Direct observation of quantum coherence in single-molecule magnets

The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes

The correct interpretation of magnetic properties in the weak-exchange regime has remained a challenging task for several decades. In this regime, the effective exchange interaction between local spins is quite weak, of the same order of magnitude or smaller than the various anisotropic terms, which generates a complex set of levels characterized by spin mixing. Although the model multispin Hamiltonian in the absence of local orbital momentum, , is considered good enough to map the experimental energies at zero field and in the strong-exchange limit, theoretical works pointed out limitations of this simple model. This work revives the use of ĤMS from a new theoretical perspective, detailing point-by-point a strategy to correctly map the computational energies and wave functions onto ĤMS, thus validating it regardless of the exchange limit. We will distinguish two cases, based on experimentally characterized dicobalt(II) complexes from the literature. If centrosymmetry imposes alignment of the various rank-2 tensors constitutive of ĤMS in the first case, the absence of any symmetry element prevents such alignment in the second case. In such a context, the strategy provided herein becomes a powerful tool to rationalize the experimental magnetic data, since it is capable of fully and rigorously extracting the multispin model without any assumption on the orientation of its constitutive tensors. Furthermore, the strategy allows to question the use of the spin Hamiltonian approach by explicitly controlling the projection norms on the model space, which is showcased in the second complex where local orbital momentum could have occurred (distorted octahedra). Finally, previous theoretical data related to a known dinickel(II) complex is reinterpreted, clarifying initial wanderings regarding the weak exchange limit.

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.

A Combined Synthetic, Magnetic, and Theoretical Study on Enhancing Ligand-Field Axiality for Dy(III) Single-Molecule Magnets Supported by Ferrocene Diamide Ligands

Molecular design is crucial for improving the performance of single-molecule magnets (SMMs). For dysprosium(III) SMMs, enhancing ligand-field axiality is a well-suited strategy to achieve high-performance SMMs. We synthesized a series of dysprosium(III) complexes, (NN^TIPS)DyBr(THF)₂ (1, NN^TIPS = fc(NSiⁱPr₃)₂; fc = 1,1'-ferrocenediyl, THF = tetrahydrofuran), [(NN^TIPS)Dy(THF)₃][BPh₄] (2), (NN^TIPS)DyI(THF)₂ (3), and [(NN^TBS)Dy(THF)₃][BPh₄] (4, NN^TBS = fc(NSi^tBuMe₂)₂), supported by ferrocene diamide ligands. X-ray crystallography shows that the rigid ferrocene backbone enforces a nearly axial ligand field with weakly coordinating equatorial ligands. Dysprosium(III) complexes 1-4 all exhibit slow magnetic relaxation under zero fields and possess high effective barriers (U_eff) around 1000 K, comparable to previously reported (NN^TBS)DyI(THF)₂ (5). We probed the influences of structural variations on SMM behaviors by theoretical calculations and found that the distribution of negative charges defined by r_q, i.e., the ratio of the charges on the axial ligands to the charges on the equatorial ligands, plays a decisive role. Moreover, theoretical calculations on a series of model complexes 1'-5' without equatorial ligands unveil that the axial crystal-field parameters B₂⁰ are directly proportional to the N-Dy-N angles and support the hypothesis that enhancing the ligand-field axiality could improve SMM performance.

Long-lived electronic spin qubits in single-walled carbon nanotubes

Electron spins in solid-state systems offer the promise of spin-based information processing devices. Single-walled carbon nanotubes (SWCNTs), an all-carbon one-dimensional material whose spin-free environment and weak spin-orbit coupling promise long spin coherence times, offer a diverse degree of freedom for extended range of functionality not available to bulk systems. A key requirement limiting spin qubit implementation in SWCNTs is disciplined confinement of isolated spins. Here, we report the creation of highly confined electron spins in SWCNTs via a bottom-up approach. The record long coherence time of 8.2 µs and spin-lattice relaxation time of 13 ms of these electronic spin qubits allow demonstration of quantum control operation manifested as Rabi oscillation. Investigation of the decoherence mechanism reveals an intrinsic coherence time of tens of milliseconds. These findings evident that combining molecular approaches with inorganic crystalline systems provides a powerful route for reproducible and scalable quantum materials suitable for qubit applications.

