Modulating quantum tunnelling of magnetization in Dy isotopologue dimers

Qudits are anticipated to streamline quantum computation by minimizing iterations, lowering error rates, and facilitating error correction. It has been shown that Dy(III)-based molecular systems can act as qudits with expanded Hilbert spaces. Achieving a robust intramolecular interaction, whether exchange or dipolar, is crucial for spanning the Hilbert space of qudits; hence, short Dy(III)⋯Dy(III) distances are required. Looking for multilevel systems that can be employed as qudits, we have synthesized and characterized two dysprosium-based isotopologues: [163Dy2(BTFA)4(PHZP)2]0 (1(I=5/2)) and [164Dy2(BTFA)4(PHZP)2]0 (2(I=0)), where BTFA = 3-benzoyl-1,1,1-trifluoroacetone and PHZP = N'-[(E)-(pyrazin-2-yl)methylidene]pyrazine-2-carbohydrazonate. Both complexes showed slow magnetic relaxation at zero applied magnetic field. μSQUID investigations, at milli-Kelvin temperatures, and direct and alternating current magnetic measurements reveal distinctions in the magnetic behavior between the two complexes and an operative interaction between the Dy(III) centers. We find that the presence or absence of the nuclear spin plays a minor role in the magnetic properties above 2 K. On the contrary, at milli-Kelvin temperatures, μSQUID studies show enhanced relaxation in 1(I=5/2), attributed to several quantum tunnelling pathways enabled by hyperfine and quadrupole interactions. The interplay between the antiferromagnetic coupling and enhanced relaxation indicates that the exchange coupling influences the relaxation mechanisms at different temperature ranges.

Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets

Single-molecule magnets are among the most promising platforms for achieving molecular-scale data storage and processing. Their magnetisation dynamics are determined by the interplay between electronic and vibrational degrees of freedom, which can couple coherently, leading to complex vibronic dynamics. Building on an ab initio description of the electronic and vibrational Hamiltonians, we formulate a non-perturbative vibronic model of the low-energy magnetic degrees of freedom in monometallic single-molecule magnets. Describing their low-temperature magnetism in terms of magnetic polarons, we are able to quantify the vibronic contribution to the quantum tunnelling of the magnetisation, a process that is commonly assumed to be independent of spin-phonon coupling. We find that the formation of magnetic polarons lowers the tunnelling probability in both amorphous and crystalline systems by stabilising the low-lying spin states. This work, thus, shows that spin-phonon coupling subtly influences magnetic relaxation in single-molecule magnets even at extremely low temperatures where no vibrational excitations are present.

Zero-Field SMM Behavior Triggered by Magnetic Exchange Interactions and a Collinear Arrangement of Local Anisotropy Axes in a Linear Co3II Complex

A new linear trinuclear Co(II)3 complex with a formula of [{Co(μ-L)}2Co] has been prepared by self-assembly of Co(II) ions and the N3O3-tripodal Schiff base ligand H3L, which is obtained from the condensation of 1,1,1-tris(aminomethyl)ethane and salicylaldehyde. Single X-ray diffraction shows that this compound is centrosymmetric with triple-phenolate bridging groups connecting neighboring Co(II) ions, leading to a paddle-wheel-like structure with a pseudo-C3 axis lying in the Co-Co-Co direction. The Co(II) ions at both ends of the Co(II)3 molecule exhibit distorted trigonal prismatic CoN3O3 geometry, whereas the Co(II) at the middle presents an elongated trigonal antiprismatic CoO6 geometry. The combined analysis of the magnetic data and theoretical calculations reveal strong easy-axis magnetic anisotropy for both types of Co(II) ions (|D| values higher than 115 cm-1) with the local anisotropic axes lying on the pseudo-C3 axis of the molecule. The magnetic exchange interaction between the middle and ends Co(II) ions, extracted by using either a Hamiltonian accounting for the isotropic magnetic coupling and ZFS or the Lines' model, was found to be medium to strong and antiferromagnetic in nature, whereas the interaction between the external Co(II) ions is weak antiferromagnetic. Interestingly, the compound exhibits slow relaxation of magnetization and open hysteresis at zero field and therefore SMM behavior. The significant magnetic exchange coupling found for [{Co(μ-L)}2Co] is mainly responsible for the quenching of QTM, which combined with the easy-axis local anisotropy of the CoII ions and the collinearity of their local anisotropy axes with the pseudo-C3 axis favors the observation of SMM behavior at zero field.

