The Rise of Single-Ion Magnets as Spin Qubits

Fault-tolerant computing with single-qudit encoding in a molecular spin

We show that molecular spins represent ideal materials to realize a fault-tolerant quantum computer, in which all quantum operations include protection against leading (dephasing) errors. This is achieved by pursuing a qudit approach, in which logical error-corrected qubits are encoded in a single multi-level molecule (a qudit) and not in a large collection of two-level systems, as in standard codes. By preventing such an explosion of resources, this emerging way of thinking about quantum error correction makes its actual implementation using molecular spins much closer. We show how to perform all quantum computing operations (logical gates, corrections and measurements) without propagating errors. We achieve a quasi-exponential error correction with only linear qudit size growth, i.e. a higher efficiency than the standard approach based on stabilizer codes and concatenation.

Levamisole Based Co(II) Single-Ion Magnet

A new Co(II) complex, [Co(NCS)2(L)2] (1) has been synthesized based on levamisole (L) as a new ligand. Single-crystal X-ray diffraction analyses confirm that the Co(II) ion is having a distorted tetrahedral coordination geometry in the complex. Notably strong intramolecular S⋅⋅⋅S and S⋅⋅⋅N interactions has been confirmed by employing Quantum Theory of Atoms in Molecules (QTAIM). These intramolecular interactions occur among the sulfur and nitrogen atoms of the levamisole ligands and also the nitrogen atoms of the thiocyanate. Direct current (dc) magnetic analyses reveal presence of zero field splitting (ZFS) and large magnetic anisotropy on Co(II). Detailed ab initio ligand field theory calculations quantitatively predicted the magnitude of ZFS. Prominent field-induced single-ion magnet (SIM) behavior was observed for 1 from dynamic magnetization measurements. Slow magnetic relaxation follows an Orbach mechanism with the effective energy barrier Ueff=29.6 (7) K and relaxation time τo=1.4 (4)×10-9 s.

An approach for patterned molecular adsorption on ferromagnets, achieved via Moiré superstructures

We have used a scanning tunneling microscope operated under ultrahigh vacuum conditions to investigate an oxo-vanadium-salen complex V(O)salen, that has potential applications as qubits in future quantum-based technologies. The adsorption and self-assembly of V(O)salen on a range of single crystal metal surfaces and nanoislands and the influence of substrate morphology and reactivity has been measured. On the close-packed flat Ag(111) and Cu(111) surfaces, the molecules adsorb isolated or form small clusters arranged randomly on the surface, whereas structured adsorption occurs on two types of Co nanoislands; Co grown on Ag(111) and Ag capped Co islands grown on Cu(111), both forming a Moiré pattern at the surface. The adsorption configuration can by scanning tunneling spectroscopy be linked to the geometric and electronic properties of the substrates and traced back to a Co d-related surface state, illustrating how the modulated reactivity can be used to engineer a pattern of adsorbed molecules on the nanoscale.

Overdestabilization vs Overstabilization in the Theoretical Analysis of f-Orbital Covalency

The complex nature of the f-orbital electronic structures and their interaction with the chemical environment pose significant computational challenges. Advanced computational techniques that variationally include scalar relativities and spin-orbit coupling directly at the molecular orbital level have been developed to address this complexity. Among these, variational relativistic multiconfigurational multireference methods stand out for their high accuracy and systematic improvement in studies of f-block complexes. Additionally, these advanced methods offer the potential for calibrating low-scaling electronic structure methods such as density functional theory. However, studies on the Cl K-edge X-ray absorption spectra of the [Ce(III)Cl6]3- and [Ce(IV)Cl6]2- complexes show that time-dependent density functional theory with approximate exchange-correlation kernels can lead to inaccuracies, resulting in an overstabilization of 4f orbitals and incorrect assessments of covalency. In contrast, approaches utilizing small active space wave function methods may understate the stability of these orbitals. The results herein demonstrate the need for large active space, multireference, and variational relativistic methods in studying f-block complexes.

