnetic relaxation behavior. Different fluoro-substituted phenoxyl co-ligands have phenoloxy oxygen atoms with different electrostatic potentials as well as a different number of phenoloxy coligands along the magnetic axis, resulting in different ligand field strengths and coordination symmetries.

Eight-coordinate mono- and dinuclear Dy(III) complexes containing a rigid equatorial plane and an anisobidentate carboxylate ligand in the axial position: synthesis, structure and magnetism

A rigid pentadentate chelating ligand (H2L) has been utilized to synthesize a series of octacoordinate mononuclear complexes, [Dy(L)(Ph3PO)(OOCR)] (where R = C6H5 (1), C(CH3)3 (2), CF3 (3)) and a dinuclear complex, [Dy2(L)2(Ph3PO)2{(OOC)2C6H4}] (4) based on the highly anisotropic Dy(III) ion. All the complexes were structurally characterized by single-crystal X-ray diffraction studies. The complexes were formed by the coordination action of the dianionic pentadentate ligand [L]2-, one phosphine oxide, and carboxylate ligands. DC and AC magnetic measurements were performed on 1-4. Complexes 1-4 show SMM behaviour, under zero DC field for 1 and 4, and under 500 Oe and 1000 Oe DC fields for 2 and 3 respectively, with thermally activated, Raman, and Raman and quantum tunnelling dominant relaxation mechanisms for 1 and 2, 3 and 4, respectively.

Halobenzene Adducts of a Dysprosocenium Single-Molecule Magnet

Dysprosium complexes with strong axial crystal fields are promising candidates for single-molecule magnets (SMMs), which could be used for high-density data storage. Isolated dysprosocenium cations, [Dy(CpR)2]+ (CpR = substituted cyclopentadienyl), have recently shown magnetic hysteresis (a memory effect) above the temperature of liquid nitrogen. Synthetic efforts have focused on reducing strong transverse ligand fields in these systems as they are known to enhance magnetic relaxation by spin-phonon mechanisms. Here we show that equatorial coordination of the halobenzenes PhX (X = F, Cl, Br) and o-C6H4F2 to the cation of a recently reported dysprosocenium complex [Dy(Cpttt)(Cp*)][Al{OC(CF3)3}4] (Cpttt = C5H2tBu3-1,2,4; Cp* = C5Me5) reduces magnetic hysteresis temperatures compared to that of the parent cation. We find that this is due to increased effectiveness of both one- (Orbach) and two-phonon (Raman) relaxation mechanisms, which correlate with the electronegativity and number of interactions with the halide despite κ1-coordination of a single halobenzene having a minimal effect on the metrical parameters of [Dy(Cpttt)(Cp*)(PhX-κ1-X)]+ cations vs the isolated [Dy(Cpttt)(Cp*)]+ cation. We observe unusual divergent behavior of relaxation rates at low temperatures in [Dy(Cpttt)(Cp*)(PhX)][Al{OC(CF3)3}4], which we attribute to a phonon bottleneck effect. We find that, despite the transverse fields introduced by the monohalobenzenes in these cations, the interactions are sufficiently weak that the effective barriers to magnetization reversal remain above 1000 cm-1, being only ca. 100 cm-1 lower than for the parent complex, [Dy(Cpttt)(Cp*)][Al{OC(CF3)3}4].

Synthesis and Magnetic Properties of Bis-Halobenzene Decamethyldysprosocenium Cations

The decamethyldysprosocenium cation, [Dy(Cp*)2]+ (Cp* = {C5Me5}), was a target single-molecule magnet (SMM) prior to the isolation of larger dysprosocenium cations, which have recently shown magnetic memory effects up to 80 K. However, the relatively short Dy···Cp*centroid distances of [Dy(Cp*)2]+, together with the reduced resonance of its vibrational modes with electronic states compared to larger dysprosocenium cations, could lead to more favorable SMM behavior. Here, we report the synthesis and magnetic properties of a series of solvated adducts containing bis-halobenzene decamethyldysprosocenium cations, namely [Dy(Cp*)2(PhX-κ-X)2][Al{OC(CF3)3}4] (X = F or Cl) and [Dy(Cp*)2(C6H4F2-κ2-F,F)(C6H4F2-κ-F)][Al{OC(CF3)3}4]. These complexes were prepared by the sequential reaction of [Dy(Cp*)2(μ-BH4)]∞ with allylmagnesium chloride and [NEt3H][Al{OC(CF3)3}4], followed by recrystallization from parent halobenzenes. The complexes were characterized by powder and single crystal X-ray diffraction, NMR and ATR-IR spectroscopy, elemental analysis, and SQUID magnetometry; experimental data were rationalized by a combination of density functional theory and ab initio calculations. We find that bis-halobenzene adducts of the [Dy(Cp*)2]+ cation exhibit highly bent Cp*···Dy···Cp* angles; these cations are also susceptible to decomposition by C-X (X = F, Cl, Br) activation and displacement of halobenzenes by O-donor ligands. The effective energy barrier to reversal of magnetization measured for [Dy(Cp*)2(PhF-κ-F)2][Al{OC(CF3)3}4] (930(6) cm-1) sets a new record for SMMs containing {Dy(Cp*)2} fragments, though all SMM parameters are lower than would be predicted for an isolated [Dy(Cp*)2]+ cation, as expected due to transverse ligand fields introduced by halobenzenes and the large deviation of the Cp*···Dy···Cp* angle from linearity promoting magnetic relaxation.

