Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets.

Paramagnetic molecules with a metal ion as an electron spin center are promising building blocks for molecular qubits and high-density memory arrays. However, fast spin relaxation and decoherence in these molecules lead to a rapid loss of magnetization and quantum information. Nonadiabatic coupling (NAC), closely related to spin-vibrational coupling, is the main source of spin relaxation and decoherence in paramagnetic molecules at higher temperatures. Predicting these couplings using numerical differentiation requires a large number of computationally intensive ab initio or crystal field electronic structure calculations. To reduce computational cost and improve accuracy, we derive and implement analytical NAC and state-specific energy gradient for the ab initio parametrized crystal field Hamiltonian describing single-ion molecular magnets. Our implementation requires only a single crystal field calculation. In addition, the accurate NACs and state-specific energy gradients can be used to model spin relaxation using sophisticated nonadiabatic molecular dynamics, which avoids the harmonic approximation for molecular vibrations. To test our implementation, we calculate the NAC values for three lanthanide complexes. The predicted values support the relaxation mechanisms reported in previous studies.

Data-driven design of molecular nanomagnets.

Three decades of research in molecular nanomagnets have raised their magnetic memories from liquid helium to liquid nitrogen temperature thanks to a wise choice of the magnetic ion and coordination environment. Still, serendipity and chemical intuition played a main role. In order to establish a powerful framework for statistically driven chemical design, here we collected chemical and physical data for lanthanide-based nanomagnets, catalogued over 1400 published experiments, developed an interactive dashboard (SIMDAVIS) to visualise the dataset, and applied inferential statistical analysis. Our analysis shows that the Arrhenius energy barrier correlates unexpectedly well with the magnetic memory. Furthermore, as both Orbach and Raman processes can be affected by vibronic coupling, chemical design of the coordination scheme may be used to reduce the relaxation rates. Indeed, only bis-phthalocyaninato sandwiches and metallocenes, with rigid ligands, consistently present magnetic memory up to high temperature. Analysing magnetostructural correlations, we offer promising strategies for improvement, in particular for the preparation of pentagonal bipyramids, where even softer complexes are protected against molecular vibrations.

Exchange-induced spin polarization in a single magnetic molecule junction.

Many spintronic devices rely on the presence of spin-polarized currents at zero magnetic field. This is often obtained by spin exchange-bias, where an element with long-range magnetic order creates magnetized states and displaces the hysteresis loop. Here we demonstrate that exchange-split spin states are observable and usable in the smallest conceivable unit: a single magnetic molecule. We use a redox-active porphyrin as a transport channel, coordinating a dysprosium-based single-molecule-magnet inside a graphene nano-gap. Single-molecule transport in magnetic field reveals the existence of exchange-split channels with different spin-polarizations that depend strongly on the field orientation, and comparison with the diamagnetic isostructural compound and milikelvin torque magnetometry unravels the role of the single-molecule anisotropy and the molecular orientation. These results open a path to using spin-exchange in molecular electronics, and offer a method to quantify the internal spin structure of single molecules in multiple oxidation states.

Spectroscopic Analysis of Vibronic Relaxation Pathways in Molecular Spin Qubit [Ho(W5O18)2]9-: Sparse Spectra Are Key.

Vibrations play a prominent role in magnetic relaxation processes of molecular spin qubits as they couple to spin states, leading to the loss of quantum information. Direct experimental determination of vibronic coupling is crucial to understand and control the spin dynamics of these nano-objects, which represent the limit of miniaturization for quantum devices. Herein, we measure the magneto-infrared properties of the molecular spin qubit system Na9[Ho(W5O18)2]·35H2O. Our results place significant constraints on the pattern of crystal field levels and the vibrational excitations allowing us to unravel vibronic decoherence pathways in this system. We observe field-induced spectral changes near 63 and 370 cm-1 that are modeled in terms of odd-symmetry vibrations mixed with f-manifold crystal field excitations. The overall extent of vibronic coupling in Na9[Ho(W5O18)2]·35H2O is limited by a modest coupling constant (on the order of 0.25) and a transparency window in the phonon density of states that acts to keep the intramolecular vibrations and MJ levels apart. These findings advance the understanding of vibronic coupling in a molecular magnet with atomic clock transitions and suggest strategies for designing molecular spin qubits with improved coherence lifetimes.

Insights on the coupling between vibronically active molecular vibrations and lattice phonons in molecular nanomagnets.

