Molecular spin qudits for quantum algorithms

A Stable Chichibabin Diradicaloid with Near-Infrared Emission

Conjugated molecules with multiple radical centers such as the iconic Chichibabin diradicaloid hold promise as building blocks in materials for quantum sensing and quantum information processing. However, it is a considerable challenge to design simple analogues of the Chichibabin hydrocarbon that are chemically inert, exhibit high diradical character and emit light at a distinct wavelength that may offer an optical readout of the spin state in functional ensembles. Here we describe the serendipitous discovery of the stable TTM-TTM diradicaloid, which exhibits high diradical character, a striking sky-blue color and near-infrared (NIR) emission (in solution). This combination of properties is unique among related diradicaloids and is due to the presence of hydrogen and chlorine atoms in "just the right positions", allowing a perfectly planar, yet predominantly benzenoid bridge to connect the two sterically stabilized radical centers. In-depth studies of the optical and magnetic properties suggest that this structural motif could become a mainstay building block of organic spin materials.

Ligand Effects on the Spin Relaxation Dynamics and Coherent Manipulation of Organometallic La(II) Potential Qudits

We present pulsed electron paramagnetic resonance (EPR) studies on three La(II) complexes, [K(2.2.2-cryptand)][La(Cp')3] (1), [K(2.2.2-cryptand)][La(Cp″)3] (2), and [K(2.2.2-cryptand)][La(Cptt)3] (3), which feature cyclopentadienyl derivatives as ligands [Cp' = C5H4SiMe3; Cp″ = C5H3(SiMe3)2; Cptt = C5H3(CMe3)2] and display a C3 symmetry. Long spin-lattice relaxation (T1) and phase memory (Tm) times are observed for all three compounds, but with significant variation in T1 among 1-3, with 3 being the slowest relaxing due to higher s-character of the SOMO. The dephasing times can be extended by more than an order of magnitude via dynamical decoupling experiments using a Carr-Purcell-Meiboom-Gill (CPMG) sequence, reaching 161 μs (5 K) for 3. Coherent spin manipulation is performed by the observation of Rabi quantum oscillations up to 80 K in this nuclear spin-rich environment (1H, 13C, and 29Si). The high nuclear spin of 139La (I = 7/2), and the ability to coherently manipulate all eight hyperfine transitions, makes these molecules promising candidates for application as qudits (multilevel quantum systems featuring d quantum states; d >2) for performing quantum operations within a single molecule. Application of HYSCORE techniques allows us to quantify the electron spin density at ligand nuclei and interrogate the role of functional groups to the electron spin relaxation properties.

A continuous-wave and pulsed X-band electron spin resonance spectrometer operating in ultra-high vacuum for the study of low dimensional spin ensembles

We report the development of a continuous-wave and pulsed X-band electron spin resonance (ESR) spectrometer for the study of spins on ordered surfaces down to cryogenic temperatures. The spectrometer operates in ultra-high vacuum and utilizes a half-wavelength microstrip line resonator realized using epitaxially grown copper films on single crystal Al2O3 substrates. The one-dimensional microstrip line resonator exhibits a quality factor of more than 200 at room temperature, close to the upper limit determined by radiation losses. The surface characterizations of the copper strip of the resonator by atomic force microscopy, low-energy electron diffraction, and scanning tunneling microscopy show that the surface is atomically clean, flat, and single crystalline. Measuring the ESR spectrum at 15 K from a few nm thick molecular film of YPc2, we find a continuous-wave ESR sensitivity of 2.6 × 1011 spins/G · Hz1/2, indicating that a signal-to-noise ratio of 3.9 G · Hz1/2 is expected from a monolayer of YPc2 molecules. Advanced pulsed ESR experimental capabilities, including dynamical decoupling and electron-nuclear double resonance, are demonstrated using free radicals diluted in a glassy matrix.

Dual Structure of a Vanadyl-Based Molecular Qubit Containing a Bis(β-diketonato) Ligand

We designed [VO(bdhb)] (1') as a new electronic qubit containing an oxovanadium(IV) ion (S = 1/2) embraced by a single bis(β-diketonato) ligand [H2bdhb = 1,3-bis(3,5-dioxo-1-hexyl)benzene]. The synthesis afforded three different crystal phases, all of which unexpectedly contain dimers with formula [(VO)2(bdhb)2] (1). A trigonal form (1h) with a honeycomb structure and 46% of solvent-accessible voids quantitatively transforms over time into a monoclinic solvatomorph 1m and minor amounts of a triclinic solventless phase (1a). In a static magnetic field, 1h and 1m have detectably slow magnetic relaxation at low temperatures through quantum tunneling and Raman mechanisms. Angle-resolved electron paramagnetic resonance (EPR) spectra on single crystals revealed signatures of low-dimensional magnetic behavior, which is solvatomorph-dependent, being the closest interdimer V···V separations (6.7-7.5 Å) much shorter than intramolecular V···V distances (11.9-12.1 Å). According to 1H diffusion ordered spectroscopy (DOSY) and EPR experiments, the complex adopts the desired monomeric structure in organic solution and its geometry was inferred from density functional theory (DFT) calculations. Spin relaxation measurements in a frozen toluene-d8/CD2Cl2 matrix yielded Tm values reaching 13 μs at 10 K, and coherent spin manipulations were demonstrated by Rabi nutation experiments at 70 K. The neutral quasi-macrocyclic structure, featuring nuclear spin-free donors and additional possibilities for chemical functionalization, makes 1' a new convenient spin-coherent building block in quantum technologies.