Spectroscopic techniques to probe magnetic anisotropy and spin-phonon coupling in metal complexes

Magnetism of molecular quantum materials such as single-molecule magnets (SMMs) has been actively studied for potential applications in the new generation of high-density data storage using SMMs and quantum information science. Magnetic anisotropy and spin-phonon coupling are two key properties of d- and f-metal complexes. Here, phonons refer to both intermolecular and intramolecular vibrations. Direct determination of magnetic anisotropy and experimental studies of spin-phonon coupling are critical to the understanding of molecular magnetism. This article discusses our recent approach in using three complementary techniques, far-IR and Raman magneto-spectroscopies (FIRMS and RaMS, respectively) and inelastic neutron scatterings (INS), to determine magnetic excited states. Spin-phonon couplings are observed in FIRMS and RaMS. DFT phonon calculations give energies and symmetries of phonons as well as calculated INS spectra which help identify magnetic peaks in experimental INS spectra.

The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes

The correct interpretation of magnetic properties in the weak-exchange regime has remained a challenging task for several decades. In this regime, the effective exchange interaction between local spins is quite weak, of the same order of magnitude or smaller than the various anisotropic terms, which generates a complex set of levels characterized by spin mixing. Although the model multispin Hamiltonian in the absence of local orbital momentum, , is considered good enough to map the experimental energies at zero field and in the strong-exchange limit, theoretical works pointed out limitations of this simple model. This work revives the use of ĤMS from a new theoretical perspective, detailing point-by-point a strategy to correctly map the computational energies and wave functions onto ĤMS, thus validating it regardless of the exchange limit. We will distinguish two cases, based on experimentally characterized dicobalt(II) complexes from the literature. If centrosymmetry imposes alignment of the various rank-2 tensors constitutive of ĤMS in the first case, the absence of any symmetry element prevents such alignment in the second case. In such a context, the strategy provided herein becomes a powerful tool to rationalize the experimental magnetic data, since it is capable of fully and rigorously extracting the multispin model without any assumption on the orientation of its constitutive tensors. Furthermore, the strategy allows to question the use of the spin Hamiltonian approach by explicitly controlling the projection norms on the model space, which is showcased in the second complex where local orbital momentum could have occurred (distorted octahedra). Finally, previous theoretical data related to a known dinickel(II) complex is reinterpreted, clarifying initial wanderings regarding the weak exchange limit.

Isolation of a Bent Dysprosium Bis(amide) Single-Molecule Magnet

The isolation of formally two-coordinate lanthanide (Ln) complexes is synthetically challenging, due to predominantly ionic Ln bonding regimes favoring high coordination numbers. In 2015, it was predicted that a near-linear dysprosium bis(amide) cation [Dy{N(SiiPr3)2}2]+ could provide a single-molecule magnet (SMM) with an energy barrier to magnetic reversal (Ueff) of up to 2600 K, a 3-fold increase of the record Ueff for a Dy SMM at the time; this work showed a potential route to SMMs that can provide high-density data storage at higher temperatures. However, synthetic routes to a Dy complex containing only two monodentate ligands have not previously been realized. Here, we report the synthesis of the target bent dysprosium bis(amide) complex, [Dy{N(SiiPr3)2}2][Al{OC(CF3)3}4] (1-Dy), together with the diamagnetic yttrium analogue. We find Ueff = 950 ± 30 K for 1-Dy, which is much lower than the predicted values for idealized linear two-coordinate Dy(III) cations. Ab initio calculations of the static electronic structure disagree with the experimentally determined height of the Ueff barrier, thus magnetic relaxation is faster than expected based on magnetic anisotropy alone. We propose that this is due to enhanced spin-phonon coupling arising from the flexibility of the Dy coordination sphere, in accord with ligand vibrations being of equal importance to magnetic anisotropy in the design of high-temperature SMMs.

Understanding electrostatics and covalency effects in highly anisotropic organometallic sandwich dysprosium complexes [Dy(CmRm)2] (where R = H, SiH3, CH3 and m = 4 to 9): a computational perspective

