Hilbert Space in Isotopologue Dy(III) SMM Dimers: Dipole Interaction Limit in [163/164Dy2(tmhd)6(tape)]0 Complexes

Single-molecule magnets are molecular complexes proposed to be useful for information storage and quantum information processing applications. In the quest for multilevel systems that can act as Qudits, two dysprosium-based isotopologues were synthesized and characterized. The isotopologues are [164Dy2(tmhd)6(tape)] (1(I=0)) and [163Dy2(tmhd)6(tape)] (2(I=5/2)), where tmhd = 2,2,6,6-tetramethylheptandionate and tape = 1,6,7,12-tetraazaperylene. Both complexes showed slow relaxation at a zero applied magnetic field with dominant Orbach and Raman relaxation mechanisms. μSQUID studies at milli-Kelvin temperatures reveal quasi-single ion loops, in contrast with the expected S-shape (near zero field) butterfly loops, characteristic of antiferromagnetically coupled dimeric complexes. Through analysis of the low-temperature data, we find that the interaction operating between Dy(III) is small, leading to a small exchange biasing from the zero-field transition. The resulting indirectly coupled nuclear states are degenerate or possess a small energy difference between them. We, therefore, conclude that for the creation of Qudits with enlarged Hilbert spaces, shorter Dy(III)···Dy(III) distances are deemed essential.

Strategies to quench quantum tunneling of magnetization in lanthanide single molecule magnets

Enhancing blocking temperature (T_B) is one of the holy grails in Single Molecule Magnets(SMMs), as any future potential application in this class of molecules is directly correlated to this parameter. Among many factors contributing to a reduction of T_B value, Quantum Tunnelling of Magnetisation (QTM), a phenomenon that is a curse or a blessing based on the application sought after, tops the list. Theoretical tools based on density functional and ab initio CASSCF/RASSI-SO methods have played a prominent role in estimating various spin Hamiltonian parameters and establishing the mechanism of magnetization relaxation in this class of molecules. Particularly, various strategies to quench QTM effects go hand-in-hand with experiments, and different methods proposed to quell QTM effects are scattered in the literature. In this perspective, we have explored various approaches that are proposed in the literature to quench QTM effects, and these include the role of (i) local symmetry of lanthanides, (ii) super-exchange interaction in {3d-4f} complexes, (iii) direct-exchange interaction in {radical-4f} and metal-metal bonded complexes to suppress the QTM, (iv) utilizing external stimuli such as an electric field or pressure to modulate the QTM and (v) avoiding QTM effects by stabilising toroidal states in 4f and {3d-4f} clusters. We believe the strategies summarized here will help to design new-generation SMMs.

Magnetization Dynamics on Isotope-Isomorphic Holmium Single-Molecule Magnets

Here we reported the deuteration of the metal-binding equatorial water molecules in a reported Ho^III single-molecule magnet (SMM) with pentagonal-bipyramidal geometry, from [Ho(CyPh₂ PO)₂ (H₂ O)₅ ]³⁺ to [Ho(CyPh₂ PO)₂ (D₂ O)₅ ]³⁺ . The hyperfine structures originating from the nuclear spin of ¹⁶⁵ Ho^III can be clearly observed. Moreover, the resulting magnetization dynamics revealed the switch of the relative relaxation rates for the two isotope-isomorphic complexes-respectively faster/slower at low/high temperature. The noticeable isotope effect arises from not only the paramagnetic metal center but also the diamagnetic ligands, which can be explained by the ab initio calculated tunnel splitting and the involvement of the super-hyperfine interaction related to the difference in the nuclear spin number of protium (¹ H, I=¹ /₂ ) and deuterium (² H, I=1).