How the spin state tunes the slow magnetic relaxation field dependence in spin crossover cobalt(II) complexes

A novel family of cobalt(II) compounds with tridentate pyridine-2,6-diiminephenyl type ligands featuring electron-withdrawing substituents of general formula [Co(n-XPhPDI)2](ClO4)2·S [n-XPhPDI = 2,6-bis(N-n-halophenylformimidoyl)pyridine with n = 4 (1-3) and 3 (4); X = I (1), Br (2 and 4) and Cl (3); S = MeCN (1 and 2) and EtOAc (3)] has been synthesised and characterised by single-crystal X-ray diffraction, electron paramagnetic resonance, and static (dc) and dynamic (ac) magnetic measurements combined with theoretical calculations. The structures of 1-4 consist of mononuclear bis(chelating) cobalt(II) complex cations, [CoII(n-XPhPDI)2]2+, perchlorate anions, and acetonitrile (1 and 2) or ethyl acetate (3) molecules of crystallisation. This unique series of mononuclear six-coordinate octahedral cobalt(II) complexes displays both thermally-induced low-spin (LS)/high-spin (HS) transition and field-induced slow magnetic relaxation in both LS and HS states. A complete LS ↔ HS transition occurs for 1 and 2, while it is incomplete for 4, one-third of the complexes being HS at low temperatures. In contrast, 3 remains HS in all the temperature range. 1 and 2 show dual spin relaxation dynamics under the presence of an applied dc magnetic field (Hdc), with the occurrence of faster- (FR) and slower-relaxing (SR) processes at lower (Hdc = 1.0 kOe) and higher fields (Hdc = 2.5 kOe), respectively. On the contrary, 3 and 4 exhibit only SR and FR relaxations, regardless of Hdc. Overall, the distinct field-dependence of the single-molecule magnet (SMM) behaviour along with this family of spin-crossover (SCO) cobalt(II)-n-XPhPDI complexes is dominated by Raman mechanisms and, occasionally, with additional temperature-independent Intra-Kramer [LS or HS (D > 0)] or Quantum Tunneling of Magnetisation mechanisms [HS (D < 0)] also contributing.

Molecular nanomagnets: a viable path toward quantum information processing?

Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.

Proof-of-Concept Quantum Simulator Based on Molecular Spin Qudits

The use of d-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Magnetic molecules are ideal spin systems to realize these large-dimensional qudits. Indeed, their Hamiltonian can be engineered to an unparalleled extent and can yield a spectrum with many low-energy states. In particular, in the past decade, intense theoretical, experimental, and synthesis efforts have been devoted to develop quantum simulators based on molecular qubits and qudits. However, this remarkable potential is practically unexpressed, because no quantum simulation has ever been experimentally demonstrated with these systems. Here, we show the first prototype quantum simulator based on an ensemble of molecular qudits and a radiofrequency broadband spectrometer. To demonstrate the operativity of the device, we have simulated quantum tunneling of the magnetization and the transverse-field Ising model, representative of two different classes of problems. These results represent an important step toward the actual use of molecular spin qudits in quantum technologies.

Molecular elastic crystals exhibiting slow magnetic relaxations

We report an elastic crystal of a copper(II) porphyrinato complex that exhibits slow magnetic relaxations and is a promising candidate for an external-force-responsive spin qubit.

Spin Qubit in a 2D GdIII NaI -Based Oxamato Supramolecular Coordination Framework

Qubits are the basic unit of quantum information and computation. To realize quantum computing and information processing, the decoherence times of qubits must be long enough. Among the studies of molecule-based electron spin qubits, most of the work focused on the ions with the spin S=1/2, where only single-bit gates can be constructed. However, quantum operations require the qubits to interact with each other, so people gradually carry out relevant research in ions or systems with S>1/2 and multilevel states. In this work, a two-dimensional (2D) oxygen-coordinated GdIII NaI -based oxamato supramolecular coordination framework, Na[Gd(4-HOpa)4 (H2 O)] ⋅ 2H2 O (1, 4-HOpa=N-4-hydroxyphenyloxamate), was selected as a possible carrier of qubit. The field-induced slow magnetic relaxation shows this system has phonon bottleneck (PB) effect at low temperatures with a very weak magnetic anisotropy. The pulse electron paramagnetic resonance studies show the spin-lattice and spin-spin relaxation times are T1 =1.66 ms at 4 K and Tm =4.25 μs at 8 K for its diamagnetically diluted sample (1Gd0.12 %). It suggested that the relatively long decoherence time is mainly ascribed to its near isotropic and the PB effect from resonance phonon trapped for pure sample, while the dilution further improves its qubit performance.

Quantum Mimicry With Inorganic Chemistry

Quantum objects, such as atoms, spins, and subatomic particles, have important properties due to their unique physical properties that could be useful for many different applications, ranging from quantum information processing to magnetic resonance imaging. Molecular species also exhibit quantum properties, and these properties are fundamentally tunable by synthetic design, unlike ions isolated in a quadrupolar trap, for example. In this comment, we collect multiple, distinct, scientific efforts into an emergent field that is devoted to designing molecules that mimic the quantum properties of objects like trapped atoms or defects in solids. Mimicry is endemic in inorganic chemistry and featured heavily in the research interests of groups across the world. We describe a new field of using inorganic chemistry to design molecules that mimic the quantum properties (e.g. the lifetime of spin superpositions, or the resonant frequencies thereof) of other quantum objects, "quantum mimicry." In this comment, we describe the philosophical design strategies and recent exciting results from application of these strategies.

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.

Multireference Study of Optically Addressable Vanadium-Based Molecular Qubit Candidates

Molecular electron spin qubits with optical manipulation schemes are some of the most promising candidates for modern quantum technologies. Key values that determine a compound's viability for optical-spin initialization and readout include its singlet-triplet gap and zero-field splitting (ZFS) parameters. Generally, these values are very small in magnitude and are thus difficult to reproduce with theoretical methods. Here, we study a previously identified optically addressable molecular qubit, (C₆F₅)₃trenVCN^tBu (tren = tris(2-aminoethyl)amine), using the complete active space self-consistent field (CASSCF) and post-CASSCF methods: complete active space second-order perturbation theory (CASPT2), multiconfiguration pair-density functional theory (MC-PDFT), and hybrid MC-PDFT (HMC-PDFT). Of those methods, we successfully reproduce the singlet-triplet gap and ZFS parameters with reasonable accuracy using 0.5 HMC-PDFT and CASPT2. Four additional V³⁺ complexes with differing ligands were also investigated. We found that the ligands have minimal effect on the spin properties of the molecule and propose them to be optically addressable qubit candidates. These potential qubits are further analyzed in terms of ab initio ligand field theory (AILFT) to understand the influence of the ligands on the singlet-triplet gap and ZFS parameters.

Quantum error correction with molecular spin qudits

Molecular multi-level spin qudits are very promising for quantum computing, embedding quantum error correction within single objects. We compare the performance of electronic/nuclear molecular qudits in the implementation of quantum error correction.

Molecular Approach to Engineer Two-Dimensional Devices for CMOS and beyond-CMOS Applications

Two-dimensional materials (2DMs) have attracted tremendous research interest over the last two decades. Their unique optical, electronic, thermal, and mechanical properties make 2DMs key building blocks for the fabrication of novel complementary metal-oxide-semiconductor (CMOS) and beyond-CMOS devices. Major advances in device functionality and performance have been made by the covalent or noncovalent functionalization of 2DMs with molecules: while the molecular coating of metal electrodes and dielectrics allows for more efficient charge injection and transport through the 2DMs, the combination of dynamic molecular systems, capable to respond to external stimuli, with 2DMs makes it possible to generate hybrid systems possessing new properties by realizing stimuli-responsive functional devices and thereby enabling functional diversification in More-than-Moore technologies. In this review, we first introduce emerging 2DMs, various classes of (macro)molecules, and molecular switches and discuss their relevant properties. We then turn to 2DM/molecule hybrid systems and the various physical and chemical strategies used to synthesize them. Next, we discuss the use of molecules and assemblies thereof to boost the performance of 2D transistors for CMOS applications and to impart diverse functionalities in beyond-CMOS devices. Finally, we present the challenges, opportunities, and long-term perspectives in this technologically promising field.

Simulating Static and Dynamic Properties of Magnetic Molecules with Prototype Quantum Computers

Magnetic molecules are prototypical systems to investigate peculiar quantum mechanical phenomena. As such, simulating their static and dynamical behavior is intrinsically difficult for a classical computer, due to the exponential increase of required resources with the system size. Quantum computers solve this issue by providing an inherently quantum platform, suited to describe these magnetic systems. Here, we show that both the ground state properties and the spin dynamics of magnetic molecules can be simulated on prototype quantum computers, based on superconducting qubits. In particular, we study small-size anti-ferromagnetic spin chains and rings, which are ideal test-beds for these pioneering devices. We use the variational quantum eigensolver algorithm to determine the ground state wave-function with targeted ansatzes fulfilling the spin symmetries of the investigated models. The coherent spin dynamics are simulated by computing dynamical correlation functions, an essential ingredient to extract many experimentally accessible properties, such as the inelastic neutron cross-section.

