Spin coherence and magnetization dynamics of TMA2[KCo1-xFex(CN)6] toward coordination-framework spin qubits

Metal compounds with S = 1/2 coordination-frameworks have been emerging as new powerful qubit candidates. In this study, we have reported the CN-based coordination framework TMA2[KCo1-xFex(CN)6] to be a qubit. We explored the magnetization dynamics and spin coherence of the magnetic dilution of the S = 1/2 Fe(III) complex TMA2[KFe(CN)6] (TMA = tetramethylammonium) in its Co(III)-based diamagnetic analogue TMA2[KCo(CN)6]. Alternating-current (AC) susceptibility data illustrate a slow magnetic relaxation upon applying a field of 0.1 T, which follows the phonon-bottleneck relaxation mechanism along with the Raman process. A magnetic relaxation time (τ) of 0.3 s (2% Fe) was realized at 1.8 K. Moreover, pulsed EPR data reveal a coherence duration of 1 μs (0.1% Fe) at 4 K with successful observation of Rabi oscillation at 4 K and 13 K (2% Fe) using MW pulses with variable irradiation-field strengths. The overall results indicate that TMA2[KCo1-xFex(CN)6] represents a promising qubit candidate, as it is capable of being placed in any superposition of the two distinct Ms states (Ms = +1/2 and Ms = -1/2).

Trityl-Based Lanthanide-Supramolecular Assemblies Exhibiting Slow Magnetic Relaxation

The triphenylmethane (trityl) group has been recognized as a supramolecular synthon in crystal engineering, molecular machine rotors and stereochemical chirality inductors in materials science. Herein we demonstrate for the first time how it can be utilized in the domain of molecular magnetic materials through shaping of single molecule magnet (SMM) properties within the lanthanide complexes in tandem with other non-covalent interactions. Trityl-appended mono- (HL1 ) and bis-compartmental (HL2 ) hydrazone ligands were synthesized and complexated with Dy(III) and Er(III) triflate and nitrate salts to generate four monometallic (1-4) and two bimetallic (5, 6) complexes. The static and dynamic magnetic properties of 1-6 were investigated, revealing that only ligand HL1 induces assemblies (1-4) capable of showing SMM behaviour, with Dy(III) congeners (1, 2) able to exhibit the phenomenon also under zero field conditions. Theoretical ab initio studies helped in determination of Dy(III) energetic levels, magnetic anisotropic axes and corroborated magnetic relaxation mechanisms to be a combination of Raman and quantum tunnelling in zero dc field, the latter being cancelled in the optimum non-zero dc field. Our work represents the first study of magneto-structural correlations within the trityl Ln-SMMs, leading to generation of slowly relaxing zero-field dysprosium complexes within the hydrogen-bonded assemblies.

Tailored Lewis Acid Sites for High-Temperature Supported Single-Molecule Magnetism

Generating or even retaining slow magnetic relaxation in surface immobilized single-molecule magnets (SMMs) from promising molecular precursors remains a great challenge. Illustrative examples are organolanthanide compounds that show promising SMM properties in molecular systems, though surface immobilization generally diminishes their magnetic performance. Here, we show how tailored Lewis acidic Al(III) sites on a silica surface enable generation of a material with SMM characteristics via chemisorption of (Cp^ttt)₂DyCl ((Cp^ttt)^- = 1,2,4-tri(tert-butyl)-cyclopentadienide). Detailed studies of this system and its diamagnetic Y analogue indicate that the interaction of the metal chloride with surface Al sites results in a change of the coordination sphere around the metal center inducing for the dysprosium-containing material slow magnetic relaxation up to 51 K with hysteresis up to 8 K and an effective energy barrier (U_eff) of 449 cm^-1, the highest reported thus far for a supported SMM.

Unveiling the Decisive Factor for the Sharp Transition in the Scanning Tunneling Spectroscopy of a Single Nickelocene Molecule

Scanning tunneling microscopy (STM) has been utilized to realize the precise measurement and control of local spin states. Experiments have demonstrated that when a nickelocene (Nc) molecule is attached to the apex of an STM tip, the dI/dV spectra exhibit a sharp or a smooth transition when the tip is displaced toward the substrate. However, what leads to the two distinct types of transitions remains unclear, and more intriguingly, the physical origin of the abrupt change in the line shape of dI/dV spectra remains unclear. To clarify these intriguing issues, we perform first-principles-based simulations on the STM tip control process for the Cu tip/Nc/Cu(100) junction. In particular, we find that the suddenly enhanced hybridization between the d orbitals on the Ni ion and the metallic bands in the substrate leads to Kondo correlation overwhelming spin excitation, which is the main cause of the sharp transition in the dI/dV spectra observed experimentally.

