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.

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.

Efficient Spin-Selective Electron Transport at Low Voltages of Thia-Bridged Triarylamine Hetero[4]helicenes Chemisorbed Monolayer.

The Chirality Induced Spin Selectivity (CISS) effect describes the capability of chiral molecules to act as spin filters discriminating flowing electrons according to their spin state. Within molecular spintronics, efforts are focused on developing chiral-molecule-based technologies to control the injection and coherence of spin-polarized currents. Herein, for this purpose, we study spin selectivity properties of a monolayer of a thioalkyl derivative of a thia-bridged triarylamine hetero[4]helicene chemisorbed on a gold surface. A stacked device assembled by embedding a monolayer of these molecules between ferromagnetic and diamagnetic electrodes exhibits asymmetric magnetoresistance with inversion of the signal according to the handedness of molecules, in line with the presence of the CISS effect. In addition, magnetically conductive atomic force microscopy reveals efficient electron spin filtering even at unusually low potentials. Our results demonstrate that thia[4]heterohelicenes represent key candidates for the development of chiral spintronic devices.

Chirality-Induced Spin Selectivity: An Enabling Technology for Quantum Applications.

Molecular spins are promising building blocks of future quantum technologies thanks to the unparalleled flexibility provided by chemistry, which allows the design of complex structures targeted for specific applications. However, their weak interaction with external stimuli makes it difficult to access their state at the single-molecule level, a fundamental tool for their use, for example, in quantum computing and sensing. Here, an innovative solution exploiting the interplay between chirality and magnetism using the chirality-induced spin selectivity effect on electron transfer processes is foreseen. It is envisioned to use a spin-to-charge conversion mechanism that can be realized by connecting a molecular spin qubit to a dyad where an electron donor and an electron acceptor are linked by a chiral bridge. By numerical simulations based on realistic parameters, it is shown that the chirality-induced spin selectivity effect could enable initialization, manipulation, and single-spin readout of molecular qubits and qudits even at relatively high temperatures.

VdW Mediated Strong Magnetic Exchange Interactions in Chains of Hydrogen-Free Sublimable Molecular Qubits.

Sulfur-rich molecular complexes of dithiolene-like ligands are appealing candidates as molecular spin qubits because spin coherence properties are enhanced in hydrogen-free environments. Herein, we employ the hydrogen-free mononegative 1,3,2-dithiazole-4-thione-5-thiolate (dttt-) ligand as an alternative to common dinegative dithiolate ligands. We report the first synthesis and structural characterization of its Cu2+, Ni2+, and Pt2+ neutral complexes. The XPS analysis of thermal deposition of [Cu(dttt)2] in UHV conditions indicates that films of intact molecules can be deposited on surfaces by sublimation. Thanks to a combined approach employing DC magnetometry and DFT calculations, we highlighted AF exchange interactions of 108 cm-1 and 36 cm-1 attributed to the two different polymorph phases. These couplings are exclusively mediated by S···S VdW interactions, which are facilitated by the absence of counterions and made particularly efficient by the diffuse electron density on S atoms. Furthermore, the spin dynamics of solid-state magnetically diluted samples was investigated. The longest observed T m is 2.3 µs at 30 K, which significantly diverges from the predicted T m > 100 µs. These results point to the diluting matrix severely affecting the coherence lifetime of Cu2+ species via different factors, such as the contributions of neighboring 14N nuclei and the formation of radical impurities in a non-completely controllable way. However, the ease of processing [Cu(dttt)2] via thermal sublimation can allow dispersion in matrices better suited for coherent spin manipulation of isolated molecules and the realization of AF-coupled VdW structures on surfaces.

Direct detection of spin polarization in photoinduced charge transfer through a chiral bridge.

