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 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.

Paramagnetic spherical nanoparticles by the self-assembly of persistent trityl radicals

The self-association of a water-soluble persistent trityl radical gives rise to paramagnetic nanoparticles: a new class of non-metallic high spin systems.

Magnetic relaxation versus 3D long-range ordering in {Dy₂Ba(α-fur)₈}n furoate polymers

A novel Dy-complex formulated as {[Dy2Ba(α-C4H3OCOO)8·(H2O)4]·2H2O}n, {Dy2Ba(α-fur)8}n, has been synthesized, structurally characterized, and magnetically and thermally investigated as a function of field and temperature, down to 85 mK. The α-furoate ligands consolidate 1D zig-zag chains formed by Dy2 dimers separated by Ba ions. Ab initio calculations were used to determine the easy anisotropy axis direction, the gyromagnetic tensor components and the energy levels of each Dy. The heat capacity and susceptibility measurements allowed us to conclude that intradimer and interdimer interactions are ferromagnetic and of the same order, J'/k(B) ≈ J''/k(B) = +0.55 K. In the absence of an applied magnetic field, the dynamic relaxation of the magnetization occurs through the fast (τ(T) ~ 10(-5) s) spin-reversal of each of the individual Dys through a quantum tunneling (QT) process. A long-range 3D ordered state is achieved at T(N) = 0.25 K, in which the ferromagnetically coupled zig-zag chains (J'/k(B) ≈ J''/k(B) = +0.528(1) K) running along the c-axis are antiferromagnetically coupled to the adjacent chains (J'''/k(B) = -0.021(1) K). Critical slowing down of the QT time constant is observed when the temperature approaches T(N). Under the application of a magnetic field, the QT relaxation is replaced by an Orbach process (with energy barrier U/k(B) = 68 K and τ0 ~ 10(-9) s at H = 2 kOe) and a very slow (τ(s) ∼ 0.2 s) relaxation process. We propose and demonstrate the proof of concept of a spintronic device, in which two different relaxation rates can be selected, and on/off switched by magnetic field biasing. The dynamical behavior of this compound is compared with another furoate to discuss the effect of competitive interactions.

Self-assembled trityl radical capsules – implications for dynamic nuclear polarization

The OX63 radical forms supramolecular capsules hosting tetraalkylammonium cations. Extensive self-association is also observed under standard dynamic nuclear polarization conditions.

Correction: Magnetic relaxation versus 3D long-range ordering in {Dy2Ba(α-fur)8}n furoate polymers

Correction for ‘Magnetic relaxation versus 3D long-range ordering in {Dy₂Ba(α-fur)₈}_n furoate polymers’ by E. Bartolomé et al., Dalton Trans., 2014, 43, 10999–11013.

Quantum interference oscillations of the superparamagnetic blocking in an Fe8 molecular nanomagnet

We show that the dynamic magnetic susceptibility and the superparamagnetic blocking temperature of an Fe(8) single molecule magnet oscillate as a function of the magnetic field H(x) applied along its hard magnetic axis. These oscillations are associated with quantum interferences, tuned by H(x), between different spin tunneling paths linking two excited magnetic states. The oscillation period is determined by the quantum mixing between the ground S=10 and excited multiplets. These experiments enable us to quantify such mixing. We find that the weight of excited multiplets in the magnetic ground state of Fe(8) amounts to approximately 11.6%.

Strong paramagnetism of gold nanoparticles deposited on a Sulfolobus acidocaldarius S layer

Magnetic properties of Au nanoparticles deposited on an archaeal S layer are reported. X-ray magnetic circular dichroism and superconducting quantum interference device magnetometries demonstrate that the particles are strongly paramagnetic, without any indication of magnetic blocking down to 16 mK. The average magnetic moment per particle is M(part)=2.36(7) μ(B). This contribution originates at the particle's Au 5d band, in which an increased number of holes with respect to the bulk value is observed. The magnetic moment per Au atom is 25 times larger than any measured in other Au nanoparticles or any other configurations up to date.