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.

Isotopic enrichment in lanthanide coordination complexes: contribution to single-molecule magnets and spin qudit insights

Lanthanide Single-Molecule Magnets (SMMs) fascinate the scientific community due to their plethora of potential applications ranging from data storage to spintronic devices and quantum computing. This review article proposes a comprehensive description of the influence of the nuclear spin, i.e. hyperfine interaction, on the magnetic properties of lanthanide SMMs and on quantum information processing of qudit. This influence is analysed for non-Kramers and Kramers lanthanide SMMs as well as for the electronic distribution of the electron in 4f orbitals i.e. oblate and prolate ions. Then the role of magnetic interactions in isotopically enriched polynuclear Dy(III) SMMs is discussed. Finally the possible effect of superhyperfine interaction due to the nuclear spin of elements originating from the surrounding of the lanthanide centre is analyzed. The effect of nuclear spin on the dynamics of the lanthanide SMMs is demonstrated using different techniques such as magnetometry, muon spectroscopy (μ-SR), and Mössbauer and Resonance Vibrational Spectroscopies.

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.

Polymorphism modulates photoluminescence and magnetic dynamics of mononuclear dysprosium-anthracene complexes

Complexes α-Dy(depma)₃Cl₃ (α-DyCl), β-Dy(depma)₃Cl₃ (β-DyCl) and β-Dy(depma)₃Br₃ (β-DyBr) (depma = 9-diethylphosphono-methylanthracene) are reported. α-DyCl and β-DyCl are polymorphs showing distinct magnetic dynamics with energy barriers of 32.3 K and 66.6 K. They also show distinct luminescence properties with emission peaks at 487 nm and 530 nm, respectively.

Synthesis, Structure, and Zero-Field SMM Behavior of Homometallic Dy2, Dy4, and Dy6 Complexes

The synthesis, structure, and magnetic properties of three Dy^III complexes of different nuclearity, [Dy₂(H₂L)₂(NO₃)] [NO₃]·2H₂O·CH₃OH (1), [Dy₄(HL)₂(piv)₄(OH)₂] (2), and [Dy₆(H₂L)₃(μ₃-OH)(μ₃-CO₃)₃(CH₃OH)₄(H₂O)₈] 5Cl·3H₂O (3) [(H₄L) = 6-((bis(2-hydroxyethyl)amino)-N'-(2-hydroxybenzylidene)picolinohydrazide)], are described. This variety of complexes with the same ligand could be obtained by playing with the metal-to-ligand molar ratio, the type of Dy^III salt, the kind of base, and the presence/absence of coligand. 1 is a dinuclear complex, while 2 is a tetranuclear assembly with a butterfly-shaped topology. 3 is a homometallic hexanuclear complex that exhibits a propeller-shaped topology. Interestingly, in this complex 3, three atmospheric carbon dioxide molecules are trapped in the form of carbonate ions, which assist in holding the hexanuclear complex together. All of the complexes reveal a slow relaxation of magnetization even in zero applied field. Complex 1 is a zero-field SMM with an effective energy barrier (U_eff) of magnetization reversal equal to 87(1) K and a relaxation time of τ₀ = 6.4(3) × 10^-9 s. Under an applied magnetic field of 0.1 T, these parameters change to U_eff = 101(3) K, τ₀ = 2.5(1) × 10^-9 s. Complex 2 shows zero-field SMM behavior with U_eff = 31(2) K, τ₀ = 4.2(1) × 10^-7 s or τ₀₁ = 2(1) × 10^-7 s, U_eff1 = 37(8) K, τ₀₂ = 5(6) × 10^-5 s, and U_eff2 = 8(4) by considering two Orbach relaxation processes, while 3, also a zero-field SMM, shows a double relaxation of magnetization [U_eff1 = 62.4(3) K, τ₀₁ = 4.6(3) × 10^-8 s, and U_eff1 = 2(1) K, τ₀₂ = 4.6(2) × 10^-5 s]. The ab initio calculations indicated that in these complexes, the Kramer's ground doublet is characterized by an axial g-tensor with the prevalence of the m_J = ±15/2 component, as well as that due to the weak magnetic coupling between the metal centers, the magnetic relaxation, which is dominated by the single Dy^III centers rather than by the exchange-coupled states, takes place via Raman/Orbach or TA-QTM. Moreover, theoretical calculations support a toroidal magnetic state for complex 2.

