Magnetic Exchange Interactions in the Molecular Nanomagnet Mn_{12}

Ab initio-based determination of lanthanoid-radical exchange as visualised by inelastic neutron scattering

Magnetic exchange coupling can modulate the slow magnetic relaxation in single-molecule magnets. Despite this, elucidation of exchange coupling remains a significant challenge for the lanthanoid(iii) ions, both experimentally and computationally. In this work, the crystal field splitting and 4f-π exchange coupling in the erbium-semiquinonate complex [ErTp2dbsq] (Er-dbsq; Tp- = hydro-tris(1-pyrazolyl)borate, dbsqH2 = 3,5-di-tert-butyl-1,2-semiquinone) have been determined by inelastic neutron scattering (INS), magnetometry, and CASSCF-SO ab initio calculations. A related complex with a diamagnetic ligand, [ErTp2trop] (Er-trop; tropH = tropolone), has been used as a model for the crystal field splitting in the absence of coupling. Magnetic and INS data indicate antiferromagnetic exchange for Er-dbsq with a coupling constant of Jex = -0.23 meV (-1.8 cm-1) (-2Jex formalism) and good agreement is found between theory and experiment, with the low energy magnetic and spectroscopic properties well modelled. Most notable is the ability of the ab initio modelling to reproduce the signature of interference between localised 4f states and delocalised π-radical states that is evident in the Q-dependence of the exchange excitation. This work highlights the power of combining INS with EPR and magnetometry for determination of ground state properties, as well as the enhanced capability of CASSCF-SO ab initio calculations and purposely developed ab initio-based theoretical models. We deliver an unprecedentedly detailed representation of the entangled character of 4f-π exchange states, which is obtained via an accurate image of the spin-orbital transition density between the 4f-π exchange coupled wavefunctions.

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.

Dipole Switching by Intramolecular Electron Transfer in Single-Molecule Magnetic Complex [Mn12O12(O2CR)16(H2O)4]

We study intramolecular electron transfer in the single-molecule magnetic complex [Mn₁₂O₁₂(O₂CR)₁₆ (H₂O)₄] for R = -H, -CH₃, -CHCl₂, -C₆H₅, and -C₆H₄F ligands as a mechanism for switching of the molecular dipole moment. Energetics is obtained using the density functional theory (DFT) with onsite Coulomb energy correction (DFT + U). Lattice distortions are found to be critical for localizing an extra electron on one of the easy sites on the outer ring in which localized states can be stabilized. We find that the lowest-energy path for charge transfer is for the electron to go through the center via superexchange-mediated tunneling. The energy barrier for such a path ranges from 0.4 to 54 meV depending on the ligands and the isomeric form of the complex. The electric field strength needed to move the charge from one end to the other, thus reversing the dipole moment, is 0.01-0.04 V/Å.

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

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

Radiofrequency to Microwave Coherent Manipulation of an Organometallic Electronic Spin Qubit Coupled to a Nuclear Qudit

We report here a comprehensive characterization of a 3d organometallic complex, [V(Cp)2Cl2] (Cp = cyclopentadienyl), which can be considered as a prototypical multilevel nuclear qudit (nuclear spin I = 7/2) hyperfine coupled to an electronic qubit (electronic spin S = 1/2). By combining complementary magnetic resonant techniques, such as pulsed electron paramagnetic resonance (EPR) and broadband nuclear magnetic resonance (NMR), we extensively characterize its Spin Hamiltonian parameters and its electronic and nuclear spin dynamics. Moreover, we demonstrate the possibility to manipulate the qubit-qudit multilevel structure by resonant microwave and radiofrequency pulses, driving coherent Rabi oscillations between targeted electronuclear states. The obtained results demonstrate that this simple complex is a promising candidate for quantum computing applications.