Assessing the Nature of Chiral-Induced Spin Selectivity by Magnetic Resonance

Understanding chiral-induced spin selectivity (CISS), resulting from charge transport through helical systems, has recently inspired many experimental and theoretical efforts but is still the object of intense debate. In order to assess the nature of CISS, we propose to focus on electron-transfer processes occurring at the single-molecule level. We design simple magnetic resonance experiments, exploiting a qubit as a highly sensitive and coherent magnetic sensor, to provide clear signatures of the acceptor polarization. Moreover, we show that information could even be obtained from time-resolved electron paramagnetic resonance experiments on a randomly oriented solution of molecules. The proposed experiments will unveil the role of chiral linkers in electron transfer and could also be exploited for quantum computing applications.

Tailoring Valence Tautomerism by Using Redox Potentials: Studies on Ferrocene-Based Triarylmethylium Dyes with Electron-Poor Fluorenylium and Thioxanthylium Acceptors

Three new electrochromic ferrocenyl triarylmethylium dyes with fluorenylium (1 a⁺ , 1 b⁺ ) or thioxanthylium (1 c⁺ ) residues were selected in order to keep the intrinsic differences of redox potentials for ferrocene oxidation and triarylmethylium reduction small and to trigger valence tautomerism (VT). UV/Vis/NIR and quantitative EPR spectroscopy identified paramagnetic diradical isomers 1 a^..+ -1 c^..+ alongside diamagnetic forms 1 a⁺ -1 c⁺ , which renders these complexes magnetochemical switches. The diradical forms 1 a^..+ -1 c^..+ as well as the one-electron-reduced triarylmethyl forms of the complexes were found to dimerize in solution. For radical 1 a^. , dimerization occurs on the timescale of cyclic voltammetry; this allowed us to determine the kinetics and equilibrium constant for this process by digital simulation. Mößbauer spectroscopy indicated that 1 a⁺ and 1 b⁺ retain VT even in the solid state. UV/Vis/NIR spectro-electrochemistry revealed the poly-electrochromic behaviour of these complexes by establishing the distinctly different electronic absorption profiles of the corresponding oxidized and reduced forms.

Design of pure heterodinuclear lanthanoid cryptate complexes

Heterolanthanide complexes are difficult to synthesize owing to the similar chemistry of the lanthanide ions. Consequently, very few purely heterolanthanide complexes have been synthesized. This is despite the fact that such complexes hold interesting optical and magnetic properties. To fine-tune these properties, it is important that one can choose complexes with any given combination of lanthanides. Herein we report a synthetic procedure which yields pure heterodinuclear lanthanide cryptates LnLn*LX3 (X = NO3 - or OTf-) based on the cryptand H3L = N[(CH2)2N[double bond, length as m-dash]CH-R-CH[double bond, length as m-dash]N-(CH2)2]3N (R = m-C6H2OH-2-Me-5). In the synthesis the choice of counter ion and solvent proves crucial in controlling the Ln-Ln* composition. Choosing the optimal solvent and counter ion afford pure heterodinuclear complexes with any given combination of Gd(iii)-Lu(iii) including Y(iii). To demonstrate the versatility of the synthesis all dinuclear combinations of Y(iii), Gd(iii), Yb(iii) and Lu(iii) were synthesized resulting in 10 novel complexes of the form LnLn*L(OTf)3 with LnLn* = YbGd 1, YbY 2, YbLu 3, YbYb 4, LuGd 5, LuY 6, LuLu 7, YGd 8, YY 9 and GdGd 10. Through the use of 1H, 13C NMR and mass spectrometry the heterodinuclear nature of YbGd, YbY, YbLu, LuGd, LuY and YGd was confirmed. Crystal structures of LnLn*L(NO3)3 reveal short Ln-Ln distances of ∼3.5 Å. Using SQUID magnetometry the exchange coupling between the lanthanide ions was found to be anti-ferromagnetic for GdGd and YbYb while ferromagnetic for YbGd.