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.

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.

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).

Counterintuitive Single-Molecule Magnet Behaviour in Two Polymorphs of One-Dimensional Compounds Involving Chiral BINOL-Derived Bisphosphate Ligands

The coordination reaction of the [Dy(hfac)3(H2O)2] units (hfac− = 1,1,1,5,5,5-hexafluoroacetylacetonate) with the [8′-(Diphenoxylphosphinyl)[1,1′-binaphthalen]-8-yl]diphenoxylphosphine oxide ligand (L) followed by a crystallisation in a 1:3 CH2Cl2:n-hexane solvent mixture led to the isolation of a new polymorph of formula [(Dy(hfac)3((S)-L))3]n (1). The X-ray structure on single crystal of 1 revealed the formation of a mono-dimensional coordination polymer with three crystallographically independent DyIII centres, which crystallised in the polar chiral P21 space group. Ac magnetic measurements highlighted single-molecule magnet behaviour under both zero and 1000 Oe applied magnetic field with magnetic relaxation through quantum tunneling of the magnetisation (QTM, zero field only) and Raman processes. Despite the three crystallographically independent DyIII centres adopting a distorted D4d coordination environment, a single slow magnetic relaxation contribution was observed at a slower rate than its previously studied [(Dy(hfac)3((S)-L))]n (2) polymorph.

Study of the influence of nuclear spin and dilution over the slow relaxation in a 3d4f heterobimetallic single-molecule magnet

The effects of isotopic enrichment and magnetic dilution have been investigated in a heterobimetallic complex of formula [Zn₂L₂^ADyCl₃]·2H₂O (^ADyZn₂) (A = 162 and 163) presenting slow relaxation of the magnetization. Isotopic substitution for ¹⁶²Dy (I = 0) and ¹⁶³Dy (I = 5/2) leads to a shift in the relaxation times depending on the suppression or enhancement of the hyperfine interactions. The release of the dipolar interactions through magnetic dilution in a Y(iii)-based matrix enhances the slow relaxation of the magnetization and the visibility of the nuclear spin effect. A comparison of the hysteresis loop at 0.5 K for bulk and diluted analogues of pure isotopically enriched complexes suggested a role of the nuclear spin in the interaction between the active system and the matrix.

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.

The anisotropy of the internal magnetic field on the central ion is capable of imposing great impact on the quantum tunneling of magnetization of Kramers single-ion magnets

In this work, a theoretical method, taking into account the anisotropy of the internal magnetic field (B[combining right harpoon above]int), is proposed to predict the rate of quantum tunneling of magnetization (QTM), i.e., τQTM-1, for Kramers single-ion magnets (SIMs). Direct comparison to both experimental and previous theoretical results of three typical Kramers SIMs indicates the necessity of the inclusion of the anisotropy of B[combining right harpoon above]int for accurate description of QTM. The predictions of the method here are consistent with the theory proposed by Prokof'ev and Stamp (PS). For Kramers SIMs of high magnetic axiality, the QTM rates, predicted by the method here, are almost linearly proportional to the results by the PS method. The dependence of τQTM-1 on various parameters is analyzed for model systems. The averaged magnitude of B[combining right harpoon above]int (Bave) and principal g value of the axial direction (gZ) are the parameters on which τQTM-1 is linearly dependent. The ones on which τQTM-1 is quadratically dependent are gXY, i.e., the principal g value of the transversal direction, and xaniso characterizing the anisotropy of B[combining right harpoon above]int. Compared to Bave and gZ, gXY and xaniso provide a higher order of dependence for QTM. Therefore regulation of the SMM property via introduction of desired values of gXY and xaniso ought to be a strategy more efficient than the one via Bave and gZ. Being different from the one via gXY, the strategy via xaniso to regulate the QTM has been rarely touched upon according to our best knowledge. However, this strategy could also lead to significant improvement since it is the same as gXY in the aspect of the dependence of τQTM-1.

A Journey in Lanthanide Coordination Chemistry: From Evaporable Dimers to Magnetic Materials and Luminescent Devices

ConspectusLanthanide ions are prime ingredients for the design of compounds, materials, and devices with unique magnetic and optical properties. Accordingly, coordination chemistry is one of the best tools for building molecular edifices from these ions because it allows careful control of the ions' environment and of the dimensionality of the final compound.In this Account, we review our results on lanthanide-based dimers. We show how a pure fundamental study on lanthanide coordination chemistry allows the investigation of a full continuum of results from the compound to materials and then to devices. The conversion of molecules into materials is a tricky task because it requires strong molecular robustness toward the surface deposition processes as well as the preservation and detectability of the molecular properties in the material. Additionally, the passage of a material toward a device implies a material with a given function, for example, a tailored response to an external stimulus.To do so, we targeted neutral and isolated molecules whose transfer on surfaces by chemi- or physisorption is much easier than that of charged molecules or extended coordination networks. Then, we focused on molecules with very strong evaporability to avoid wet chemistry deposition processes that are more likely to damage the molecules and/or distort their geometries.We thus designed lanthanide dimers based on fluorinated β-diketonates and pyridine-N-oxide ligands. As expected, they show remarkable evaporability but also strong luminescence and interesting magnetic behavior because they behave as single-molecule magnets (SMMs). Ligand substitutions and stoichiometric modifications allow the optimization of the geometric organization of the dimers in the crystal packing as well as their evaporability, SMM behavior, luminescent properties, or their ability to be anchored on surfaces. Most of all, this family of molecules shows a strong ability to form thick films on various substrates. This allows converting these molecules to magnetic materials and luminescent devices.Magnetic materials can be designed by creating thick films of the dimers deposited on gold. These films have been designed and investigated with the most advanced techniques of on-surface imaging (atomic force microscopy, AFM), on-surface physicochemical characterization (X-ray photoelectron spectroscopy (XPS), time of flight-secondary ion mass spectroscopy (Tof-SIMS)), and on-surface magnetic investigation (low-energy muon spin relaxation (LE-μSR)). Contrary to what was previously observed on other SMM films, no depth dependence of the SMM behavior was observed. This means that the dimers do not suffer from the vacuum or substrate interface and behave similarly, whatever their localization. This exceptional magnetic robustness is a key ingredient in the creation of materials for molecular magnetic data storage.Luminescent devices can be obtained by layering molecular films of the dimers with a copper-rich solid-state electrolyte between ITO/Pt electrodes. The electromigration of Cu²⁺ ions into films of Eu³⁺, Tb³⁺, and Dy³⁺ dimers quenches their luminescence. This luminescence tuning by electromigration is reversible, and this setup can be considered to be a proof of concept of full solid-state luminescent device where reversible coding can be tailored by an electric field. It is envisioned for optical data storage purposes. In the future, it could also benefit from the SMM properties of the molecules to pave the way toward multifunctional molecular data storage devices.

Ytterbium-Centered Isotopic Enrichment Leading to a Zero-Field Single-Molecule Magnet

An unprecedented combination of isotopic enrichment and magnetic dilution approaches for a prolate ytterbium(III)-based complex was performed. It results in the appearance of the first observations of a nuclear spin effect on both quantum tunneling of magnetization and slow magnetic relaxation for an ytterbium complex under a zero applied field.