Neutron Studies of a High Spin Fe19 Molecular Nanodisc

The molecular cluster system [Fe19(metheidi)10(OH)14O6(H2O)12]NO3·24H2O, abbreviated as Fe19, contains nineteen Fe(III) ions arranged in a disc-like structure with the total spin S = 35/2. For the first order, it behaves magnetically as a single molecule magnet with a 16 K anisotropy barrier. The high spin value enhances weak intermolecular interactions for both dipolar and superexchange mechanisms and an eventual transition to antiferromagnetic order occurs at 1.2 K. We used neutron diffraction to determine both the mode of ordering and the easy spin axis. The observed ordering was not consistent with a purely dipolar driven order, indicating a significant contribution from intermolecular superexchange. The easy axis is close to the molecular Fe1–Fe10 axis. Inelastic neutron scattering was used to follow the magnetic order parameter and to measure the magnetic excitations. Direct transitions to at least three excited states were found in the 2 to 3 meV region. Measurements below 0.2 meV revealed two low energy excited states, which were assigned to S = 39/2 and S = 31/2 spin states with respective excitation gaps of 1.5 and 3 K. Exchange interactions operating over distances of order 10 Å were determined to be on the order of 5 mK and were eight-times stronger than the dipolar coupling.

Unveiling phonons in a molecular qubit with four-dimensional inelastic neutron scattering and density functional theory

Phonons are the main source of relaxation in molecular nanomagnets, and different mechanisms have been proposed in order to explain the wealth of experimental findings. However, very limited experimental investigations on phonons in these systems have been performed so far, yielding no information about their dispersions. Here we exploit state-of-the-art single-crystal inelastic neutron scattering to directly measure for the first time phonon dispersions in a prototypical molecular qubit. Both acoustic and optical branches are detected in crystals of [VO(acac)[Formula: see text]] along different directions in the reciprocal space. Using energies and polarisation vectors calculated with state-of-the-art Density Functional Theory, we reproduce important qualitative features of [VO(acac)[Formula: see text]] phonon modes, such as the presence of low-lying optical branches. Moreover, we evidence phonon anti-crossings involving acoustic and optical branches, yielding significant transfers of the spin-phonon coupling strength between the different modes.

Magnetic properties of transition metal dimers probed by inelastic neutron scattering

The physical characterisation and understanding of molecular magnetic materials is one of the most important steps towards the integration of such systems in hybrid spintronic devices. Amongst the many characterisation techniques employed in such a task, Inelastic Neutron Scattering (INS) stands as one of the most powerful and sensitive tools to investigate their spin dynamics. Herein, the magnetic properties and spin dynamics of two dinuclear complexes, namely [(M(hfacac)2)2(bpym)] (where M = Ni2+, Co2+, abbreviated in the following as Ni2, Co2) are reported. These are model systems that could constitute fundamental units of future spintronic devices. By exploiting the highly sensitive IN5 Cold INS spectrometer, we are able to gain a deep insight into the spin dynamics of Ni2 and to fully obtain the microscopic spin Hamiltonian parameters; while for Co2, a multitude of INS transitions are observed demonstrating the complexity of the magnetic properties of octahedral cobalt-based systems.

Anisotropy of CoII transferred to the Cr7Co polymetallic cluster via strong exchange interactions

In the Cr₇Co model-system the anisotropy of Co^II is effectively transferred to the whole cluster through strong and anisotropic exchange interactions.

The Cr₇Co ring represents a model system to understand how the anisotropy of a Co^II ion is transferred to the effective anisotropy of a polymetallic cluster by strong exchange interactions. Combining sizeable anisotropy with exchange interactions is an important point in the understanding and design of new anisotropic molecular nanomagnets addressing fundamental and applicative issues. By combining electron paramagnetic resonance and inelastic neutron scattering measurements with spin Hamiltonian and ab initio calculations, we have investigated in detail the anisotropy of the Co^II ion embedded in the antiferromagnetic ring. Our results demonstrate a strong and anisotropic exchange interaction between the Co and the neighbouring Cr ions, which effectively transmits the anisotropy to the whole molecule.

Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians

Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl]₄ ('Ni₄ ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp^- is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni₄ , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings.