Determining Key Local Vibrations in the Relaxation of Molecular Spin Qubits and Single-Molecule Magnets

Origins of Slow Magnetic Relaxation in Single-Molecule Magnets

Exponential and power law temperature dependences are widely used to fit experimental data of magnetic relaxation time in single molecular magnets. We derived a theory to show how these rules arise from the underling relaxation mechanisms and to clarify the conditions for their occurrence. The theory solves the puzzle of lower-than-expected Orbach barriers found in recent experiments, and elucidates it as a result of the Raman process in disguise. Our results highlight the importance of reducing the rate of direct tunneling between the ground state doublet so as to achieve longtime coherence in magnetic molecules. To this end, large spin and small transverse magnetic anisotropy can reduce magnitude of the transition operator, and rigid ligands may weaken the spin-phonon coupling in that they raise the energy of vibrational modes and better screen the acoustic phonons.

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.

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.

Exploring the Vibrational Side of Spin-Phonon Coupling in Single-Molecule Magnets via 161 Dy Nuclear Resonance Vibrational Spectroscopy

Synchrotron-based nuclear resonance vibrational spectroscopy (NRVS) using the Mössbauer isotope 161 Dy has been employed for the first time to study the vibrational properties of a single-molecule magnet (SMM) incorporating DyIII , namely [Dy(Cy3 PO)2 (H2 O)5 ]Br3 ⋅2 (Cy3 PO)⋅2 H2 O ⋅2 EtOH. The experimental partial phonon density of states (pDOS), which includes all vibrational modes involving a displacement of the DyIII ion, was reproduced by means of simulations using density functional theory (DFT), enabling the assignment of all intramolecular vibrational modes. This study proves that 161 Dy NRVS is a powerful experimental tool with significant potential to help to clarify the role of phonons in SMMs.

Spin-phonon coupling and dynamic zero-field splitting contributions to spin conversion processes in iron(II) complexes

Magnetization dynamics of transition metal complexes manifest in properties and phenomena of fundamental and applied interest [e.g., slow magnetic relaxation in single molecule magnets, quantum coherence in quantum bits (qubits), and intersystem crossing (ISC) rates in photophysics]. While spin-phonon coupling is recognized as an important determinant of these dynamics, additional fundamental studies are required to unravel the nature of the coupling and, thus, leverage it in molecular engineering approaches. To this end, we describe here a combined ligand field theory and multireference ab initio model to define spin-phonon coupling terms in S = 2 transition metal complexes and demonstrate how couplings originate from both the static and dynamic properties of ground and excited states. By extending concepts to spin conversion processes, ligand field dynamics manifest in the evolution of the excited state origins of zero-field splitting (ZFS) along specific normal mode potential energy surfaces. Dynamic ZFSs provide a powerful means to independently evaluate contributions from spin-allowed and/or spin-forbidden excited states to spin-phonon coupling terms. Furthermore, ratios between various intramolecular coupling terms for a given mode drive spin conversion processes in transition metal complexes and can be used to analyze the mechanisms of ISC. Variations in geometric structure strongly influence the relative intramolecular linear spin-phonon coupling terms and will define the overall spin state dynamics. While the findings of this study are of general importance for understanding magnetization dynamics, they also link the phenomenon of spin-phonon coupling across fields of single molecule magnetism, quantum materials/qubits, and transition metal photophysics.

Inter-Kramers Transitions and Spin-Phonon Couplings in a Lanthanide-Based Single-Molecule Magnet

Spin-phonon coupling plays a critical role in magnetic relaxation in single-molecule magnets (SMMs) and molecular qubits. Yet, few studies of its nature have been conducted. Phonons here refer to both intermolecular and intramolecular vibrations. In the current work, we show spin-phonon couplings between IR-active phonons in a lanthanide molecular complex and Kramers doublets (from the crystal field). For the SMM Er[N(SiMe₃)₂]₃ (1, Me = methyl), the couplings are observed in the far-IR magnetospectroscopy (FIRMS) of crystals with coupling constants ≈ 2-3 cm^-1. In particular, one of the magnetic excitations couples to at least two phonon excitations. The FIRMS reveals at least three magnetic excitations (within the ⁴I_15/2 ground state/manifold; hereafter, manifold) at 0 T at 104, ∼180, and 245 cm^-1, corresponding to transitions from the ground state, M_J = ±15/2, to the first three excited states, M_J = ±13/2, ±11/2, and ±9/2, respectively. The transition between the ground and first excited Kramers doublet in 1 is also observed in inelastic neutron scattering (INS) spectroscopy, moving to a higher energy with an increasing magnetic field. INS also gives complete phonon spectra of 1. Periodic DFT computations provide the energies of all phonon excitations, which compare well with the spectra from INS, supporting the assignment of the inter-Kramers doublet (magnetic) transitions in the spectra. The current studies unveil and measure the spin-phonon couplings in a typical lanthanide complex and throw light on the origin of the spin-phonon entanglement.