Blocking like it's hot: a synthetic chemists' path to high-temperature lanthanide single molecule magnets

Progress in the synthesis, design, and characterisation of single-molecule magnets (SMMs) has expanded dramatically from curiosity driven beginnings to molecules that retain magnetization above the boiling point of liquid nitrogen. This is in no small part due to the increasingly collaborative nature of this research where synthetic targets are guided by theoretical design criteria. This article aims to summarize these efforts and progress from the perspective of a synthetic chemist with a focus on how chemistry can modulate physical properties. A simple overview is presented of lanthanide electronic structure in order to contextualize the synthetic advances that have led to drastic improvements in the performance of lanthanide-based SMMs from the early 2000s to the late 2010s.

Spin dynamics in single-molecule magnets and molecular qubits

Over recent decades, much effort has been made to lengthen spin relaxation/decoherence times of single-molecule magnets and molecular qubits by following different chemical design rules such as maximizing the total spin value, controlling symmetry, enhancing the ligand field or inhibiting key vibrational modes. Simultaneously, electronic structure calculations have been employed to provide an understanding of the processes involved in the spin dynamics of molecular systems and served to refine or introduce new design rules. This review focuses on contemporary theoretical approaches focused on the calculation of spin relaxation/decoherence times, highlighting their main features and scope. Fundamental aspects of experimental techniques for the determination of key Single Molecule Magnet/Spin Qubit properties are also reviewed.

Redox- and solvato-magnetic switching in a tetrathiafulvalene-based triad single-molecule magnet

Simultaneous redox and solvato-magnetic switching was achieved for a dinuclear dysprosium single-molecule magnet involving an extended tetrathiafulvalene fused semiquinone based triad.

A method to predict both the relaxation time of quantum tunneling of magnetization and the effective barrier of magnetic reversal for a Kramers single-ion magnet

A method to predict the relaxation time of quantum tunneling of magnetization and the magnetic reversal barrier with efficiency and reliability.

Synthetic Hilbert Space Engineering of Molecular Qudits: Isotopologue Chemistry

One of the most ambitious technological goals is the development of devices working under the laws of quantum mechanics. Among others, an important challenge to be resolved on the way to such breakthrough technology concerns the scalability of the available Hilbert space. Recently, proof-of-principle experiments were reported, in which the implementation of quantum algorithms (the Grover's search algorithm, iSWAP-gate, etc.) in a single-molecule nuclear spin qudit (with d = 4) known as ¹⁵⁹ TbPc₂ was described, where the nuclear spins of lanthanides are used as a quantum register to execute simple quantum algorithms. In this progress report, the goal of linear and exponential up-scalability of the available Hilbert space expressed by the qudit-dimension "d" is addressed by synthesizing lanthanide metal complexes as quantum computing hardware. The synthesis of multinuclear large-Hilbert-space complexes has to be carried out under strict control of the nuclear spin degree of freedom leading to isotopologues, whereby electronic coupling between several nuclear spin units will exponentially extend the Hilbert space available for quantum information processing. Thus, improved multilevel spin qudits can be achieved that exhibit an exponentially scalable Hilbert space to enable high-performance quantum computing and information storage.

Quantum tunnelling of the magnetisation in single-molecule magnet isotopologue dimers

Quantum tunnelling of the magnetisation plays a major role in the magnetic properties of lanthanide Single-Molecule Magnets: while it is considered a problem for data storage device applications since it leads to information loss, it is an essential pre-requisite for the read-out and manipulation of the nuclear states in Quantum Information Processing schemes. Here we describe two isotopologue dysprosium dimers, i.e. [(163Dy(tmhd)3)2(bpym)] and [(164Dy(tmhd)3)2(bpym)] (tmd = tris(tetramethylheptanedionato) and bpym = bipyrimidine), where the nuclear spin presence or absence clearly affects the magnetic properties of the systems. Through μ-SQUID studies at milli-Kelvin temperatures and alternating current magnetic measurements, we find significant differences in the magnetic behaviour of both complexes. While simulation of the hysteresis loops at 30 mK reveals that the presence of nuclear spin does not influence the tunnelling rate, we find that it facilitates the coupling to the phonon bath enhancing the direct relaxation process; an observation reflected in the temperature and field dependence of the relaxation rates.