Effect of diamagnetic Zn(II) ions on the SMM properties of a series of trinuclear ZnDy2 and tetranuclear Zn2Dy2 (LnIII = Dy, Tb, Gd) complexes: combined experimental and theoretical studies

To study the effect of diamagnetic ions on magnetic interactions, utilizing a compartmental ligand (Z)-2-(hydroxymethyl)-4-methyl-6-((quinolin-8-ylimino)methyl)phenol (LH2), two different series of ZnII-LnIII complexes, namely the trinuclear series of [DyZn2(L)2(μ2-OAc)2(CH3OH)2]·NO3·MeOH (1), [TbZn2(L)2(μ2-OAc)2(CH3OH)2]·NO3·5MeOH·H2O (2), and [GdZn2(L)2(μ2-OAc)2(CH3OH)2]·NO3·MeOH·CHCl3 (3) and the tetranuclear series of [Dy2Zn2(LH)4(NO3)4(μ2OAc)]·NO3·MeOH·H2O (4), [Tb2Zn2(LH)4(NO3)4(μ2-OAc)]·NO3·MeOH·2H2O (5), and [Gd2Zn2(LH)4(NO3)4(μ2-OAc)]·NO3·MeOH·2H2O (6), were synthesized. Trinuclear ZnII-LnIII complexes 1-3 consist of one LnIII ion sandwiched between two peripheral ZnII ions forming a bent type ZnII-DyIII-ZnII array with an angle of 110.64°. Tetranuclear ZnII-LnIII complexes 4-6 are basically a combination of two dinuclear moieties of [LnZn(LH)2(NO3)2]+ connected by one bidentate bridging acetate ion in μ2-OAc coordination mode. The detailed magnetic analysis reveals that complexes 1 and 4 are single molecule magnets having energy barriers of 34.98 K and 46.71 K with relaxation times (τ0) of 5.05 × 10-4 s and 5.24 × 10-4 s, respectively. Ab initio calculations were employed to analyze the magnetic anisotropy and magnetic exchange interaction between the ZnII and LnIII centers with the aim of gaining better insights into the magnetic dynamics of complexes 1-6.

Selective Transition Enhancement in a g-Engineered Diradical

A diradical with engineered g-asymmetry was synthesized by grafting a nitroxide radical onto the [Y(Pc)2]⋅ radical platform. Various spectroscopic techniques and computational studies revealed that the electronic structures of the two spin systems remained minimally affected within the diradical system. Fluid-solution Electron Paramagnetic Resonance (EPR) experiments revealed a weak exchange coupling with |J| ~ 0.014 cm-1, subsequently rationalized by CAS-SCF calculations. Frozen solution continuous-wave (CW) EPR experiments showed a complicated and power-dependent spectrum that eluded analysis using the point-dipole model. Pulse EPR manipulations with varying microwave powers, or under varying magnetic fields, demonstrated that different resonances could be selectively enhanced or suppressed, based on their different tipping angles. In particular, Field-Swept Echo-Detected (FSED) spectra revealed absorptions of MW power-dependent intensities, while Field-Swept Spin Nutation (FSSN) experiments revealed two distinct Rabi frequencies. This study introduces a methodology to synthesize and characterize g-asymmetric two-spin systems, of interest in the implementation of spin-based CNOT gates.

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.

Spin qubits of Cu(II) doped in Zn(II) metal-organic frameworks above microsecond phase memory time

With the aim of creating Cu(II) spin qubits in a rigid metal-organic framework (MOF), this work demonstrates a doping of 5 %, 2 %, 1 %, and 0.1 % mol of Cu(II) ions into a perovskite-type MOF [CH6 N3 ][ZnII (HCOO)3 ]. The presence of dopant Cu(II) sites are confirmed with anisotropic g-factors (gx =2.07, gy =2.12, and gz =2.44) in the S=1/2 system by experimentally and theoretically. Magnetic dynamics indicate the occurrence of a slow magnetic relaxation via the direct and Raman processes under an applied field, with a relaxation time (τ) of 3.5 ms (5 % Cu), 9.2 ms (2 % Cu), and 15 ms (1 % Cu) at 1.8 K. Furthermore, pulse-ESR spectroscopy reveals spin qubit properties with a spin-spin relaxation (phase memory) time (T2 ) of 0.21 μs (2 %Cu), 0.39 μs (1 %Cu), and 3.0 μs (0.1 %Cu) at 10 K as well as Rabi oscillation between MS =±1/2 spin sublevels. T2 above microsecond is achieved for the first time in the Cu(II)-doped MOFs. It can be observed at submicrosecond around 50 K. These spin relaxations are very sensitive to the magnetic dipole interactions relating with cross-relaxation between the Cu(II) sites and can be tuned by adjusting the dopant concentration.

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.

Oriented Triplet Excitons as Long-Lived Electron Spin Qutrits in a Molecular Donor-Acceptor Single Cocrystal

The photogeneration of multiple unpaired electron spins within molecules is a promising route to applications in quantum information science because they can be initialized into well-defined, multilevel quantum states (S > 1/2) and reproducibly fabricated by chemical synthesis. However, coherent manipulation of these spin states is difficult to realize in typical molecular systems due to the lack of selective addressability and short coherence times of the spin transitions. Here, these challenges are addressed by using donor-acceptor single cocrystals composed of pyrene and naphthalene dianhydride to host spatially oriented triplet excitons, which exhibit promising photogenerated qutrit properties. Time-resolved electron paramagnetic resonance (TREPR) spectroscopy demonstrates that spatially orienting triplet excitons in a single crystal platform imparts narrow, well-resolved, tunable resonances in the triplet EPR spectrum, allowing selective addressability of the spin sublevel transitions. Pulse-EPR spectroscopy reveals that at temperatures above 30 K, spin decoherence of these triplet excitons is driven by exciton diffusion. However, coherence is limited by electronic spin dipolar coupling below 30 K, where T2 varies nonlinearly with the optical excitation density due to exciton annihilation. Overall, an optimized coherence time of T2 = 7.1 μs at 20 K is achieved. These results provide important insights into designing solid-state molecular excitonic materials with improved spin qutrit properties.