Single-Molecule Magnets DyM2 N@C80 and Dy2 MN@C80 (M=Sc, Lu): The Impact of Diamagnetic Metals on Dy3+ Magnetic Anisotropy, Dy⋅⋅⋅Dy Coupling, and Mixing of Molecular and Lattice Vibrations

The substitution of scandium in fullerene single-molecule magnets (SMMs) DySc2 N@C80 and Dy2 ScN@C80 by lutetium has been studied to explore the influence of the diamagnetic metal on the SMM performance of dysprosium nitride clusterfullerenes. The use of lutetium led to an improved SMM performance of DyLu2 N@C80 , which shows a higher blocking temperature of magnetization (TB =9.5 K), longer relaxation times, and broader hysteresis than DySc2 N@C80 (TB =6.9 K). At the same time, Dy2 LuN@C80 was found to have a similar blocking temperature of magnetization to Dy2 ScN@C80 (TB =8 K), but substantially different interactions between the magnetic moments of the dysprosium ions in the Dy2 MN clusters. Surprisingly, although the intramolecular dipolar interactions in Dy2 LuN@C80 and Dy2 ScN@C80 are of similar strength, the exchange interactions in Dy2 LuN@C80 are close to zero. Analysis of the low-frequency molecular and lattice vibrations showed strong mixing of the lattice modes and endohedral cluster librations in k-space. This mixing simplifies the spin-lattice relaxation by conserving the momentum during the spin flip and helping to distribute the moment and energy further into the lattice.

Design of high-temperature f-block molecular nanomagnets through the control of vibration-induced spin relaxation

One of the main roadblocks that still hamper the practical use of molecular nanomagnets is their cryogenic working temperature. In the pursuit of rational strategies to design new molecular nanomagnets with increasing blocking temperature, ab initio methodologies play an important role by guiding synthetic efforts at the lab stage. Nevertheless, when evaluating vibration-induced spin relaxation, these methodologies are still far from being computationally fast enough to provide a useful predictive framework. Herein, we present an inexpensive first-principles method devoted to evaluating vibration-induced spin relaxation in molecular f-block single-ion magnets, with the important advantage of requiring only one CASSCF calculation. The method is illustrated using two case studies based on uranium as the magnetic centre. Finally, we propose chemical modifications in the ligand environment with the aim of suppressing spin relaxation.

High performance single-molecule magnets, Orbach or Raman relaxation suppression?

Relaxation mechanisms limiting the blocking temperature for high-performance single molecule magnets (SMMs) are investigated. Best SMMs are limited by the exponential regime. Current ab initio methods can yield accurate estimations for this limit.

Regulating the structural dimensionality and dynamic properties of a porous dysprosium coordination polymer through solvent molecules

The solvent molecules can regulate the structural dimensionality of a porous dysprosium coordination polymer from three to two and its dynamic behavior, as evidenced by the increase of the effective energy barriers and slowdown of quantum tunneling.

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.

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.

Relaxation dynamics in see-saw shaped Dy(iii) single-molecule magnets

Unusual see-saw shaped Dy(iii) single-molecule magnets, [K(DME)_n][L^ArDy(X)₂] (L^Ar = {C₆H₄[(2,6-ⁱPrC₆H₃)NC₆H₄]₂}²⁻), X = Cl (1) and X = I (2) were synthesized and display high effective energy barriers (U_eff = 1278–1334 K) in zero field.