Series of Chloranilate-Bridged Dinuclear Lanthanide Complexes: Kramers Systems Showing Field-Induced Slow Magnetic Relaxation

A series of chloralilate-bridged dinuclear lanthanide complexes of formula [{LnIII(Tp)2}2(μ-Cl2An)]·2CH2Cl2, where Cl2An2− and Tp− represent the chloranilate and hydrotris (pyrazolyl)borate ligands, respectively, and Ln = Gd (1), Tb (2), Ho (3), Er (4), and Yb (5) was synthesized. All five complexes were characterized by an elemental analysis, infrared spectroscopy, single crystal X-ray diffraction, and SQUID measurements. The complexes 1–5 in the series were all isostructural. A comparison of the temperature dependence of the dc magnetic susceptibility data of these complexes revealed clear differences depending on the lanthanide center. Ac magnetic susceptibility measurements revealed that none of the five complexes exhibited a slow magnetic relaxation under a zero applied dc field. On the other hand, the Kramers systems (complexes 4 and 5) clearly displayed a slow magnetic relaxation under applied dc fields, suggesting field-induced single-molecule magnets that occur through Orbach and Raman relaxation processes.

Studies of hysteresis and quantum tunnelling of the magnetisation in dysprosium(iii) single molecule magnets

We report a study of quantum tunneling of the magnetisation in three Dy(iii) single-molecule magnets.

Hyperfine coupling and slow magnetic relaxation in isotopically enriched DyIII mononuclear single-molecule magnets

On the role of hyperfine coupling constant on the relaxation time of single-molecule magnets.

Electro-activity and magnetic switching in lanthanide-based single-molecule magnets

The present work reviews switching of single-molecule magnetic behaviour achieved through various stimuli such as temperature, light irradiation, redox processes, solvation/desolvation, and magnetic field.

Slow relaxation of magnetization in a {Fe6Dy} complex deriving from a family of highly symmetric metallacryptands

A novel family of combined 9-MC-3/12-MC-4 {Fe₆Ln} metallacrown-like complexes or else a new form of metallacryptates is reported, while the {Fe₆Dy} analogue shows SMM behavior.

Ab Initio Prediction of Tunneling Relaxation Times and Effective Demagnetization Barriers in Kramers Lanthanide Single-Molecule Magnets

Single-molecule magnets (SMMs) are promising candidates for molecule-based quantum information devices. Their main limitation is their cryogenic operative temperature. To achieve devices performing at higher temperatures, demagnetization mechanisms must be suppressed by chemical tuning. Electronic structure calculations can provide useful information to rationalize SMM behavior, but they do not provide a direct prediction for the key experimental parameters describing magnetic relaxation (i.e., tunneling relaxation time (τ_QT) and effective demagnetization barrier ( U_eff)). In this Letter, a first-principles model is proposed to predict τ_QT and U_eff for mononuclear, half-integer spin SMMs, allowing direct comparison with experiment. Model accuracy was assessed against experimental data for 18 mononuclear Ln^III complexes (15 Dy^III and 3 Er^III) and applied to 3 of the current best-performing SMMs, correctly predicting nontrivial relaxation pathways. The model shows that the combination of single-ion anisotropy and spin-spin dipolar coupling can account for the major part of tunneling demagnetization for the studied systems.