Spin-lattice relaxation is a key open problem to understand the spin dynamics of single-molecule magnets and molecular spin qubits. While modelling the coupling between spin states and local vibrations allows to determine the more relevant molecular vibrations for spin relaxation, this is not sufficient to explain how energy is dissipated towards the thermal bath. Herein, we employ a simple and efficient model to examine the coupling of local vibrational modes with long-wavelength longitudinal and transverse phonons in the clock-like spin qubit [Ho(W5O18)2]9-. We find that in crystals of this polyoxometalate the vibrational mode previously found to be vibronically active at low temperature does not couple significantly to lattice phonons. This means that further intramolecular energy transfer via anharmonic vibrations is necessary for spin relaxation in this system. Finally, we discuss implications for the spin-phonon coupling of [Ho(W5O18)2]9- deposited on a MgO (001) substrate, offering a simple methodology that can be extrapolated to estimate the effects on spin relaxation of different surfaces, including 2D materials.

Binding Sites, Vibrations and Spin-Lattice Relaxation Times in Europium(II)-Based Metallofullerene Spin Qubits.

To design molecular spin qubits with enhanced quantum coherence, a control of the coupling between the local vibrations and the spin states is crucial, which could be realized in principle by engineering molecular structures via coordination chemistry. To this end, understanding the underlying structural factors that govern the spin relaxation is a central topic. Here, we report the investigation of the spin dynamics in a series of chemically designed europium(II)-based endohedral metallofullerenes (EMFs). By introducing a unique structural difference, i. e. metal-cage binding site, while keeping other molecular parameters constant between different complexes, these manifest the key role of the three low-energy metal-displacing vibrations in mediating the spin-lattice relaxation times (T1 ). The temperature dependence of T1 can thus be normalized by the frequencies of these low energy vibrations to show an unprecedentedly universal behavior for EMFs in frozen CS2 solution. Our theoretical analysis indicates that this structural difference determines not only the vibrational rigidity but also spin-vibration coupling in these EMF-based qubit candidates.

Near Isotropic D4d Spin Qubits as Nodes of a Gd(III)-Based Metal-Organic Framework.

Embedding coherent spin motifs in reproducible molecular building blocks is a promising pathway for the realization of quantum technologies. Three-dimensional (3D) MOFs are a versatile platform for the rational design of extended structures employing coordination chemistry. Here, we report the synthesis and characterization of a gadolinium(III)-based MOF, [Gd(bipyNO)4](TfO)3·xMeOH (bipyNO = bipyridine,N,N'-dioxide; TfO = triflate; and MeOH = methanol) (quMOF-1), which presents a unique coordination geometry that leads to a tiny magnetic anisotropy (in terms of D, an equivalent zero-field splitting would be achieved by D = 0.006 cm-1) even compared with regular Gd(III) complexes. Pulsed electron paramagnetic resonance experiments on its magnetically diluted samples confirm the preservation of quantum coherence of single Gd(III) qubit units in this 3D extended molecular architecture (T2 = 612 ns and T1 = 66 µs at 3.5 K), which allows for the detection of Rabi oscillations at 40 K.

Towards peptide-based tunable multistate memristive materials.

Development of new memristive hardware is a technological requirement towards widespread neuromorphic computing. Molecular spintronics seems to be a fertile field for the design and preparation of this hardware. Within molecular spintronics, recent results on metallopeptides demonstrating the interaction between paramagnetic ions and the chirality induced spin selectivity effect hold particular promise for developing fast (ns-µs) operation times. [R. Torres-Cavanillas et al., J. Am. Chem. Soc., 2020, DOI: 10.1021/jacs.0c07531]. Among the challenges in the field, a major highlight is the difficulty in modelling the spin dynamics in these complex systems, but at the same time the use of inexpensive methods has already allowed progress in that direction. Finally, we discuss the unique potential of biomolecules for the design of multistate memristors with a controlled- and indeed, programmable-nanostructure, allowing going beyond anything that is conceivable by employing conventional coordination chemistry.

Reinforced Room-Temperature Spin Filtering in Chiral Paramagnetic Metallopeptides.

Chirality-induced spin selectivity (CISS), whereby helical molecules polarize the spin of electrical current, is an intriguing effect with potential applications in nanospintronics. In this nascent field, the study of the CISS effect using paramagnetic chiral molecules, which could introduce another degree of freedom in controlling the spin transport, remains so far unexplored. To address this challenge, herein we propose the use of self-assembled monolayers (SAMs) of helical lanthanide-binding peptides. To elucidate the effect of the paramagnetic nuclei, monolayers of the peptide coordinating paramagnetic or diamagnetic ions are prepared. By means of spin-dependent electrochemistry, the CISS effect is demonstrated by cyclic voltammetry and electrochemical impedance measurements for both samples. Additionally, an implementation of the standard liquid-metal drop electron transport setup has been carried out, and this process helped to demonstrate the peptides' suitability for solid-state devices. Remarkably, the inclusion of a paramagnetic center in the peptide increases the spin polarization as was independently proved by different techniques. These findings permit the inclusion of magnetic biomolecules in the CISS field and pave the way to their implementation in a new generation of (bio)spintronic nanodevices.