In Silico Molecular Engineering of Dysprosocenium-Based Complexes to Decouple Spin Energy Levels from Molecular Vibrations

Molecular nanomagnets hold great promise for spintronics and quantum technologies, provided that their spin memory can be preserved above liquid-nitrogen temperatures. In the past few years, the magnetic hysteresis records observed for two related dysprosocenium-type complexes have highlighted the potential of molecular engineering to decouple vibrational excitations from spin states and thereby enhance magnetic memory. Herein, we study the spin-vibrational coupling in [(Cp^iPr5)Dy(Cp*)]⁺ (Cp^iPr5 = pentaisopropylcyclopentadienyl, Cp* = pentamethylcyclopentadienyl), which currently holds the hysteresis record (80 K), by means of a computationally affordable methodology that combines first-principles electronic structure calculations with a phenomenological ligand field model. Our analysis is in good agreement with the previously reported state-of-the-art ab initio calculations, with the advantage of drastically reducing the computation time. We then apply the proposed methodology to three alternative dysprosocenium-type complexes, extracting physical insights that demonstrate the usefulness of this strategy to efficiently engineer and screen magnetic molecules with the potential of retaining spin information at higher temperatures.

Coligand Effects on the Field-Induced Double Slow Magnetic Relaxation in Six-Coordinate Cobalt(II) Single-Ion Magnets (SIMs) with Positive Magnetic Anisotropy

Two mononuclear cobalt(II) compounds of formula [Co(dmphen)₂(OOCPh)]ClO₄·1/2H₂O·1/2CH₃OH (1) and [Co(dmbipy)₂(OOCPh)]ClO₄ (2) (dmphen = 2,9-dimethyl-1,10-phenanthroline, dmbipy = 6,6'-dimethyl-2,2'-bipyridine and HOOCPh = benzoic acid) are prepared and magnetostructurally investigated. Each cobalt(II) ion is six-coordinate with a distorted octahedral CoN₄O₂ environment. The complex cations are interlinked leading to supramolecular chains (1) and pairs (2) that grow along the crystallographic c-axis with racemic mixtures of (Δ,Λ)-Co units. FIRMS allowed us to directly measure the zero-field splitting between the two lowest Kramers doublets, which led to axial anisotropy values of 58.3 cm^-1 ≤ D < 60.7 cm^-1 (1) and 63.8 cm^-1 ≤ D < 64.1 cm^-1 (2). HFEPR spectra of polycrystalline samples of 1 and 2 at low temperatures confirm the positive sign of D and provide an estimate of the E/D quotient [0.147/0.187 (1) and 0.052 (2)]. Detailed ac and dc magnetic studies reveal that 1 and 2 are new examples of field-induced single-ion magnets (SIMs) with small transversal anisotropy. CASSCF/NEVPT2 calculations support these results. Two Orbach processes or one Orbach plus a direct relaxation mechanism provide similar agreements with the nonlinear experimental Arrhenius plots at H_dc = 500 and 2500 G for 1. Two independent relaxation processes occur in 2, but in contrast to 1, an observed linear dependence of ln(τ) vs 1/T substantiates Orbach processes against the most widely proposed Raman and direct mechanisms. The analysis of each relaxation process in 2 provided values for E_a and τ₀ that are very close to those found for 1, validating the predominant role of the Orbach relaxations in both compounds and, probably, also in other cobalt(II) SIMs. A mechanism based on a spin-phonon coupling is proposed to account for the SIM behavior in 1 and 2 with any Raman or direct processes being discarded.

Unveiling the Effect of Magnetic Noise in the Coherence of Single-Molecule Quantum Processors

Quantum bits (qubits) constitute the most elementary building-blocks of any quantum technology, where information is stored and processed in the form of quantum superpositions between discrete energy levels. In particular, the fabrication of quantum processors is a key long-term goal that will allow us conducting specific tasks much more efficiently than the most powerful classical computers can do. Motivated by recent experiments in which three addressable spin qubits are defined on a potential single-molecule quantum processor, namely the [Gd(H₂O)P₅W₃₀O₁₁₀]^12- polyoxometalate, we investigate the decohering effect of magnetic noise on the encoded quantum information. Our state-of-the-art model, which provides more accurate results than previous estimates, show a noticeable contribution of magnetic noise in limiting the survival timescale of the qubits. Yet, our results suggest that it might not be the only dephasing mechanism at play but other mechanisms, such as lattice vibrations and physical movement of magnetic nuclei, must be considered to understand the whole decoherence process.