In this article, we have thoroughly studied the electronic structure and 4f-ligand covalency of six mononuclear dysprosium organometallic sandwich complexes [Dy(CmRm)2]n+/- (where R = H, SiH3, CH3; m = 4 to 9; n = 1, 3) using both the scalar relativistic density functional and complete active space self-consistent field (CASSCF) and N-electron valence perturbation theory (NEVPT2) method to shed light on the ligand field effects in fine-tuning the magnetic anisotropy of these complexes. Energy decomposition analysis (EDA) and ab initio-based ligand field theory AILFT calculations predict the sizable 4f-ligand covalency in all these complexes. The analysis of CASSCF/NEVPT2 computed spin-Hamiltonian (SH) parameters indicates the stabilization of mJ |±15/2〉 for [Dy(C4(SiH3)4)2]- (1), [Dy(C5(CH3)5)2]+ (2) and [Dy(C6H6)2]3+ (3) complexes with the Ucal value of 1867.5, 1621.5 and 1070.8 cm-1, respectively. On the other hand, we observed mJ |±9/2〉 as the ground state for [Dy(C7H7)2]3- (4) and [Dy(C8H8)2]- (5) complexes with significantly smaller Ucal values of 237.1 and 38.6 cm-1 respectively. For the nine-membered ring [Dy(C9H9)2]+ (6) complex, we observed the stabilization of the mJ |±1/2〉 ground state, with the first excited state being located ∼29 cm-1 higher in energy. AILFT-NEVPT2 ligand field splitting analysis indicates that the presence of π-type 4f-ligand interactions in complexes 1-3 help generate the axial-ligand field, while the δ-type interactions in complexes 4-5 generate the equatorial ligand field despite the ligands approaching from the axial direction. As the ring size increases, φ-type interactions dominate, generating a pure equatorial ligand field stabilising mJ |±1/2〉 as the ground state for 6. Calculations suggest that the nature of the ligand field mainly governs the Ucal values in the following order: 4f-Lσ > 4f-Lπ > 4f-Lδ > 4f-Lφ. Calculations were performed by replacing ligands with CHELPG charges to access the crystal field (CF) effects which suggests the stabilization of pure mJ |±15/2〉 in all the charge-embedded models (1Q-6Q). Our findings point out that the crystal field and ligand field effects complement each other and generate a giant barrier for magnetic relaxation in the small ring complexes 1-3, while a relatively weak crystal field and adverse 4f-Lδ/4f-Lφ interactions diminish the SMM behaviour in the large ring complexes 4-6.

AtomAccess: A Predictive Tool for Molecular Design and Its Application to the Targeted Synthesis of Dysprosium Single-Molecule Magnets

Isolated dysprosocenium cations, [Dy(CpR)2]+ (CpR = substituted cyclopentadienyl), have recently been shown to exhibit superior single-molecule magnet (SMM) properties over closely related complexes with equatorially bound ligands. However, gauging the crossover point at which the CpR substituents are large enough to prevent equatorial ligand binding, but small enough to approach the metal closely and generate strong crystal field splitting has required laborious synthetic optimization. We therefore created the computer program AtomAccess to predict the accessibility of a metal binding site and its ability to accommodate additional ligands. Here, we apply AtomAccess to identify the crossover point for equatorial coordination in [Dy(CpR)2]+ cations in silico and hence predict a cation that is at the cusp of stability without equatorial interactions, viz., [Dy(Cpttt)(Cp*)]+ (Cpttt = C5H2tBu3-1,2,4, Cp* = C5Me5). Upon synthesizing this cation, we found that it crystallizes as either a contact ion-pair, [Dy(Cpttt)(Cp*){Al[OC(CF3)3]4-κ-F}], or separated ion-pair polymorph, [Dy(Cpttt)(Cp*)][Al{OC(CF3)3}4]·C6H6. Upon characterizing these complexes, together with their precursors, yttrium and yttrium-doped analogues, we find that the contact ion-pair shows inferior SMM properties to the separated ion-pair, as expected, due to faster Raman and quantum tunneling of magnetization relaxation processes, while the Orbach region is relatively unaffected. The experimental verification of the predicted crossover point for equatorial coordination in this work tests the limitations of the use of AtomAccess as a predictive tool and also indicates that the application of this type of program shows considerable potential to boost efficiency in exploratory synthetic chemistry.

Pyrrolyl-Bridged Metallocene Complexes: From Synthesis, Electronic Structure, to Single-Molecule Magnetism

The π- and σ-basicity of the pyrrolyl ligand affords several coordination modes. A sterically encumbering coordination sphere around metal centers may foster new coordination modes for the pyrrolyl ligand. Here, we present three dinuclear rare earth complexes [Cp*2RE(μ-pyr)]2, [RE = Y (1), La (2), Dy (3); Cp* = pentamethylcyclopentadienyl, pyr = pyrrolyl], which were synthesized through a protonolysis reaction between allyl complexes and H-pyrrole. Each metal is ligated by two Cp* ligands and the N atom of the pyrrolyl ring while interacting with the π-system of the other pyrrolyl ligand, yielding an unprecedented coordination mode for pyrrolyl best described as [((η5-Cp*)2RE)2(μ-1η2-pyr-2κN)(μ-2η2-pyr-1κN)]. The steric congestion implemented by the Cp* ligands forces this asymmetric coordination of the pyrrolyl ligand. 1-3 were characterized by crystallography, electrochemistry, and spectroscopy. Density functional theory calculations on 1 uncovered the bonding situation between the pyrrolyl ligand and the yttrium(III) ion. Excitingly, 3 displays slow magnetic relaxation under zero dc field with Ueff = 98.9(7) cm-1 and τo = 6.7(1) × 10-8 s, placing it among coveted dinuclear metallocene single-molecule magnets. CASSCF calculations provided the energy of the crystal field states of DyIII and confirmed the barrier height.

Observation of High Magnetic Bistability in Lanthanide (Ln = Gd, Tb and Dy)-Grafted Carbon Nanotube Hybrid Molecular System

There is an immense research interest in molecular hybrid materials posing novel magnetic properties for usage in spintronic devices and quantum technological applications. Although grafting magnetic molecules onto carbon nanotubes (CNTs) is nontrivial, there is a need to explore their single molecule magnetic (SMM) properties post-grafting to a greater degree. Here, we report a one-step chemical approach for lanthanide-EDTA (Ln = GdIII, 1; TbIII, 2 and DyIII, 3) chelate synthesis and their effective grafting onto MWCNT surfaces with high magnetic bistability retention. The magnetic anisotropy of an Ln-CNT hybrid molecular system by replacing the central ions in the hybrid complex was studied and it was found that system 1 exhibited a magnetization reversal from positive to negative values at 70 K with quasi-anti-ferromagnetic ordering, 2 showed diamagnetism to quasi-ferromagnetism and 3 displayed anti-ferromagnetic ordering as the temperature was lowered at an applied field of 200 Oe. A further analysis of magnetization (M) vs. field (H) revealed 1 displaying superparamagnetic behavior, and 2 and 3 displaying smooth hysteresis loops with zero-field slow magnetic relaxation. The present work highlights the importance of the selection of lanthanide ions in designing SMM-CNT hybrid molecular systems with multi-functionalities for building spin valves, molecular transistors, switches, etc.

Ab initio prediction of key parameters and magneto-structural correlation of tetracoordinated lanthanide single-ion magnets

Single-molecule magnets (SMMs) have great potential in becoming revolutionary materials for micro-electronic devices. As one type of SMM and holding the performance record, lanthanide single-ion magnets (Ln-SIMs) stand at the forefront of the family. Lowering the coordination number (CN) is an important strategy to improve the performance of Ln-SIMs. Here, we report a theoretical study on a typical group of low-CN Ln-SIMs, i.e., tetracoordinated structures. Our results are consistent with those of experiments and they identify the same three best Ln-SIMs via a concise criterion, i.e., the co-existence of long τ_QTM and high U_eff. Compared to the record-holding dysprosocenium systems, the best SIMs here possess τ_QTM values that are shorter by several orders of magnitude and U_eff values that are lower by ∼1000 Kelvin (K). These are important reasons for the fact that the tetracoordinated Ln-SIMs are clearly inferior to dysprosocenium. A simple but intuitive crystal-field analysis leads to several routes to improve the performance of a given Ln-SIM, including compression of the axial bond length, widening the axial bond angle, elongation of the equatorial bond length and usage of weaker equatorial donor ligands. Although these routes are not brand-new, the most efficient option and the degree of improvement resulting from it are not known in advance. Consequently, a theoretical magneto-structural study, covering various routes, is carried out for the best Ln-SIM here and the most efficient route is shown to be widening the axial ∠O-Dy-O angle. The most optimistic case, having a ∠O-Dy-O of 180°, could have a τ_QTM (up to 10³ s) and U_eff (∼2400 K) close to those of the record-holders. Subsequently, a blocking temperature (T_B) of 64 K is predicted to be possible for it. A more practical case, with ∠O-Dy-O being 160°, could have a τ_QTM of up to 400 s, U_eff of around 2200 K and the possibility of a T_B of 57 K. Although having an inherent precision limit, these predictions provide a guide to performance improvement, starting from an existing system.

Spin-state energetics and magnetic anisotropy in penta-coordinated Fe(III) complexes with different axial and equatorial ligand environments

The penta-coordinated trigonal-bi-pyramidal (TBP) Fe(III) complex (PMe₂Ph)₂FeCl₃ shows a reduced magnetic anisotropy in its intermediate-spin (IS) state as compared to its methyl-analog (PMe₃)₂Fe(III)Cl₃. In this work, the ligand environment in (PMe₂Ph)₂FeCl₃ is systematically altered by replacing the axial -P with -N and -As, the equatorial -Cl with other halides, and the axial methyl group with an acetyl group. This has resulted in a series of Fe(III) TBP complexes modelled in their IS and high-spin (HS) states. Lighter ligands -N and -F stabilize the complex in the HS state, while the magnetically anisotropic IS state is stabilized by -P and -As at the axial site, and -Cl, -Br, and -I at the equatorial site. Larger magnetic anisotropies appear for complexes with nearly degenerate ground electronic states that are well separated from the higher excited states. This requirement, largely controlled by the d-orbital splitting pattern due to the changing ligand field, is achieved with a certain combination of axial and equatorial ligands, such as -P and -Br, -As and -Br, and -As and -I. In most cases, the acetyl group at the axial site enhances the magnetic anisotropy compared to its methyl counterpart. In contrast, the presence of -I at the equatorial site compromises the uniaxial type of anisotropy of the Fe(III) complex leading to an enhanced rate of quantum tunneling of magnetization.