Gd-based single-ion magnets with tunable magnetic anisotropy: molecular design of spin qubits

We report ac susceptibility and continuous wave and pulsed EPR experiments performed on GdW10 and GdW30 polyoxometalate clusters, in which a Gd3+ ion is coordinated to different polyoxometalate moieties. Despite the isotropic character of gadolinium as a free ion, these molecules show slow magnetic relaxation at very low temperatures, characteristic of single molecule magnets. For T≲200  mK, the spin-lattice relaxation becomes dominated by pure quantum tunneling events, with rates that agree quantitatively with those predicted by the Prokof'ev and Stamp model [Phys. Rev. Lett. 80, 5794 (1998)]. The sign of the magnetic anisotropy, the energy level splittings, and the tunneling rates strongly depend on the molecular structure. We argue that GdW30 molecules are also promising spin qubits with a coherence figure of merit Q(M)≳50.

Molecular prototypes for spin-based CNOT and SWAP quantum gates

We show that a chemically engineered structural asymmetry in [Tb2] molecular clusters renders the two weakly coupled Tb3+ spin qubits magnetically inequivalent. The magnetic energy level spectrum of these molecules meets then all conditions needed to realize a universal CNOT quantum gate. A proposal to realize a SWAP gate within the same molecule is also discussed. Electronic paramagnetic resonance experiments confirm that CNOT and SWAP transitions are not forbidden.

Magnetic dipolar ordering and quantum phase transition in an Fe8 molecular magnet

We show that a crystal of mesoscopic Fe(8) single-molecule magnets is an experimental realization of the quantum Ising model in a transverse field, with dipolar interactions. Quantum annealing has enabled us to explore the quantum and classical phase transitions between the paramagnetic and ferromagnetic phases, at thermodynamical equilibrium. The phase diagram and critical exponents that we obtain agree with expectations for the mean-field universality class.

Size-dependent properties of magnetoferritin

We report a detailed experimental study of maghemite nanoparticles, with sizes ranging from 1.6 to 6 nm, synthesized inside a biological mould of apoferritin. The structural characterization of the inorganic cores, using TEM and x-ray diffraction, reveals a low degree of crystalline order, possibly arising from the nucleation and growth of multiple domains inside each molecule. We have also investigated the molecular structure by means of atomic force microscopy in liquid. We find that the synthesis of nanoparticles inside apoferritin leads to a small, but measurable, decrease in the external diameter of the protein, probably associated with conformational changes. The magnetic response of the maghemite cores has been studied by a combination of techniques, including ac susceptibility, dc magnetization and Mössbauer spectroscopy. From the equilibrium magnetic response, we have determined the distribution of magnetic moments per molecule. The results show highly reduced magnetic moments. This effect cannot be ascribed solely to the canting of spins located at the particle surface but, instead, it suggests that magnetoferritin cores have a highly disordered magnetic structure in which the contributions of different domains compensate each other. Finally, we have also determined, for each sample, the distribution of the activation energies required for the magnetization reversal and, from this, the size-dependent magnetic anisotropy constant K. We find that K is enormously enhanced with respect to the maghemite bulk value and that it increases with decreasing size. The Mössbauer spectra suggest that low-symmetry atomic sites, probably located at the particle surface and at the interfaces between different crystalline domains, are the likely source of the enhanced magnetic anisotropy.

Note: Highly sensitive superconducting quantum interference device microsusceptometers operating at high frequencies and very low temperatures inside the mixing chamber of a dilution refrigerator

We report the experimental results that show the operation of superconducting quantum interference device (SQUID) microsusceptometers immersed in the (3)He-(4)He mixture inside the mixing chamber of a dilution refrigerator at high frequency (1 MHz) and down to very low temperatures (13 mK). The devices are based on highly sensitive and easy-to-use commercial SQUID sensors. The integrated susceptometers are fabricated by rerouting some connections of the SQUID's input circuit. Examples of measurements on molecular magnets Mn(12) and HoW(10) are shown.