Exploring the High-Temperature Frontier in Molecular Nanomagnets: From Lanthanides to Actinides

Molecular nanomagnets based on mononuclear metal complexes, also known as single-ion magnets (SIMs), are crossing challenging boundaries in molecular magnetism. From an experimental point of view, this class of magnetic molecules has expanded from lanthanoid complexes to both d-transition metal and actinoid complexes. From a theoretical point of view, more and more improved models have been developed, and we are now able not only to calculate the electronic structure of these systems on the basis of their molecular structures but also to unveil the role of vibrations in the magnetic relaxation processes, at least for lanthanoid and d-transition metal SIMs. This knowledge has allowed us to optimize the behavior of dysprosocenium-based SIMs until reaching magnetic hysteresis above liquid-nitrogen temperature. In this contribution, we offer a brief perspective of the progress of theoretical modeling in this field. We start by reviewing the developed methodologies to investigate the electronic structures of these systems and then move on focus to the open problem of understanding and optimizing the vibrationally induced spin relaxation, especially in uranium-based molecular nanomagnets. Finally, we discuss the differences in the design strategies for 4f and 5f SIMs, including an analysis of the metallocenium family.

Detection of Spin-Vibration States in Single Magnetic Molecules

The spin states of magnetic molecules have advantageous attributes as carriers of quantum information. However, spin-vibration coupling in molecules causes a decay of excited spin states and a loss of spin coherence. Here, we detect excitations of spin-vibration states in single nickelocene molecules on Ag(110) with a scanning tunneling microscope. By transferring a nickelocene to the tip, the joint spin-vibration states with an adsorbed nickelocene were measured. Chemical variations in magnetic molecules offer the opportunity to tune spin-vibration coupling for controlling the spin coherence.

The Role of Vibrational Anharmonicity in the Computational Study of Thermal Spin Crossover

Spin crossover in transition metal complexes can be studied in great detail with computational chemistry. Over the years, the understanding has grown that the relative stability of high-spin (HS) versus low-spin (LS) states is a subtle balance of many factors that all need to be taken into account for a reliable description. Among the different contributions, the zero-point energy (ZPE) and the entropy play key roles. These quantities are usually calculated assuming a harmonic oscillator model for the molecular vibrations. We investigated the impact of including anharmonic corrections on the ZPE and the entropy and indirectly on the critical temperature of spin crossover. As test systems, we used a set of ten Fe(II) complexes and one Fe(III) complex, covering different coordination modes (mono-, bi-, and tri-dentate ligands), decreasing coordination number upon spin crossover, coordination by second- and third-row atoms, and changes in the oxidation state. The results show that the anharmonicity has a measurable effect, but it is in general rather small, and tendencies are not easily recognized. As a conclusion, we put forward that for high precision results, one should be aware of the anharmonic effects, but as long as computational chemistry is still struggling with other larger factors like the influence of the environment and the accurate determination of the electronic energy difference between HS and LS, the anharmonicity of the vibrational modes is a minor concern.

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.

An imido ligand significantly enhances the effective energy barrier of dysprosium(iii) single-molecule magnets

We report herein an imido ligand 1,3-bis(2,6-diisopropylphenyl) imidazolin-2-imine (Im^DippNH) that can form a very short Dy-N bond (2.12 Å) with the dysprosium(iii) ion, which leads to a much larger effective energy barrier for magnetisation reversal (803 K) compared to the analogous alkoxide ligand (53 K). Moreover, we predict that a linear two-coordinate [Dy(Im^DippN)₂]⁺ complex may have an effective energy barrier larger than 4000 K.

In-depth investigation of large axial magnetic anisotropy in monometallic 3d complexes using frequency domain magnetic resonance and ab initio methods: a study of trigonal bipyramidal Co(ii)

The magnetic properties of 3d monometallic complexes can be tuned through geometric control, owing to their synthetic accessibility and relative structural simplicity. Monodentate ligands offer great potential for fine-tuning the coordination environment to engineer both the axial and rhombic zero-field splitting (ZFS) parameters. In [CoCl3(DABCO)(HDABCO)] (1), the trigonal bipyramidal Co(ii) centre has two bulky axial ligands and three equatorial chloride ligands. An in-depth experimental and theoretical study of 1 reveals a large easy-plane magnetic anisotropy (+ve D) with a negligible rhombic zero-field splitting (E) due to the strict axial symmetry imposed by the C 3 symmetric ligand and trigonal space group. The large easy-plane magnetic anisotropy (D = +44.5 cm-1) is directly deduced using high-field EPR and frequency-domain magnetic resonance (FDMR) studies. Ab initio calculations reveal a large positive contribution to the D term arising from ground state/excited state mixing of the 4E'' states at ∼4085 cm-1 and a minor contribution from the spin-flip transition as well. The nature of the slow relaxation in 1 is elucidated through analysis of the rates of relaxation of magnetisation, taking into account Raman and direct spin-lattice relaxation processes and Quantum Tunnelling of the Magnetisation (QTM). The terms relating to the direct process and QTM were found based on the fit of the field-dependence of τ at 2 K. Subsequently, these were used as fixed parameters in the fit of the temperature-dependence of τ to obtain the Raman terms. This experimental-theoretical investigation provides further insight into the power of FDMR and ab initio methods for the thorough investigation of magnetic anisotropy. Thus, these results contribute to design criteria for high magnetic anisotropy systems.

Metal-ligand covalency enables room temperature molecular qubit candidates

Metal–ligand covalency enables observation of coherent spin dynamics to room temperature in a series of vanadium(iv) and copper(ii) catechol complexes.

Harnessing synthetic chemistry to design electronic spin-based qubits, the smallest unit of a quantum information system, enables us to probe fundamental questions regarding spin relaxation dynamics. We sought to probe the influence of metal–ligand covalency on spin–lattice relaxation, which comprises the upper limit of coherence time. Specifically, we studied the impact of the first coordination sphere on spin–lattice relaxation through a series of four molecules featuring V–S, V–Se, Cu–S, and Cu–Se bonds, the Ph₄P⁺ salts of the complexes [V(C₆H₄S₂)₃]^2– (1), [Cu(C₆H₄S₂)₂]^2– (2), [V(C₆H₄Se₂)₃]^2– (3), and [Cu(C₆H₄Se₂)₂]^2– (4). The combined results of pulse electron paramagnetic resonance spectroscopy and ac magnetic susceptibility studies demonstrate the influence of greater M–L covalency, and consequently spin-delocalization onto the ligand, on elongating spin–lattice relaxation times. Notably, we observe the longest spin–lattice relaxation times in 2, and spin echos that survive until room temperature in both copper complexes (2 and 4).

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.

Molecular spins for quantum computation

Spins in solids or in molecules possess discrete energy levels, and the associated quantum states can be tuned and coherently manipulated by means of external electromagnetic fields. Spins therefore provide one of the simplest platforms to encode a quantum bit (qubit), the elementary unit of future quantum computers. Performing any useful computation demands much more than realizing a robust qubit-one also needs a large number of qubits and a reliable manner with which to integrate them into a complex circuitry that can store and process information and implement quantum algorithms. This 'scalability' is arguably one of the challenges for which a chemistry-based bottom-up approach is best-suited. Molecules, being much more versatile than atoms, and yet microscopic, are the quantum objects with the highest capacity to form non-trivial ordered states at the nanoscale and to be replicated in large numbers using chemical tools.

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.

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.

Bromine-bridged Dy2 single-molecule magnet: magnetic anisotropy driven by cis/trans stereoisomers

The peculiar cis/trans stereoisomers in a bromine-bridged Dy2 single-molecule magnet drive the orthogonal magnetic moments and tune the magnetic interactions, leading to a large energy barrier of 684 K.

Field-induced slow magnetic relaxation in pseudooctahedral cobalt(ii) complexes with positive axial and large rhombic anisotropy

The preparation, X-ray crystal structure, spectroscopic and variable-temperature dc and ac magnetic properties of two six-coordinate cobalt(ii) complexes of formula [Co(bim)₄(tcm)₂] (1) and [Co(bmim)₄(tcm)₂] (2) are reported.

Tetrathiafulvalene-Based Helicene Ligand in the Design of a Dysprosium Field-Induced Single-Molecule Magnet

The design of a coordination complex that involves a ligand combining both a tetrathiafulvalene core and a helicene fragment was achieved thanks to the reaction between the new 2-{1-[2-methyl[6]helicene]-4,5-[4,5-bis(propylthio)tetrathiafulvalenyl]-1H-benzimidazol-2-yl}pyridine ligand (L) and the Dy(hfac)₃·2H₂O metalloprecursor. Magnetic investigations showed field-induced single-molecule-magnet (SMM) behavior under an applied magnetic field of 1000 Oe for [Dy(hfac)₃(L)]·0.5CH₂Cl₂, while experimentally oriented single-crystal magnetic measurements allowed for determination of the magnetic anisotropy orientation. The magnetic behavior was rationalized through ab initio CASSCF/SI-SO calculations. This redox-active chiral-field-induced SMM paves the way for the design of switchable-multiproperty SMMs.

