Many-Body Models for Chirality-Induced Spin Selectivity in Electron Transfer.

We present the first microscopic model for the chirality-induced spin selectivity effect in electron-transfer, in which the internal degrees of freedom of the chiral bridge are explicitly included. By exactly solving this model on short chiral chains we demonstrate that a sizable spin polarization on the acceptor arises from the interplay of coherent and incoherent dynamics, with strong electron-electron correlations yielding many-body states on the bridge as crucial ingredients. Moreover, we include the coherent and incoherent dynamics induced by interactions with vibrational modes and show that they can play an important role in determining the long-time polarized state probed in experiments.

Weak Exchange Interactions in Multispin Systems: EPR Studies of Metalloporphyrins Decorated with {Cr7Ni} Rings.

Both metalloporphyrins and heterometallic {Cr7Ni} rings are of significant research interest due to their proposed roles in quantum information processing devices. In this study, we present a series of complexes in which [Cr7NiF3(Etglu)(O2CtBu)15] (N-EtgluH5 = N-ethyl-d-glucamine) heterometallic rings are coordinated to metalloporphyrin linkers: the symmetric [M(TPyP)] for M = Cu2+, VO2+, and H2TPyP = 5,10,15,20-tetra(4-pyridyl)porphyrin; and the asymmetric [{VO}(TrPPyP)] for H2(TrPPyP) = 5,10,15-(triphenyl)-20-(4-pyridyl)porphyrin. The magnetic interactions present in these complexes are unraveled using the continuous wave (CW) electron paramagnetic resonance (EPR) technique. The nature of the coupling between the {Cr7Ni} rings and the central metalloporphyrin is assessed by numerical simulations of CW EPR spectra and determined to be on the order of 0.01 cm-1, larger than the dipolar ones and suitable for individual spin addressability in multiqubit architectures.

Challenges in the Direct Detection of Chirality-induced Spin Selectivity: Investigation of Foldamer-based Donor-acceptor Dyads.

Over the past two decades, the chirality-induced spin selectivity (CISS) effect was reported in several experiments disclosing a unique connection between chirality and electron spin. Recent theoretical works highlighted time-resolved Electron Paramagnetic Resonance (trEPR) as a powerful tool to directly detect the spin polarization resulting from CISS. Here, we report a first attempt to detect CISS at the molecular level by linking the pyrene electron donor to the fullerene acceptor with chiral peptide bridges of different length and electric dipole moment. The dyads are investigated by an array of techniques, including cyclic voltammetry, steady-state and transient optical spectroscopies, and trEPR. Despite the promising energy alignment of the electronic levels, our multi-technique analysis reveals no evidence of electron transfer (ET), highlighting the challenges of spectroscopic detection of CISS. However, the analysis allows the formulation of guidelines for the design of chiral organic model systems suitable to directly probe CISS-polarized ET.

Mixed-Sandwich Titanium(III) Qubits on Au(111): Electron Delocalization Ruled by Molecular Packing.

Organometallic sandwich complexes are versatile molecular systems that have been recently employed for single-molecule manipulation and spin sensing experiments. Among related organometallic compounds, the mixed-sandwich S = 1/2 complex (η8-cyclooctatetraene)(η5-cyclopentadienyl)titanium, here [CpTi(cot)], has attracted interest as a spin qubit because of the long coherence time. Here the structural and chemical properties of [CpTi(cot)] on Au(111) are investigated at the monolayer level by experimental and computational methods. Scanning tunneling microscopy suggests that adsorption occurs in two molecular orientations, lying and standing, with a 3:1 ratio. XPS data evidence that a fraction of the molecules undergo partial electron transfer to gold, while our computational analysis suggests that only the standing molecules experience charge delocalization toward the surface. Such a phenomenon depends on intermolecular interactions that stabilize the molecular packing in the monolayer. This orientation-dependent molecule-surface hybridization opens exciting perspectives for selective control of the molecule-substrate spin delocalization in hybrid interfaces.