Enhancing Coherence Times of Chromophore-Radical Molecular Qubits and Qudits by Rational Design

An important criterion for quantum operations is long qubit coherence times. To elucidate the influence of molecular structure on the coherence times of molecular spin qubits and qudits, a series of molecules featuring perylenediimide (PDI) chromophores covalently linked to stable nitroxide radicals were synthesized and investigated by pulse electron paramagnetic resonance spectroscopy. Photoexcitation of PDI in these systems creates an excited quartet state (Q) followed by a spin-polarized doublet ground state (D0), which hold promise as spin qudits and qubits, respectively. By tailoring the molecular structure of these spin qudit/qubit candidates by selective deuteration and eliminating intramolecular motion, coherence times of Tm = 9.1 ± 0.3 and 4.2 ± 0.3 μs at 85 K for D0 and Q, respectively, are achieved. These coherence times represent a nearly 3-fold enhancement compared to those of the initial molecular design. This approach offers a rational structural design protocol for effectively extending coherence times in molecular spin qudits/qubits.

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.

Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets

Paramagnetic molecules with a metal ion as an electron spin center are promising building blocks for molecular qubits and high-density memory arrays. However, fast spin relaxation and decoherence in these molecules lead to a rapid loss of magnetization and quantum information. Nonadiabatic coupling (NAC), closely related to spin-vibrational coupling, is the main source of spin relaxation and decoherence in paramagnetic molecules at higher temperatures. Predicting these couplings using numerical differentiation requires a large number of computationally intensive ab initio or crystal field electronic structure calculations. To reduce computational cost and improve accuracy, we derive and implement analytical NAC and state-specific energy gradient for the ab initio parametrized crystal field Hamiltonian describing single-ion molecular magnets. Our implementation requires only a single crystal field calculation. In addition, the accurate NACs and state-specific energy gradients can be used to model spin relaxation using sophisticated nonadiabatic molecular dynamics, which avoids the harmonic approximation for molecular vibrations. To test our implementation, we calculate the NAC values for three lanthanide complexes. The predicted values support the relaxation mechanisms reported in previous studies.

PDI-trityl dyads as photogenerated molecular spin qubit candidates

Owing to their potential applications in the field of quantum information science, photogenerated organic triplet-radical conjugates have attracted an increasing amount of attention recently. Typically, these compounds are composed of a chromophore appended to a stable radical. After initialisation of the system by photoexcitation, a highly spin-polarised quartet state may be generated, which serves as a molecular spin qubit candidate. Here, we investigate three perylene diimide (PDI)-based chromophore-radical systems with different phenylene linkers and radical counterparts by both optical spectroscopy and transient electron paramagnetic resonance (EPR) techniques. Femtosecond transient absorption measurements demonstrate chromophore triplet state formation on a picosecond time scale for PDI-trityl dyads, while excited state deactivation is found to be slowed down considerably in a PDI-nitroxide analogue. The subsequent investigation of the coherent spin properties by transient EPR confirms quartet state formation by triplet-doublet spin mixing for all investigated dyads and the suitability of the two studied PDI-trityl dyads as spin qubit candidates. In particular, we show that using tetrathiaryl trityl as the radical counterpart, an intense spin polarisation is observed even at room temperature and quartet state coherence times of 3.0 μs can be achieved at 80 K, which represents a considerable improvement compared to previously studied systems.

Vertical molecular transistors: a new strategy towards practical quantum devices

Considerable effort has been dedicated to improving molecular devices since they were initially proposed by Aviram and Ratner in 1974. Organic molecules are small and have discrete molecular orbitals. These features can facilitate fascinating quantum transport phenomena, such as single-carrier tunneling, resonant tunneling, and quantum interference. The effective gate modulation of these quantum transport phenomena holds the promise of realizing a new computing architecture that differs from that of current Si electronics. In this article, we review the recent research progress on molecular transistors, specifically vertical molecular transistors (VMTs). First, we discuss the benefits of VMTs for future molecular-scale transistors compared with the currently dominant lateral molecular transistors. Subsequently, we describe representative examples of VMTs, where single molecules, self-assembled monolayers, and isolated molecules are used as transistor channels. Finally, we present our conclusions and perspectives about the use of VMTs for attractive quantum devices.

Laser Scheme for Doppler Cooling of the Hydroxyl Cation (OH+)

We report on a cycling scheme for Doppler cooling of trapped OH+ ions using transitions between the electronic ground state X3Σ- and the first excited triplet state A3Π. We have identified relevant transitions for photon cycling and repumping, have found that coupling into other electronic states is strongly suppressed, and have calculated the number of photon scatterings required to cool OH+ to a temperature where Raman sideband cooling can take over. In contrast to the standard approach, where molecular ions are sympathetically cooled, our scheme does not require co-trapping of another species and opens the door to the creation of pure samples of cold molecular ions with potential applications in quantum information, quantum chemistry, and astrochemistry. The laser cooling scheme identified for OH+ is efficient despite the absence of near-diagonal Franck-Condon factors, suggesting that broader classes of molecules and molecular ions are amenable to laser cooling than commonly assumed.

Single molecule magnet features in luminescent lanthanide coordination polymers with heptacoordinate Dy/Yb(III) ions as nodes

Two sets of 1D/2D lanthanide coordination polymers with formulas of Ln(oqa)3·2H2O [Hoqa = 2-(4-oxoquinolin-1(4H)-yl) acetic acid, Ln = Dy (1), Yb (2)] and Ln(oaa)2(HCOO)(H2O) [Hoaa = 2-(9-oxoacridin-10(9H)-yl) acetic acid, Ln = Dy (3), Yb (4)] have been synthesized and their physical properties were investigated. All four complexes are constructed from seven-coordinate lanthanide ions and corresponding organic linkers. The lanthanide ions in 1 and 2 adopt a pentagonal bipyramid coordination geometry, whereas the coordination geometry of lanthanide ions in 3 and 4 can be described as a capped octahedron. Slow magnetic relaxation behaviors were observed in these four products at a zero/non-zero static magnetic field. Complexes 1, 2 and 4 exhibit the characteristic emission of Ln(III) ions, whereas complex 3 shows ligand-based emission. Bright yellow light emission was also observed when a voltage was applied, demonstrating the potential of 1 for application in light-emitting diodes (LEDs). Compounds 3 and 4 are the first examples of lanthanide complexes based on Hoaa ligands.

