Penta- and Hexacoordinated Copper(II) Complexes with Azido and 4-amino-3,5-di-2-pyridyl-4H-1,2,4-triazole Ligands with Field-Induced Slow Magnetic Relaxation

Two new Cu(II) complexes with abpt (4-amino-3,5-di-2-pyridyl-4H-1,2,4-triazole) and azido ligands, [Cu(abpt)2(N3)]NO3 (1) and [Cu(abpt)2(N3)2]⋅2H2O (2), have been prepared and characterized by crystal structure analysis, spectral and magnetic measurements. The presence of neutral abpt, as well as azido ligands was proved by IR spectroscopy and the composition of the complexes confirmed an elemental analysis. Monocrystal X-ray structure analysis revealed that 1 is an ionic pentacoordinated Cu(II) complex, exhibiting a distorted tetragonal pyramidal geometry of the coordination polyhedron, while 2 is a neutral molecular complex with a distorted octahedral environment of the Cu(II) atom. The structures are stabilized by π-π stacking interactions between the aromatic rings of abpt, as well as various intra- and intermolecular hydrogen bonds involving nitrate ions and molecules of solvated water in 1 and 2, respectively. A field-induced slow magnetic relaxation was observed at low temperatures in 1, described by the direct and Raman process involving low-energy intramolecular vibrational modes, which were predicted by the DFT calculations.

Phase-dependent polymerization isomerism in the coordination complexes of a flexible bis(β-diketonato) ligand

First prepared in the late 70s, the pro-ligand 1,3-bis(3,5-dioxo-1-hexyl)benzene (H2bdhb) contains two acetoacetyl terminations linked to a central 1,3-phenylene unit through dimethylene bridges. Since each termination can be either in diketonic or keto-enolic form, in organic solution it exists as a mixture of three spectroscopically resolvable tautomers. In the presence of pyridine, Co2+ and the bdhb2- anion form a crystalline dimeric compound with formula [Co2(bdhb)2(py)4] (2) and a Co⋯Co separation of more than 11 Å. Complex 2 contains two pseudo-octahedrally coordinated and non-interacting high-spin cobalt(II) ions (S = 3/2) displaying a large easy-plane anisotropy (D ∼ 70 cm-1), as consistently indicated by magnetic measurements, X-band EPR spectra, and complete active space self-consistent field/N-electron valence state perturbation theory (CASSCF/NEVPT2) calculations. At cryogenic temperatures (T < 7 K) and in an applied static magnetic field, the compound shows detectably slow magnetic relaxation, which occurs through direct and Raman mechanisms. Combined mass spectrometry, UV-Vis, and 1H/2H NMR data, including an isotopic labelling experiment and a determination of molecular weight by diffusion ordered spectroscopy (DOSY), show that 2 rearranges to monomeric high-spin [Co(bdhb)(py)x] species (x = 0, 1, or 2) in organic solution (CH2Cl2, THF) with concomitant partial dissociation of the py ligands. The X-band EPR spectra in a frozen CH2Cl2/toluene matrix concurrently suggest a significant alteration of the coordination environment upon dissolution. These observations are fairly well reproduced by density functional theory (DFT) and CASSCF/NEVPT2 calculations on the lowest Gibbs free energy conformers of each species, as provided by an extensive conformational search based on meta-dynamics simulations and semiempirical tight-binding methods. After the vanadyl analogue, compound 2 provides the second example of polymerization isomerism in the 1 : 1 adducts of bdhb2- with divalent metal ions.

Modulation of the magnetic properties of mononuclear Dy(III) complexes by tuning the coordination geometry and local symmetry

Precise control of the crystal field and local symmetry around the paramagnetic spin center is crucial for the design and synthesis of single-molecule magnets (SMMs). Herein, three mononuclear Dy(III)-based complexes, [Dy(LN6)(CH3COO)2](BPh4)(CH2Cl2) (1), [Dy(LN6)(2,6-Cl-4-NO2-PhO)(H2O)2]2(PF6)2(H2O)(2,6-Cl-4-NO2-PhO)2 (2) and [Dy(LN6)(2,6-Cl-4-NO2-PhO)2](BPh4)(CH2Cl2)2 (3) (LN6 = N6-hexagonal plane accomplished by a neutral Schiff base ligand formed from 2,6-diacetylpyridine and ethylenediamine), are successfully isolated. In these complexes, the Dy(III) centers are coordinated with six neutral N atoms from a nonrigid equatorial ligand, while different oxygen-bearing ligands are arranged at the axial positions of the central ions by gradual regularization of the axial ligands. As a result, Dy(III) ions in the three complexes exhibit various coordination geometries, forming a ten-coordinate tetradecahedron for 1, a nine-coordinate muffin configuration for 2 and a distorted eight-coordinate hexagonal bipyramid for 3. Magnetic studies reveal that all complexes exhibit no SIM behaviour under zero dc field, due to the predominant quantum tunneling of magnetization (QTM), which can be effectively suppressed by additional dc fields. Experiments, coupled with theoretical calculations, demonstrate that varying local symmetries and coordination geometries are synergistically responsible for the disparities of QTM and uniaxial anisotropy, resulting in notably different magnetic properties.