A Heterometallic Porphyrin Dimer as a Potential Quantum Gate: Magneto-Structural Correlations and Spin Coherence Properties.

In the development of two-qubit quantum gates, precise control over the intramolecular spin-spin interaction between molecular spin units plays a pivotal role. A weak but measurable exchange coupling is especially important for achieving selective spin addressability that allows controlled manipulation of the computational basis states |00⟩ |01⟩ |10⟩ |11⟩ by microwave pulses. Here, we report the synthesis and Electron Paramagnetic Resonance (EPR) study of a heterometallic meso-meso (m-m) singly-linked VIV O-CuII porphyrin dimer. X-band continuous wave EPR measurements in frozen solutions suggest a ferromagnetic exchange coupling of ca. 8 ⋅ 10-3  cm-1 . This estimation is supported by Density Functional Theory calculations, which also allow disentangling the ferro- and antiferromagnetic contributions to the exchange. Pulsed EPR experiments show that the dimer maintains relaxation times similar to the monometallic CuII porphyrins. The addressability of the two individual spins is made possible by the different g-tensors of VIV and CuII -ions, in contrast to homometallic dimers where tilting of the porphyrin planes plays a key role. Therefore, single-spin addressability in the heterometallic dimer can be maintained even with small tilting angles, as expected when deposited on surface, unlocking the full potential of molecular quantum gates for practical applications.

A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound.

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion's first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

Magnetic Anisotropy Trends along a Full 4f-Series: The fn+7 Effect.

The combined experimental and computational study of the 13 magnetic complexes belonging to the Na[LnDOTA(H2O)] (H4DOTA = tetraazacyclododecane-N,N',N″,N‴-tetraacetic acid and Ln = Ce-Yb) family allowed us to identify a new trend: the orientation of the magnetic anisotropy tensors of derivatives differing by seven f electrons practically coincide. We name this trend the fn+7 effect. Experiments and theory fully agree on the match between the magnetic reference frames (e.g., the easy, intermediate, and hard direction). The shape of the magnetic anisotropy of some couples of ions differing by seven f electrons might seem instead different at first look, but our analysis explains a hidden similarity. We thus pave the way toward a reliable predictivity of the magnetic anisotropy of lanthanide complexes with a consequent reduced need of computational and synthetical efforts. We also offer a way to gain information on ions with a relatively small total angular momentum (i.e., Sm3+ and Eu3+) and on the radioactive Pm3+, which are difficult to investigate experimentally.

Quantum dynamics of a single molecule magnet on superconducting Pb(111).

Magnetic materials interfaced with superconductors may reveal new physical phenomena with potential for quantum technologies. The use of molecules as magnetic components has already shown great promise, but the diversity of properties offered by the molecular realm remains largely unexplored. Here we investigate a submonolayer of tetrairon(III) propeller-shaped single molecule magnets deposited on a superconducting lead surface. This material combination reveals a strong influence of the superconductor on the spin dynamics of the single molecule magnet. It is shown that the superconducting transition to the condensate state switches the single molecule magnet from a blocked magnetization state to a resonant quantum tunnelling regime. Our results open perspectives to control single molecule magnetism via superconductors and to use single molecule magnets as local probes of the superconducting state.

Probing Vibrational Symmetry Effects and Nuclear Spin Economy Principles in Molecular Spin Qubits.