Equilibrium susceptibilities of superparamagnets: longitudinal and transverse, quantum and classical

The equilibrium susceptibility of uniaxial paramagnets is studied in a unified framework which permits us to connect traditional results of the theory of quantum paramagnets, S = 1/2,1,3/2,..., with molecular magnetic clusters, S∼5,10,20 all the way up (S = 30,50,100,...,) to the theory of classical superparamagnets. This is done using standard tools of quantum statistical mechanics and linear-response theory (the Kubo correlator formalism). Several features of the temperature dependence of the susceptibility curves (crossovers, peaks, deviations from Curie law) are studied and their scalings with S identified and characterized. Both the longitudinal and transverse susceptibilities are discussed, as well as the response of the ensemble with anisotropy axes oriented at random. For the latter case a simple approximate formula is derived too, and its range of validity assessed, which could be used in the modelization of experiments.

Giant isotope effect in the incoherent tunneling specific heat of the molecular nanomagnet Fe8

Time-dependent specific heat experiments on the molecular nanomagnet Fe8 and the isotopic enriched analogue 57Fe8 are presented. The inclusion of the 57Fe nuclear spins leads to a huge enhancement of the specific heat below 1 K, ascribed to a strong increase in the spin-lattice relaxation rate gamma arising from incoherent, nuclear-spin-mediated magnetic quantum tunneling (MQT) in the ground doublet. Since gamma is found comparable to the expected tunneling rate, the MQT process has to be inelastic. A model for the coupling of the tunneling spins to the lattice is presented. Under transverse field, a crossover from nuclear-spin-mediated to phonon-induced tunneling is observed.

Long-range ferromagnetism of Mn12 acetate single-molecule magnets under a transverse magnetic field

We use neutron diffraction to probe the magnetization components of a crystal of Mn12 single-molecule magnets. Each of these molecules behaves, at low temperatures, as a nanomagnet with spin S = 10 and strong anisotropy along the crystallographic c axis. The application of a magnetic field H(perpendicular) perpendicular to c induces quantum tunneling between opposite spin orientations, enabling the spins to attain thermal equilibrium. For T approximately < 0.9(1) K, this equilibrium state shows spontaneous magnetization, indicating the onset of ferromagnetism. These long-range magnetic correlations nearly disappear for mu0H(perpendicular) approximately > 5.5 T, possibly suggesting the existence of a quantum critical point.

Magnetic long-range order induced by quantum relaxation in single-molecule magnets

Can magnetic interactions between single-molecule magnets (SMMs) in a crystal establish long-range magnetic order at low temperatures deep in the quantum regime, where the only electron spin fluctuations are due to incoherent magnetic quantum tunneling (MQT)? Put inversely: can MQT provide the temperature dependent fluctuations needed to destroy the ordered state above some finite T(c), although it should basically itself be a T-independent process? Our experiments on two novel Mn4 SMMs provide a positive answer to the above, showing at the same time that MQT in the SMMs has to involve spin-lattice coupling at a relaxation rate equaling that predicted and observed recently for nuclear-spin-mediated quantum relaxation.

Large quantum nonlinear dynamic susceptibility of single-molecule magnets

The nonlinear dynamical response of Mn12 single-molecule magnets is experimentally found to be very large, quite insensitive to the spin-lattice coupling constant, and displaying peaks reversed with respect to classical superparamagnets. It is shown that these features are caused by the strong field dependence of the relaxation rate due to the detuning of energy levels between which tunneling takes place. The nonlinear susceptibility technique, previously overlooked, is thus proposed as a privileged probe to ascertain the occurrence of quantum effects in mesoscopic magnetic systems.