Hilbert Space in Isotopologue Dy(III) SMM Dimers: Dipole Interaction Limit in [163/164Dy2(tmhd)6(tape)]0 Complexes

Single-molecule magnets are molecular complexes proposed to be useful for information storage and quantum information processing applications. In the quest for multilevel systems that can act as Qudits, two dysprosium-based isotopologues were synthesized and characterized. The isotopologues are [164Dy2(tmhd)6(tape)] (1(I=0)) and [163Dy2(tmhd)6(tape)] (2(I=5/2)), where tmhd = 2,2,6,6-tetramethylheptandionate and tape = 1,6,7,12-tetraazaperylene. Both complexes showed slow relaxation at a zero applied magnetic field with dominant Orbach and Raman relaxation mechanisms. μSQUID studies at milli-Kelvin temperatures reveal quasi-single ion loops, in contrast with the expected S-shape (near zero field) butterfly loops, characteristic of antiferromagnetically coupled dimeric complexes. Through analysis of the low-temperature data, we find that the interaction operating between Dy(III) is small, leading to a small exchange biasing from the zero-field transition. The resulting indirectly coupled nuclear states are degenerate or possess a small energy difference between them. We, therefore, conclude that for the creation of Qudits with enlarged Hilbert spaces, shorter Dy(III)···Dy(III) distances are deemed essential.

Creation of a Field-Induced Co(II) Single-Ion Magnet by Doping into a Zn(II) Diamagnetic Metal-Organic Framework

The combination of single-ion magnets (SIMs) and metal-organic frameworks (MOFs) is expected to produce new quantum materials. The principal issue to be solved in this regard is the development of new strategies for the synthesis of SIM-MOFs. This work demonstrates a new simple strategy for the synthesis of SIM-MOFs where a diamagnetic MOF is used as the framework into which the SIM sites are doped. 1, 0.5, and 0.2 mol% of the Co(II) ions are doped into the Zn(II) sites of [CH6 N3 ][ZnII (HCOO)3 ]. The doped Co(II) sites in the MOFs perform as SIM with a positive D term of zero-field splitting. The longest magnetic relaxation time is 150 ms (0.2 mol% Co) at 1.8 K under a static field of 0.1 T. Temperature dependency of the relaxation time suggests suppressing magnetic relaxation by reduction of spin-spin interaction upon doping in the rigid framework. Thus, this work represents a proof of concept for the creation of a single-ion doped magnet in the MOF. This simple synthetic strategy will be widely applied for the creation of quantum magnetic materials.

Reversible spin-optical interface in luminescent organic radicals

Molecules present a versatile platform for quantum information science1,2 and are candidates for sensing and computation applications3,4. Robust spin-optical interfaces are key to harnessing the quantum resources of materials5. To date, carbon-based candidates have been non-luminescent6,7, which prevents optical readout via emission. Here we report organic molecules showing both efficient luminescence and near-unity generation yield of excited states with spin multiplicity S > 1. This was achieved by designing an energy resonance between emissive doublet and triplet levels, here on covalently coupled tris(2,4,6-trichlorophenyl) methyl-carbazole radicals and anthracene. We observed that the doublet photoexcitation delocalized onto the linked acene within a few picoseconds and subsequently evolved to a pure high-spin state (quartet for monoradical, quintet for biradical) of mixed radical-triplet character near 1.8 eV. These high-spin states are coherently addressable with microwaves even at 295 K, with optical readout enabled by reverse intersystem crossing to emissive states. Furthermore, for the biradical, on return to the ground state the previously uncorrelated radical spins either side of the anthracene shows strong spin correlation. Our approach simultaneously supports a high efficiency of initialization, spin manipulations and light-based readout at room temperature. The integration of luminescence and high-spin states creates an organic materials platform for emerging quantum technologies.

Ultrafast Jahn-Teller Photoswitching in Cobalt Single-Ion Magnets

Single-ion magnets (SIMs) constitute the ultimate size limit in the quest for miniaturizing magnetic materials. Several bottlenecks currently hindering breakthroughs in quantum information and communication technologies could be alleviated by new generations of SIMs displaying multifunctionality. Here, ultrafast optical absorption spectroscopy and X-ray emission spectroscopy are employed to track the photoinduced spin-state switching of the prototypical complex [Co(terpy)2 ]2+ (terpy = 2,2':6',2″-terpyridine) in solution phase. The combined measurements and their analysis supported by density functional theory (DFT), time-dependent-DFT (TD-DFT) and multireference quantum chemistry calculations reveal that the complex undergoes a spin-state transition from a tetragonally elongated doublet state to a tetragonally compressed quartet state on the femtosecond timescale, i.e., it sustains ultrafast Jahn-Teller (JT) photoswitching between two different spin multiplicities. Adding new Co-based complexes as possible contenders in the search for JT photoswitching SIMs will greatly widen the possibilities for implementing magnetic multifunctionality and eventually controlling ultrafast magnetization with optical photons.

Isotopic enrichment in lanthanide coordination complexes: contribution to single-molecule magnets and spin qudit insights

Lanthanide Single-Molecule Magnets (SMMs) fascinate the scientific community due to their plethora of potential applications ranging from data storage to spintronic devices and quantum computing. This review article proposes a comprehensive description of the influence of the nuclear spin, i.e. hyperfine interaction, on the magnetic properties of lanthanide SMMs and on quantum information processing of qudit. This influence is analysed for non-Kramers and Kramers lanthanide SMMs as well as for the electronic distribution of the electron in 4f orbitals i.e. oblate and prolate ions. Then the role of magnetic interactions in isotopically enriched polynuclear Dy(III) SMMs is discussed. Finally the possible effect of superhyperfine interaction due to the nuclear spin of elements originating from the surrounding of the lanthanide centre is analyzed. The effect of nuclear spin on the dynamics of the lanthanide SMMs is demonstrated using different techniques such as magnetometry, muon spectroscopy (μ-SR), and Mössbauer and Resonance Vibrational Spectroscopies.