The selection of molecular spin qubits with a long coherence time, Tm, is a central task for implementing molecule-based quantum technologies. Even if a sufficiently long Tm can be achieved through an efficient synthetic strategy and ad hoc experimental measurement procedures, many factors contributing to the loss of coherence still need to be thoroughly investigated and understood. Vibrational properties and nuclear spins of hydrogens are two of them. The former plays a paramount role, but a detailed theoretical investigation aimed at studying their effects on the spin dynamics of molecular complexes such as the benchmark phthalocyanine (Pc) is still missing, whereas the effect of the latter deserves to be examined in detail for such a class of compounds. In this work, we adopted a combined theoretical and experimental approach to investigate the relaxation properties of classical [Cu(Pc)] and a CuII complex based on the ligand tetrakis(thiadiazole)porphyrazine (H2TTDPz), characterized by a hydrogen-free molecular structure. Systematic calculations of molecular vibrations exemplify the effect of normal modes on the spin-lattice relaxation process, unveiling a different contribution to T1 depending on the symmetry of normal modes. Moreover, we observed that an appreciable Tm enhancement could be achieved by removing hydrogens from the ligand.

Substrate mediated interaction of terbium(III) double-deckers with the TiO2(110) surface.

A terbium(iii)-bis(phthalocyaninato) neutral complex was deposited on the rutile TiO2(110) surface, and their interaction was studied by Scanning Tunneling Microscopy (STM) and X-ray Photoelectron Spectroscopy (XPS). It was found that the TiO2 rutile surface favours the adsorption of isolated molecules adopting a lying down configuration with the phthalocyanine planes tilted by about 30° when they lie in the first layer. The electronic and chemical properties of the molecules on the surface were studied by XPS as a function of the TiO2(110) substrate preparation. This study evidences that strong molecule-substrate interactions are present and a charge transfer process occurs from the molecule to the surface.

Longitudinal and transverse NMR relaxivities of Ln(III)-DOTA complexes: A comprehensive investigation.

Longitudinal and transverse 1H nuclear magnetic resonance relaxivities of Ln(III)-DOTA complexes (with Ln = Gd, Tb, Dy, Er; DOTA = 1,4,7,10-tetraazacyclododecane-N,N',N″,N‴-tetraacetic acid) and Mn(II) aqueous solutions were measured in a wide range of frequencies, 10 kHz to 700 MHz. The experimental data were interpreted by means of models derived from the Solomon-Bloembergen-Morgan theory. The data analysis was performed assuming the orbital angular momentum L = 0 for Gd-DOTA and the aqua ion [Mn(H2O)6]2+ and L ≠ 0 for Dy-, Tb-, and Er-DOTA. A refined estimation of the zero-field-splitting barrier Δ and of the modulation correlation time τv was obtained for [Mn(H2O)6]2+ by extending the fitting of nuclear magnetic relaxation dispersion profiles to the low-field regime. The Gd-DOTA fitting parameters resulted in good agreement with the literature, and the fit of transverse relaxivity data confirmed the negligibility of the scalar interaction in the nuclear relaxation mechanism. Larger transverse relaxivities of Dy-DOTA and Tb-DOTA (∼10 mM-1 s-1) with respect to Er-DOTA (∼1 mM-1 s-1) were observed at 16 T. Such higher values are suggested to be due to a shorter residence time τm that is possibly linked to the fluctuations of the hyperfine interaction and the different shape of the magnetic anisotropy. The possible employment of Dy-DOTA, Tb-DOTA, and Er-DOTA as negative magnetic resonance imaging contrast agents for high-field applications was envisaged by collecting spin-echo images at 7 T. Particularly in Dy- and Tb-derivatives, the transverse relaxivity at 16 T is of the order of the Gd-one at 1.5 T.

Spin-Electric Coupling in a Cobalt(II)-Based Spin Triangle Revealed by Electric-Field-Modulated Electron Spin Resonance Spectroscopy.

A cobalt(II)-based spin triangle shows a significant spin-electric coupling. [Co3 (pytag)(py)6 Cl3 ]ClO4 ⋅3 py crystallizes in the acentric monoclinic space group P21 . The intra-triangle antiferromagnetic interaction, of the order of ca. -15 cm-1 (H=-JSa Sb ), leads to spin frustration. The two expected energy-degenerate ground doublets are, however, separated by a few wavenumbers, as a consequence of magnetic anisotropy and deviations from threefold symmetry. The Co3  planes of symmetry-related molecules are almost parallel, allowing for the determination of the spin-electric properties of single crystals by EFM-ESR spectroscopy. The spin-electric effect detected when the electric field is applied in the Co3  plane was revealed by a shift in the resonance field. It was quantified as ΔgE /E=0.11×10-9  m V-1 , which in terms of frequency corresponds to approximately 0.3 Hz m V-1 . This value is comparable to what was determined for a Cu3  triangle despite the antiferromagnetic interaction being 20 times larger for the latter.