Magneto-thermal properties and slow magnetic relaxation in Mn(II)Ln(III) complexes: influence of magnetic coupling on the magneto-caloric effect

A family of Mn(II)Ln(III) dinuclear and tetranuclear complexes (Ln = Gd and Dy) has been prepared from the compartmental ligands N,N'-dimethyl-N,N'-bis(2-hydroxy-3-formyl-5-bromobenzyl)ethylenediamine (H₂L¹) and N,N',N''-trimethyl-N,N''-bis(2-hydroxy-3-methoxy-5-methylbenzyl)diethylenetriamine (H₂L²). The Mn(II)Gd(III) complexes exhibit antiferromagnetic interactions between Mn(II) and Gd(III) ions in most cases, which are supported by Density Functional Theory (DFT) calculations. Experimental magneto-structural correlations carried out for the reported complexes and other related complexes found in bibliography show that the highest ferromagnetic coupling constants are observed in di-μ-phenoxido bridged complexes, which is due to the planarity of the Mn-(μ-O)₂-Gd bridging fragment and to the high Mn-O-Gd angles. The effect of these angles has been studied by DFT calculations performed on a di-μ-phenoxido doubly bridged model. The magneto-thermal properties of the Mn(II)Gd(III) based complexes have also been measured, concluding that the magnitude of the Magneto-Caloric Effect (MCE) is due to the strength rather than to the nature of the magnetic coupling. Moreover, when two Mn(II)Gd(III) dinuclear units are connected by two carbonato-bridging ligands the MCE is enhanced, obtaining a maximum magnetic entropy change of 36.4 Jkg^-1 K^-1 at ΔB = 7 T and T = 2.2 K. On the other hand, one of the dinuclear Mn(II)Dy(III) complexes displays Single-Molecule Magnet (SMM) behaviour with an energy barrier of 14.8 K under an applied external field of 1000 Oe.

Understanding the effect of structural changes on slow magnetic relaxation in mononuclear octahedral copper(II) complexes

Current advances in molecular magnetism are aimed at the construction of molecular nanomagnets and spin qubits for their utilization as high-density data storage materials and quantum computers. Mononuclear coordination compounds with low spin values of S = ½ are excellent candidates for this endeavour, but knowledge of their construction via rational design is limited. This particularly applies to the single copper(II) spin center, having been only recently demonstrated to exhibit slow relaxation of magnetisation in the appropriate octahedral environment. We have thus prepared a unique organic scaffold that would allow one to gain in-depth insight into how purposeful structural differences affect the slow magnetic relaxation in monometallic, transition metal complexes. As a proof-of-principle, we demonstrate how one can construct two, structurally very similar complexes with isolated Cu(II) ions in an octahedral ligand environment, the magnetic properties of which differ significantly. The differences in structural symmetry effects and in magnetic relaxation are corroborated with a series of experimental techniques and theoretical approaches, showing how symmetry distortions and crystal packing affect the relaxation behaviour in these isolated Cu(II) systems. Our unique organic platform can be efficiently utilized for the construction of various transition-metal ion systems in the future, effectively providing a model system for investigation of magnetic relaxation via targeted structural distortions.

Engineering Periodic Dinuclear Lanthanide-Directed Networks Featuring Tunable Energy Level Alignment and Magnetic Anisotropy by Metal Exchange

The design of lanthanide multinuclear networks is an emerging field of research due to the potential of such materials for nanomagnetism, spintronics, and quantum information. Therefore, controlling their electronic and magnetic properties is of paramount importance to tailor the envisioned functionalities. In this work, a multidisciplinary study is presented combining scanning tunneling microscopy, scanning tunneling spectroscopy, X-ray absorption spectroscopy, X-ray linear dichroism, X-ray magnetic circular dichroism, density functional theory, and multiplet calculations, about the supramolecular assembly, electronic and magnetic properties of periodic dinuclear 2D networks based on lanthanide-pyridyl interactions on Au(111). Er- and Dy-directed assemblies feature identical structural architectures stabilized by metal-organic coordination. Notably, despite exhibiting the same +3 oxidation state, there is a shift of the energy level alignment of the unoccupied molecular orbitals between Er- and Dy-directed networks. In addition, there is a reorientation of the easy axis of magnetization and an increment of the magnetic anisotropy when the metallic center is changed from Er to Dy. Thus, the results show that it is feasible to tune the energy level alignment and magnetic anisotropy of a lanthanide-based metal-organic architecture by metal exchange, while preserving the network design.

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.