Room Temperature Electron Spin Coherence in Photogenerated Molecular Spin Qubit Candidates

One of the main challenges in the emerging field of molecular spintronics is the identification of new spin qubit materials for quantum information applications. In this regard, recent work has shown that photoexcited chromophore-radical systems are promising candidates to expand our repertoire of suitable candidate molecules. Here, we investigate a series of three chromophore-radical compounds composed of a perylene diimide (PDI) chromophore and a stable 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO) radical by transient electron paramagnetic resonance (EPR) techniques. We explore the influence of isotope labeling of the TEMPO moiety on the EPR spectra and electron spin coherence times of the molecular quartet states generated upon photoexcitation and illustrate that (i) a coherent manipulation of the spin state is possible in these systems even at room temperature and that (ii) a spin coherence time of 0.7 μs can be achieved under these conditions. This demonstration of electron spin coherence at ambient temperatures paves the way for practical applications of such systems in functional molecular devices.

Direct determination of high-order transverse ligand field parameters via µSQUID-EPR in a Et4N[160GdPc2] SMM

The development of quantum technologies requires a thorough understanding of systems possessing quantum effects that can ultimately be manipulated. In the field of molecular magnetism, one of the main challenges is to measure high-order ligand field parameters, which play an essential role in the relaxation properties of SMMs. The development of highly advanced theoretical calculations has allowed the ab-initio determination of such parameters; however, currently, there is a lack of quantitative assessment of how good the ab-initio parameters are. In our quest for technologies that can allow the extraction of such elusive parameters, we develop an experimental technique that combines the EPR spectroscopy and µSQUID magnetometry. We demonstrate the power of the technique by performing EPR-µSQUID measurement of a magnetically diluted single crystal of Et₄N[GdPc₂], by sweeping the magnetic field and applying a range of multifrequency microwave pulses. As a result, we were able to directly determine the high-order ligand field parameters of the system, enabling us to test theoretical predictions made by state-of-the-art ab-initio methods.

Thermalization of Nuclear Spins in Lanthanide Molecular Magnets

Single-molecule magnets (SMMs) distinguish themselves in the field of quantum magnetism through the ability to combine fundamental research with promising applications. The evolution of quantum spintronics in the last decade exemplifies the potential held by molecular-based quantum devices. Notably, the readout and manipulation of the nuclear spin states embedded in a lanthanide-based SMM hybrid device were employed in proof of principle studies of quantum computation at the single-molecule level. In the quest for further understanding of the relaxation behavior in SMMs for their integration in novel applications, herein, we study the relaxation dynamics of the ¹⁵⁹Tb nuclear spins in a diluted molecular crystal employing the recently acquired understanding of the nonadiabatic dynamics of TbPc₂ molecules. Through numerical simulation, we find that phonon-modulated hyperfine interaction opens a direct relaxation channel between the nuclear spins and the phonon bath. The mechanism is of potential importance for the theory of spin bath and the relaxation dynamics of the molecular spins.

Lanthanide-radical single-molecule magnets: current status and future challenges

In the field of molecular magnetism, the lanthanide-radical (Ln-Rad) method has become one of the most appealing tactics for introducing strong magnetic interactions and has spurred on the booming development of heterospin single-molecule magnets (SMMs). The article is a timely retrospect on the research progress of Ln-Rad heterospin systems and special attention is invested on low dimensional Ln-Rad compounds with SMM behavior, primarily concerning with nitrogen-based radicals, semiquinone and nitroxide radicals. Rational design, molecular structures, magnetic behaviors and magneto-structural correlations are highlighted. Meanwhile, particular attention is focused on the influence of exchange couplings on the dynamic magnetic properties, with the purpose of helping to guide the design of prospective radical-based Ln-SMMs.

Binuclear spin-crossover [Fe(bt)(NCS)2]2(bpm) complex: A study using first principles calculations

The spin-crossover [Fe(bt)(NCS)₂]₂(bpm) complex is studied using spin-polarized density functional theory within the generalized gradient approximation, the Hubbard U and the weak van der Waals interactions in conjunction with the projector augmented wave method in its molecular and periodic arrangements. It is shown that the considered complex has three magnetic configurations [high spin state (HS)-HS, HS-low spin state (LS), and LS-LS] corresponding to those observed experimentally after two transition temperatures T_c ⁽¹⁾ of 163 K and T_c ⁽²⁾ of 197 K. For the HS-HS magnetic state, we found that the two Fe centers are antiferromagnetically coupled for both molecular and periodic structures in good agreement with the experimental observations. Our results show that the computed total energy difference between the magnetic state configurations of the considered Fe₂ complex is significantly smaller compared to those reported in the literature for other mono- or binuclear compounds.

The critical role of ultra-low-energy vibrations in the relaxation dynamics of molecular qubits

Improving the performance of molecular qubits is a fundamental milestone towards unleashing the power of molecular magnetism in the second quantum revolution. Taming spin relaxation and decoherence due to vibrations is crucial to reach this milestone, but this is hindered by our lack of understanding on the nature of vibrations and their coupling to spins. Here we propose a synergistic approach to study a prototypical molecular qubit. It combines inelastic X-ray scattering to measure phonon dispersions along the main symmetry directions of the crystal and spin dynamics simulations based on DFT. We show that the canonical Debye picture of lattice dynamics breaks down and that intra-molecular vibrations with very-low energies of 1-2 meV are largely responsible for spin relaxation up to ambient temperature. We identify the origin of these modes, thus providing a rationale for improving spin coherence. The power and flexibility of our approach open new avenues for the investigation of magnetic molecules with the potential of removing roadblocks toward their use in quantum devices.

Controlled Hydrolysis of Phosphate Esters: A Route to Calixarene-Supported Rare-Earth Clusters

Phosphate ester bonds are widely present in nature (e. g. DNA/RNA) and can be extremely stable against hydrolysis without the help of catalysts. Previously, we showed how the combination of phosphoryl and calix[4]arene moieties in the same organic framework (L_PO ) allows isolation of single lanthanide (Ln) metal ions as [Ln^III (L_PO )₂ ](O₃ SCF₃ )₃ . Here we report how by controlling the reaction conditions a new hydrolyzed phosphoryl-calix[4]arene ligand (H₃ L_HPO ) is formed as a result of Ln^III -mediated P-OEt bond cleavage in three out of the eight possible sites in L_PO . The chelating nature of H₃ L_HPO traps the Ln^III species in the form of [Ln^III (L_HPO )((EtO)₂ P(O)OH)]₂ dimers (Ln=La, Dy, Tb, Gd), where the Dy derivative shows slow magnetization relaxation. The strategy presented herein could be extended to access a broader library of hydrolyzed platforms (H_x L_HPO ; x=1-8) that may represent mimics of nuclease enzymes.

