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.

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

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

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.

Ultralow-temperature device dedicated to soft X-ray magnetic circular dichroism experiments.

A new ultralow-temperature setup dedicated to soft X-ray absorption spectroscopy and X-ray magnetic circular dichroism (XMCD) experiments is described. Two experiments, performed on the DEIMOS beamline (SOLEIL synchrotron), demonstrate the outstanding performance of this new platform in terms of the lowest achievable temperature under X-ray irradiation (T = 220 mK), the precision in controlling the temperature during measurements as well as the speed of the cooling-down and warming-up procedures. Moreover, owing to the new design of the setup, the eddy-current power is strongly reduced, allowing fast scanning of the magnetic field in XMCD experiments; these performances lead to a powerful device for X-ray spectroscopies on synchrotron-radiation beamlines facilities.

Magnetic bistability of a TbPc2 submonolayer on a graphene/SiC(0001) conductive electrode.

The alteration of the properties of single-molecule magnets (SMMs) due to the interaction with metallic electrodes is detrimental to their employment in spintronic devices. Conversely, herein we show that the terbium(iii) bis-phthalocyaninato complex, TbPc2, maintains its SMM behavior up to 9 K on a graphene/SiC(0001) substrate, making this alternative conductive layer highly promising for molecular spintronic applications.

Coherent coupling between Vanadyl Phthalocyanine spin ensemble and microwave photons: towards integration of molecular spin qubits into quantum circuits.

Electron spins are ideal two-level systems that may couple with microwave photons so that, under specific conditions, coherent spin-photon states can be realized. This represents a fundamental step for the transfer and the manipulation of quantum information. Along with spin impurities in solids, molecular spins in concentrated phases have recently shown coherent dynamics under microwave stimuli. Here we show that it is possible to obtain high cooperativity regime between a molecular Vanadyl Phthalocyanine (VOPc) spin ensemble and a high quality factor superconducting YBa2Cu3O7 (YBCO) coplanar resonator at 0.5 K. This demonstrates that molecular spin centers can be successfully integrated in hybrid quantum devices.

Giant spin-phonon bottleneck effects in evaporable vanadyl-based molecules with long spin coherence.

Vanadium(iv) complexes have recently shown record quantum spin coherence times that in several circumstances are limited by spin-lattice relaxation. The role of the environment and vibronic properties in the low temperature dynamics is here investigated by a comparative study of the magnetization dynamics as a function of crystallite size and the steric hindrance of the ß-diketonate ligands in VO(acac)2 (1), VO(dpm)2 (2) and VO(dbm)2 (3) evaporable complexes (acac- = acetylacetonate, dpm- = dipivaloylmethanate, and dbm- = dibenzoylmethanate). A pronounced crystallite size dependence of the relaxation time is observed at unusually high temperatures (up to 40 K), which is associated with a giant spin-phonon bottleneck effect. We model this behaviour by an ad hoc force field approach derived from density functional theory calculations, which evidences a correlation of the intensity of the phenomenon with ligand dimensions and the unit cell size.

Magnetism of TbPc2 SMMs on ferromagnetic electrodes used in organic spintronics.

Structural features and magnetic behaviour of TbPc2 thin films sublimated on LSMO and on cobalt surfaces have been investigated by synchrotron-based XNLD and XMCD techniques. Different orientation of the molecules is observed for the two substrates. No significant magnetic interaction with the ferromagnetic substrates is detected.

Quantum tunnelling of the magnetization in a monolayer of oriented single-molecule magnets.

A fundamental step towards atomic- or molecular-scale spintronic devices has recently been made by demonstrating that the spin of an individual atom deposited on a surface, or of a small paramagnetic molecule embedded in a nanojunction, can be externally controlled. An appealing next step is the extension of such a capability to the field of information storage, by taking advantage of the magnetic bistability and rich quantum behaviour of single-molecule magnets (SMMs). Recently, a proof of concept that the magnetic memory effect is retained when SMMs are chemically anchored to a metallic surface was provided. However, control of the nanoscale organization of these complex systems is required for SMMs to be integrated into molecular spintronic devices. Here we show that a preferential orientation of Fe(4) complexes on a gold surface can be achieved by chemical tailoring. As a result, the most striking quantum feature of SMMs-their stepped hysteresis loop, which results from resonant quantum tunnelling of the magnetization-can be clearly detected using synchrotron-based spectroscopic techniques. With the aid of multiple theoretical approaches, we relate the angular dependence of the quantum tunnelling resonances to the adsorption geometry, and demonstrate that molecules predominantly lie with their easy axes close to the surface normal. Our findings prove that the quantum spin dynamics can be observed in SMMs chemically grafted to surfaces, and offer a tool to reveal the organization of matter at the nanoscale.

Field induced 4f5d [Re(salen)]2O3[Dy(hfac)3(H2O)]2 single molecule magnet.

The reaction between the mononuclear [ReO(salen)(OMe)] (salen(2-) = N,N'-ethan-1,2-diylbis(salicylidenamine) dianion) and Dy(hfac)(3).2H(2)O (hfac(-) = 1,1,1,5,5,5-hexafluoroacetylacetonate anion) complexes lead to the formation of a compound with the formula {[Re(salen)](2)O(3)[Dy(hfac)(3)(H(2)O)](2)}(CHCl(3))(2)(CH(2)Cl(2))(2) noted (Dy(2)Re(2)). This compound has been characterized by single crystal and powder X-ray diffraction and has been found isostructural to the Y(III) derivative (Y(2)Re(2)) that we previously reported. The cyclic voltammetry demonstrates the redox activity of the system. The characterization of both static and dynamic magnetic properties is reported. Static magnetic data has been analyzed after the cancellation of the crystal field contribution by two different methods. Weak ferromagnetic exchange interactions between the Dy(III) ions are highlighted. The compound Dy(2)Re(2) displays slow relaxation of the magnetization when an external magnetic field is applied. Alternating current susceptibility shows a thermally activated behavior with pre-exponential factors of 7.13 (+/-0.10) x 10(-6) and 5.76 (+/-0.27) x 10(-7) s, and energy barriers of 4.19 (+/-0.02) and 8.52 (+/-0.55) K respectively for low and high temperature regimes.

Molecular nanomagnets and magnetic nanoparticles: the EMR contribution to a common approach.

The current status and future developments of the use of electron magnetic resonance (EMR) for the investigation of magnetic nano-systems is here reviewed. The aim is to stimulate efforts to provide a unified view of the properties of magnetic nanoparticles (MNP) comprising a few hundred magnetic centres, and molecular nanomagnets which contain up to ca. one hundred magnetic centres (MNM). The size of the systems is becoming the same but the approaches to the interpretation of their properties are still different, being bottom up for the latter and top down for the former. We make the point here of the need for a common viewpoint, highlighting the status of the two fields and giving some hints for the future developments. EMR has been a powerful tool for the investigation of magnetic nano-objects and it can provide a tool of fundamental importance for the development of a unified view.

Local magnetic properties of a monolayer of Mn12 single molecule magnets.

The magnetic properties of a monolayer of Mn12 single molecule magnets grafted onto a silicon (Si) substrate have been investigated using depth-controlled beta-detected nuclear magnetic resonance. A low-energy beam of spin-polarized radioactive 8Li was used to probe the local static magnetic field distribution near the Mn12 monolayer in the Si substrate. The resonance line width varies strongly as a function of implantation depth as a result of the magnetic dipolar fields generated by the Mn12 electronic magnetic moments. The temperature dependence of the line width indicates that the magnetic properties of the Mn12 moments in this low-dimensional configuration differ from bulk Mn12.

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.

High-field/high-frequency EPR studies of spin clusters with integer spin: the multi-frequency approach.

In this paper a rapid overview of the main results obtained from the study with multi-frequency HF-EPR of molecular spin clusters possessing integer spin values is presented. In the first part, two antiferromagnetic rings with zero ground spin state are reported. It is illustrated how the HF-EPR study of the first excited states allows obtaining important information on this kind of spin clusters. In the second part, selected examples of single-molecule magnets (SMM) are treated, starting with complexes involving only a few magnetic ions and going on to more complex systems. Indeed, because of their large zero-field energy gaps, EPR studies of SMM deserve the use of high frequencies and high fields. The approach presented here is twofold. First the interest of studying a series of 'simple' SMM in order to understand the subtle mechanisms underlying their properties is stressed. Then a summary of our HF-EPR studies of the most investigated SMM, Mn12ac and Fe8 is presented.

Nuclear spin dynamics in the quantum regime of a single-molecule magnet.

