Matrix effects on the magnetic properties of a molecular spin triangle embedded in a polymeric film.

Molecular triangles with competing Heisenberg interactions and significant Dzyaloshinskii-Moriya interactions (DMI) exhibit high environmental sensitivity, making them potential candidates for active elements for quantum sensing. Additionally, these triangles exhibit magnetoelectric coupling, allowing their properties to be controlled using electric fields. However, the manipulation and deposition of such complexes pose significant challenges. This work explores a solution by embedding iron-based molecular triangles in a polymer matrix, a strategy that offers various deposition methods. We investigate how the host matrix alters the magnetic properties of the molecular triangle, with specific focus on the magnetic anisotropy, aiming to advance its practical applications as quantum sensors.

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

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

Modular Approach to Creating Functionalized Surface Arrays of Molecular Qubits.

The quest for developing quantum technologies is driven by the promise of exponentially faster computations, ultrahigh performance sensing, and achieving thorough understanding of many-particle quantum systems. Molecular spins are excellent qubit candidates because they feature long coherence times, are widely tunable through chemical synthesis, and can be interfaced with other quantum platforms such as superconducting qubits. A present challenge for molecular spin qubits is their integration in quantum devices, which requires arranging them in thin films or monolayers on surfaces. However, clear proof of the survival of quantum properties of molecular qubits on surfaces has not been reported so far. Furthermore, little is known about the change in spin dynamics of molecular qubits going from the bulk to monolayers. Here, a versatile bottom-up method is reported to arrange molecular qubits as functional groups of self-assembled monolayers (SAMs) on surfaces, combining molecular self-organization and click chemistry. Coherence times of up to 13 µs demonstrate that qubit properties are maintained or even enhanced in the monolayer.

A mesoionic carbene complex of manganese in five oxidation states.

Reaction between a carbazole-based mesoionic carbene ligand and manganese(II) iodide results in the formation of a rare air-stable manganese(IV) complex after aerobic workup. Cyclic voltammetry reveals the complex to be stable in five oxidation states. The electronic structure of all five oxidation states is elucidated chemically, spectroscopically (NMR, high-frequency EPR, UV-Vis, MCD), magnetically, and computationally (DFT, CASSCF).

Plasmonic Metasurface Resonators to Enhance Terahertz Magnetic Fields for High-Frequency Electron Paramagnetic Resonance.

Nanoscale magnetic systems play a decisive role in areas ranging from biology to spintronics. Although, in principle, THz electron paramagnetic resonance (EPR) provides high-resolution access to their properties, lack of sensitivity has precluded realizing this potential. To resolve this issue, the principle of plasmonic enhancement of electromagnetic fields that is used in electric dipole spectroscopies with great success is exploited, and a new type of resonators for the enhancement of THz magnetic fields in a microscopic volume is proposed. A resonator composed of an array of diabolo antennas with a back-reflecting mirror is designed and fabricated. Simulations and THz EPR measurements demonstrate a 30-fold signal increase for thin film samples. This enhancement factor increases to a theoretical value of 7500 for samples confined to the active region of the antennas. These findings open the door to the elucidation of fundamental processes in nanoscale samples, including junctions in spintronic devices or biological membranes.

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.

Single-Ion Anisotropy and Intramolecular Interactions in CeIII and NdIII Dimers.

This article reports the syntheses, characterization, structural description, together with magnetic and spectroscopic properties of two isostructural molecular magnets based on the chiral ligand N,N'-bis((1,2-diphenyl-(pyridine-2-yl)methylene)-(R,R/S,S)-ethane-1,2-diamine), L1, of general formula [Ln2(RR-L1)2(Cl6)]·MeOH·1.5H2O, (Ln = Ce (1) or Nd (2)). Multifrequency electron paramagnetic resonance (EPR), cantilever torque magnetometry (CTM) measurements, and ab initio calculations allowed us to determine single-ion magnetic anisotropy and intramolecular magnetic interactions in both compounds, evidencing a more important role of the anisotropic exchange for the NdIII derivative. The comparison of experimental and theoretical data indicates that, in the case of largely rhombic lanthanide ions, ab initio calculations can fail in determining the orientation of the weakest components, while being reliable in determining their principal values. However, they remain of paramount importance to set the analysis of EPR and CTM on sound basis, thus obtaining a very precise picture of the magnetic interactions in these systems. Finally, the electronic structure of the two complexes, as obtained by this approach, is consistent with the absence of zero-field slow relaxation observed in ac susceptibility.

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.

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.

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.

Isotope effects on the spin dynamics of single-molecule magnets probed using muon spin spectroscopy.