Intramolecular Ferromagnetism in Di-Nuclear 3 d-Transition-Metal Single-Molecule Magnets by Pseudo-Serial Arrangement

Di-nuclear citrate complexes, [CH₆ N₃ ]₂ [M₂ (citH)₂ (H₂ O)₄ ] ⋅ 2H₂ O (citH₄ =citric acid; M=Fe^II (Fe-2), Co^II (Co-2), and Ni^II (Ni-2)), are synthesized. The ligand, citH^3- , is deprotonated only at the three carboxy groups, which is different from the previously reported tetra-nuclear structures with cit^4- ligands. Magnetic measurements reveal that these complexes have intramolecular ferromagnetism with J=∼0 cm^-1 (Ni-2), 0.02 cm^-1 (Co-2), and 0.04 cm^-1 (Fe-2). Co-2 and Fe-2 show slow magnetic relaxation, and are field-induced SMMs with activation energy of spin-reversal U_eff =27 cm^-1 (Co-2) and 4.2 cm^-1 (Fe-2). Density functional theory calculations indicate that the uniaxial anisotropy along the z-axis of each metal ion center forms the pseudo-serial arrangement, leading to intramolecular ferromagnetism via the magnetic dipole interaction. This work demonstrates the creation of ferromagnetic SMMs by the magnetic dipole engineering of 3d di-nuclear metal ion centers.

Molecular cyclo-P3 complexes of the rare-earth elements via a one-pot reaction and selective reduction

Synthesis of new organo-lanthanide polyphosphides with an aromatic cyclo-[P₄]^2- moiety and a cyclo-[P₃]^3- moiety is presented. For this purpose, the divalent Ln^II-complexes [(NON)Ln^II(thf)₂] (Ln = Sm, Yb) ((NON)^2- = 4,5-bis(2,6-diisopropylphenyl-amino)-2,7-di-tert-butyl-9,9-dimethylxanthene) and trivalent Ln^III-complexes [(NON)Ln^IIIBH₄(thf)₂] (Ln = Y, Sm, Dy) were used as precursors in the reduction process of white phosphorus. While using [(NON)Ln^II(thf)₂] as a one-electron reducing agent the formation of organo-lanthanide polyphosphides with a cyclo-[P₄]^2- Zintl anion was observed. For comparison, we investigated a multi-electron reduction of P₄ by a one-pot reaction of [(NON)Ln^IIIBH₄(thf)₂] with elemental potassium. As products molecular polyphosphides with a cyclo-[P₃]^3- moiety were isolated. The same compound could also be obtained by reducing the cyclo-[P₄]^2- Zintl anion within the coordination sphere of Sm^III in [{(NON)Sm^III(thf)₂}₂(μ-η⁴:η⁴-P₄)]. Reduction of a polyphosphide within the coordination sphere of a lanthanide complex is unprecedented. Additionally, the magnetic properties of the dinuclear Dy^III-compound bearing a bridging cyclo-[P₃]^3- moiety were investigated.

Heterometallic clusters based on an uncommon asymmetric "V-shaped" [Fe3+(μ-OR)Ln3+(μ-OR)2Fe3+]6+ (Ln = Gd, Tb, Dy, Ho) structural core and the investigation of the slow relaxation of the magnetization behaviour of the [Fe2Dy] analogue

The synthesis, crystal structures, Mössbauer spectra and variable temperature dc and ac magnetic susceptibility studies of a new family of trinuclear heterometallic Fe³⁺/Ln³⁺ complexes, [Fe₂Ln(PhCO₂)₃((py)₂CO₂)((py)₂C(OMe)O)₂(NO₃)Cl] (Ln = Gd (1/Gd), Tb (1/Tb), Dy (1/Dy), and Ho (1/Ho)), where (py)₂CO₂^2- and (py)₂C(OMe)O^- are the anions of the gem-diol and hemiketal derivatives of di-2-pyridyl ketone, are reported. Compounds 1/Ln are based on an asymmetric "V-shaped" [Fe³⁺(μ-OR)Ln(μ-OR)₂Fe³⁺]⁶⁺ structural core formed from the connection of the two terminal Fe³⁺ centers to the central Ln³⁺ ion either through one or two alkoxide groups originating from the alkoxide-type bridging ligands. Direct current magnetic susceptibility studies reveal the presence of weak antiferromagnetic interactions between the Fe³⁺ ions. Alternating current magnetic studies indicate the presence of a slow-magnetic relaxation process in 1/Dy with an energy barrier U_eff = 6.7 (±0.3) K and a pre-exponential factor, τ₀ = 2.2 (±0.4) × 10^-7 s. The electronic, magnetic and relaxation properties of the complexes were further monitored by variable temperature ⁵⁷Fe Mössbauer spectroscopy. At T > 80 K the spectra from the complexes comprise two quadrupole doublets the hyperfine parameters of which reflect the distinct coordination environment of the two Fe³⁺ terminal sites. At T < 20 K, the Mössbauer spectra for 1/Dy are affected by magnetic relaxation effects. At 1.5 K, the spectrum of 1/Dy comprises well defined magnetic sextets indicating relaxation times slower than the characteristic time of the Mössbauer technique (10^-7 s) in agreement with the dynamic magnetic measurements. 1/Gd exhibits broad unresolved magnetic sextets at 1.5 K indicating that the spin relaxation time is of the order of the Mössbauer characteristic time at this temperature. For 1/Tb, 1/Ho the Mössbauer spectra exhibit slight broadening even at the lowest available temperature consistent with magnetic relaxation times less than 10^-7 s.

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.