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin-flip DFT and Heisenberg effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For 12 binuclear complexes with J-values ranging from -6 to -132 cm^-1 , our benchmark calculations using the short-range hybrid ωPBEh functional and 6-31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm^-1 ). For the tetranuclear SMMs, the computed J constants are within 6 cm^-1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

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.

Zero-Field Splitting Calculations by Multiconfiguration Pair-Density Functional Theory

Zero-field splitting (ZFS) is a fundamental molecular property that is especially relevant for single-molecule magnets (SMMs), electron paramagnetic resonance spectra, and quantum computing. Developing a method that can accurately predict ZFS parameters can be very powerful for designing new SMMs. One of the challenges is to include external correlation in an inherently multiconfigurational open-shell species for the accurate prediction of magnetic properties. Previously available methods depend on expensive multireference perturbation theory calculations to include external correlation. In this paper, we present spin-orbit-inclusive multiconfiguration and multistate pair-density functional theory (MC-PDFT) calculations of ZFSs; these calculations have a cost comparable to complete-active-space self-consistent field (CASSCF) theory, but they include correlation external to the active space. We found that combining a multistate formulation of MC-PDFT, namely, compressed-state multistate pair-density functional theory, with orbitals optimized by weighted-state-averaged CASSCF, yields reasonably accurate ZFS results.

A cyanide-bridged Fe-Co pearl-chain-like single-chain magnet containing 4-coordinate cobalt(II) ions

Treatment of CoCl₂·6H₂O and tris(pyrazolyl-1-yl)borate tricyanoiron(III) anions at an elevated temperature (55 °C) afforded two less-common pearl-chain-like compounds, {[(Tp^R)Fe(CN)₃CoCl₂]₂Co(DMF)₄}·nDMF (1, Tp^R = Tp^4-Me = hydridotris(4-methylpyrazol-1-yl)borate, n = 1 and 2, Tp^R = Tp*^Me = hydridotris(3,4,5-trimethylpyrazol-1-yl)borate, n = 4.5), in which the 4-coordinate Co(II) ions and [(Tp^R)Fe^III(CN)₃]^- units are alternately bridged by cyanide groups into squares, which are further linked with the 6-coordinate Co(II) ions into an infinite chain. Interestingly, the magnetic study revealed that 1 exhibits a typical single-chain magnet behaviour with an effective energy barrier of 28.0 K, while surprisingly no Glauber dynamics was observed for 2 despite their very similar structures. The variations of the local coordination environments of the cobalt ions and the cyanide linkages were evidenced, and they may account for the significant difference in their magnetic properties related to the global magnetic anisotropy and magnetic exchange of the chain.

Lanthanide Complexes with a Tripodal Nitroxyl Radical Showing Strong Magnetic Coupling

A series of isomorphous mononuclear complexes of Ln(III) ions comprising one stable tripodal oxazolidine nitroxyl radical were obtained in acetonitrile media starting from nitrates. The compounds, [LnRad(NO₃)₃] (Ln = Gd, Tb, Dy, Tm, Y; Rad = 4,4-dimethyl-2,2-bis(pyridin-2-yl)-1,3-oxazolidine-3-oxyl), have a molecular structure. Their coordination polyhedron, LnO₇N₂, can be described as a tricapped trigonal prism with symmetry not far from D_3h. The extracted value of 23 cm^-1 for the antiferromagnetic coupling of Gd-Rad established from the DC magnetic and EPR data is a record strength for the complexes of 4f elements with nitroxyl radicals. The terbium derivative displays frequency-dependent out-of-phase signals in zero field, indicating single-molecule magnetic behavior. With an applied field of 0.1 T, an effective barrier of 57 cm^-1 is found.

Toward Long-Range Entanglement between Electrically Driven Single-Molecule Magnets

Over the past two decades, several molecules have been explored as possible building blocks of a quantum computer, a device that would provide exponential speedups for a number of problems, including the simulation of large, strongly correlated chemical systems. Achieving strong interactions and entanglement between molecular qubits remains an outstanding challenge. Here, we show that the TbPc₂ single-molecule magnet has the potential to overcome this obstacle because of its sensitivity to electric fields stemming from the hyperfine Stark effect. We show how this feature can be leveraged to achieve long-range entanglement between pairs of molecules using a superconducting resonator as a mediator. Our results suggest that the molecule-resonator interaction is near the edge of the strong-coupling regime and could potentially pass into it given a more detailed, quantitative understanding of the TbPc₂ molecule.