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.

Exploiting clock transitions for the chemical design of resilient molecular spin qubits.

Molecular spin qubits are chemical nanoobjects with promising applications that are so far hampered by the rapid loss of quantum information, a process known as decoherence. A strategy to improve this situation involves employing so-called Clock Transitions (CTs), which arise at anticrossings between spin energy levels. At CTs, the spin states are protected from magnetic noise and present an enhanced quantum coherence. Unfortunately, these optimal points are intrinsically hard to control since their transition energy cannot be tuned by an external magnetic field; moreover, their resilience towards geometric distortions has not yet been analyzed. Here we employ a python-based computational tool for the systematic theoretical analysis and chemical optimization of CTs. We compare three relevant case studies with increasingly complex ground states. First, we start with vanadium(iv)-based spin qubits, where the avoided crossings are controlled by hyperfine interaction and find that these S = 1/2 systems are very promising, in particular in the case of vanadyl complexes in an L-band pulsed EPR setup. Second, we proceed with a study of the effect of symmetry distortions in a holmium polyoxotungstate of formula [Ho(W5O18)2]9- where CTs had already been experimentally demonstrated. Here we determine the relative importance of the different structural distortions that causes the anticrossings. Third, we study the most complicated case, a polyoxopalladate cube [HoPd12(AsPh)8O32]5- which presents an unusually rich ground spin multiplet. This system allows us to find uniquely favorable CTs that could nevertheless be accessible with standard pulsed EPR equipment (X-band or Q-band) after a suitable chemical distortion to break the perfect cubic symmetry. Since anticrossings and CTs constitute a rich source of physical phenomena in very different kinds of quantum systems, the generalization of this study is expected to have impact not only in molecular spin science but also in other related fields such as molecular photophysics and photochemistry.

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 [(CpiPr5)Dy(Cp*)]+ (CpiPr5 = 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.

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.

Experimental determination of single molecule toroic behaviour in a Dy8 single molecule magnet.

The enhancement of toroic motifs through coupling toroidal moments within molecular nanomagnets is a new, interesting and relevant approach for both fundamental research and potential quantum computation applications. We investigate a Dy8 molecular cluster and discover it has a antiferrotoroic ground state with slow magnetic relaxation. The experimental characterization of the magnetic anisotropy axes of each magnetic center and their exchange interactions represents a considerable challenge due to the non-magnetic nature of the toroidal motif. To overcome this and obtain access to the low energy states of Dy8 we establish a multi-orientation single-crystal micro Hall sensor magnetometry approach. Using an effective Hamiltonian model we then unpick the microscopic spin structure of Dy8, leading to a canted antiferrotoroidic tetramer molecular ground state. These findings are supported with electrostatic calculations that independently confirm the experimentally determined magnetic anisotropy axes for each DyIII ion within the molecule.

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.

Sublimable Single Ion Magnets Based on Lanthanoid Quinolinate Complexes: The Role of Intermolecular Interactions on Their Thermal Stability.

We report the design, preparation, and characterization of two families of thermally robust coordination complexes based on lanthanoid quinolinate compounds: [Ln(5,7-Br2q)4]- and [Ln(5,7-ClIq)4]-, where q = 8-hydroquinolinate anion and Ln = DyIII, TbIII, ErIII, and HoIII. The sodium salt of [Dy(5,7-Br2q)4]- decomposes upon sublimation, whereas the sodium salt of [Dy(5,7-ClIq)4]-, which displays subtly different crystalline interactions, is sublimable under gentle conditions. The resulting film presents low roughness with high coverage, and the molecular integrity of the coordination complex is verified through AFM, MALDI-TOF, FT-IR, and microanalysis. Crucially, the single-molecule magnet behavior exhibited by [Dy(5,7-ClIq)4]- in bulk remains detectable by ac magnetometry in the sublimated film.

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.

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.

Sublimable chloroquinolinate lanthanoid single-ion magnets deposited on ferromagnetic electrodes.

A new family of chloroquinolinate lanthanoid complexes of the formula A+[Ln(5,7Cl2q)4]-, with Ln = Y3+, Tb3+ and Dy3+ and A+ = Na+, NEt4+ and K0.5(NEt4)0.5+, is studied, both in bulk and as thin films. Several members of the family are found to present single-molecule magnetic behavior in bulk. Interestingly, the sodium salts can be sublimed under high vacuum conditions retaining their molecular structures and magnetic properties. These thermally stable compounds have been deposited on different substrates (Al2O3, Au and NiFe). The magnetic properties of these molecular films show the appearance of cusps in the zero-field cooled curves when they are deposited on permalloy (NiFe). This indicates a magnetic blocking caused by the interaction between the single-ion magnet and the ferromagnet. X-ray absorption spectroscopy confirms the formation of hybrid states at the molecule/metal interface.