Modern physical methods for the molecular design of single-molecule magnets

Many paramagnetic metal complexes have emerged as unique magnetic materials (single-molecule magnets), which behave as conventional magnets at the single-molecule level, thereby making it possible to use them in modern devices for data storage and processing. The rational design of these complexes, however, requires a deep understanding of the physical laws behind a single-molecule magnet behaviour, the mechanisms of magnetic relaxation that determines the magnetic properties and the relationship of these properties with the structure of single-molecule magnets. This review focuses on the physical methods providing such understanding, including different versions and various combinations of magnetometry, electron paramagnetic and nuclear magnetic resonance spectroscopy, optical spectroscopy and X-ray diffraction. Many of these methods are traditionally used to determine the composition and structure of new chemical compounds. However, they are rarely applied to study molecular magnetism.

The bibliography includes 224 references.

Solvato Modulation of the Magnetic Memory in Isotopically Enriched Erbium Polyoxometalate

Single-Molecule Magnet (SMM) property is by essence molecular, while commonly measured in solid crystalline state. Solvent crystallization molecules are usually neglected in the analysis and interpretation of solid-state properties. The solvation/desolvation process in the polyoxometalate(POM)-based Na₉ [Er(W₅ O₁₈ )₂ ] ⋅ 35 H₂ O SMM demonstrates that the dehydrated form relaxes more than 1000 times faster than the initial state, while the rehydration process allows the quasi complete recovering of the initial magnetic behaviour. This dehydration process is monitored by thermogravimetric analysis (TGA) and temperature-dependent X-ray powder diffraction, and rationalized by periodic quantum chemical calculations evidencing the tremendous role of the labile water molecules in the stability of the edifice. Ab-initio calculations highlight that sodium ions localization in the structure drive the magnetic responses. Isotopic enrichment with nuclear spin free (¹⁶⁶ Er, I=0) Er^III ions shows that the relaxation dynamics in the quantum regime depends on the nuclear spin.

Manipulation of the Coordination Geometry along the C4 Rotation Axis in a Dinuclear Tb3+ Triple-Decker Complex via a Supramolecular Approach

A supramolecular complex (1⋅C₆₀ ) was prepared by assembling (C60-Ih)[5,6]fullerene (C₆₀ ) with the dinuclear Tb³⁺ triple-decker complex [(TPP)Tb(Pc)Tb(TPP)] (1: Tb³⁺ =trivalent terbium ion, Pc^2- =phthalocyaninato, TPP^2- =tetraphenylporphyrinato) with quasi-D_4h symmetry to investigate the relationship between the coordination symmetry and single-molecule magnet (SMM) properties. Tb³⁺ -Pc triple-decker complexes (Tb₂ Pc₃ ) have an important advantage over Tb³⁺ -Pc double-decker complexes (TbPc₂ ) since the magnetic relaxation processes correspond to the Zeeman splitting when there are two 4f spin systems. The two Tb³⁺ sites of 1 are equivalent, and the twist angle (φ) was determined to be 3.62°. On the other hand, the two Tb³⁺ sites of 1⋅C₆₀ are not equivalent. The φ values for sites Tb1 and Tb2 were determined to be 3.67° and 33.8°, respectively, due to a change in the coordination symmetry of 1 upon association with C₆₀ . At 1.8 K, 1 and 1⋅C₆₀ undergo different magnetic relaxations, and the changes in the ground state affect the spin dynamics. Although 1 and 1⋅C₆₀ relax via QTM in a zero applied magnetic field (H), H dependencies of the magnetic relaxation times (τ) for H>1500 Oe are similar. On the other hand, for H<1500 Oe, the τ values have different behaviors since the off-diagonal terms ( B k q ; q ≠ 0 ) affect the magnetic relaxation mechanism. From temperature (T) and H dependences of τ, spin-phonon interactions along with direct and Raman mechanisms explain the spin dynamics. We believe that a supramolecular method can be used to control the magnetic anisotropy along the C₄ rotation axis and the spin dynamic properties in dinuclear Ln³⁺ -Pc multiple-decker complexes.