Magnetic anisotropy in YbIII complex candidates for molecular qubits: a theoretical analysis

The magnetic properties of mononuclear YbIII complexes have been explored by using multiconfigurational CASPT2/RASSI calculations. Such complexes, in particular the case of [Yb(trensal)] complex, have been proposed as molecular qubits due to their spin dynamics properties. We have verified the accuracy of the theoretical approach to study such systems by comparing with experimental magnetic data. In order to have a wide overview of the magnetic properties of mononuclear YbIII complexes, we have considered simple charged and neutral models, [Yb(H2O)n]3+ and [Yb(OH)3(H2O)n-3], for many coordination modes. Thus, the results for more than 100 models allow extraction of some conclusions about the best ligand distributions in the coordination sphere to tailor the magnetic properties. Some low coordination, between 3 and 5, complexes that have no experimental magnetic data have been studied computationally to check if they can present high magnetic anisotropy.

When Molecular Magnetism Meets Supramolecular Chemistry: Multifunctional and Multiresponsive Dicopper(II) Metallacyclophanes as Proof-of-Concept for Single-Molecule Spintronics and Quantum Computing Technologies?

Molecular magnetism has made a long journey, from the fundamental studies on through-ligand electron exchange magnetic interactions in dinuclear metal complexes with extended organic bridges to the more recent exploration of their electron spin transport and quantum coherence properties. Such a field has witnessed a renaissance of dinuclear metallacyclic systems as new experimental and theoretical models for single-molecule spintronics and quantum computing, due to the intercrossing between molecular magnetism and metallosupramolecular chemistry. The present review reports a state-of-the-art overview as well as future perspectives on the use of oxamato-based dicopper(II) metallacyclophanes as promising candidates to make multifunctional and multiresponsive, single-molecule magnetic (nano)devices for the physical implementation of quantum information processing (QIP). They incorporate molecular magnetic couplers, transformers, and wires, controlling and facilitating the spin communication, as well as molecular magnetic rectifiers, transistors, and switches, exhibiting a bistable (ON/OFF) spin behavior under external stimuli (chemical, electronic, or photonic). Special focus is placed on the extensive research work done by Professor Francesc Lloret, an outstanding chemist, excellent teacher, best friend, and colleague, in recognition of his invaluable contributions to molecular magnetism on the occasion of his 65th birthday.

Molecular Nanomagnets as Qubits with Embedded Quantum-Error Correction

We show that molecular nanomagnets have a potential advantage in the crucial rush toward quantum computers. Indeed, the sizable number of accessible low-energy states of these systems can be exploited to define qubits with embedded quantum error correction. We derive the scheme to achieve this crucial objective and the corresponding sequence of microwave/radiofrequency pulses needed for the error correction procedure. The effectiveness of our approach is shown already with a minimal S = 3/2 unit corresponding to an existing molecule, and the scaling to larger spin systems is quantitatively analyzed.

Molecular Nanomagnets as Qubits with Embedded Quantum-Error Correction

We show that molecular nanomagnets have a potential advantage in the crucial rush toward quantum computers. Indeed, the sizable number of accessible low-energy states of these systems can be exploited to define qubits with embedded quantum error correction. We derive the scheme to achieve this crucial objective and the corresponding sequence of microwave/radiofrequency pulses needed for the error correction procedure. The effectiveness of our approach is shown already with a minimal S = 3/2 unit corresponding to an existing molecule, and the scaling to larger spin systems is quantitatively analyzed.

Spin dynamics in single-molecule magnets and molecular qubits

Over recent decades, much effort has been made to lengthen spin relaxation/decoherence times of single-molecule magnets and molecular qubits by following different chemical design rules such as maximizing the total spin value, controlling symmetry, enhancing the ligand field or inhibiting key vibrational modes. Simultaneously, electronic structure calculations have been employed to provide an understanding of the processes involved in the spin dynamics of molecular systems and served to refine or introduce new design rules. This review focuses on contemporary theoretical approaches focused on the calculation of spin relaxation/decoherence times, highlighting their main features and scope. Fundamental aspects of experimental techniques for the determination of key Single Molecule Magnet/Spin Qubit properties are also reviewed.

Single molecule magnet behaviour in a square planar S = 1/2 Co(ii) complex and spin-state assignment of multiple relaxation modes

We report the first example of field-induced single molecule magnet (SMM) behaviour in a square-planar S = 1/2 Co(ii) pincer complex [(PNNNP)CoBr]Br (2). The related five-coordinate complexes [(PCNCP)CoBr2] (1) and [(PONOP)CoBr2] (3) also exhibit SMM properties. Partial spin crossover displayed by 3 allows for assignment of distinct relaxation modes to each spin state.