Stabilization of an Enantiopure Sub-monolayer of Helicene Radical Cations on a Au(111) Surface through Noncovalent Interactions.

In the past few years, the chirality and magnetism of molecules have received notable interest for the development of novel molecular devices. Chiral helicenes combine both these properties, and thus their nanostructuration is the first step toward developing new multifunctional devices. Here, we present a novel strategy to deposit a sub-monolayer of enantiopure thia[4]helicene radical cations on a pre-functionalized Au(111) substrate. This approach results in both the paramagnetic character and the chemical structure of these molecules being maintained at the nanoscale, as demonstrated by in-house characterizations. Furthermore, synchrotron-based X-ray natural circular dichroism confirmed that the handedness of the thia[4]helicene is preserved on the surface.

Exploring the Organometallic Route to Molecular Spin Qubits: The [CpTi(cot)] Case.

The coherence time of the 17-electron, mixed sandwich complex [CpTi(cot)], (η8 -cyclooctatetraene)(η5 -cyclopentadienyl)titanium, reaches 34 µs at 4.5 K in a frozen deuterated toluene solution. This is a remarkable coherence time for a highly protonated molecule. The intramolecular distances between the Ti and H atoms provide a good compromise between instantaneous and spin diffusion sources of decoherence. Ab initio calculations at the molecular and crystal packing levels reveal that the characteristic low-energy ring rotations of the sandwich framework do not yield a too detrimental spin-lattice relaxation because of their small spin-phonon coupling. The volatility of [CpTi(cot)] and the accessibility of the semi-occupied, non-bonding d z 2 orbital make this neutral compound an ideal candidate for single-qubit addressing on surface and quantum sensing in combination with scanning probe microscopy.

Magnetic Anisotropy Drives Magnetochiral Dichroism in a Chiral Molecular Helix Probed with Visible Light.

Magnetochiral dichroism (MChD) is a nonreciprocal manifestation of light-matter interaction that can be observed in chiral magnetized systems. It features a differential absorption of unpolarized light depending on the relative orientation of the magnetic field and the light wavevector and on the absolute configuration of the system. The relevance of this effect for optical readout of magnetic data calls for a complete understanding of the microscopic parameters driving MChD with an easy-accessible and nondamaging light source, such as visible light. For this purpose, here we report on MChD detected with visible light on a chiral magnetic helix formulated as [MnIII(cyclam)(SO4)]ClO4·H2O (cyclam = 1,4,8,11-tetraazacyclotetradecane) featuring antiferromagnetically coupled anisotropic MnIII ions. Alternate current susceptibility measurements revealed the existence of a single-chain magnet behavior hidden below the canted antiferromagnetism (TN = 5.8 K) already evidenced by direct current magnetometry. A detailed analysis of the optical absorption gives access to the value of the zero-field splitting parameter D (2.9 cm-1), which quantifies the magnetic anisotropy of the MnIII centers. Below the magnetic ordering temperature of the material, the MChD spectra exhibit intense absolute configuration dependent MChD signals reaching record values of ca. 12% of the absorbed intensity for the two electronic transitions most influenced by the spin-orbit coupling of the MnIII ion. These findings set a clear route toward the design and preparation of highly MChD-responsive molecular materials.

Electric field modulation of magnetic exchange in molecular helices.