Photoluminescence and magnetic properties of isostructural europium(III), gadolinium(III) and terbium(III) oxamate-based coordination polymers

Developing and investigating advanced multifunctional materials with magnetic properties as candidates for assembling spin qubits for quantum computing is imperative. A new polytopic ligand based on oxamate and aniline was used to promote the synthesis of three neutral homometallic lanthanide-coordinated polymers. New complexes with the formula {Ln(phox)3(DMSO)2(H2O)}n, where Ln = Eu3+ (1), Gd3+ (2), and Tb3+ (3) [phox = N-(phenyl)oxamate and DMSO = dimethylsulfoxide], were synthesized and well characterized by spectroscopic methods as well as X-ray crystallographic analysis. All crystalline structures comprise neutral zigzag chains. The lanthanide ions are linked by three phox ligands, in which two oxygen atoms from two different ligands are responsible for connecting the trivalent lanthanide ions, and one phox ligand completes the coordination sphere in a bis-bidentate mode, together with two DMSO molecules and one water coordination molecule. The coordination sphere of lanthanide ions consisted of spherical capped square antiprism (CSAPR-9) symmetry. The magnetic properties of 1-3 were investigated in the 2-300 K temperature range. The dynamic (ac) magnetic properties of 2 reveal a frequency dependence involving the phonon bottleneck mechanism below 33 K under nonzero applied dc magnetic fields, resulting in an example of a field-induced single-molecule magnet. Solid-state photophysical measurements for Eu3+ (1) and Tb3+ (3) complexes indicate that the N-(phenyl)oxamate ligands are very efficient in sensitizing the lanthanide(III) ions in the visible region of the electromagnetic spectrum. Compounds 1 and 3 exhibited an emission in the red and green regions, respectively. Experimental results and theoretical calculations using the Sparkle/RM1 method support a quantum efficiency of ∼72% for 1, suggesting its potential as a candidate for light conversion molecular devices (LCMDs).

Six-Coordinated CoII Single-Molecule Magnets: Synthetic Strategy, Structure and Magnetic Properties

The pursuit of molecule-based magnetic memory materials contributes significantly to high-density information storage research in the frame of the ongoing information technologies revolution. Remarkable progress has been achieved in both transition metal (TM) and lanthanide based single-molecule magnets (SMMs). Notably, six-coordinated CoII SMMs hold particular research significance owing to the economic and abundant nature of 3d TM ions compared to lanthanide ions, the substantial spin-orbit coupling of CoII ions, the potential for precise control over coordination geometry, and the air-stability of coordination-saturated structures. In this review, we will summarize the progress made in six-coordinated CoII SMMs, organized by their coordination geometry and molecular structure similarity. Valuable insights, principles, and new mechanism gleaned from this research and remaining issues that need to be addressed will also be discussed to guide future optimization.

Stable organic radical qubits and their applications in quantum information science

The past century has witnessed the flourishing of organic radical chemistry. Stable organic radicals are highly valuable for quantum technologies thanks to their inherent room temperature quantum coherence, atomic-level designability, and fine tunability. In this comprehensive review, we highlight the potential of stable organic radicals as high-temperature qubits and explore their applications in quantum information science, which remain largely underexplored. Firstly, we summarize known spin dynamic properties of stable organic radicals and examine factors that influence their electron spin relaxation and decoherence times. This examination reveals their design principles and optimal operating conditions. We further discuss their integration in solid-state materials and surface structures, and present their state-of-the-art applications in quantum computing, quantum memory, and quantum sensing. Finally, we analyze the primary challenges associated with stable organic radical qubits and provide tentative insights to future research directions.

Structural, optical and magnetic properties of a new metal-organic CoII-based complex

A mononuclear cobalt(ii) complex [C5H8N3]2[CoCl4(C5H7N3)2] (I) was synthesized and structurally characterized. Single crystal X-ray diffraction analysis indicates that monometallic Co(ii) ions acted as coordination nodes in a distorted octahedral geometry, giving rise to a supramolecular architecture. The latter is made up of a ½ unit form composed of an anionic element [Co0.5Cl2(C5H7N3)]- and one 2-amino-4-methylpyrimidinium cation [C5H8N3]+. The crystalline arrangement of this compound adopts the sandwich form where inorganic parts are sandwiched between the organic sheets following the [100] direction. More information regarding the structure hierarchy has been supplied based on Hirshfeld surface analysis; the X⋯H (X = N, Cl) interactions play a crucial role in stabilizing the self-assembly process of I, complemented by the intervention of π⋯π electrostatic interaction created between organic entities. Thermal analyses were carried out to study the thermal behavior process. Static magnetic measurements and ab initio calculations of compound I revealed the easy-axis anisotropy character of the central Co(ii) ion. Two-channel field-induced slow-magnetic relaxation was observed; the high-frequency channel is characterized by underbarrier relaxation with U eff = 16.5 cm-1, and the low-frequency channel involves a direct relaxation process affected by the phonon-bottleneck effect.

Inductive detection of temperature-induced magnetization dynamics of molecular spin systems

The development and technological applications of molecular spin systems require versatile experimental techniques to characterize and control their static and dynamic magnetic properties. In the latter case, bulk spectroscopic and magnetometric techniques, such as AC magnetometry and pulsed electron paramagnetic resonance, are usually employed, showing high sensitivity, wide dynamic range, and flexibility. They are based on creating a nonequilibrium state either by changing the magnetic field or by applying resonant microwave radiation. Another possible source of perturbation is a laser pulse that rapidly heats the sample. This approach has proven to be one of the most useful techniques for studying the kinetics and mechanism of chemical and biochemical reactions. Inspired by these works, we propose an inductive detection of temperature-induced magnetization dynamics as applied to the study of molecular spin systems and describe the general design and construction of a particular induction probehead, taking into account the constraints imposed by the cryostat and electromagnet. To evaluate the performance, several coordination compounds of VO2+, Co2+, and Dy3+ were investigated using low-energy pulses of a terahertz free electron laser of the Novosibirsk free electron laser facility as a heat source. All measured magnetization dynamics were qualitatively or quantitatively described using a proposed basic theoretical model and compared with the data obtained by alternating current magnetometry. Based on the results of the research, the possible scope of applications of inductive detection and its advantages and disadvantages in comparison with standard methods are discussed.