Molecular Lanthanide Switches for Magnetism and Photoluminescence

Solvation of [(CNT)Ln(η⁸ -COT)] (Ln=La, Ce, Nd, Tb, Er; CNT=cyclononatetraenyl, i.e., C₉ H₉ ^- ; COT=cyclooctatetraendiid, i.e., C₈ H₈ ^2- ) complexes with tetrahydrofuran (THF) gives rise to neutral [(η⁴ -CNT)Ln(thf)₂ (η⁸ -COT)] (Ln=La, Ce) and ionic [Ln(thf)_x (η⁸ -COT)][CNT] (x=4 (Ce, Nd, Tb), 3 (Er)) species in a solid-to-solid transformation. Due to the severe distortion of the ligand sphere upon solvation, these species act as switchable luminophores and single-molecule magnets. The desolvation of the coordinated solvents can be triggered by applying a dynamic vacuum, as well as a temperature gradient stimulus. Raman spectroscopic investigations revealed fast and fully reversible solvation and desolvation processes. Moreover, we also show that a Nd:YAG laser can induce the necessary temperature gradient for a self-sufficient switching process of the Ce(III) analogue in a spatially resolved manner.

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.

Self-assembly of fish-bone and grid-like CoII-based single-molecule magnets using dihydrazone ligands with NNN and NNO pockets

Three Co^II complexes, [Co₂(H₂L¹)₂](ClO₄)₄·4CH₃OH (1), [Co₂(H₄L²)₂](ClO₄)₄ (2) and [Co₄(H₄L²)₄](ClO₄)₈ (3), were constructed by the self-assembly of the symmetrical dihydrazone ligands H2L1 and H4L2 with Co^II ions under different synthetic conditions. The fish-bone-like complex 1 was obtained using the ligand H2L1 in methanol via the solvothermal method, while the self-assembly of H4L2 with Co^II ions is solvent-dependent, producing the fish-bone-like complex 2 and [2 × 2] grid-like complex 3. Magnetic susceptibility measurements and theoretical calculations reveal that the large negative D values for the three complexes stem from their easy-axis magnetic anisotropy. Ac magnetic susceptibility measurements disclosed field-induced slow magnetic relaxation behaviors and the presence of Raman and/or direct processes of the three complexes at various applied dc fields.

Five-Spin Supramolecule for Simulating Quantum Decoherence of Bell States

We report a supramolecule that contains five spins of two different types and with, crucially, two different and predictable interaction energies between the spins. The supramolecule is characterized, and the interaction energies are demonstrated by electron paramagnetic resonance (EPR) spectroscopy. Based on the measured parameters, we propose experiments that would allow this designed supramolecule to be used to simulate quantum decoherence in maximally entangled Bell states that could be used in quantum teleportation.

Extending the Spin Excitation Lifetime of a Magnetic Molecule on a Proximitized Superconductor

Molecular spins on surfaces potentially used in quantum information processing and data storage require long spin excitation lifetimes. Normally, coupling of the molecular spin with the conduction electrons of metallic surfaces causes fast relaxation of spin excitations. However, the presence of superconducting pairing effects in the substrate can protect the excited spin from decaying. In this work, we show that a proximity-induced superconducting gold film can sustain spin excitations of a FeTPP-Cl molecule for more than 80 ns. This long value was determined by studying inelastic spin excitations of the S = 5/2 multiplet of FeTPP-Cl on Au films over V(100) using scanning tunneling spectroscopy. The spin lifetime decreases with increasing film thickness, along with the decrease of the effective superconducting gap. Our results elucidate the use of proximitized gold electrodes for addressing quantum spins on surfaces, envisioning new routes for tuning the value of their spin lifetime.

Theoretical Design of Optimal Molecular Qudits for Quantum Error Correction

We pinpoint the key ingredients ruling decoherence in multispin clusters, and we engineer the system Hamiltonian to design optimal molecules embedding quantum error correction. These are antiferromagnetically coupled systems with competing exchange interactions, characterized by many low-energy states in which decoherence is dramatically suppressed and does not increase with the system size. This feature allows us to derive optimized code words, enhancing the power of the quantum error correction code by orders of magnitude. We demonstrate this by a complete simulation of the system dynamics, including the effect of decoherence driven by a nuclear spin bath and the full sequence of pulses to implement error correction and logical gates between protected states.

Correlation anisotropy driven Kosterlitz-Thouless-type quantum phase transition in a Kondo simulator

The precise manipulation of the quantum states of individual atoms/molecules adsorbed on metal surfaces is one of the most exciting frontiers in nanophysics, enabling us to realize novel single molecular logic devices and quantum information processing. Herein, by modeling an iron phthalocyanine molecule adsorbed on the Au(111) surface with a two-impurity Anderson model, we demonstrate that the quantum states of such a system could be adjusted by the uniaxial magnetic anisotropy D_z. For negative D_z, the ground state is dominated by a parallel configuration of the z component of local spins, whereas it turns to be an antiparallel one when D_z becomes positive. Interestingly, we found that these two phases are separated by a Kosterlitz-Thouless-type quantum phase transition, which is confirmed by the critical behaviors of the transmission coefficient and the local magnetic moment. Both phases are associated with spin correlation anisotropy, thus move against the Kondo effect. When the external magnetic field is applied, it first plays a role in compensating for the effect of D_z, and then it contributes significantly to the Zeeman effect for positive D_z, accompanied by the reappearance and the splitting of the Kondo peak, respectively. For fixed negative D_z, only the Zeeman behavior is revealed. Our results provide deep insights into the manipulation of the quantum phase within a single molecular junction.

Spin-State Modulation in FeII -Based Hofmann-Type Coordination Polymers: From Molecules to Materials

Spin crossover complexes that reversibly interconvert between two stable states imitate a binary state of 0 and 1, delivering a promising possibility to address the data processing concept in smart materials. Thus, a comprehensive understanding of the modulation of magnetic transition between high spin and low spin and the factors responsible for stabilizing the spin states is an essential theme in modern materials design. In this context, the present review attempts to provide a concise outline of the design strategy employed at the molecular level for fine-tuning the spin-state switching in Fe^II -based Hofmann-type coordination polymers and their effects on the optical and magnetic response. In addition, development towards the nanoscale architectures of HCPs, i. e., in terms of nanoparticles and thin films, are emphasized to bridge the gap between the laboratory and reality.