Long-range ferromagnetic dipolar ordering of high-spin molecular clusters

We report the first example of a transition to long-range magnetic order in a purely dipolarly interacting molecular magnet. For the magnetic cluster compound Mn6O4Br4(Et2dbm)6, the anisotropy experienced by the total spin S = 12 of each cluster is so small that spin-lattice relaxation remains fast down to the lowest temperatures, thus enabling dipolar order to occur within experimental times at T(c) = 0.16 K. In high magnetic fields, the relaxation rate becomes drastically reduced and the interplay between nuclear- and electron-spin lattice relaxation is revealed.

Magnetic relaxation of interacting co clusters: crossover from two- to three-dimensional lattices

The influence that dipole-dipole interactions exert on the dynamics of the magnetization of nanometer-sized Co clusters has been studied by means of ac and dc susceptibility experiments. These clusters grow in a quasiordered layered structure, where all relevant parameters can be tailored and measured independently. Our data show without ambiguity that the magnetic relaxation becomes slower as the degree of interaction increases. The effective activation energy increases linearly with the number of nearest neighbor clusters, evolving from the value for a 2D layer to the fully 3D behavior, which is nearly reached for five layers. The experimental results agree quantitatively with the predictions of a simple model.

Metallorganic routes to nanoscale iron and titanium oxide particles encapsulated in mesoporous alumina: formation, physical properties, and chemical reactivity

Iron and titanium oxide nanoparticles have been synthesized in parallel mesopores of alumina by a novel organometallic "chimie douce" approach that uses bis(toluene)iron(0) (1) and bis(toluene)titanium(0) (2) as precursors. These complexes are molecular sources of iron and titanium in a zerovalent atomic state. In the case of 1, core shell iron/iron oxide particles with a strong magnetic coupling between both components, as revealed by magnetic measurements, are formed. Mössbauer data reveal superparamagnetic particle behavior with a distinct particle size distribution that confirms the magnetic measurements. The dependence of the Mössbauer spectra on temperature and particle size is explained by the influence of superparamagnetic relaxation effects. The coexistence of a paramagnetic doublet and a magnetically split component in the spectra is further explained by a distribution in particle size. From Mössbauer parameters the oxide phase can be identified as low-crystallinity ferrihydrite oxide. In agreement with quantum size effects observed in UV-visible studies, TEM measurements determine the size of the particles in the range 5-8 nm. The particles are mainly arranged alongside the pore walls of the alumina template. TiO2 nanoparticles are formed by depositing 2 in mesoporous alumina template. This produces metallic Ti, which is subsequently oxidized to TiO2 (anatase) within the alumina pores. UV-visible studies show a strong quantum confinement effect for these particles. From UV-visible investigations the particle size is determined to be around 2 nm. XPS analysis of the iron- and titania- embedded nanoparticles reveal the presence of Fe2O3 and TiO2 according to experimental binding energies and the experimental line shapes. Ti4+ and Fe3+ are the only oxidation states of the particles which can be determined by this technique. Hydrogen reduction of the iron/iron-oxide nanoparticles at 500 degrees C under flowing H2/N2 produces a catalyst, which is active towards formation of carbon nanotubes by a CVD process. Depending on the reaction conditions, the formation of smaller carbon nanotubes inside the interior of larger carbon nanotubes within the alumina pores can be achieved. This behavior can be understood by means of selectively turning on and off the iron catalyst by adjusting the flow rate of the gaseous carbon precursor in the CVD process.

Observation of quantum coherence in mesoscopic molecular magnets

By applying a transverse magnetic field B( perpendicular) of sufficient strength to the uniaxial molecular magnets Fe8 and Mn12, the tunneling splitting Delta(t) of their S = +/-10 magnetic ground states can be made large compared to perturbations such as hyperfine and dipolar interactions. We present evidence for such a Delta(t) from magnetic specific heat data below 1 K that is consistent with coherent quantum mechanical tunneling in a "mesoscopic" system under such conditions.