Magnetization Dynamics and Coherent Spin Manipulation of a Propeller Gd(III) Complex with the Smallest Helicene Ligand

A homoleptic gadolinium(III) complex with the smallest helicene-type ligand, 1,10-phenanthroline-N,N'-dioxide (phendo) [Gd(phendo)₄](NO₃)₃·xMeOH (phendo = 1,10-phenanthroline-N,N'-dioxide, MeOH = methanol), shows slow relaxation of the magnetization characteristic for Single Ion Magnets (SIM), despite negligible magnetic anisotropy, confirmed by ab initio calculations. Solid state dilution magnetic and EPR studies reveal that the magnetization dynamics of the [Gd(phendo)₄]³⁺ cation is controlled mainly by a Raman process. Pulsed EPR experiments demonstrate long phase memory times (up to 2.7 μs at 5 K), enabling the detection of Rabi oscillations at 20 K, which confirms coherent control of its spin state.

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.

Detection of Spin-Vibration States in Single Magnetic Molecules

The spin states of magnetic molecules have advantageous attributes as carriers of quantum information. However, spin-vibration coupling in molecules causes a decay of excited spin states and a loss of spin coherence. Here, we detect excitations of spin-vibration states in single nickelocene molecules on Ag(110) with a scanning tunneling microscope. By transferring a nickelocene to the tip, the joint spin-vibration states with an adsorbed nickelocene were measured. Chemical variations in magnetic molecules offer the opportunity to tune spin-vibration coupling for controlling the spin coherence.

Probing and imaging spin interactions with a magnetic single-molecule sensor

Magnetic single atoms and molecules are receiving intensifying research focus because of their potential as the smallest possible memory, spintronic, and qubit elements. Scanning probe microscopes used to study these systems have benefited greatly from new techniques that use molecule-functionalized tips to enhance spatial and spectroscopic resolutions and enable new sensing capabilities. We demonstrate a microscopy technique that uses a magnetic molecule, Ni(cyclopentadienyl)₂, adsorbed at the apex of a scanning probe tip, to sense exchange interactions with another molecule adsorbed on a Ag(110) surface in a continuously tunable fashion in all three spatial directions. We further used the probe to image contours of exchange interaction strength, revealing angstrom-scale regions where the quantum states of two magnetic molecules strongly mix. Our results pave the way for new nanoscale imaging capabilities based on magnetic single-molecule sensors.

Three Dy(iii) single-ion magnets bearing the tropolone ligand: structure, magnetic properties and theoretical elucidation

Three Dy(iii) SIMs bearing the tropolone ligand are reported here with the tuning effect on their performances by ancillary ligands revealed via experimental magnetic investigations and theoretical calculations.

Electronic Structures, and Optical and Magnetic Properties of Quadruple-Decker Phthalocyanines

For applications of magnetic devices with operating nuclear-spin-based quantum bits in quantum computing, electronic structures, and magnetic and optical properties of quadruple-decker phthalocyanines with 3d transition metals, such as scandium, yttrium, and lanthanum atoms (M3Pc4: M = Sc, Y, and La), were studied by quantum calculation using density function theory. Electron density distributions at the highest occupied molecular orbital and lowest unoccupied molecular orbital were considerably delocalized on the phthalocyanine ring with considerable bias of the electrostatic potential. The wide energy gaps and the ultraviolet-visible-near infrared spectra of the systems were based on the phthalocyanine ring-ring interactions with overlapping π-orbitals on the phthalocyanine rings. The chemical shift behavior of 13C and 14N-NMR of Sc3(Pc)4, Y3(Pc)4, and La3(Pc)4 depended on the deformation of their structures owing to Jahn-Teller splitting of the d-orbital in the metal ligand field, the considerable perturbation of the metal ligand crystal field on the phthalocyanine ring, the electronic structure based on the electron density distribution, and the magnetic interaction of the nuclear quadrupole interaction. The magnetic parameters of the principle g-tensor, the V-tensor of the electronic field gradient, and the asymmetric parameters were influenced by the deformed structures of the complex with the considerable deviation of the charge density distribution. The quadruple-decker metal phthalocyanines using 3d transition metals have an advantage in controlling the electronic structure and magnetic parameters based on the nuclear spin interaction in spin lattice relaxation with respect to applications of single-molecular magnets.