The possibility to operate on magnetic materials through the application of electric rather than magnetic fields-promising faster, more compact and energy efficient circuits-continues to spur the investigation of magnetoelectric effects. Symmetry considerations, in particular the lack of an inversion centre, characterize the magnetoelectric effect. In addition, spin-orbit coupling is generally considered necessary to make a spin system sensitive to a charge distribution. However, a magnetoelectric effect not relying on spin-orbit coupling is appealing for spin-based quantum technologies. Here, we report the detection of a magnetoelectric effect that we attribute to an electric field modulation of the magnetic exchange interaction without atomic displacement. The effect is visible in electron paramagnetic resonance absorption of molecular helices under electric field modulation and confirmed by specific symmetry properties and spectral simulation.

The Second Quantum Revolution: Role and Challenges of Molecular Chemistry.

Implementation of modern Quantum Technologies might benefit from the remarkable quantum properties shown by molecular spin systems. In this Perspective, we highlight the role that molecular chemistry can have in the current second quantum revolution, i.e., the use of quantum physics principles to create new quantum technologies, in this specific case by means of molecular components. Herein, we briefly review the current status of the field by identifying the key advances recently made by the molecular chemistry community, such as for example the design of molecular spin qubits with long spin coherence and the realization of multiqubit architectures for quantum gates implementation. With a critical eye to the current state-of-the-art, we also highlight the main challenges needed for the further advancement of the field toward quantum technologies development.

First-Principles Investigation of Spin-Phonon Coupling in Vanadium-Based Molecular Spin Quantum Bits.

Paramagnetic molecules can show long spin-coherence times, which make them good candidates as quantum bits (qubits). Reducing the efficiency of the spin-phonon interaction is the primary challenge toward achieving long coherence times over a wide temperature range in soft molecular lattices. The lack of a microscopic understanding about the role of vibrations in spin relaxation strongly undermines the possibility of chemically designing better-performing molecular qubits. Here we report a first-principles characterization of the main mechanism contributing to the spin-phonon coupling for a class of vanadium(IV) molecular qubits. Post-Hartree-Fock and density functional theory methods are used to determine the effect of both intermolecular and intramolecular vibrations on modulation of the Zeeman energy for four molecules showing different coordination geometries and ligands. This comparative study provides the first insight into the role played by coordination geometry and ligand-field strength in determining the spin-lattice relaxation time of molecular qubits, opening an avenue to the rational design of new compounds.

Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules.

Atomic-scale magnetic moments in contact with superconductors host rich physics based on the emergence of Yu-Shiba-Rusinov (YSR) magnetic bound states within the superconducting condensate. Here, we focus on a magnetic bound state induced into Pb nanoislands by individual vanadyl phthalocyanine (VOPc) molecules deposited on the Pb surface. The VOPc molecule is characterized by a spin magnitude of 1/2 arising from a well-isolated singly occupied d xy-orbital and is a promising candidate for a molecular spin qubit with long coherence times. X-ray magnetic circular dichroism (XMCD) measurements show that the molecular spin remains unperturbed even for molecules directly deposited on the Pb surface. Scanning tunneling spectroscopy and density functional theory (DFT) calculations identify two adsorption geometries for this "asymmetric" molecule (i.e., absence of a horizontal symmetry plane): (a) oxygen pointing toward the vacuum with the Pc laying on the Pb, showing negligible spin-superconductor interaction, and (b) oxygen pointing toward the Pb, presenting an efficient interaction with the Pb and promoting a Yu-Shiba-Rusinov bound state. Additionally, we find that in the first case a YSR state can be induced smoothly by exerting mechanical force on the molecules with the scanning tunneling microscope (STM) tip. This allows the interaction strength to be tuned continuously from an isolated molecular spin case, through the quantum critical point (where the bound state energy is zero) and beyond. DFT indicates that a gradual bending of the VO bond relative to the Pc ligand plane promoted by the STM tip can modify the interaction in a continuously tunable manner. The ability to induce a tunable YSR state in the superconductor suggests the possibility of introducing coupled spins on superconductors with switchable interaction.

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.