Chemical control of spin-lattice relaxation to discover a room temperature molecular qubit

The second quantum revolution harnesses exquisite quantum control for a slate of diverse applications including sensing, communication, and computation. Of the many candidates for building quantum systems, molecules offer both tunability and specificity, but the principles to enable high temperature operation are not well established. Spin-lattice relaxation, represented by the time constant T ₁, is the primary factor dictating the high temperature performance of quantum bits (qubits), and serves as the upper limit on qubit coherence times (T ₂). For molecular qubits at elevated temperatures (>100 K), molecular vibrations facilitate rapid spin-lattice relaxation which limits T ₂ to well below operational minimums for certain quantum technologies. Here we identify the effects of controlling orbital angular momentum through metal coordination geometry and ligand rigidity via π-conjugation on T ₁ relaxation in three four-coordinate Cu²⁺ S = ½ qubit candidates: bis(N,N'-dimethyl-4-amino-3-penten-2-imine) copper(ii) (Me₂Nac)₂ (1), bis(acetylacetone)ethylenediamine copper(ii) Cu(acacen) (2), and tetramethyltetraazaannulene copper(ii) Cu(tmtaa) (3). We obtain significant T ₁ improvement upon changing from tetrahedral to square planar geometries through changes in orbital angular momentum. T ₁ is further improved with greater π-conjugation in the ligand framework. Our electronic structure calculations reveal that the reduced motion of low energy vibrations in the primary coordination sphere slows relaxation and increases T ₁. These principles enable us to report a new molecular qubit candidate with room temperature T ₂ = 0.43 μs, and establishes guidelines for designing novel qubit candidates operating above 100 K.

A Tetranuclear Dysprosium Schiff Base Complex Showing Slow Relaxation of Magnetization

A tetranuclear dysprosium Schiff base complex was isolated by reacting dysprosium chloride with 2-hydroxy-3-methoxybenzaldehyde and 2-(aminomethyl)pyridine in-situ under basic conditions. The isolated Dy(III) complex was characterized by elemental analyses, single crystal X-ray diffraction and molecular spectroscopy. The complex crystallizes in the triclinic space group P-1 with unit cell parameters of a = 10.2003 (4), b = 13.8602 (5), c = 14.9542 (6), α = 94.523 (3), β = 109.362 (4), and γ = 99.861 (3). The magnetic properties of 1 have been investigated by DC and AC susceptibility measurements. The DC measurements reveal weak exchange coupling of antiferromagnetic nature. In the AC measurement, the complex shows a slow relaxation of magnetization in the absence of an external magnetic field.

Harnessing Colossal Magnetic Anisotropy in Sandwiched 3d2-Metallocenes

Single-molecule magnets are gaining attention in recent years with the growing focus on achieving higher barriers of magnetization reversal. Metallocenes, owing to their unique sandwiched structure, assure themselves as plausible molecular systems for the development of novel single-molecule magnets (SMMs). Here in this work, we have explicitly investigated metallocenes of first-row transition elements, along with their one-electron-oxidized (cationic) and -reduced (anionic) analogues, for their magnetic anisotropies by adopting multireference ab initio calculations. Herein, we report a high magnetic anisotropy for 3d² systems among all 3d-metallocenes.

An All-Organic Photochemical Magnetic Switch with Bistable Spin States

Controlling the electronic spin state in single molecules through an external stimulus is of interest in developing devices for information technology, such as data storage and quantum computing. We report the synthesis and operation mode of two all-organic molecular spin-state switches that can be photochemically switched from a diamagnetic [electron paramagnetic resonance (EPR)-silent] to a paramagnetic (EPR-active) form at cryogenic temperatures due to a reversible electrocyclic reaction of its carbon skeleton. Facile synthetic substitution of a configurationally stable 1,14-dimethyl-[5]helicene with radical stabilizing groups at the 4,11-positions afforded two spin-state switches as 4,11-dioxo or 4,11-bis(dicyanomethylidenyl) derivatives in a closed diamagnetic form. After irradiation with an LED light source at cryogenic temperatures, a stable paramagnetic state is readily obtained, making this system a bistable magnetic switch that can reversibly react back to its diamagnetic form through a thermal stimulus. The switching can be monitored with UV/vis spectroscopy and EPR spectroscopy or induced by electrochemical reduction and reoxidation. Variable-temperature EPR spectroscopy of the paramagnetic species revealed an open-shell triplet ground state with an experimentally determined triplet-singlet energy gap of ΔE_T-S < 0.1 kcal mol^-1. The inherent chirality and the ability to separate the enantiomers turns this helical motif into a potential chiroptical spin-state switch. The herein developed 4,11-substitution pattern on the dimethyl[5]helicene introduces a platform for designing future generations of organic molecular photomagnetic switches that might find applications in spintronics and related fields.

Spin-Electric Coupling with Anisotropy-Induced Vanishment and Enhancement in Molecular Ferroelectrics

Manipulating quantum properties by electric fields using spin-electric coupling (SEC) effects promises spatial addressability. While several studies about inorganic materials showing the SEC functionality have been reported, the vastly tunable crystal structures of molecular ferroelectrics provide a range of rationally designable materials yet to be exploited. In this work, Mn²⁺-doped molecular ferroelectrics are chosen to experimentally demonstrate the feasibility of achieving the quantum coherent SEC effect in molecular ferroelectrics for the first time. The electric field pulse applied between Hahn-echo pulses in electron paramagnetic resonance (EPR) experiments causes controllable phase shifts via manipulating of the zero-field splitting (ZFS) of the Mn(II) ions. Detailed investigations of the aMn crystal showed unexpected SEC vanishment and enhancement at different crystal orientations, which were elucidated by studying the spin Hamiltonian and magnetic anisotropy. With the enhanced SEC efficiency being achieved (0.68 Hz m/V), this work discovers an emerging material library of molecular ferroelectrics to implement coherent quantum control with selective and tunable SEC effects toward highly scalable quantum gates.