It is well assessed that the charge transport through a chiral potential barrier can result in spin-polarized charges. The possibility of driving this process through visible photons holds tremendous potential for several aspects of quantum information science, e.g., the optical control and readout of qubits. In this context, the direct observation of this phenomenon via spin-sensitive spectroscopies is of utmost importance to establish future guidelines to control photo-driven spin selectivity in chiral structures. Here, we provide direct proof that time-resolved electron paramagnetic resonance (EPR) can be used to detect long-lived spin polarization generated by photoinduced charge transfer through a chiral bridge. We propose a system comprising CdSe quantum dots (QDs), as a donor, and C60, as an acceptor, covalently linked through a saturated oligopeptide helical bridge (χ) with a rigid structure of ∼10 Å. Time-resolved EPR spectroscopy shows that the charge transfer in our system results in a C60 radical anion, whose spin polarization maximum is observed at longer times with respect to that of the photogenerated C60 triplet state. Notably, the theoretical modelling of the EPR spectra reveals that the observed features may be compatible with chirality-induced spin selectivity, but the electronic features of the QD do not allow the unambiguous identification of the CISS effect. Nevertheless, we identify which parameters need optimization for unambiguous detection and quantification of the phenomenon. This work lays the basis for the optical generation and direct manipulation of spin polarization induced by chirality.

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.

Magnetic molecules as local sensors of topological hysteresis of superconductors.

Superconductors and magnetic materials, including molecules, are key ingredients for quantum computing and spintronics. However, only a little is known about how these materials interact in multilayer nanostructures like the hybrid architectures nowadays under development for such advanced applications. Here, we show that a single layer of magnetic molecules, Terbium(III) bis-phthalocyaninato (TbPc2) complexes, deposited under controlled UHV conditions on a superconducting Pb(111) surface is sensitive to the topology of the intermediate state of the superconductor, namely to the presence and evolution of superconducting and normal domains due to screening and penetration of an external magnetic field. The topological hysteresis of the superconducting substrate imprints a local evolution of the magnetisation of the TbPc2 molecules in the monolayer. Element and surface selective detection is achieved by recording the X-ray magnetic circular dichroism of the Tb atoms. This study reveals the impressive potential of magnetic molecules for sensing local magnetic field variations in molecular/superconductor hybrid devices, including spin resonators or spin injecting and spin filtering components for spintronics applications.

A dysprosium single molecule magnet outperforming current pseudocontact shift agents.

A common criterion for designing performant single molecule magnets and pseudocontact shift tags is a large magnetic anisotropy. In this article we present a dysprosium complex chemically designed to exhibit strong easy-axis type magnetic anisotropy that is preserved in dichloromethane solution at room temperature. Our detailed theoretical and experimental studies on the magnetic properties allowed explaining several features typical of highly performant SMMs. Moreover, the NMR characterization shows remarkably large chemical shifts, outperforming the current state-of-the art PCS tags.

An exchange coupled meso-meso linked vanadyl porphyrin dimer for quantum information processing.

We report here the synthesis of a new meso-meso (m-m) singly linked vanadyl-porphyrin dimer that crystallizes in two different pseudo-polymorphs. The single crystal continuous-wave electron paramagnetic resonance investigation evidences a small but crucial isotropic exchange interaction, J, between the two tilted, and thus distinguishable, spin centers of the order of 10-2 cm-1. The experimental and DFT studies evidence a correlation between J values and porphyrin plane tilting angle and distortion. Pulsed EPR analysis shows that the two vanadyl dimers maintain the coherence time of the monomer. With the obtained spin Hamiltonian parameters, we identify suitable transitions that could be used as computational basis states. Our results, coupled with the evaporability of porphyrin systems, establish this class of dimers as extremely promising for quantum information processing applications.

Correction: An exchange coupled meso-meso linked vanadyl porphyrin dimer for quantum information processing.

[This corrects the article DOI: 10.1039/D2SC04969D.].

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.

Quantum-coherent nanoscience.

For the past three decades nanoscience has widely affected many areas in physics, chemistry and engineering, and has led to numerous fundamental discoveries, as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing, has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this Review according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system, such as charge, spin, mechanical motion and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations.

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.

Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla.

We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds a nuclear spin 7/2 coupled to an electronic spin 1/2 by hyperfine interaction. This qubit-qudit unit can be exploited to implement quantum error correction and quantum simulation algorithms. Through a combined theoretical and broadband nuclear magnetic resonance study, we demonstrate that the elementary operations of such algorithms can be efficiently implemented on the nuclear spin qudit. Manipulation of the nuclear qudit can be achieved by resonant radio-frequency pulses, thanks to the remarkably long coherence times and the effective quadrupolar coupling induced by the strong hyperfine interaction. This approach may open new perspectives for developing new molecular qubit-qudit systems.

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.

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.

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.