Muon spin relaxation (µSR) experiments on a single-molecule magnet enriched in different Dy isotopes detect unambiguously the slowing down of the zero field spin dynamics for the non-magnetic isotope. This occurs in the low temperature regime dominated by quantum tunnelling, in agreement with previous ac susceptibility investigations. In contrast to the latter, however, µSR is sensitive to all fluctuation modes affecting the lifetime of the spin levels.

A Pseudo-Octahedral Cobalt(II) Complex with Bispyrazolylpyridine Ligands Acting as a Zero-Field Single-Molecule Magnet with Easy Axis Anisotropy.

The homoleptic mononuclear compound [Co(bpp-COOMe)2 ](ClO4 )2  (1) (bpp-COOMe=methyl 2,6-di(pyrazol-1-yl)pyridine-4-carboxylate) crystallizes in the monoclinic C2/c space group, and the cobalt(II) ion possesses a pseudo-octahedral environment given by the two mer-coordinated tridentate ligands. Direct-current magnetic data, single-crystal torque magnetometry, and EPR measurements disclosed the easy-axis nature of this cobalt(II) complex, which shows single-molecule magnet behavior when a static field is applied in alternating-current susceptibility measurements. Diamagnetic dilution in the zinc(II) analogue [Zn(bpp-COOMe)2 ](ClO4 )2  (2) afforded the derivative [Zn0.95 Co0.05 (bpp-COOMe)2 ](ClO4 )2  (3), which exhibits slow relaxation of magnetization even in zero field thanks to the reduction of dipolar interactions. Theoretical calculations confirmed the overall electronic structure and the magnetic scenario of the compound as drawn by experimental data, thus confirming the spin-phonon Raman relaxation mechanism, and a direct quantum tunneling in the ground state as the most plausible relaxation pathway in zero field.

Structural Effects on the Spin Dynamics of Potential Molecular Qubits.

Control of spin-lattice magnetic relaxation is crucial to observe long quantum coherence in spin systems at reasonable temperatures. Such a control is most often extremely difficult to achieve, because of the coexistence of several relaxation mechanisms, that is direct, Raman, and Orbach. These are not always easy to relate to the energy states of the investigated system, because of the contribution to the relaxation of additional spin-phonon coupling phenomena mediated by intramolecular vibrations. In this work, we have investigated the effect of slight changes on the molecular structure of four vanadium(IV)-based potential spin qubits on their spin dynamics, studied by alternate current (AC) susceptometry. The analysis of the magnetic field dependence of the relaxation time correlates well with the low-energy vibrational modes experimentally detected by time-domain THz spectroscopy. This confirms and extends our preliminary observations on the role played by spin-vibration coupling in determining the fine structure of the spin-lattice relaxation time as a function of the magnetic field, for S = 1/2 potential spin qubits. This study represents a step forward in the use of low-energy vibrational spectroscopy as a prediction tool for the design of molecular spin qubits with long-lived quantum coherence. Indeed, quantum coherence times of ca. 4.0-6.0 µs in the 4-100 K range are observed for the best performing vanadyl derivatives identified through this multitechnique approach.

Spin Dynamics and Low Energy Vibrations: Insights from Vanadyl-Based Potential Molecular Qubits.

Here we report the investigation of the magnetization dynamics of a vanadyl complex with diethyldithiocarbamate (Et2dtc-) ligands, namely [VO(Et2dtc)2] (1), in both solid-state and frozen solution. This showed an anomalous and unprecedentedly observed field dependence of the relaxation time, which was modeled with three contributions to the relaxation mechanism. The temperature dependence of the weight of the two processes dominating at low fields was found to well correlate with the low energy vibrations as determined by THz spectroscopy. This detailed experimental comparative study represents a fundamental step to understand the spin dynamics of potential molecular quantum bits, and enriches the guidelines to design molecule-based systems with enhanced quantum coherence.

Quantum Coherence Times Enhancement in Vanadium(IV)-based Potential Molecular Qubits: the Key Role of the Vanadyl Moiety.