A trivalent 4f complex with two bis-silylamide ligands displaying slow magnetic relaxation

The best-performing single-molecule magnets (SMMs) have historically relied on pseudoaxial ligands delocalized across several coordinated atoms. This coordination environment has been found to elicit strong magnetic anisotropy, but lanthanide-based SMMs with low coordination numbers have remained synthetically elusive species. Here we report a cationic 4f complex bearing only two bis-silylamide ligands, Yb(III)[{N(SiMePh₂)₂}₂][Al{OC(CF₃)₃}₄], which exhibits slow relaxation of its magnetization. The combination of the bulky silylamide ligands and weakly coordinating [Al{OC(CF₃)₃}₄]^- anion provides a sterically hindered environment that suitably stabilizes the pseudotrigonal geometry necessary to elicit strong ground-state magnetic anisotropy. The resolution of the m_J states by luminescence spectroscopy is supported by ab initio calculations, which show a large ground-state splitting of approximately 1,850 cm^-1. These results provide a facile route to access a bis-silylamido Yb(III) complex, and further underline the desirability of axially coordinated ligands with well-localized charges for high-performing SMMs.

Search for Toroidal Ground State and Magnetoelectric Effects in Molecular Spin Triangles with Antiferromagnetic Exchange

Using first-principles methods and spin models, we investigate the magnetic properties of transition-metal trimers Cr₃ and Cu₃. We calculate exchange coupling constants and zero-field splitting parameters using density functional theory and, with these parameters, determine the ground spin state as well as thermodynamic properties via spin models. Results for Cr₃ indicate uniaxial magnetic anisotropy with a magnetic easy axis aligned along the 3-fold rotational symmetry axis and a mostly isotropic exchange interaction. The Cu₃ molecule lacks rotational symmetry and our results show strong antisymmetric interactions for three distinct exchange couplings within the molecule. We are able to reproduce experimental findings on magnetic susceptibility and magnetization of Cr₃ with the first-principles spin-Hamiltonian parameters. Our results show no presence of a toroidal ordering of spins for Cr₃ and a finite toroidal moment for Cu₃ in the ground state. We apply an external electric field up to 0.08 V/Å to each system to reveal the field dependence of exchange coupling as magnetoelectric effects. Finally, we scan the parameter space of a spin Hamiltonian to gain insights into which parameters would lead to a sizable toroidal moment in such systems.

Influence of pressure on a dysprosocenium single-molecule magnet

The effects of external pressure on a high-performing dysprosocenium single-molecule magnet are investigated using a combination of X-ray diffraction, magnetometry and theoretical calculations. The effective energy barrier (U_eff) decreases from ca. 1300 cm^-1 at ambient pressure to ca. 1125 cm^-1 at 3 GPa. Our results indicate that compression < 1.2 GPa has a negligible effect on the Orbach process, but magnetic relaxation > 1 GPa increases via Raman relaxation and/or quantum tunnelling of magnetisation.

Axial Ligand as a Critical Factor for High-Performance Pentagonal Bipyramidal Dy(III) Single-Ion Magnets

The choice of axial ligands is of great importance for the construction of high-performance Dy-based single-molecule magnets (SMMs). Here, combining axial ligands Ph₃SiO^- (anion of triphenylsilanol) and 2,6-dichloro-4-nitro-PhO^- (the anion of 2,6-dichloro-4-nitrophenol) with a neutral macrocyclic ligand 2,14-dimethyl-3,6,10,13,19-pentaazabicyclo[13.3.1]nonadeca-1(19),2,13,15,17-pentaene (L₂^N5) generates two new pentagonal bipyramidal Dy(III) complexes [Dy^III(L₂^N5) (X)₂](BPh₄) (X = Ph₃SiO^-, 1; 2,6-dichloro-4-nitro-PhO^-, 2) with strong axial ligand fields. Magnetic characterizations show that 1 possesses a large energy barrier above 1000 K and a magnetic hysteresis up to 9 K, whereas 2 only displays field-induced peaks of alternating-current susceptibilities without the hysteresis loop, even though 2 has a similar coordination geometry with 1. Detailed Ab initio calculations indicate an apparent difference in the axial negative charge between both complexes, which is caused by the diverse electron-donating properties of the axial ligands. The present work provides an efficient strategy to enhance the SMMs' properties, which highlights that the electron-donating property of the axial ligands is especially important for constructing the high-performance Dy-based SMMs.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Lanthanide SMMs Based on Belt Macrocycles: Recent Advances and General Trends

Enhancement of axial magnetic anisotropy is the central objective to push forward the performance of Single-Molecule Magnet (SMM) complexes. In the case of mononuclear lanthanide complexes, the chemical environment around the paramagnetic ion must be tuned to place strongly interacting ligands along either the axial positions or the equatorial plane, depending on the oblate or prolate preference of the selected lanthanide. One classical strategy to achieve a precise chemical environment for a metal centre is using highly structured, chelating ligands. A natural approach for axial-equatorial control is the employment of macrocycles acting in a belt conformation, providing the equatorial coordination environment, and leaving room for axial ligands. In this review, we present a survey of SMMs based on the macrocycle belt motif. Literature systems are divided in three families (crown ether, Schiff-base and metallacrown) and their general properties in terms of structural stability and SMM performance are briefly discussed.