Nuclear-spin-pattern control of electron-spin dynamics in a series of V(iv) complexes

Achieving control of phase memory relaxation times (T m) in metal ions is an important goal of molecular spintronics. Herein we provide the first evidence that nuclear-spin patterning in the ligand shell is an important handle to modulate T m in metal ions. We synthesized and studied a series of five V(iv) complexes with brominated catecholate ligands, [V(C6H4-n Br n O2)3]2- (n = 0, 1, 2, and 4), where the 79/81Br and 1H nuclear spins are arranged in different substitutional patterns. High-field, high-frequency (120 GHz) pulsed electron paramagnetic resonance spectroscopic analysis of this series reveals a pattern-dependent variation in T m for the V(iv) ion. Notably, we show that it is possible for two molecules to have starkly different (by 50%) T m values despite the same chemical composition. Nuclear magnetic resonance analyses of the protons on the ligand shell suggest that relative chemical shift (δ), controlled by the patterning of nuclear spins, is an important underlying design principle. Here, having multiple ligand-based protons with nearly identical chemical shift values in the ligand shell will, ultimately, engender a short T m for the bound metal ion.

Sub-Kelvin (100 mK) time resolved electron paramagnetic resonance spectroscopy for studies of quantum dynamics of low-dimensional spin systems at low frequencies and magnetic fields

This article presents a time-resolved electron paramagnetic resonance spectrometry setup designed to work at frequencies below 20 GHz and temperatures down to 50 mK. The setup consists of an on-chip microstrip resonator (Q < 100) placed in a dilution cryostat located within a superconducting 3D vector magnet. A housemade spin echo circuitry controlled by a microwave network analyzer, a pulse pattern generator, and an oscilloscope connects to the microstrip through a series of copper, stainless steel, and superconducting semirigid coaxial lines which are thermally anchored to the different cooling stages of the fridge by means of power attenuators, circulators, and a cryogenic amplifier. Spin echo experiments were performed at a 0.5-T magnetic field on a spin 1 2 paramagnetic coal marker sample mounted on a 15 GHz microstrip resonator at temperatures ranging from 100 to 800 mK. The results show an increase in echo signal intensity as temperature is decreased until saturation as theoretically expected in reaching 99% spin polarization at 100 mK. Our technique allows tuning of the spin system in the pure-state regime and minimizing dipolar fluctuations, which are the main contribution to decoherence in solid-state samples of single-molecule magnets (SMMs) - molecular spin systems that are currently being tested for applications in quantum computation. The achievement of full spin polarization at 100 mK will allow for coherent control over the time evolution of spin systems without the need for large magnetic fields (commonly used to polarize the dipolar bath at higher temperatures) and high frequencies.

General framework for calculating spin-orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions

Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., M_s = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner-Eckart's theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin-orbit matrix elements by applying Wigner-Eckart's theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born-Oppenheimer's separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin-orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin-orbit treatment. Intrinsic issues of constructing spin-orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

Chromium(iii)-based potential molecular quantum bits with long coherence times

Molecular quantum bits based on copper(ii) or vanadium(iv) have been shown to possess long coherence times on multiple occasions. In contrast, studies in which non-spin-½ ions are employed are relatively scarce. High-spin ions provide additional states that can be used to encode further quantum bits. Furthermore, an optical rather than a microwave readout of molecular quantum bits is highly desirable, because in principle it could allow addressing at the single quantum bit level. The chromium(iii) complex [Cr(ddpd)2]3+ (ddpd = N,N'-dimethyl-N,N'-dipyridine-2-yl-pyridine-2,6-diamine) combines both the large spin (S = 3/2) and optical activity (strong, long lived luminescence). Here we demonstrate that the compound possesses coherence times of up to 8.4(1) μs, which are much longer (at least three times) than those for other chromium(iii)-based compounds. On the other hand, it is proved to be impossible to read out or influence the quantum state by optical means, underlining that further work is needed in this direction.