Leveraging Surface Siloxide Electronics to Enhance the Relaxation Properties of a Single-Molecule Magnet

Single-molecule magnets (SMMs) hold promise for unmatched information storage density as well as for applications in quantum computing and spintronics. To date, the most successful SMMs have been organometallic lanthanide complexes. However, their surface immobilization, one of the requirements for device fabrication and commercial application, remains challenging due to the sensitivity of the magnetic properties to small changes in the electronic structure of the parent SMM. Thus, finding controlled approaches to SMM surface deposition is a timely challenge. In this contribution we apply the concept of isolobality to identify siloxides present at the surface of partially dehydroxylated silica as a suitable replacement for archetypal ligand architectures in organometallic SMMs. We demonstrate theoretically and experimentally that isolated siloxide anchoring sites not only enable successful immobilization but also lead to a 2 orders of magnitude increase in magnetization relaxation times.

Tb-based silicate apatites showing slow magnetization relaxation with identical parameters for the Tb3+ and Dy3+ counter ions

Tb-diluted and Tb-rich apatite-type silicates with compositions Y7.75Tb0.25Ca2(SiO4)6O2 and Tb8Ca2(SiO4)6O2, respectively, exhibit field induced multiple slow relaxation of magnetization. The former reveals two slow relaxation paths, the latter only one with a longer relaxation time of several seconds. The relaxation features of the Tb-diluted one are comparable with those of analogue compounds, where Tb is replaced by Dy, as well as with those of a Tb-doped calcium phosphate apatite. The relaxation parameters of the Tb-rich compound virtually match those of the Dy-based analogue Dy8Ca2(SiO4)6O2. The latter represents the first instance of independence of magnetization relaxation on the nature of a paramagnetic rare-earth metal ion in single ion magnet like materials.

Hard X-ray magnetochiral dichroism in a paramagnetic molecular 4f complex

Magnetochiral dichroism (MΧD) originates in the coupling of local electric fields and magnetic moments in systems where a simultaneous break of space parity and time-reversal symmetries occurs. This magnetoelectric coupling, displayed by chiral magnetic materials, can be exploited to manipulate the magnetic moment of molecular materials at the single molecule level. We demonstrate herein the first experimental observation of X-ray magnetochiral dichroism in enantiopure chiral trigonal single crystals of a chiral mononuclear paramagnetic lanthanide coordination complex, namely, holmium oxydiacetate, at the Ho L₃-edge. The observed magnetochiral effect is opposite for the two enantiomers and is rationalised on the basis of a multipolar expansion of the matter–radiation interaction. These results demonstrate that 4f–5d hybridization in chiral lanthanoid coordination complexes is at the origin of magnetochiral dichroism, an effect that could be exploited for addressing of their magnetic moment at the single molecule level.

Magnetochiral Dichroism of chiral mononuclear lanthanoid complexes is for the first time detected by X-ray absorption measurements on single crystals of Holmium oxydiacetate, at the Ho L₃-edge. The effect is of opposite sign for the two enantiomers.

All-Inorganic Single-Ion Magnets in Ceramic Matrices

All-inorganic single-ion magnets representing paramagnetic ions incorporated in a crystalline diamagnetic matrix are reviewed. Key results and advantages of this approach in comparison with the common strategy based on molecular metal-organic complexes are considered, and some unsolved problems and future perspectives are discussed.

Slow magnetic relaxation in hexacoordinated cobalt(ii) field-induced single-ion magnets

To gain an insight into the factors affecting the enhancement of the energy barrier in SMM/SIM, hexacoordinate pseudohalide Co(ii) complexes based on the tridentate ligand were investigated.

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

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

Molecular spins for quantum computation

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

Hybrid organic–inorganic mononuclear lanthanoid single ion magnets

The plasticity of the coordination chemistry of lanthanoid ions has allowed the design and synthesis for the first time of a family of mononuclear hybrid organic–inorganic lanthanoid complexes with slow relaxation of the magnetization.

Exploring High-Symmetry Lanthanide-Functionalized Polyoxopalladates as Building Blocks for Quantum Computing

The structural, electronic, and magnetochemical properties of the star-shaped polyoxopalladate [Pd15O10(SeO3)10]10− (POPd) and its lanthanide-functionalized derivatives have been investigated on the basis of density functional theory, followed by a ligand field analysis using the Radial Effective Charge (REC) model. Our study predicts that heteroPOPd is a robust cryptand that enforces D5h symmetry around the encapsulated Ln3+ centers. This rigid coordination environment favors an interesting potential magnetic behavior in the Er and Ho derivatives, and the presence of a cavity in the structure suggests an effective insulation of the electronic system from the lattice phonons, which may be of interest for molecular spintronics and quantum computing applications.