Rigid N3O2-Pentadentate Ligand-Assisted Octacoordinate Mononuclear Ln(III) Complexes: Syntheses, Characterization, and Slow Magnetization Relaxation

A series of air-stable mononuclear octacoordinate Ln(III) complexes, [(L)Ln(TPPO)₃]OTf (Ln = Y (1·Y); Gd (1·Gd); Tb (1·Tb); Dy (1·Dy); Ho (1·Ho); and Er (1·Er)) and [(L)Ln(TPPO)(NO₃)] (Ln = Y (2·Y) and Dy (2·Dy)), are synthesized employing a rigid N₃O₂-pentadentate chelating ligand as the basis ligand and meridional ancillary ligands (where H₂L = 2,6-diacetylpyridine bis-benzoylhydrazone, TPPO = triphenylphosphine oxide, and OTf^- = trifluoromethanesulfonate). All the complexes are synthesized under aerobic conditions and characterized comprehensively by spectroscopic and X-ray crystallographic techniques. Magnetic property investigation on the polycrystalline solid samples of 1·Ln (Ln = Gd, Tb, Dy, Ho, and Er) and 2·Dy are reported. A field-induced single-molecule magnet behavior was observed for the Dy derivatives. 1·Dy exhibits the highest effective energy barrier of magnetization reversal, U _eff/k _B = 47 K under H _dc = 1 kOe among the complexes presented herein.

Conformational preferences of endohedral metallofullerenes on Ag, Au, and MgO surfaces: Theoretical studies

In this report, we study the ordering of C₆₀ , Sc₃ N@C₈₀ , and Dy₂ ScN@C₈₀ molecules on different metallic and dielectric surfaces such as Ag(100), Au(111), and MgO(100). By using DFT techniques, we can classify different types of cage-to-surface arrangements and their relative energies. Using a proposed homogenous sampling of the conformational space for the M₃ N cluster, we determine a potential energy map that is capable of providing a structural distribution for a given energy window. We find that Coulomb interaction is a dominant force that governs the system's stability and order. However, a deep analysis of the charge density rearrangements reveals that even though the integral charges may be considered as a qualitative control parameter, it fails to provide quantitative data due to the importance of spatial characteristics of charge densities.

In silico design criteria for high blocking barrier uranium (III) SIMs

A combination of DFT and ab initio CASSCF/PT2 calculations on U(III) fictitious models and numerous reported X-ray structures unveils several geometries from coordination number 1 to 12 that can be targeted to design potential U(III) SIMs with attractive barrier heights. Among the geometries studied, the T-shaped and capped pentagonal antiprism geometries yield values exceeding 1500 cm^-1 - a value that is elusive for any uranium SIMs.

The coexistence of long τQTM and high Ueff as a concise criterion for a good single-molecule magnet: a theoretical case study of square antiprism dysprosium single-ion magnets

A systematic theoretical study is performed on a group of 16 square antiprism dysprosium single-ion magnets. Based on ab initio calculations, the quantum tunneling of magnetization (QTM) time, i.e., τ_QTM, and effective barrier of magnetic reversal, U_eff, are theoretically predicted. The theoretical τ_QTM is able to identify the ones with the longest QTM time with small numerical deviations. Similar results occur with respect to U_eff too. The systems possessing the best single-molecule magnet (SMM) properties here are just the ones having both the longest τ_QTM and the highest U_eff, from either experiment or theory. Thus, our results suggest the coexistence of long τ_QTM and high U_eff to be a criterion for high-performance SMMs. Although having its own limits, this criterion is easy to be applied in a large number of systems since both τ_QTM and U_eff could be predicted by theory with satisfactory efficiency and reliability. Therefore, this concise criterion could provide screened candidates for high-performance SMMs quickly and, hence, ease the burden of further exploration aiming for a higher degree of precision. This screening is important since the further exploration could easily demand tens or even hundreds of ab initio calculations for a single SMM. A semi-quantitative crystal field (CF) analysis is performed and shown here to be capable of indicating the general trends in a more chemically intuitive way. This analysis could help to identify the most important coordinating atoms for both diagonal and non-diagonal CF components. Thus, it could give some direct clues for improving the SMM properties: reducing the distance of the axial atom to the central ion, rotating the axial atom closer to the easy axis or increasing the amount of its negative charge. Correspondingly, opposite operations on the equatorial atom could give the same result.