Unravelling the role of spin-vibrational coupling in designing high-performance pentagonal bipyramidal Dy(iii) single ion magnets

At the cutting edge of high-performance single-molecule magnets (SMMs) lie lanthanide-based complexes, renowned for their potent magnetic anisotropy. SMMs containing one metal centre are defined as single-ion magnets (SIMs). The performance of SMMs is measured generally via the barrier height for magnetisation reversal (Ueff) and blocking temperature (TB), below which the magnetisation is fully frozen. To enhance the Ueff and TB values in lanthanide-based SMMs, the static crystal field splitting of mJ levels has been effectively adjusted through ligand design, leveraging the oblate/prolate ground state 4f electron density shape. However, the maximum fine-tuning achievable through ligand design, known as the axial limit, has already been reached in this class of compounds. This necessitates new design principles to enhance SMM characteristics to better suit end-user applications. Among other avenues that can be explored to improve SMM characteristics, a deeper understanding of spin-phonon coupling is critical to advancing TB values. However, there are only a handful of examples where this has been deciphered. In this work, using a combination of DFT and ab initio CASSCF calculations, we have performed spin-phonon calculations on five classes of pentagonal bipyramidal Dy(iii) SIMs exhibiting TB values in the range of 4.5 K to 36 K ([Dy(bbpen)Br] (1, H2bbpen = N,N'-bis(2-hydroxybenzyl)-N,N'-bis(2-methylpyridyl)ethylenediamine), [Dy(OCMe3)Br(THF)5][BPh4] (2) [Dy(OSiMe3)Br(THF)5] [BPh4] (3), [Dy(LN5)(Ph3SiO)2](BPh4)·CH2Cl2 (4) and [L2Dy(H2O)5][I]3·L2·H2O (5, L = tBuPO(NHiPr)2)). Unlike the method employed elsewhere for the calculation of spin-phonon coupling, in this work, we have employed a set of criteria and intuitively selected vibrational modes to perform the spin-phonon coupling analysis. The approach provided here not only reduces the computational cost significantly but also suggests chemical intuition to improve the performance of this class of compounds. Our calculations reveal that low-energy vibrational modes govern the magnetisation relaxation in these SIMs. A flexible first coordination sphere found on some of the complexes was found to be responsible for low-energy vibrations that flip the magnetisation, reducing the TB values drastically (complexes 2 and 3). On the other hand, a rigid first coordination sphere and a stiff ligand framework move the spin-vibrational coupling that causes the relaxation to lie beyond the secondary coordination sphere, resulting in an increase in TB values. Our calculations also reveal that not only the atoms in the first coordination sphere but also those in the secondary coordination sphere affect the performance of the SMMs. Learning from this exercise, we have undertaken several in silico models based on these vibrations to improve the TB values. Some of these predictions were correlated with literature precedents, offering confidence in the methodology employed. To this end, our comprehensive investigation, involving twenty-three molecules/models and five sets of geometries for pentagonal bipyramidal Dy(iii) single-ion magnets (SIMs), unveils a treasure trove of chemically sound design clues, poised to enhance the TB values in this fascinating molecular realm.

Modulated spin dynamics of [Co2] coordination helicates via differential strand composition

Coordination supramolecular chemistry provides a versatile entry into materials with functionalities of technological relevance at the nanoscale. Here, we describe how two different bis-pyrazolylpyridine ligands (L1 and L2) assemble with Co(II) ions into dinuclear triple-stranded helicates, in turn, encapsulating different anionic guests. These constructs are described as (Cl@[Co2(L1)3])3+, (SiF6@[Co2(L1)(L2)3])2+ and (ClO4@[Co2(L2)3])3+, as established by single-crystal X-ray diffraction. Extensive magnetic and calorimetric measurements, numerical treatments and theoretical calculations reveal that the individual Co(II) centers of these supramolecular entities exhibit field-induced slow relaxation of magnetization, dominated by direct and Raman mechanisms. While the small variations in the spin dynamics are not easily correlated with the evident structural differences among the three species, the specific heat measurements suggest two vibronic pathways of magnetic relaxation: one that would be associated with the host lattice and another linked with the guest.

Dual Structure of a Vanadyl-Based Molecular Qubit Containing a Bis(β-diketonato) Ligand

We designed [VO(bdhb)] (1') as a new electronic qubit containing an oxovanadium(IV) ion (S = 1/2) embraced by a single bis(β-diketonato) ligand [H2bdhb = 1,3-bis(3,5-dioxo-1-hexyl)benzene]. The synthesis afforded three different crystal phases, all of which unexpectedly contain dimers with formula [(VO)2(bdhb)2] (1). A trigonal form (1h) with a honeycomb structure and 46% of solvent-accessible voids quantitatively transforms over time into a monoclinic solvatomorph 1m and minor amounts of a triclinic solventless phase (1a). In a static magnetic field, 1h and 1m have detectably slow magnetic relaxation at low temperatures through quantum tunneling and Raman mechanisms. Angle-resolved electron paramagnetic resonance (EPR) spectra on single crystals revealed signatures of low-dimensional magnetic behavior, which is solvatomorph-dependent, being the closest interdimer V···V separations (6.7-7.5 Å) much shorter than intramolecular V···V distances (11.9-12.1 Å). According to 1H diffusion ordered spectroscopy (DOSY) and EPR experiments, the complex adopts the desired monomeric structure in organic solution and its geometry was inferred from density functional theory (DFT) calculations. Spin relaxation measurements in a frozen toluene-d8/CD2Cl2 matrix yielded Tm values reaching 13 μs at 10 K, and coherent spin manipulations were demonstrated by Rabi nutation experiments at 70 K. The neutral quasi-macrocyclic structure, featuring nuclear spin-free donors and additional possibilities for chemical functionalization, makes 1' a new convenient spin-coherent building block in quantum technologies.

Influence of the phonon-bottleneck effect and low-energy vibrational modes on the slow spin-phonon relaxation in Kramers-ions-based Cu(II) and Co(II) complexes with 4-amino-3,5-bis-(pyridin-2-yl)-1,2,4-triazole and dicyanamide

Two new complexes, bis-[4-amino-3,5-bis-(pyridin-2-yl)-1,2,4-triazole-κ2N2,N6]bis-(dicyanamide-κN8)copper(II), [Cu(abpt)2(dca)2] (1) and bis-[4-amino-3,5-bis-(pyridin-2-yl)-1,2,4-triazole-κ2N2,N6]bis-(dicyanamide-κN8)cobalt(II), [Co(abpt)2(dca)2] (2), have been prepared and magneto-structurally characterised. Single crystal studies of both complexes have shown that their crystal structures are molecular, in which the central atoms are six-coordinated in the form of a distorted octahedron by two bidentate abpt and two monodentate dca ligands. Even if both complexes have the same composition and crystallize in the same P1̄ space group, they are not isostructural. Both structures contain strong intermolecular N-H⋯N hydrogen bonds and π-π stacking interactions. IR spectra are consistent with the solved structures of both complexes and confirmed the terminal character of the dca ligands and the bidentate coordination of the abpt ligands. The analysis of the magnetic properties showed that both complexes exhibit field-induced slow spin-phonon relaxation. In both complexes, the slow spin-phonon relaxation is influenced by a severe phonon-bottleneck effect that affects the direct process, a dominant relaxation mechanism at low temperatures in both complexes. The phonon-bottleneck effect in 1 was suppressed by simply reducing the crystallite size, and further analysis of the field dependence of the relaxation time yielded the characteristic energy of vibrational modes of 11 cm-1 participating in the Raman process at low magnetic fields. The analysis of magnetic properties and ab initio calculations confirmed that 2 represents a system with a moderate uniaxial anisotropy yielding an average energy barrier of 82 cm-1 (from all four nonequivalent Co(II) sites in the structure of 2).

Magnetic Relaxations of Chromium Nitride Porphyrinato Complexes Driven by the Anisotropic g-Factor

Molecule-based magnetic materials are useful candidates as the spin qubit due to their long coherence time and high designability. The anisotropy of the g-values of the metal complexes can be utilized to access the individual spin of the metal complexes, making it possible to achieve the scalable molecular spin qubit. For this goal, it is important to evaluate the effect of g-value anisotropy on the magnetic relaxation behaviour. This study reports the slow magnetic relaxation behaviour of chromium nitride (CrN2+ ) porphyrinato complex (1), which is structurally and magnetically similar with the vanadyl (VO2+ ) porphyrinato complex (2) which is known as the excellent spin qubit. Detailed analyses for vibrational and dynamical magnetism of 1 and 2 revealed that g-value anisotropy accelerates magnetic relaxations greater than the internal magnetic field from nuclear spin does. These results provide a design criterion for construction of multiple spin qubit based on g-tensor engineering.

Molecular One- and Two-Qubit Systems with Very Long Coherence Times

General-purpose quantum computation and quantum simulation require multi-qubit architectures with precisely defined, robust interqubit interactions, coupled with local addressability. This is an unsolved challenge, primarily due to scalability issues. These issues often derive from poor control over interqubit interactions. Molecular systems are promising materials for the realization of large-scale quantum architectures, due to their high degree of positionability and the possibility to precisely tailor interqubit interactions. The simplest quantum architecture is the two-qubit system, with which quantum gate operations can be implemented. To be viable, a two-qubit system must possess long coherence times, the interqubit interaction must be well defined and the two qubits must also be addressable individually within the same quantum manipulation sequence. Here results are presented on the investigation of the spin dynamics of chlorinated triphenylmethyl organic radicals, in particular the perchlorotriphenylmethyl (PTM) radical, a mono-functionalized PTM, and a biradical PTM dimer. Extraordinarily long ensemble coherence times up to 148 µs are found at all temperatures below 100 K. Two-qubit and, importantly, individual qubit addressability in the biradical system are demonstrated. These results underline the potential of molecular materials for the development of quantum architectures.

Observation of slow magnetic relaxation phenomena in spatially isolated π-radical ions

The use of molecular spins as quantum bits is fascinating because it offers a wide range of strategies through chemical modifications. In this regard, it is very interesting to search for organic radical ions that have small spin-orbit coupling values. On the other hand, the feature of the magnetic relaxation of π-organic radical ions is rarely exploited due to the difficulty of spin dilution, and π-stacking interaction. In this study, we focus on N,N',N''-tris(2,6-dimethylphenyl)benzenetriimide (BTI-xy), where three xylene moieties connected to the imide groups cover the π-plane of the BTI core. As a result, BTI-xy radical anions without π-stacking interaction were obtained. This led to the slow magnetization relaxation, which is reported for the first time in organic radicals. Furthermore, the relaxation times in a solution state revealed the importance of spin interaction.