We show that the nuclear spin dynamics in the single-molecule magnet Mn12-ac below 1 K is governed by quantum tunneling fluctuations of the cluster spins, combined with intercluster nuclear spin diffusion. We also obtain the first experimental proof that-surprisingly-even deep in the quantum regime the nuclear spins remain in good thermal contact with the lattice phonons. We propose a simple model for how T-independent tunneling fluctuations can relax the nuclear polarization to the lattice that may serve as a framework for more sophisticated theories.

Finite-size effects in single chain magnets: an experimental and theoretical study.

The problem of finite-size effects in s=1/2 Ising systems showing slow dynamics of the magnetization is investigated introducing diamagnetic impurities in a Co2+-radical chain. The static magnetic properties have been measured and analyzed considering the peculiarities induced by the ferrimagnetic character of the compound. The dynamic susceptibility shows that an Arrhenius law is observed with the same energy barrier for the pure and the doped compounds while the prefactor decreases, as theoretically predicted. Multiple spin reversal has also been investigated.

Origin of second-order transverse magnetic anisotropy in Mn12-acetate.

The symmetry breaking effects for quantum tunneling of the magnetization in Mn12-acetate, a molecular nanomagnet, represent an open problem. We present structural evidence that the disorder of the acetic acid of crystallization induces sizable distortion of the Mn(III) sites, giving rise to six different isomers. Four isomers have symmetry lower than tetragonal and a nonzero second-order transverse magnetic anisotropy, which has been evaluated using a ligand field approach. The result of the calculation leads to an improved simulation of electron paramagnetic resonance spectra and justifies the tunnel splitting distribution derived from the field sweep rate dependence of the hysteresis loops.

Ising-type magnetic anisotropy in a cobalt(II) nitronyl nitroxide compound: a key to understanding the formation of molecular magnetic nanowires.

The compound [Co(hfac)2-(NITPhOMe)2] (2) (hfac = hexafluoroacetylacetonate, NITPhOMe = 4'-methoxyphenyl-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide) crystallizes in the triclinic P1 space group, a= 10.870(5), b = 11.520(5), c = 19.749(5) A, alpha = 78.05(5), beta = 84.20(5), gamma = 64.51(5) degrees, Z = 2. It can be considered a model system for studying the nature of the magnetic anisotropy of [Co(hfac)2(NITPhOMe)] (1), which was recently reported to behave as a molecular magnetic wire. The magnetic anisotropy of 2 was investigated by EPR spectroscopy and SQUID magnetometry both in the polycrystalline powder and in a single crystal. The experimental magnetic anisotropy was related to the anisotropy of the central ion and to the exchange interaction between the cobalt(II) ion and the radicals.

Tuning the magnetic properties of the high-spin molecular cluster Fe8.

The synthesis, crystal structure, and magnetic characterization of a high-spin cluster comprising eight iron ions are presented in this contribution. The cluster has formula [(tacn)6Fe8O2(OH)12Br4.3(ClO4)3.7]·6H2O (Fe8pcl), where tacn is the organic ligand 1,4,7-triazacyclononane. It can be considered a derivative of Fe8 Br8 , a cluster whose low-temperature magnetization dynamics has been extensively investigated, in which four of the bromide ions have been replaced by perchlorate anions. The structure of the central core of the two molecules, [Fe8O(OH)12(tacn)6](8+), is essentially the same, but Fe8pcl has a higher symmetry (the bromide derivative crystallizes in the acentric P1 space group while Fe8pcl crystallizes in the monoclinic P2(1)/c space group). The magnetic properties of Fe8pcl suggest it is very similar to Fe8Br8 having a S=10 ground state as well. The zero-field splitting parameters were accurately determined by high field-high frequency EPR (HF-EPR) measurements. The two clusters have similar axial anisotropy D but Fe8pcl has a larger transverse anisotropy E: The value of E/D is 0.21 for the perchlorate derivative but 0.19 for Fe8Br8. AC susceptibility measurements revealed the cluster behaves like a superparamagnetic particle. However, due to the occurrence of large terms in the transverse anisotropy, the temperature dependence of the relaxation time cannot be reproduced by a simple Arrhenius law model. As observed in the bromide derivative, below 350 mK the relaxation time becomes temperature independent and indicating that a pure tunneling regime is attained. The comparison of the tunneling rate in the two clusters shows that in the perchlorate derivative the relaxation process is 35 times faster. The observed ratio of the tunneling rates is in reasonable agreement with that calculated from the tunneling splitting, namely the energy difference between the two almost-degenerate lowest levels Ms =±10, in the two clusters.