Dominance of Cyclobutadienyl Over Cyclopentadienyl in the Crystal Field Splitting in Dysprosium Single-Molecule Magnets

Replacing a monoanionic cyclopentadienyl (Cp) ligand in dysprosium single-molecule magnets (SMMs) with a dianionic cyclobutadienyl (Cb) ligand in the sandwich complexes [(η4 -Cb'''')Dy(η5 -C5 Me4 t Bu)(BH4 )]- (1), [(η4 -Cb'''')Dy(η8 -Pn† )K(THF)] (2) and [(η4 -Cb'''')Dy(η8 -Pn† )]- (3) leads to larger energy barriers to magnetization reversal (Cb''''=C4 (SiMe3 )4 , Pn† =1,4-di(tri-isopropylsilyl)pentalenyl). Short distances to the Cb'''' ligands and longer distances to the Cp ligands in 1-3 are consistent with the crystal field splitting being dominated by the former. Theoretical analysis shows that the magnetic axes in the ground Kramers doublets of 1-3 are oriented towards the Cb'''' ligands. The theoretical axiality parameter and the relative axiality parameter Z and Zrel are introduced to facilitate comparisons of the SMM performance of 1-3 with a benchmark SMM. Increases in Z and Zrel when Cb''' replaces Cp signposts a route to SMMs with properties that could surpass leading systems.

Effect of an axial coordination environment on quantum tunnelling of magnetization for dysprosium single-ion magnets with theoretical insight

Herein, we report two mononuclear dysprosium complexes [Dy(H₄L){B(OMe)₂(Ph)₂}₂](Cl)·MeOH (1) and [Dy(H₄L){MeOH)₂(NCS)₂}](Cl) (2) [where H₄L = 2,2'-(pyridine-2,6-diylbis(ethan-1-yl-1-ylidene))bis(N-phenylhydrazinecarboxamide)] with different axial coordination environments. The structural analysis revealed that the pentadentate H₄L ligand binds through the equatorial position in both complexes. In complex 1, the axial positions are occupied by bidentate dimethoxydiphenyleborate [B(OMe)₂(Ph)₂]^-. On the other hand, in complex 2, one axial position is occupied by two NCS^- and one MeOH molecule while another MeOH molecule is coordinated to the other axial position. Magnetic measurements disclose the presence of field-induced slow relaxation of magnetization with an energy barrier of U_eff = 30 K for 1 whereas no such effective barrier was observed in complex 2. Detailed analysis of field and temperature dependence of the relaxation time confirms the major role of Raman, QTM, and direct processes rather than the Orbach process in complex 1. It was observed that [B(OMe)₂(Ph)₂]^- provides higher axial anisotropy which slows down the QTM process (relaxation time for the QTM process is 2.70 × 10^-5 s) in 1 as compared to NCS anions and MeOH molecules in 2 (1.03 × 10^-8 s), and is responsible for the absence of an effective energy barrier in the latter complex as confirmed by ab initio calculations. The calculations also show that the presence of a large bidentate dimethoxydiphenyleborate ligand in axial positions may result in high-performance Dy-based single-ion magnets.

Ultrahard magnetism from mixed-valence dilanthanide complexes with metal-metal bonding

Magnetic effects of lanthanide bonding Lanthanide coordination compounds have attracted attention for their persistent magnetic properties near liquid nitrogen temperature, well above alternative molecular magnets. Gould et al. report that introducing metal-metal bonding can enhance coercivity. Reduction of iodide-bridged terbium or dysprosium dimers resulted in a single electron bond between the metals, which enforced alignment of the other valence electrons. The resultant coercive fields exceeded 14 tesla below 50 and 60 kelvin for the terbium and dysprosium compounds, respectively. —JSY

Pseudo-mono-axial ligand fields that support high energy barriers in triangular dodecahedral Dy(iii) single-ion magnets

Air-stable triangular dodecahedral Dy(iii) single-ion magnets with pseudo-mono-axial linear ligand fields exhibit high energy barrier exceeding 600 K, which represent the highest energy barrier for mononuclear SMMs with triangular dodecahedron.

The interpretation and prediction of lanthanide single-ion magnet from ab initio electronic structure calculation: The capability and limit

Single-molecule magnet (SMM) is a fascinating system holding the potential of being revolutionary micro-electronic device in information technology. However current SMMs are still far away from real-life application due to...

Metal–metal bond in lanthanide single-molecule magnets

This review surveys recent critical advances in lanthanide SMMs, highlighting the influences of metal–metal bonds on the magnetization dynamics.

Slow relaxation of Dy(III) single-ion magnets dominated by the simultaneous binding of chelating ligands in low-symmetry ligand-fields

Electronic effect and geometry distortion of low-symmetry ligand-field on the anisotropy barrier (U_eff) of spin reversal have been compared in three Dy(III) single-ion magnets through the simultaneous binding of chelating ligands. The substitution of N,O-salicylaldoxime by N,N'-1,10-phenanthroline in the distorted triangular-dodecahedronal field sharply decreases the U_eff by 286 K due to an increase in non-preferred transverse anisotropy, while the geometry distortion with CShM = 1.569 went down to 1.376 only lowering the U_eff by 12 K. The co-coordination strategy of heterodonor ligands highlights the importance of ligand-surroundings on the relaxation dynamics.