Single Ion Magnets from 3d to 5f: Developments and Strategies

Single-ion magnets (SIMs), exhibiting slow magnetization relaxation in the absence of the magnetic field, originate from their single spin-carrier centre. In pursuit of high-performance magnetic properties, such as high spin-reversal barrier and high blocking temperature, various metal centres were investigated to establish SIMs, including 3d and 5d transition metal ions, 4f lanthanide ions, and 5f actinide ions, which possess unique zero-field splitting and magnetic properties. Therefore, proper ligand field is of great importance to different types of metals. In the given great breakthroughs since the first SIM, [Pc₂ Tb]^- (Pc=dianion of phthalocyanine), was reported, strategies of ligand field design have emerged. In this review, the developments of SIMs with different metal centres are summarized, as well as the possible strategies.

A Terminal Fluoride Ligand Generates Axial Magnetic Anisotropy in Dysprosium Complexes

The first dysprosium complexes with a terminal fluoride ligand are obtained as air-stable compounds. The strong, highly electrostatic dysprosium-fluoride bond generates a large axial crystal-field splitting of the J=15/2 ground state, as evidenced by high-resolution luminescence spectroscopy and correlated with the single-molecule magnet behavior through experimental magnetic susceptibility data and ab initio calculations.

Elucidation of Dual Magnetic Relaxation Processes in Dinuclear Dysprosium(III) Phthalocyaninato Triple-Decker Single-Molecule Magnets Depending on the Octacoordination Geometry

When applying single-molecule magnets (SMMs) to spintronic devices, control of the quantum tunneling of the magnetization (QTM) as well as a spin-lattice interactions are important. Attempts have been made to use not only coordination geometry but also magnetic interactions between SMMs as an exchange bias. In this manuscript, dinuclear dysprosium(III) (Dy^III ) SMMs with the same octacoordination geometry undergo dual magnetic relaxation processes at low temperature. In the dinuclear Dy^III phthalocyaninato (Pc^2- ) triple-decker type complex [(Pc)Dy(ooPc)Dy(Pc)] (1) (ooPc^2- =2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato) with a square-antiprismatic (SAP) geometry, the ground state is divided by the Zeeman effect, and level intersection occurs when a magnetic field is applied. Due to the ground state properties of 1, since the Zeeman diagram where the levels intersect in an H_dc of 2500 Oe, two kinds of QTM and direct processes occur. However, dinuclear Dy^III -Pc systems with C₄ geometry, which have a twist angle (ϕ) of less than 45° do not undergo dual magnetic relaxation processes. From magnetic field and temperature dependences, the dual magnetic relaxation processes were clarified.

Nuclear Spin Isomers: Engineering a Et4 N[DyPc2 ] Spin Qudit

Two dysprosium isotopic isomers were synthesized: Et₄ N[¹⁶³ DyPc₂ ] (1) with I=5/2 and Et₄ N[¹⁶⁴ DyPc₂ ] (2) with I=0 (where Pc=phthalocyaninato). Both isotopologues are single-molecule magnets (SMMs); however, their relaxation times as well as their magnetic hystereses differ considerably. Quantum tunneling of the magnetization (QTM) at the energy level crossings is found for both systems via ac-susceptibility and μ-SQUID measurements. μ-SQUID studies of 1^(I=5/2) reveal several nuclear-spin-driven QTM events; hence determination of the hyperfine coupling and the nuclear quadrupole splitting is possible. Compound 2^(I=0) shows only strongly reduced QTM at zero magnetic field. 1^(I=5/2) could be used as a multilevel nuclear spin qubit, namely qudit (d=6), for quantum information processing (QIP) schemes and provides an example of novel coordination-chemistry-discriminating nuclear spin isotopes. Our results show that the nuclear spin of the lanthanide must be included in the design principles of molecular qubits and SMMs.