Porous Mn2+ Magnet with a Pt-Cl Framework: Correlation between Water Vapor Adsorption/Desorption and Slow Magnetic Relaxation

We report the water adsorption/desorption behavior and dynamic magnetic properties of the Pt-Cl chain complex [{[Pt(en)₂ ][PtCl₂ (en)₂ ]}₃ ][{(MnCl₅ )Cl₃ }₂ ] ⋅ 12H₂ O (1). Upon heating 1 in a vacuum, we obtained the dehydrated form [{[Pt(en)₂ ][PtCl₂ (en)₂ ]}₃ ][{(MnCl₅ )Cl₃ }₂ ] (1DH). The framework structures of 1 and 1DH are identical, and both complexes underwent slow magnetic relaxation. However, the magnetic relaxation times for 1DH were shorter than those for 1, meaning that the dynamic magnetic properties were controlled upon water vapor adsorption/desorption. From detailed analyses of the dynamic magnetic behavior, a phonon-bottleneck effect contributes to the magnetic relaxation processes. We discuss the mechanism for the changes in the magnetic relaxation processes upon dehydration in terms of the heat capacity and thermal conductivity.

Slow magnetic relaxation of a S = 1/2 copper(II)-substituted Keggin-type silicotungstate

This is the first report on slow magnetic relaxation in an S = 1/2 system based on a first-row transition metal ion with the polyoxometalate skeleton [(n-C₄H₉)₄N]₄H₂[SiW₁₁O₃₉Cu] (1). The X-band electron-spin-resonance spectrum of 1 measured at room temperature indicates that the copper ion experiences significantly reduced intermolecular interactions compared to the potassium salt and that it adopts a five-coordinated square-pyramidal coordination geometry. The AC magnetic-susceptibility measurements revealed that 1 undergoes slow magnetic relaxation in an applied static magnetic field (H_dc). The extracted spin-lattice relaxation time (92 ms at 1.8 K and H_dc = 5000 Oe) for 5% magnetically diluted 1, [(n-C₄H₉)₄N]₄H₂[SiW₁₁O₃₉Cu_0.05Zn_0.95] (dil.1), is comparable to those of other potential S = 1/2 spin qubits. A relaxation-time analysis indicated that Raman spin-lattice relaxation dominates even at low temperatures in an optimized field. The extracted Raman exponent (n = 2.30) is smaller than those of other S = 1/2 complexes that carry organic ligands, which implies that the decrease in relaxation time at higher temperatures is likely to be moderate.

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.

Toward exact predictions of spin-phonon relaxation times: An ab initio implementation of open quantum systems theory

Spin-phonon coupling is the main driver of spin relaxation and decoherence in solid-state semiconductors at finite temperature. Controlling this interaction is a central problem for many disciplines, ranging from magnetic resonance to quantum technologies. Spin relaxation theories have been developed for almost a century but often use a phenomenological description of phonons and their coupling to spin, resulting in a nonpredictive tool and hindering our detailed understanding of spin dynamics. Here, we combine time-local master equations up to the fourth order with advanced electronic structure methods and perform predictions of spin-phonon relaxation time for a series of solid-state coordination compounds based on both transition metals and lanthanide Kramers ions. The agreement between experiments and simulations demonstrates that an accurate, universal, and fully ab initio implementation of spin relaxation theory is possible, thus paving the way to a systematic study of spin-phonon relaxation in solid-state materials.

Studies of the Temperature Dependence of the Structure and Magnetism of a Hexagonal-Bipyramidal Dysprosium(III) Single-Molecule Magnet

The hexagonal-bipyramidal lanthanide(III) complex [Dy(O^tBu)Cl(18-C-6)][BPh₄] (1; 18-C-6 = 1,4,7,10,13,16-hexaoxacyclooctadecane ether) displays an energy barrier for magnetization reversal (U_eff) of ca. 1000 K in a zero direct-current field. Temperature-dependent X-ray diffraction studies of 1 down to 30 K reveal bending of the Cl-Ln-O^tBu angle at low temperature. Using ab initio calculations, we show that significant bending of the O-Dy-Cl angle upon cooling from 273 to 100 K leads to a ca. 10% decrease in the energy of the excited electronic states. A thorough exploration of the temperature and field dependencies of the magnetic relaxation rate reveals that magnetic relaxation is dictated by five mechanisms in different regimes: Orbach, Raman-I, quantum tunnelling of magnetization, and Raman-II, in addition to the observation of a phonon bottleneck effect.

Temperature Dependence of Spin-Phonon Coupling in [VO(acac)2]: A Computational and Spectroscopic Study

Molecular electronic spins are good candidates as qubits since they are characterized by a large tunability of their electronic and magnetic properties through a rational chemical design. Coordination compounds of light transition metals are promising systems for spin-based quantum information technologies, thanks to their long spin coherence times up to room temperature. Our work aims at presenting an in-depth study on how the spin-phonon coupling in vanadyl-acetylacetonate, [VO(acac)₂], can change as a function of temperature using terahertz time-domain spectroscopy and density functional theory (DFT) calculations. Powder THz spectra were recorded between 10 and 300 K. The temperature dependence of vibrational frequencies was then accounted for in the periodic DFT calculations using unit-cell parameters measured at two different temperatures and the optimized ones, as usually reported in the literature. In this way, it was possible to calculate the observed THz anharmonic frequency shift with high accuracy. The overall differences in the spin-phonon coupling magnitudes as a function of temperature were also highlighted showing that the computed trends have to be ascribed to the anisotropic variation of cell parameters.

Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach

In the past decade, transition metal complexes have gained momentum as electron spin-based quantum bit (qubit) candidates due to their synthetic tunability and long achievable coherence times. The decoherence of magnetic quantum states imposes a limit on the use of these qubits for quantum information technologies, such as quantum computing, sensing, and communication. With rapid recent development in the field of molecular quantum information science, a variety of chemical design principles for prolonging coherence in molecular transition metal qubits have been proposed. Here the spin-spin, motional, and spin-phonon regimes of decoherence are delineated, outlining design principles for each. It is shown how dynamic ligand field models can provide insights into the intramolecular vibrational contributions in the spin-phonon decoherence regime. This minireview aims to inform the development of molecular quantum technologies tailored for different environments and conditions.

A reaction-coordinate perspective of magnetic relaxation

Understanding and utilizing the dynamic quantum properties of metal ions is the frontier of many next generation technologies. One property in particular, magnetic relaxation, is a complicated physical phenomenon that is scarcely treated in undergraduate coursework. Consequently, principles of magnetic relaxation are nearly impenetrable to starting synthetic chemists, who ultimately design the molecules that fuel new discoveries. In this Tutorial Review, we describe a new paradigm for thinking of magnetic relaxation in metal complexes in terms of a simple reaction-coordinate diagram to facilitate access to the field. We cover the main mechanisms of both spin-lattice (T1) and spin-spin (T2) relaxation times within this conceptual framework and how molecular and environmental design affects these times. Ultimately, we show that many of the scientific methods used by inorganic chemists to study and manipulate reactivity are also useful for understanding and controlling magnetic relaxation. We also describe the cutting edge of magnetic relaxation within this paradigm.

Magnetic anisotropy in YbIII complex candidates for molecular qubits: a theoretical analysis

The magnetic properties of mononuclear YbIII complexes have been explored by using multiconfigurational CASPT2/RASSI calculations. Such complexes, in particular the case of [Yb(trensal)] complex, have been proposed as molecular qubits due to their spin dynamics properties. We have verified the accuracy of the theoretical approach to study such systems by comparing with experimental magnetic data. In order to have a wide overview of the magnetic properties of mononuclear YbIII complexes, we have considered simple charged and neutral models, [Yb(H2O)n]3+ and [Yb(OH)3(H2O)n-3], for many coordination modes. Thus, the results for more than 100 models allow extraction of some conclusions about the best ligand distributions in the coordination sphere to tailor the magnetic properties. Some low coordination, between 3 and 5, complexes that have no experimental magnetic data have been studied computationally to check if they can present high magnetic anisotropy.

Non-traditional thermal behavior of Co(ii) coordination networks showing slow magnetic relaxation

Three new Co(ii) coordination polymers show the DC magnetic data consistent with the S = 3/2 spin system with large zero-field splitting D > 0, which was confirmed by HF EPR and FIRMS measurements.

The Limit of Spin Lifetime in Solid-State Electronic Spins

The development of spin qubits for quantum technologies requires their protection from the main source of finite-temperature decoherence: atomic vibrations. Here we eliminate one of the main barriers to the progress in this field by providing a complete first-principles picture of spin relaxation that includes up to two-phonon processes. Our method is based on machine learning and electronic structure theory and makes the prediction of spin lifetime in realistic systems feasible. We study a prototypical vanadium-based molecular qubit and reveal that the spin lifetime at high temperature is limited by Raman processes due to a small number of THz intramolecular vibrations. These findings effectively change the conventional understanding of spin relaxation in this class of materials and open new avenues for the rational design of long-living spin systems.

Coexistence of Spin-Lattice Relaxation and Phonon-Bottleneck Processes in GdIII -Phthlocyaninato Triple-Decker Complexes under Highly Diluted Conditions

Gd³⁺ complexes have been shown to undergo unusual slow magnetic relaxation processes similar to those of single-molecule magnets (SMMs), even though Gd³⁺ does not exhibit strong magnetic anisotropy. To reveal the origin of the slow magnetic relaxation of Gd³⁺ complexes, we have investigated the magnetic properties and heat capacities of two Gd³⁺ -phthalocyaninato triple-decker complexes, one of which has intramolecular Gd³⁺ -Gd³⁺ interactions and the other does not. It was found that the Gd³⁺ -Gd³⁺ interactions accelerate the magnetic relaxation processes. In addition, magnetically diluted samples, prepared by doping a small amount of the Gd³⁺ complexes into a large amount of diamagnetic Y³⁺ complexes, underwent dual magnetic relaxation processes. A detailed dynamic magnetic analysis revealed that the coexistence of spin-lattice relaxation and phonon-bottleneck processes is the origin of the dual magnetic relaxation processes.

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.

Unveiling phonons in a molecular qubit with four-dimensional inelastic neutron scattering and density functional theory

Phonons are the main source of relaxation in molecular nanomagnets, and different mechanisms have been proposed in order to explain the wealth of experimental findings. However, very limited experimental investigations on phonons in these systems have been performed so far, yielding no information about their dispersions. Here we exploit state-of-the-art single-crystal inelastic neutron scattering to directly measure for the first time phonon dispersions in a prototypical molecular qubit. Both acoustic and optical branches are detected in crystals of [VO(acac)[Formula: see text]] along different directions in the reciprocal space. Using energies and polarisation vectors calculated with state-of-the-art Density Functional Theory, we reproduce important qualitative features of [VO(acac)[Formula: see text]] phonon modes, such as the presence of low-lying optical branches. Moreover, we evidence phonon anti-crossings involving acoustic and optical branches, yielding significant transfers of the spin-phonon coupling strength between the different modes.