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.

Vanadyl dithiolate single molecule transistors: the next spintronic frontier?

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

Abrupt Switching of Crystal Fields during Formation of Molecular Contacts

Magnetic molecules have the potential to be used as building blocks for bits in quantum computers. The spin states of the magnetic ion in the molecule can be represented by the effective spin Hamiltonian describing the zero field splitting (ZFS) of the magnetic states. We determined the ZFS of mechanically flexible metal-chelate molecules (Co, Ni, and Cu as metal ions) adsorbed on Cu₂N/Cu(100) by inelastic tunneling spectroscopy at temperatures down to 30 mK. When moving the tip toward the molecule, the tunneling current abruptly jumps to higher values, indicating the sudden deformation of the molecule bridging the tunneling junction. Hand in hand with the formation of the contact, an abrupt change of the ZFS occurs. This work also implies that ZFS expected in mechanical break junctions can drastically deviate from that of adsorbed molecules probed by other techniques.

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.

Lanthanide-Directed Assembly of Interfacial Coordination Architectures-From Complex Networks to Functional Nanosystems

Metallo-supramolecular engineering on surfaces provides a powerful strategy toward low-dimensional coordination architectures with prospects for several application fields. To date, most efforts have relied on transition metal centers, and only recently did we pioneer lanthanide-directed assembly. Coordination spheres and motifs with rare-earth elements generally display distinct properties and structural features. The size of the cations and shielding role of the 4f orbitals induces high coordination numbers, frequently entailing flexible coordination geometries. Following Pearson's hard and soft acid-base theory, lanthanide cations are hard Lewis acids and thus feature strong affinity for nitrile, terpyridine, and carboxylate donor moieties. The prevailing oxidation state is +3, although in certain compounds stable +2 or +4 cations occur. The chemistry of rare-earth elements is currently receiving widespread attention, as they are key ingredients for established and emerging 21st century science and technology with relevance for energy conversion, sensing, catalysis, magnetism, photonics, telecommunications, superconductivity, biomedicine, and quantum engineering. In this Account, we review recent advances toward the design of interfacial supramolecular nanoarchitectures incorporating lanthanide centers. We apply controlled ultrahigh vacuum conditions whereby atomistically clean substrates are prepared and exposed to ultrapure atomic and molecular beams of the chosen sublimable constituents. We focus on direct molecular-level investigations and in situ assembly operative close to equilibrium conditions. Our scanning probe microscopy techniques provide atomistic insights regarding the formation, stability, and manipulability of metal-organic compounds and networks. In order to gain deeper insights into the experimental findings, complementary computational analysis of bond characteristics, electronic properties, and coordination motifs has been performed for several case studies. Exemplary elements under consideration include cerium, gadolinium, dysprosium, and europium. By the use of ditopic molecular linkers equipped with carbonitrile moieties, adaptive coordination spheres are unveiled, yielding vertices with two- to sixfold symmetry. The respective coordination nodes underlie the expression of complex networks, such as semiregular Archimedean tessellations for cerium- or gadolinium-directed assemblies and random-tiling quasicrystalline characteristics for europium. Tunability via constituent stoichiometry regulation is revealed for bimolecular arrangements embedding europium centers, simultaneously connecting to carbonitrile and terypyridine ligands. Ditopic carboxylate linkers yield robust reticular networks based on a lateral coordination number of 8 for either gadolinium or dysprosium complexation, featuring a prevalent ionic nature of the coordination bond. Orthogonal insertion protocols give rise to d-f reticular architectures exploiting macrocyclic tetradentate cobalt complexation and peripheral carbonitrile-gadolinium coordination, respectively. Furthermore, lanthanides may afford metalation of adsorbed free-base tetrapyrrole species and can be engaged for interfacial synthesis of sandwich compounds, thus providing prospects for columnar design of coordination architectures. Finally, direct manipulation experiments achieved lateral displacement of single supramolecules and molecular rotation of sandwich or other molecular units. These findings evidence prospects for advancing molecular machinery components. The presented accomplishements herald further advancements in metallo-supramolecular design on surfaces, with versatile nanosystems and architectures emanating from the flexible coordination spheres. The embedding and systematic rationalization of lanthanide centers in tailored interfacial environments are keys to establishing relations between structure and physicochemical characteristics toward the generation of novel functionalities with technological significance.

New field-induced single ion magnets based on prolate Er(iii) and Yb(iii) ions: tuning the energy barrierUeffby the choice of counterions within an N3-tridentate Schiff-base scaffold

Counterions modulate the structure and magnetic properties of rarely observed high-coordinate SIM species.