Singlet-triplet energy gaps and the degree of diradical character in binuclear copper molecular magnets characterized by spin-flip density functional theory

Molecular magnets, defined here as organic polyradicals, can be used as building blocks in the fabrication of novel and structurally diverse magnetic light-weight materials. We present a theoretical investigation of the lowest spin states of several binuclear copper diradicals. In contrast to previous studies, we consider not only the energetics of the low-lying states (which are related to the exchange-coupling parameter within the Heisenberg-Dirac-van-Vleck model), but also the character of the diradical states themselves. We use natural orbitals, their occupations, and the number of effectively unpaired electrons to quantify bonding patterns in these systems. We compare the performance of spin-flip time-dependent density functional theory (SF-TDDFT) using various functionals and effective core potentials against the wave function based approach, equation-of-motion spin-flip coupled-cluster method with single and double substitutions (EOM-SF-CCSD). We find that SF-TDDFT paired with the PBE50 and B5050LYP functionals performs comparably to EOM-SF-CCSD, with respect to both singlet-triplet gaps and states' characters. Visualization of frontier natural orbitals shows that the unpaired electrons are localized on copper centers, in some cases exhibiting slight through-bond interaction via copper d-orbitals and p-orbitals of neighboring ligand atoms. The analysis reveals considerable interactions between the formally unpaired electrons in the antiferromagnetic diradicaloids, meaning that they are poorly described by the Heisenberg-Dirac-van-Vleck model. Thus, for these systems the experimentally derived exchange-coupling parameters are not directly comparable with the singlet-triplet gaps. This explains systematic discrepancies between the computed singlet-triplet energy gaps and the exchange-coupling parameters extracted from experiment.

Comparison of the Magnetic Anisotropy and Spin Relaxation Phenomenon of Dinuclear Terbium(III) Phthalocyaninato Single-Molecule Magnets Using the Geometric Spin Arrangement

Herein we report the synthesis and characterization of a dinuclear Tb^III single-molecule magnet (SMM) with two [TbPc₂]⁰ units connected via a fused-phthalocyaninato ligand. The stable and robust complex [(obPc)Tb(Fused-Pc)Tb(obPc)] (1) was characterized by using synchrotron radiation measurements and other spectroscopic techniques (ESI-MS, FT-IR, UV). The magnetic couplings between the Tb^III ions and the two π radicals present in 1 were explored by means of density functional theory (DFT). Direct and alternating current magnetic susceptibility measurements were conducted on magnetically diluted and nondiluted samples of 1, indicating this compound to be an SMM with improved properties compared to those of the well-known [TbPc₂]^-/0/+ and the axially symmetric dinuclear Tb^III phthalocyaninato triple-decker complex (Tb₂(obPc)₃). Assuming that the probability of quantum tunneling of the magnetization (QTM) occurring in one TbPc₂ unit is P_QTM, the probability of QTM simultaneously occurring in 1 is P_QTM², meaning that QTM is effectively suppressed. Furthermore, nondiluted samples of 1 underwent slow magnetic relaxation times (τ ≈ 1000 s at 0.1 K), and the blocking temperature (T_B) was determined to be ca. 16 K with an energy barrier for spin reversal (U_eff) of 588 cm^-1 (847 K) due to D_4d geometry and weak inter- and intramolecular magnetic interactions as an exchange bias (H_bias), reducing QTM. Four hyperfine steps were observed by micro-SQUID measurement. Furthermore, solution NMR measurements (one-dimensional, two-dimensional, and dynamic) were done on 1, which led to the determination of the high rotation barrier (83 ± 10 kJ/mol) of the obPc ligand. A comparison with previously reported Tb^III triple-decker compounds shows that ambient temperature NMR measurements can indicate improvements in the design of coordination environments for SMMs. A large U_eff causes strong uniaxial magnetic anisotropy in 1, leading to a χ_ax value (1.39 × 10^-30 m³) that is larger than that for Tb₂(obPc)₃ (0.86 × 10^-30 m³). Controlling the coordination environment and spin arrangement is an effective technique for suppressing QTM in TbPc₂-based SMMs.