A redox-active chiral-field-induced single-molecule magnet was achieved through a coordination reaction of the [Dy(hfac)₃] precursor to a ligand that combines a redox-active tetrathiafulvalene core and a chiral carbo[6]helicene fragment. This multiproperty system was characterized using X-ray crystallography, magnetism, and ab initio calculations.

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.

Octacyanometallate qubit candidates

We report the temperature dependence of the spin dynamics of the octacyanometallates [Mo(CN)8]3- and [W(CN)8]3-. At 5 K, these complexes display remarkably long spin-lattice relaxation times of 1.05 s, and 0.63 s, respectively. We probe the contributing factors to the spin relaxation and demonstrate the impact of spin-orbit coupling as a handle to tune vibrationally mediated spin-lattice relaxation.

Slow magnetic relaxation in octahedral low-spin Ni(iii) complexes

Herein we report the first examples of single-molecule magnet (SMM) behaviour in S = 1/2 Ni(iii) complexes. We find that low-spin 3d7 trans-[NiIII(cyclam)(X)2]Y complexes (cyclam = 1,4,8,11-tetraazacyclotetradecane; X and Y are singly charged anions) exhibit field-induced slow relaxation of magnetization for O-donor axial ligands (nitrate) but not for N-donor variants (isothiocyanate). Experimental and electronic structure computational investigations indicate that intrinsic spin polarisation of low-spin Ni(iii) is modulated significantly by local coordination geometry and supramolecular interactions. Solid state dilution of Ni(iii) with diamagnetic Co(iii) ions forms a related complex salt, [Ni x Co1-x (cyclam)(NO3)2](NO3)·2HNO3 (0.1 < x < 1), which preserves slow magnetic dynamics, thus supporting a molecular component to slow relaxation. An initial analysis of magnetic relaxation lifetime fits best to a combination of Raman and direct relaxation processes.

Effect of magnetic fields on the methyl rotation in a paramagnetic cobalt(ii) complex. Quasielastic neutron scattering studies

Molecular dynamics is a fundamental property of metal complexes. These dynamic processes, especially for paramagnetic complexes under external magnetic fields, are in general not well understood. Quasielastic neutron scattering (QENS) in 0-4 T magnetic fields has been used to study the dynamics of Co(acac)2(D2O)2 (1-d4, acac = acetylacetonate). At 80-100 K, rotation of the methyl groups on the acac ligands is the dominant dynamical process. This rotation is slowed down by the magnetic field increase. Rotation times at 80 K are 5.6(3) × 10-10 s at 0 T and 2.04(10) × 10-9 s at 4 T. The QENS studies suggest that methyl groups in these paramagnetic Co(ii) molecules do not behave as isolated units, which is consistent with results from earlier magnetic susceptibility studies indicating the presence of intermolecular interactions. DFT calculations show that unpaired electron spin density in 1 is dispersed to the atoms of both acac and H2O ligands. Methyl torsions in 1-d4 have also been observed at 5-100 K in inelastic neutron spectroscopy (INS). The QENS and INS results here help understand the dynamics of the compound in the solid state.

Peptides as Versatile Platforms for Quantum Computing

The pursuit of novel functional building blocks for the emerging field of quantum computing is one of the most appealing topics in the context of quantum technologies. Herein we showcase the urgency of introducing peptides as versatile platforms for quantum computing. In particular, we focus on lanthanide-binding tags, originally developed for the study of protein structure. We use pulsed electronic paramagnetic resonance to demonstrate quantum coherent oscillations in both neodymium and gadolinium peptidic qubits. Calculations based on density functional theory followed by a ligand field analysis indicate the possibility of influencing the nature of the spin qubit states by means of controlled changes in the peptidic sequence. We conclude with an overview of the challenges and opportunities opened by this interdisciplinary field.

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.

Spin-phonon couplings in transition metal complexes with slow magnetic relaxation

Spin–phonon coupling plays an important role in single-molecule magnets and molecular qubits. However, there have been few detailed studies of its nature. Here, we show for the first time distinct couplings of g phonons of Co^II(acac)₂(H₂O)₂ (acac = acetylacetonate) and its deuterated analogs with zero-field-split, excited magnetic/spin levels (Kramers doublet (KD)) of the S = 3/2 electronic ground state. The couplings are observed as avoided crossings in magnetic-field-dependent Raman spectra with coupling constants of 1–2 cm⁻¹. Far-IR spectra reveal the magnetic-dipole-allowed, inter-KD transition, shifting to higher energy with increasing field. Density functional theory calculations are used to rationalize energies and symmetries of the phonons. A vibronic coupling model, supported by electronic structure calculations, is proposed to rationalize the behavior of the coupled Raman peaks. This work spectroscopically reveals and quantitates the spin–phonon couplings in typical transition metal complexes and sheds light on the origin of the spin–phonon entanglement.