Bulky ligands shape the separation between the large spin carriers to condition field-induced slow magnetic relaxation

Crystal engineering of magnetic relaxation in supramolecular networks based on almost isotropic cyanido-bridged {Mn9[W(CN)8]6L8(solv)8} clusters decorated by bulky 4,4'-di-tert-butyl-2,2'-bipyridine (But2bpy) and 4,7-diphenyl-1,10-phenanthroline (Ph2phen) ligands is presented. The three new compounds {MnII9[WV(CN)8]6(But2bpy)8(MeOH)8}·Pri2O·13MeOH (1), {MnII9[WV(CN)8]6(But2bpy)8(MeOH)6(H2O)2}·4Pri2O·2H2O (1a), and {MnII9[WV(CN)8]6(Ph2phen)8(MeOH)8}·29MeOH·6H2O (2) were characterized structurally and magnetically. Compound 1 exhibits unequivocal domination of repulsive intercluster contacts operating between the side But groups leading to intercluster distances exceeding 10 Å in all three dimensions. Compound 1a reveals a 1-dimensional (1D) supramolecular chain structure with very close intercluster distances of 6.7 Å realized through the direct W-CNHO-Mn hydrogen bonds along the chain, further isolated by the above repulsive ButBut synthons. Compound 2 shows significant separation in all three directions with the intercluster distances close to 10, 12 and 13.5 Å. However, in contrast to 1, these separations are accompanied by indirect hydrogen bond arrays and local π-π interactions of potential to assist in the transfer of weak magnetic interactions. The dc magnetic data show the signature of S = 39/2 in the ground state, which is typical in this group of compounds. The high-spin clusters are accompanied by different intercluster interactions, illustrated by the effective zJ' values of +0.010 cm-1 (1), +0.008 cm-1 (1a) and +0.001 cm-1 (2). The low temperature ac susceptibility measurements revealed a temperature- and field-dependent magnetic relaxation time for all 1, 1a and 2 compounds (τ1, τ1a-fast, and τ2-fast in the range 10-3-10-4 s). In contrast and only in the case of 1a and 2, an additional temperature independent slow process was detected (τ1a-slow and τ2-slow located between 0.1 s and 1 s). The magnetic relaxations were correlated with the obtained supramolecular networks, indicating the significant role of dipolar fields, weak non-covalent interactions, hydrogen bonds and π-π interactions.

The dynamic ligand field of a molecular qubit: decoherence through spin–phonon coupling

A ligand field model highlights chemical design principles for the development of room temperature coherent materials for quantum information processing.

How do phonons relax molecular spins?

The coupling between electronic spins and lattice vibrations is fundamental for driving relaxation in magnetic materials. The debate over the nature of spin-phonon coupling dates back to the 1940s, but the role of spin-spin, spin-orbit, and hyperfine interactions has never been fully established. Here, we present a comprehensive study of the spin dynamics of a crystal of Vanadyl-based molecular qubits by means of first-order perturbation theory and first-principles calculations. We quantitatively determine the role of the Zeeman, hyperfine, and electronic spin dipolar interactions in the direct mechanism of spin relaxation. We show that, in a high magnetic field regime, the modulation of the Zeeman Hamiltonian by the intramolecular components of the acoustic phonons dominates the relaxation mechanism. In low fields, hyperfine coupling takes over, with the role of spin-spin dipolar interaction remaining the less important for the spin relaxation.

Tetraoxolene-bridged rare-earth complexes: a radical-bridged dinuclear Dy single-molecule magnet

Two families of neutral tetraoxolene-bridged dinuclear rare earth complexes of general formula [((HBpz₃)₂RE)₂(μ-tetraoxolene)] (RE = Y and Dy; HBpz₃^- = hydrotris(pyrazolyl)borate; tetraoxolene = fluoranilate (fa^2-; 1-RE) or bromanilate (ba^2-; 2-RE)) have been synthesised and characterised. In each case, the bridging tetraoxolene ligand is in the diamagnetic dianionic form and each rare earth metal centre has two HBpz₃^- ligands completing the coordination. Electrochemical studies on the soluble 2-RE family reveal a tetraoxolene-based reversible one-electron reduction. Bulk chemical reduction with cobaltocene affords the cobaltocenium (CoCp⁺) salt of the 1e-reduced analogue: [CoCp][((HBpz₃)₂RE)₂(μ-ba˙)] (3-RE) that incorporates a radical trianionic form of the bromanilate bridging ligand. Alternating current (ac) magnetic susceptibility studies of 2-Dy reveal slow magnetic relaxation only in the presence of an applied magnetic field, but reduction to radical-bridged 3-Dy affords frequency-dependent peaks in the out-of-phase ac susceptibility in zero applied field. Exchange coupling between the Dy(iii) ions and the radical bridging ligand thus reduces zero-field magnetisation quantum tunnelling and confers single-molecule magnet status on the complex. Comprehensive analysis of the magnetic relaxation data indicates that a combination of Orbach, Raman and direct relaxation processes are required to fit the data for both dysprosium bromanilate complexes.

Magnetization Slow Dynamics in Ferrocenium Complexes

The single-molecule magnet (SMM) properties of a series of ferrocenium complexes, [Fe(η⁵ -C₅ R₅ )₂ ]⁺ (R=Me, Bn), are reported. In the presence of an applied dc field, the slow dynamics of the magnetization in [Fe(η⁵ -C₅ Me₅ )₂ ]BAr_F are revealed. Multireference quantum mechanical calculations show a large energy difference between the ground and first excited states, excluding the commonly invoked, thermally activated (Orbach-like) mechanism of relaxation. In contrast, a detailed analysis of the relaxation time highlights that both direct and Raman processes are responsible for the SMM properties. Similarly, the bulky ferrocenium complexes, [Fe(η⁵ -C₅ Bn₅ )₂ ]BF₄ and [Fe(η⁵ -C₅ Bn₅ )₂ ]PF₆ , also exhibit magnetization slow dynamics, however an additional relaxation process is clearly detected for these analogous systems.