Unexpected suppression of spin-lattice relaxation via high magnetic field in a high-spin iron(iii) complex

A counterintuitive three-order of magnitude slowing of the spin-lattice relaxation rate is observed in a high spin qubit at high magnetic field via multifrequency pulsed electron paramagnetic resonance measurements.

Qubit crossover in the endohedral fullerene Sc3C2@C80

The core-shell structure of endohedral fullerenes results in good protection of the encapsulated spin carriers from the environment. In this research, the quantum coherence behavior of the endohedral fullerene Sc3C2@C80 in CS2 solution is characterized from 5 K to room temperature. Below the critical temperature of around 140 K, the inner group is hindered, and the EPR spectrum consists of a single broad line. The spin carriers display a maximum phase memory time of 17.2(7) μs at 10 K. In the high temperature region, the inner group is mobile, and the EPR spectrum consists of 22 homogeneously broadened lines due to isotropic hyperfine coupling. The maximum phase memory time for each transition is around 139(1) ns at 200 K which allows arbitrary superposition state manipulations to be performed. This research demonstrates that Sc3C2@C80 displays temperature-crossover behaviour due to weak interaction between the Sc3C2 core and the C80 shell.

Elucidation of Dual Magnetic Relaxation Processes in Dinuclear Dysprosium(III) Phthalocyaninato Triple-Decker Single-Molecule Magnets Depending on the Octacoordination Geometry

When applying single-molecule magnets (SMMs) to spintronic devices, control of the quantum tunneling of the magnetization (QTM) as well as a spin-lattice interactions are important. Attempts have been made to use not only coordination geometry but also magnetic interactions between SMMs as an exchange bias. In this manuscript, dinuclear dysprosium(III) (Dy^III ) SMMs with the same octacoordination geometry undergo dual magnetic relaxation processes at low temperature. In the dinuclear Dy^III phthalocyaninato (Pc^2- ) triple-decker type complex [(Pc)Dy(ooPc)Dy(Pc)] (1) (ooPc^2- =2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato) with a square-antiprismatic (SAP) geometry, the ground state is divided by the Zeeman effect, and level intersection occurs when a magnetic field is applied. Due to the ground state properties of 1, since the Zeeman diagram where the levels intersect in an H_dc of 2500 Oe, two kinds of QTM and direct processes occur. However, dinuclear Dy^III -Pc systems with C₄ geometry, which have a twist angle (ϕ) of less than 45° do not undergo dual magnetic relaxation processes. From magnetic field and temperature dependences, the dual magnetic relaxation processes were clarified.

Tuning the spin coherence time of Cu(II)-(bis)oxamato and Cu(II)-(bis)oxamidato complexes by advanced ESR pulse protocols

We have investigated with the pulsed ESR technique at X- and Q-band frequencies the coherence and relaxation of Cu spins S = 1/2 in single crystals of diamagnetically diluted mononuclear [n-Bu4N]2[Cu(opba)] (1%) in the host lattice of [n-Bu4N]2[Ni(opba)] (99%, opba = o-phenylenebis(oxamato)) and of diamagnetically diluted mononuclear [n-Bu4N]2[Cu(opbon-Pr2)] (1%) in the host lattice of [n-Bu4N]2[Ni(opbon-Pr2)] (99%, opbon-Pr2 = o-phenylenebis(N(propyl)oxamidato)). For that we have measured the electron spin dephasing time Tm at different temperatures with the two-pulse primary echo and with the special Carr-Purcell-Meiboom-Gill (CPMG) multiple microwave pulse sequence. Application of the CPMG protocol has led to a substantial increase of the spin coherence lifetime in both complexes as compared to the primary echo results. It shows the efficiency of the suppression of the electron spin decoherence channel in the studied complexes arising due to spectral diffusion induced by a random modulation of the hyperfine interaction with the nuclear spins. We argue that this method can be used as a test for the relevance of the spectral diffusion for the electron spin decoherence. Our results have revealed a prominent role of the opba4- and opbon-Pr24- ligands for the dephasing of the Cu spins. The presence of additional 14N nuclei and protons in [Cu(opbon-Pr2)]2- as compared to [Cu(opba)]2- yields significantly shorter Tm times. Such a detrimental effect of the opbon-Pr24- ligands has to be considered when discussing a potential application of the Cu(II)-(bis)oxamato and Cu(II)-(bis)oxamidato complexes as building blocks of more complex molecular structures in prototype spintronic devices. Furthermore, in our work we propose an improved CPMG pulse protocol that enables elimination of unwanted echoes that inevitably appear in the case of inhomogeneously broadened ESR spectra due to the selective excitation of electron spins.