Effect of the Transition Metal Ions on the Single-Molecule Magnet Properties in a Family of Air-Stable 3d-4f Ion-Pair Compounds with Pentagonal Bipyramidal Ln(III) Ions

Single-molecule magnets (SMMs) are expected to be promising candidates for the applications of high-density information storage materials and quantum information processing. Lanthanide SMMs have attracted considerable interest in recent years due to their excellent performance. It has always been interesting but not straightforward to study the relaxation and blocking mechanisms by embedding 3d ions into 4f SMMs. Here we report a family of air-stable 3d-4f ion-pair compounds, YFe (1), DyCr (2), DyFe (3), DyCo (4), and Dy_0.04Y_0.96Fe (5), composed of pentagonal bipyramidal (D_5h) Ln^III cations and transition metallocyanate anions. The ion-pair nature makes the dipole-dipole interactions almost the only component of the magnetic interactions that can be clarified and analytically resolved under proper approximation. Therefore, this family provides an intuitive opportunity to investigate the effects of 3d-4f and 4f-4f magnetic interactions on the behavior of site-resolved 4f SMMs. Dynamic magnetic measurements of 1 under a 4 kOe external field reveal slow magnetic relaxation originating from the isolated [Fe^III]_LS (S = ¹/₂) ions. Under zero dc field, compounds 2-5 show similar magnetic relaxation processes coming from the separated pentagonal bipyramidal (D_5h) Dy^III ions with high Orbach barriers of 592(5), 596(4), 595(3), and 606(4) K, respectively. Comparatively, both compounds 3 and 5 exhibit two distinct relaxation processes, respectively from the [Fe^III]_LS and Dy^III [U_eff = 596(4) K for 3 and 610(7) K for 5] ions, under a 4 kOe dc field. The dipolar interactions between the neighboring TM^III (TM = transition metal, Cr^III or [Fe^III]_LS) and Dy^III ions were revealed to have little effect on the thermal relaxation in compounds 2, 3, and 5, or the coexistence of the two separate relaxation processes in compounds 3 and 5 under a 4 kOe dc field, but they significantly affect the quantum tunneling of magnetization and the magnetic hysteresis behavior of 2 and 3 at low temperatures compared to those of 4.

Deciphering the Role of Anions and Secondary Coordination Sphere in Tuning Anisotropy in Dy(III) Air-Stable D5h SIMs*

Precise control of the crystal field and symmetry around the paramagnetic spin centre has recently facilitated the engineering of high-temperature single-ion magnets (SIMs), the smallest possible units for future spin-based devices. In the present work, we report a series of air-stable seven coordinate Dy(III) SIMs {[L₂ Dy(H₂ O)₅ ][X]₃ ⋅L₂ ⋅n(H₂ O), n = 0, X = Cl (1), n=1, X = Br (2), I (3)} possessing pseudo-D_5h symmetry or pentagonal bipyramidal coordination geometry with high anisotropy energy barrier (U_eff ) and blocking temperature (T_B ). While the strong axial coordination from the sterically encumbered phosphonamide, ^t BuPO(NHⁱ Pr)₂ (L), increases the overall anisotropy of the system, the presence of high symmetry significantly quenches quantum tunnelling of magnetization, which is the prominent deactivating factor encountered in SIMs. The energy barrier (U_eff ) and the blocking temperature (T_B ) decrease in the order 3>2>1 with the change of anions from larger iodide to smaller strongly hydrogen-bonded chloride in the secondary coordination sphere, albeit the local coordination geometry and the symmetry around the Dy(III) display only slight deviations. Ab initio CASSCF/RASSI-SO/SINGLE_ANISO calculations provide deeper insights into the dynamics of magnetic relaxation in addition to the role of the secondary coordination sphere in modulating the anisotropy of the D_5h systems, using diverse models. Thus, in addition to the importance of the crystal field and the symmetry to obtain high-temperature SIMs, this study also probes the significance of the secondary coordination sphere that can be tailored to accomplish novel SIMs.

A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion's first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

Magnetic Anisotropy Trends along a Full 4f-Series: The fn+7 Effect

The combined experimental and computational study of the 13 magnetic complexes belonging to the Na[LnDOTA(H2O)] (H4DOTA = tetraazacyclododecane-N,N',N″,N‴-tetraacetic acid and Ln = Ce-Yb) family allowed us to identify a new trend: the orientation of the magnetic anisotropy tensors of derivatives differing by seven f electrons practically coincide. We name this trend the fn+7 effect. Experiments and theory fully agree on the match between the magnetic reference frames (e.g., the easy, intermediate, and hard direction). The shape of the magnetic anisotropy of some couples of ions differing by seven f electrons might seem instead different at first look, but our analysis explains a hidden similarity. We thus pave the way toward a reliable predictivity of the magnetic anisotropy of lanthanide complexes with a consequent reduced need of computational and synthetical efforts. We also offer a way to gain information on ions with a relatively small total angular momentum (i.e., Sm3+ and Eu3+) and on the radioactive Pm3+, which are difficult to investigate experimentally.