A first peek into sub-picosecond dynamics of spin energy levels in magnetic biomolecules

We estimate the time- and temperature-evolution of spin energy levels in a metallopeptide by combining molecular dynamics with crystal field analysis. Fluctuations of tens of cm^-1 for spin energy levels at fs times gradually average out at longer times. We confirm that local vibrations are key in spin dynamics.

Counterion influence on dynamic spin properties in a V(iv) complex

Using transition metal ions for spin-based applications, such as electron paramagnetic resonance imaging (EPRI) or quantum computation, requires a clear understanding of how local chemistry influences spin properties. Herein we report a series of four ionic complexes to provide the first systematic study of one aspect of local chemistry on the V(iv) spin - the counterion. To do so, the four complexes (Et3NH)2[V(C6H4O2)3] (1), (n-Bu3NH)2[V(C6H4O2)3] (2), (n-Hex3NH)2[V(C6H4O2)3] (3), and (n-Oct3NH)2[V(C6H4O2)3] (4) were probed by EPR spectroscopy in solid state and solution. Room temperature, solution X-band (ca. 9.8 GHz) continuous-wave electron paramagnetic resonance (CW-EPR) spectroscopy revealed an increasing linewidth with larger cations, likely a counterion-controlled tumbling in solution via ion pairing. In the solid state, variable-temperature (5-180 K) X-band (ca. 9.4 GHz) pulsed EPR studies of 1-4 in o-terphenyl glass demonstrated no effect on spin-lattice relaxation times (T 1), indicating little role for the counterion on this parameter. However, the phase memory time (T m) of 1 below 100 K is markedly smaller than those of 2-4. This result is counterintuitive, as 2-4 are relatively richer in 1H nuclear spin, hence, expected to have shorter T m. Thus, these data suggest an important role for counterion methyl groups on T m, and moreover provide the first instance of a lengthening T m with increasing nuclear spin quantity on a molecule.

Scaling Up Electronic Spin Qubits into a Three-Dimensional Metal-Organic Framework

Practical implementation of highly coherent molecular spin qubits for challenging technological applications, such as quantum information processing or quantum sensing, requires precise organization of electronic qubit molecular components into extended frameworks. Realization of spatial control over qubit-qubit distances can be achieved by coordination chemistry approaches through an appropriate choice of the molecular building blocks. However, translating single qubit molecular building units into extended arrays does not guarantee a priori retention of long quantum coherence and spin-lattice relaxation times due to the introduced modifications over qubit-qubit reciprocal distances and molecular crystal lattice phonon structure. In this work, we report the preparation of a three-dimensional (3D) metal-organic framework (MOF) based on vanadyl qubits, [VO(TCPP-Zn₂-bpy)] (TCPP = tetracarboxylphenylporphyrinate; bpy = 4,4'-bipyridyl) (1), and the investigation of how such structural modifications influence qubits' performances. This has been done through a multitechnique approach where the structure and properties of a representative molecular building block of formula [VO(TPP)] (TPP = tetraphenylporphyrinate) (2) have been compared with those of the 3D MOF 1. Pulsed electron paramagnetic resonance measurements on magnetically diluted samples in titanyl isostructural analogues revealed that coherence times are retained almost unchanged for 1 with respect to 2 up to room temperature, while the temperature dependence of the spin-lattice relaxation time revealed insights into the role of low-energy vibrations, detected through terahertz spectroscopy, on the spin dynamics.

A Rare Example of Four-Coordinate Nonoxido Vanadium(IV) Alkoxide in the Solid State: Structure, Spectroscopy, and Magnetization Dynamics

The distorted tetrahedral [V(OAd)₄] alkoxide (OAd = 1-adamantoxide, complex 1) is the first homoleptic, mononuclear vanadium(IV) alkoxide to be characterized in the solid state by X-ray diffraction analysis. The compound crystallizes in the cubic P4̅3 n space group with two highly disordered, crystallographically independent molecules in the asymmetric unit. Spin Hamiltonian parameters extracted from low temperature X- and Q-band electron paramagnetic resonance (EPR) experiments performed for polycrystalline samples of 1, both in the concentrated (bulk) form and diluted in the diamagnetic [Ti(OAd)₄] analogue, reveal a fully axial system with g _z < g _x, g _y and A _z ≫ A _x, A _y. Complex 1 has also been characterized by alternate current susceptometry with varying temperature (3-30 K) and static magnetic field (up to 8.5 T), showing field-induced slow relaxation of the magnetization with relaxation times ranging from ca. 3 ms at 3 K to 0.02-0.03 ms at 30 K, in line with relevant results described recently for other potential molecular quantum bits. Pulsed EPR measurements, in turn, disclosed long coherence times of ca. 4 μs at temperatures lower than 40 K, despite the presence of the H-rich ligands. The slow spin relaxation in 1 is the first observed for a tetracoordinate nonoxido vanadium(IV) complex, and results are compared here to those generated by square-pyramidal V^IV(O)²⁺ and trigonal prismatic V⁴⁺ with oxygen donor atom sets. Considering that the number of promising d¹ complexes investigated in detail for slow magnetization dynamics is still small, the present work contributes to the establishment of possible structural/electronic correlations of interest to the field of quantum information processing.

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.