Long Coherence Times in Nuclear Spin-Free Vanadyl Qubits

Quantum information processing (QIP) offers the potential to create new frontiers in fields ranging from quantum biology to cryptography. Two key figures of merit for electronic spin qubits, the smallest units of QIP, are the coherence time (T₂), the lifetime of the qubit, and the spin-lattice relaxation time (T₁), the thermally defined upper limit of T₂. To achieve QIP, processable qubits with long coherence times are required. Recent studies on (Ph₄P-d₂₀)₂[V(C₈S₈)₃], a vanadium-based qubit, demonstrate that millisecond T₂ times are achievable in transition metal complexes with nuclear spin-free environments. Applying these principles to vanadyl complexes offers a route to combine the previously established surface compatibility of the flatter vanadyl structures with a long T₂. Toward those ends, we investigated a series of four qubits, (Ph₄P)₂[VO(C₈S₈)₂] (1), (Ph₄P)₂[VO(β-C₃S₅)₂] (2), (Ph₄P)₂[VO(α-C₃S₅)₂] (3), and (Ph₄P)₂[VO(C₃S₄O)₂] (4), by pulsed electron paramagnetic resonance (EPR) spectroscopy and compared the performance of these species with our recently reported set of vanadium tris(dithiolene) complexes. Crucially we demonstrate that solutions of 1-4 in SO₂, a uniquely polar nuclear spin-free solvent, reveal T₂ values of up to 152(6) μs, comparable to the best molecular qubit candidates. Upon transitioning to vanadyl species from the tris(dithiolene) analogues, we observe a remarkable order of magnitude increase in T₁, attributed to stronger solute-solvent interactions with the polar vanadium-oxo moiety. Simultaneously, we detect a small decrease in T₂ for the vanadyl analogues relative to the tris(dithiolene) complexes. We attribute this decrease to the absence of one nuclear spin-free ligand, which served to shield the vanadium centers against solvent nuclear spins. Our results highlight new design principles for long T₁ and T₂ times by demonstrating the efficacy of ligand-based tuning of solute-solvent interactions.

Hydroxide-bridged five-coordinate DyIII single-molecule magnet exhibiting the record thermal relaxation barrier of magnetization among lanthanide-only dimers

A hydroxide-bridged five-coordinate dysprosium(iii) dimer with short Dy–O bonds was synthesized.

A hydroxide-bridged centrosymmetric Dy^III dimer with each Dy^III being five-coordinated has been synthesized using bulky hindered phenolate ligands. Magnetic studies revealed that this compound exhibits a slow magnetic relaxation of a single-ion origin together with a step-like magnetic hysteresis of the magnetic coupled cluster. The thermal relaxation barrier of magnetization is 721 K in the absence of a static magnetic field, while the intramolecular magnetic interaction is very large among reported 4f-only dimers. CASSCF calculations with a larger active space were performed to understand the electronic structure of the compound. The thermal relaxation regime and the quantum tunneling regime are well separated, representing a good model to study the relaxation mechanism of SMMs with intramolecular Dy–Dy magnetic interactions.

Observation of Tunneling-Assisted Highly Forbidden Single-Photon Transitions in a Ni_{4} Single-Molecule Magnet

Forbidden transitions between energy levels typically involve violation of selection rules imposed by symmetry and/or conservation laws. A nanomagnet tunneling between up and down states violates angular momentum conservation because of broken rotational symmetry. Here we report observations of highly forbidden transitions between spin states in a Ni_{4} single-molecule magnet in which a single photon can induce the spin to change by several times ℏ, nearly reversing the direction of the spin. These observations are understood as tunneling-assisted transitions that lift the standard Δm=±1 selection rule for single-photon transitions. These transitions are observed at low applied fields, where tunneling is dominated by the molecule's intrinsic anisotropy and the field acts as a perturbation. Such transitions can be exploited to create macroscopic superposition states that are not typically accessible through single-photon Δm=±1 transitions.