In the search for long-lived quantum coherence in spin systems, vanadium(IV) complexes have shown record phase memory times among molecular systems. When nuclear spin-free ligands are employed, vanadium(IV) complexes can show at low temperature sufficiently long quantum coherence times, Tm, to perform quantum operations, but their use in real devices operating at room temperature is still hampered by the rapid decrease of T1 caused by the efficient spin-phonon coupling. In this work we have investigated the effect of different coordination environments on the magnetization dynamics and the quantum coherence of two vanadium(IV)-based potential molecular spin qubits in the solid state by introducing a unique structural difference, i.e., an oxovanadium(IV) in a square pyramidal versus a vanadium(IV) in an octahedral environment featuring the same coordinating ligand, namely, the 1,3-dithiole-2-thione-4,5-dithiolate. This investigation, performed by a combined approach of alternate current (ac) susceptibility measurements and continuous wave (CW) and pulsed electron paramagnetic resonance (EPR) spectroscopies revealed that the effectiveness of the vanadyl moiety in enhancing quantum coherence up to room temperature is related to a less effective mechanism of spin-lattice relaxation that can be quantitatively evaluated by the exponent n (ca. 3) of the temperature dependence of the relaxation rate. A more rapid collapse is observed for the non-oxo counterpart (n = 4) hampering the observation of quantum coherence at room temperature. Record coherence time at room temperature (1.04 µs) and Rabi oscillations are also observed for the vanadyl derivative in a very high concentrated material (5 ± 1%) as a result of the additional benefit provided by the use of a nuclear spin-free ligand.

Spin Helicity in Chiral Lanthanide Chains.

We report here the determination of the helical spin structure of three Ln-based chiral chains of the formula [Ln(Hnic)(nic)2(NO3)]n (Hnic = nicotinic acid; Ln = Tb, Dy, and Er) by means of cantilever torque magnetometry. While the Dy and Er derivatives are strongly axial (easy-axis and easy-plane anisotropy, respectively), the Tb derivative is characterized by a remarkable rhombicity. In agreement with these findings, alternating-current susceptibility reveals slow magnetic relaxation only in the Dy derivative. Dilution of DyIII ions in the diamagnetic Y-based analogue shows that the weak ferromagnetic intrachain interactions do not contribute significantly to the energy barrier for the reversal of magnetization, which is better described as a single-ion process. Single crystals of the two enantiomers of the Dy derivative have also been investigated using hard X-ray synchrotron radiation at the L-edge of the metal revealing optical activity although with negligible involvement of the 4f electrons of the DyIII ion.

Room-Temperature Quantum Coherence and Rabi Oscillations in Vanadyl Phthalocyanine: Toward Multifunctional Molecular Spin Qubits.

Here we report the investigation of the magnetic relaxation and the quantum coherence of vanadyl phthalocyanine, VOPc, a multifunctional and easy-processable potential molecular spin qubit. VOPc in its pure form (1) and its crystalline dispersions in the isostructural diamagnetic host TiOPc in different stoichiometric ratios, namely VOPc:TiOPc 1:10 (2) and 1:1000 (3), were investigated via a multitechnique approach based on the combination of alternate current (AC) susceptometry, continuous wave, and pulsed electron paramagnetic resonance (EPR) spectroscopy. AC susceptibility measurements revealed a linear increase of the relaxation rate with temperature up to 20 K, as expected for a direct mechanism, but τ remains slow over a very wide range of applied static field values (up to ∼5 T). Pulsed EPR spectroscopy experiments on 3 revealed quantum coherence up to room temperature with T(m) ∼1 µs at 300 K, representing the highest value obtained to date for molecular electronic spin qubits. Rabi oscillations are observed in this nuclear spin-active environment ((1)H and (14)N nuclei) at room temperature also for 2, indicating an outstanding robustness of the quantum coherence in this molecular semiconductor exploitable in spintronic devices.

Quantum coherence in a processable vanadyl complex: new tools for the search of molecular spin qubits.

Electronic spins in different environments are currently investigated as potential qubits, i.e. the logic units of quantum computers. These have to retain memory of their quantum state for a sufficiently long time (phase memory time, Tm) allowing quantum operations to be performed. For molecular based spin qubits, strategies to increase phase coherence by removing nuclear spins are rather well developed, but it is now crucial to address the problem of the rapid increase of the spin-lattice relaxation rate, T1-1, with increasing temperature that hampers their use at room-temperature. Herein, thanks to the combination of pulsed EPR spectroscopy and AC susceptometry we evidence that an evaporable vanadyl complex of formula VO(dpm)2, where dpm- is the anion of dipivaloylmethane, presents a combination of very promising features for potential application as molecular spin-qubit. The spin-lattice relaxation time, T1, studied in detail through AC susceptometry, decreases slowly with increasing temperature and, more surprisingly, it is not accelerated by the application of an external field up to several Teslas. State-of-the art phase memory times for molecular spin systems in protiated environment are detected by pulsed EPR also in moderate dilution, with values of 2.7 µs at 5 K and 2.1 µs at 80 K. Low temperature scanning tunnel microscopy and X-ray photoelectron spectroscopy in situ investigations reveal that intact molecules sublimated in ultra-high vacuum spontaneously form an ordered monolayer on Au(111), opening the perspective of electric access to the quantum memory of ensembles of spin qubits that can be scaled down to the single molecule.