Hyperfine-Interaction-Driven Suppression of Quantum Tunneling at Zero Field in a Holmium(III) Single-Ion Magnet

An extremely rare non-Kramers holmium(III) single-ion magnet (SIM) is reported to be stabilized in the pentagonal-bipyramidal geometry by a phosphine oxide with a high energy barrier of 237(4) cm^-1 . The suppression of the quantum tunneling of magnetization (QTM) at zero field and the hyperfine structures originating from field-induced QTMs can be observed even from the field-dependent alternating-current magnetic susceptibility in addition to single-crystal hysteresis loops. These dramatic dynamics were attributed to the combination of the favorable crystal-field environment and the hyperfine interactions arising from ¹⁶⁵ Ho (I=7/2) with a natural abundance of 100 %.

A heterometallic ferrimagnet based on a new TTF-bis(oxamato) ligand

An interesting heterometallic one-dimensional complex {[Cu(TTF-opba)][Mn(CH₃OH)₂]}_n based on a π-extended TTF ligand was prepared through the method of “metalloligand”. It retains the redox activity and shows ferrimagnetic behavior.

A Low-Symmetry Dysprosium Metallocene Single-Molecule Magnet with a High Anisotropy Barrier

The single-molecule magnet (SMM) properties of the isocarbonyl-ligated dysprosium metallocene [Cp*2 Dy{μ-(OC)2 FeCp}]2 (1Dy ), which contains a rhombus-shaped Dy2 Fe2 core, are described. Combining a strong axial [Cp*](-) ligand field with a weak equatorial field consisting of the isocarbonyl ligands leads to an anisotropy barrier of 662 cm(-1) in zero applied field. The dominant thermal relaxation pathways in 1Dy involves at least the fourth-excited Kramers doublet, thus demonstrating that prominent SMM behavior can be observed for dysprosium in low-symmetry environments.

Relaxation Dynamics and Magnetic Anisotropy in a Low-Symmetry Dy(III) Complex

The magnetic behaviour of a Dy(LH)3 complex (LH(-) is the anion of 2-hydroxy-N'-[(E)-(2-hydroxy-3-methoxyphenyl)methylidene]benzhydrazide) was analysed in depth from both theoretical and experimental points of view. Cantilever torque magnetometry indicated that the complex has Ising-type anisotropy, and provided two possible directions for the easy axis of anisotropy due to the presence of two magnetically non-equivalent molecules in the crystal. Ab initio calculations confirmed the strong Ising-type anisotropy and disentangled the two possible orientations. The computed results obtained by using ab initio calculations were then used to rationalise the composite dynamic behaviour observed for both pure Dy(III) phase and Y(III) diluted phase, which showed two different relaxation channels in zero and non-zero static magnetic fields. In particular, we showed that the relaxation behaviour at the higher temperature range can be correctly reproduced by using a master matrix approach, which suggests that Orbach relaxation is occurring through a second excited doublet.

Influence of Guest Exchange on the Magnetization Dynamics of Dilanthanide Single-Molecule-Magnet Nodes within a Metal-Organic Framework

Multitopic organic linkers can provide a means to organize metal cluster nodes in a regular three-dimensional array. Herein, we show that isonicotinic acid N-oxide (HINO) serves as the linker in the formation of a metal-organic framework featuring Dy2 single-molecule magnets as nodes. Importantly, guest solvent exchange induces a reversible single-crystal to single-crystal transformation between the phases Dy2(INO)4(NO3)2⋅2 solvent (solvent=DMF (Dy2-DMF), CH3CN (Dy2-CH3CN)), thereby switching the effective magnetic relaxation barrier (determined by ac magnetic susceptibility measurements) between a negligible value for Dy2-DMF and 76 cm(-1) for Dy2-CH3CN. Ab initio calculations indicate that this difference arises not from a significant change in the intrinsic relaxation barrier of the Dy2 nodes, but rather from a slowing of the relaxation rate of incoherent quantum tunneling of the magnetization by two orders of magnitude.