Transition metal complexes that display slow magnetic relaxation show promise for information storage, but our mechanistic understanding of the magnetic relaxation of such compounds remains limited. Here, the authors spectroscopically and computationally characterize the strength of spin–phonon couplings, which play an important role in the relaxation process.

Slow Magnetic Relaxation in a Palladium-Gadolinium Complex Induced by Electron Density Donation from the Palladium Ion

Incorporating palladium in the first coordination sphere of acetato-bridged lanthanoid complexes, [Pd₂ Ln₂ (H₂ O)₂ (AcO)₁₀ ]⋅2 AcOH (Ln=Gd (1), Y (2), Gd_0.4 Y_1.6 (3), Eu (4)), led to significant bonding interactions between the palladium and the lanthanoid ions, which were demonstrated by experimental and theoretical methods. We found that electron density was donated from the d⁸ Pd²⁺ ion to Gd³⁺ ion in 1 and 3, leading to the observed slow magnetic relaxation by using local orbital locator (LOL) and X-ray absorption near-edge structure (XANES) analysis. Field-induced dual slow magnetic relaxation was observed for 1 up to 20 K. Complex 3 and frozen aqueous and acetonitrile solutions of 1 showed only one relaxation peak, which confirms the role of intermolecular dipolar interactions in slowing the magnetic relaxation of 1. The slow magnetic relaxation occurred through a combination of Orbach and Direct processes with the highest pre-exponential factor (τ_o =0.06 s) reported so far for a gadolinium complex exhibiting slow magnetic relaxation. The results revealed that transition metal-lanthanoid (TM-Ln) axial interactions indeed could lead to new physical properties by affecting both the electronic and magnetic states of the compounds.

Vanadyl dithiolate single molecule transistors: the next spintronic frontier?

On the road towards quantum devices, chemistry can offer elementary pieces with a built-in function, like [TbPc2]- which functions as a molecular transistor for nuclear spin detection. We argue that a large class of molecules have similar potential. In particular, we review the recent progress regarding highly coherent spin qubits based on vanadium dithiolate complexes. We propose their use as single molecule transistors to read and control a triple nuclear spin qubit, which could enable a low-current nuclear spin detection scheme by means of a spin valve effect.

Spin states, vibrations and spin relaxation in molecular nanomagnets and spin qubits: a critical perspective

Very recently the closely related fields of molecular spin qubits, single ion magnets and single atom magnets have been shaken by unexpected results. We have witnessed a jump in the phase memory times of spin qubits from a few microseconds to almost a millisecond in a vanadium complex, magnetic hysteresis up to 60 K in a dysprosium-based magnetic molecule and magnetic memory up to 30 K in a holmium atom deposited on a surface. With single-molecule magnets being more than two decades old, this rapid improvement in the physical properties is surprising and its explanation deserves urgent attention. The general assumption of focusing uniquely on the energy barrier is clearly insufficient to model magnetic relaxation. Other factors, such as vibrations that couple to spin states, need to be taken into account. In fact, this coupling is currently recognised to be the key factor that accounts for the slow relaxation of magnetisation at higher temperatures. Herein we will present a critical perspective of the recent advances in molecular nanomagnetism towards the goal of integrating spin-phonon interactions into the current computational methodologies of spin relaxation. This presentation will be placed in the context of the well-known models developed in solid state physics, which, as we will explain, are severely limited for molecular systems.

A neutral auxiliary ligand enhanced dysprosium(iii) single molecule magnet

An approximately equatorial three-coordinated dysprosium(iii) complex DyL₂[N(SiMe₃)₂] (L = bis(2-(2,5-dimethyl-1H-pyrrol-1-yl)ethyl)amine) with an additional neutral auxiliary pyrrole ligand was synthesised and structurally characterized.

A belt-like one-dimensional Dy chain exhibiting slow magnetic relaxation behavior

A belt-like Dy chain compound was synthesized, which exhibited slow magnetic relaxation behavior and clear hysteresis loops below 0.6 K.