A scalable architecture for quantum computation with molecular nanomagnets

A proposal for a magnetic quantum processor that consists of individual molecular spins coupled to superconducting coplanar resonators and transmission lines is carefully examined. We derive a simple magnetic quantum electrodynamics Hamiltonian to describe the underlying physics. It is shown that these hybrid devices can perform arbitrary operations on each spin qubit and induce tunable interactions between any pair of them. The combination of these two operations ensures that the processor can perform universal quantum computations. The feasibility of this proposal is critically discussed using the results of realistic calculations, based on parameters of existing devices and molecular qubits. These results show that the proposal is feasible, provided that molecules with sufficiently long coherence times can be developed and accurately integrated into specific areas of the device. This architecture has an enormous potential for scaling up quantum computation thanks to the microscopic nature of the individual constituents, the molecules, and the possibility of using their internal spin degrees of freedom.

Millisecond Coherence Time in a Tunable Molecular Electronic Spin Qubit

Quantum information processing (QIP) could revolutionize areas ranging from chemical modeling to cryptography. One key figure of merit for the smallest unit for QIP, the qubit, is the coherence time (T 2), which establishes the lifetime for the qubit. Transition metal complexes offer tremendous potential as tunable qubits, yet their development is hampered by the absence of synthetic design principles to achieve a long T 2. We harnessed molecular design to create a series of qubits, (Ph4P)2[V(C8S8)3] (1), (Ph4P)2[V(β-C3S5)3] (2), (Ph4P)2[V(α-C3S5)3] (3), and (Ph4P)2[V(C3S4O)3] (4), with T 2s of 1-4 μs at 80 K in protiated and deuterated environments. Crucially, through chemical tuning of nuclear spin content in the vanadium(IV) environment we realized a T 2 of ∼1 ms for the species (d 20-Ph4P)2[V(C8S8)3] (1') in CS2, a value that surpasses the coordination complex record by an order of magnitude. This value even eclipses some prominent solid-state qubits. Electrochemical and continuous wave electron paramagnetic resonance (EPR) data reveal variation in the electronic influence of the ligands on the metal ion across 1-4. However, pulsed measurements indicate that the most important influence on decoherence is nuclear spins in the protiated and deuterated solvents utilized herein. Our results illuminate a path forward in synthetic design principles, which should unite CS2 solubility with nuclear spin free ligand fields to develop a new generation of molecular qubits.

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

A multitechnique investigation of an evaporable vanadyl spin system with long-lived quantum coherence that self-assembles on gold.

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

Heterometallic Rings: Their Physics and use as Supramolecular Building Blocks

An enormous family of heterometallic rings has been made. The first were Cr7 M rings where M = Ni(II), Zn(II), Mn(II), and rings have been made with as many as fourteen metal centers in the cyclic structure. They are bridged externally by carboxylates, and internally by fluorides or a penta-deprotonated polyol. The size of the rings is controlled through templates which have included a range of ammonium or imidazolium ions, alkali metals and coordination compounds. The rings can be functionalized to act as ligands, and incorporated into hybrid organic-inorganic rotaxanes and into molecules containing up to 200 metal centers. Physical studies reported include: magnetic measurements, inelastic neutron scattering (including single crystal measurements), electron paramagnetic resonance spectroscopy (including measurements of phase memory times), NMR spectroscopy (both solution and solid state), and polarized neutron diffraction. The rings are hence ideal for understanding magnetism in elegant exchange-coupled systems.

Dissipative dynamics in a quantum bistable system: crossover from weak to strong damping

The dissipative dynamics of a quantum bistable system coupled to a Ohmic heat bath is investigated beyond the spin-boson approximation. Within the path-integral approach to quantum dissipation, we propose an approximation scheme which exploits the separation of time scales between intra- and interwell (tunneling) dynamics. The resulting generalized master equation for the populations in a space localized basis enables us to investigate a wide range of temperatures and system-environment coupling strengths. A phase diagram in the coupling-temperature space is provided to give a comprehensive account of the different dynamical regimes.