Field- and temperature-dependent quantum tunnelling of the magnetisation in a large barrier single-molecule magnet

Understanding quantum tunnelling of the magnetisation (QTM) in single-molecule magnets (SMMs) is crucial for improving performance and achieving molecule-based information storage above liquid nitrogen temperatures. Here, through a field- and temperature-dependent study of the magnetisation dynamics of [Dy(^tBuO)Cl(THF)₅][BPh₄]·2THF, we elucidate the different relaxation processes: field-independent Orbach and Raman mechanisms dominate at high temperatures, a single-phonon direct process dominates at low temperatures and fields >1 kOe, and a field- and temperature-dependent QTM process operates near zero field. Accounting for the exponential temperature dependence of the phonon collision rate in the QTM process, we model the magnetisation dynamics over 11 orders of magnitude and find a QTM tunnelling gap on the order of 10⁻⁴ to 10⁻⁵ cm⁻¹. We show that removal of Dy nuclear spins does not suppress QTM, and argue that while internal dipolar fields and hyperfine coupling support QTM, it is the dynamic crystal field that drives efficient QTM.

Understanding quantum tunnelling of the magnetisation in single-molecule magnets is crucial for their potential application in information storage. Here the authors conduct a field- and temperature-dependent study of the magnetisation dynamics of a dysprosium-based SMM, finding four distinct relaxation processes that dominate in different regimes.

Magnetization relaxation in the single-ion magnet DySc2N@C80: quantum tunneling, magnetic dilution, and unconventional temperature dependence

Quantum tunneling and relaxation of magnetization in single molecule magnet DySc₂N@C₈₀ is thoroughly studied as a function of magnetic dilution, temperature, and magnetic field.

Relaxation of magnetization in endohedral metallofullerenes DySc₂N@C₈₀ is studied at different temperatures, in different magnetic fields, and in different molecular arrangements. Magnetization behavior and relaxation are analyzed for powder sample, and for DySc₂N@C₈₀ diluted in non-magnetic fullerene Lu₃N@C₈₀, adsorbed in voids of a metal–organic framework, and dispersed in a polymer. The magnetic field dependence and zero-field relaxation are also studied for single-crystals of DySc₂N@C₈₀ co-crystallized with Ni(ii) octaethylporphyrin, as well as for the single crystal diluted with Lu₃N@C₈₀. Landau–Zener theory is applied to analyze quantum tunneling of magnetization in the crystals. The field dependence of relaxation rates revealed a dramatic dependence of the zero-field tunneling resonance width on the dilution and is explained with the help of an analysis of dipolar field distributions. AC magnetometry is used then to get access to the relaxation of magnetization in a broader temperature range, from 2 to 87 K. Finally, a theoretical framework describing the spin dynamics with dissipation is proposed to study magnetization relaxation phenomena in single molecule magnets.

Symmetry strategies for high performance lanthanide-based single-molecule magnets

Toward promising candidates of quantum information processing, the rapid development of lanthanide-based single-molecule magnets (Ln-SMMs) highlights design strategies in consideration of the local symmetry of lanthanide ions. In this review, crystal-field theory is employed to demonstrate the electronic structures according to the semiquantitative electrostatic model. Then, specific symmetry elements are analysed for the elimination of transverse crystal fields and quantum tunnelling of magnetization (QTM). In this way, high-performance Ln-SMMs can be designed to enable extremely slow relaxation of magnetization, namely magnetic blocking; however, their practical magnetic characterization becomes increasingly challenging. Therefore, we will attempt to interpret the experimental behaviours and clarify some issues in detail. Finally, representative Ln-SMMs with specific local symmetries are summarized in combination with the discussion on the symmetry strategies, and some of the underlying questions are put forward.

Manipulating the Relaxation of Quasi- D4 d Dysprosium Compounds through Alternation of the O-Donor Ligands

Three mononuclear Dy^III complexes with the same auxiliary ligand Lz (2,4-diamino-6-pyridyl-1,3,5-triazine), [Dy(TTA)₃Lz] (1Dy) (TTA = 4,4,4-trifluoro-1-(2-thienyl)-1,3-butanedionate), [Dy(acac)₃Lz]·CH₃OH·0.5H₂O (2Dy) (acac = acetylacetonate), and [Dy(MQ)₂Lz₂]Br·CH₃OH (3Dy) (HMQ = 2-methyl-8-quinolinol), have been synthesized through alteration of the ligands containing O donors. In all three complexes, the Dy^III ions are eight-coordinate and submitted to pseudo- D_{4 d} symmetry in the first coordination sphere. It is noteworthy that the TTA ligands in 1Dy are easily substituted by other bidentate capping ligands with O donors, leading to distinct magnetic properties, which were studied experimentally and via ab initio calculations. All three complexes were found to exhibit single-molecule magnet behavior with U_eff of 22 cm^-1 (1Dy), 112 cm^-1 (2Dy), and 56 cm^-1 (3Dy) under zero applied dc field. Complex 1Dy demonstrates inferior SIM properties compared with 2Dy and 3Dy, which can be attributed to the strong electron-withdrawing effects of TTA ligands, as confirmed by theoretical calculations. However, butterfly-shaped magnetic hysteresis in 1Dy and 3Dy was observed at 1.9 K, while not in 2Dy.

Chemical tunnel-splitting-engineering in a dysprosium-based molecular nanomagnet

Total control over the electronic spin relaxation in molecular nanomagnets is the ultimate goal in the design of new molecules with evermore realizable applications in spin-based devices. For single-ion lanthanide systems, with strong spin-orbit coupling, the potential applications are linked to the energetic structure of the crystal field levels and quantum tunneling within the ground state. Structural engineering of the timescale of these tunneling events via appropriate design of crystal fields represents a fundamental challenge for the synthetic chemist, since tunnel splittings are expected to be suppressed by crystal field environments with sufficiently high-order symmetry. Here, we report the long missing study of the effect of a non-linear (C₄) to pseudo-linear (D_4d) change in crystal field symmetry in an otherwise chemically unaltered dysprosium complex. From a purely experimental study of crystal field levels and electronic spin dynamics at milliKelvin temperatures, we demonstrate the ensuing threefold reduction of the tunnel splitting.

Isotope effects on the spin dynamics of single-molecule magnets probed using muon spin spectroscopy

Subtle isotopic effects on spin dynamics are captured using Muon Spin Relaxation experiments on isotopically enriched Dy-based single molecule magnets.

Hybrid organic–inorganic connectivity of NdIII(pyrazine-N,N′-dioxide)[CoIII(CN)6]3− coordination chains for creating near-infrared emissive Nd(iii) showing field-induced slow magnetic relaxation

Organic pzdo and inorganic hexacyanidocobaltate(iii) support the formation of Nd(iii) complexes showing NIR fluorescence and magnetic anisotropy.

Eight homodinuclear lanthanide complexes prepared from a quinoline based ligand: structural diversity and single-molecule magnetism behaviour

Eight dinuclear complexes are prepared and characterized; complex 6 exhibits SMM behavior with a U_eff value of 14.83 K.

Heteroleptic β-diketonate Ln(iii) complexes decorated with pyridyl substituted pyridazine ligands: synthesis, structure and luminescence properties

A substituted pyridazine acts as a sensitizer in mononuclear heteroleptic Ln(iii) complexes.

Unprecedented family of heterometallic LnIII[18-metallacrown-6] complexes: syntheses, structures, and magnetic properties

Herein, a new family of Ln^III[18-metallacrown-6] compounds with the formula [Fe₆O₂Ln(tBu-sao)₆(OH)(MeO)₄(MeOH)(H₂O)]·6MeOH [Ln = Dy^III (1), Tb^III (2), Gd^III (3), and Y^III (4), tBu-saoH₂ = 3,5-di-tert-butylsalicylaldoxime] was synthesized through one-pot reactions using tBu-saoH₂, Fe(ClO₄)₃·6H₂O, and Ln(NO₃)₃·6H₂O. The four compounds are isostructural, and the encapsulation of a Ln ion in the ring cavity of 18-metallacrown-6 (18-MC-6) was exhibited for the first time. The structural analysis shows a ship-like 18-MC-6 core with a beset lanthanide ion connecting six ring oxygen atoms (O_MC). Magnetic measurements reveal domain antiferromagnetic coupling interactions between metal ions and field-dependent slow magnetic relaxation in 1-3.

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.