Molecular lanthanide single-ion magnets: from bulk to submonolayers

Single-ion magnets (SIMs) are mononuclear molecular complexes exhibiting slow relaxation of magnetization. They are currently attracting a lot of interest because of potential applications in spintronics and quantum information processing. However, exploiting SIMs in, e.g. molecule-inorganic hybrid devices requires a fundamental understanding of the effects of molecule-substrate interactions on the SIM magnetic properties. In this review the properties of lanthanide SIMs in the bulk crystalline phase and deposited on surfaces in the (sub)monolayer regime are discussed. As a starting point trivalent lanthanide ions in a ligand field will be described, and the challenges in characterizing the ligand field are illustrated with a focus on several spectroscopic techniques which are able to give direct information on the ligand-field split energy levels. Moreover, the dominant mechanisms of magnetization relaxation in the bulk phase are discussed followed by an overview of SIMs relevant for surface deposition. Further, a short introduction will be given on x-ray absorption spectroscopy, x-ray magnetic circular dichroism and scanning tunneling microscopy. Finally, the recent experiments on surface-deposited SIMs will be reviewed, along with a discussion of future perspectives.

Surface Contributions to Mn(2+) Spin Dynamics in Colloidal Doped Quantum Dots

Colloidal impurity-doped quantum dots (QDs) are attractive model systems for testing the fundamental spin properties of semiconductor nanostructures relevant to future spin-based information processing technologies. Although static spin properties of this class of materials have been studied extensively in recent years, their spin dynamics remain largely unexplored. Here we use pulsed electron paramagnetic resonance (pEPR) spectroscopy to probe the spin relaxation dynamics of colloidal Mn(2+)-doped ZnO, ZnSe, and CdSe quantum dots in the limit of one Mn(2+) per QD. pEPR spectroscopy is particularly powerful for identifying the specific nuclei that accelerate electron spin relaxation in these QDs. We show that the spin-relaxation dynamics of these colloidal QDs are strongly influenced by dipolar coupling with proton nuclear spins outside the QDs and especially those directly at the QD surfaces. Using this information, we demonstrate that spin-relaxation times can be elongated significantly via ligand (or surface) deuteration or shell growth, providing two tools for chemical adjustment of spin dynamics in these nanomaterials. These findings advance our understanding of the spin properties of solution-grown semiconductor nanostructures relevant to spin-based information technologies.

Molecular nanomagnets with switchable coupling for quantum simulation

Molecular nanomagnets are attractive candidate qubits because of their wide inter- and intra-molecular tunability. Uniform magnetic pulses could be exploited to implement one- and two-qubit gates in presence of a properly engineered pattern of interactions, but the synthesis of suitable and potentially scalable supramolecular complexes has proven a very hard task. Indeed, no quantum algorithms have ever been implemented, not even a proof-of-principle two-qubit gate. Here we show that the magnetic couplings in two supramolecular {Cr7Ni}-Ni-{Cr7Ni} assemblies can be chemically engineered to fit the above requisites for conditional gates with no need of local control. Microscopic parameters are determined by a recently developed many-body ab-initio approach and used to simulate quantum gates. We find that these systems are optimal for proof-of-principle two-qubit experiments and can be exploited as building blocks of scalable architectures for quantum simulation.

Multiple quantum coherences from hyperfine transitions in a vanadium(IV) complex

We report a vanadium complex in a nuclear-spin free ligand field that displays two key properties for an ideal candidate qubit system: long coherence times that persist at high temperature, T2 = 1.2 μs at 80 K, and the observation of quantum coherences from multiple transitions. The electron paramagnetic resonance (EPR) spectrum of the complex [V(C8S8)3](2-) displays multiple transitions arising from a manifold of states produced by the hyperfine coupling of the S = ½ electron spin and I = 7/2 nuclear spin. Transient nutation experiments reveal Rabi oscillations for multiple transitions. These observations suggest that each pair of hyperfine levels hosted within [V(C8S8)3](2-) are candidate qubits. The realization of multiple quantum coherences within a transition metal complex illustrates an emerging method of developing scalability and addressability in electron spin qubits. This study presents a rare molecular demonstration of multiple Rabi oscillations originating from separate transitions. These results extend observations of multiple quantum coherences from prior reports in solid-state compounds to the new realm of highly modifiable coordination compounds.