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Molecular Nanomagnets have attracted the attention of the scientific community since the rich physics behind their magnetic behaviour make them ideal test-beds for fundamental concepts in quantum mechanics. Sophisticated experiments and targeted research activities have also unveiled their potential for several technological applications. Inelastic neutron scattering is a powerful and widely used technique to investigate the properties of these systems. The new generation of spectrometers, equipped with arrays of position-sensitive detectors, enable to efficiently measure the neutron cross-sections as a function of energy and of the three component of the momentum transfer vector Q, in vast portions of the reciprocal space. Exploiting these capabilities together with the availability of sufficiently large single-crystal samples of MNMs, it is now possible to obtain an unprecedented insight into the coherent spin dynamics of these molecular clusters. This is witnessed by several recent results, that we present in this review. By using the benchmark system Cr$_8$, it has been demonstrated that the richness of the four-dimensional inelastic neutrons scattering technique enables to extract dynamical correlation functions directly from the data. This technique has been also applied to the archetypical single-molecule magnet Mn$_{12}$ to unambiguously characterise its Spin Hamiltonian as well as to portray the entanglement between molecular qubits in (Cr$_7$Ni)$_2$.

Nine new complexes are reported involving linked heterometallic rings; one ring is designed as a ligand for the second, and the compounds produced can be regarded as molecular prototypes for implementing quantum gates featuring two subtly different qubits., We are grateful to the EPSRC (UK) for funding, especially of the National EPR Facility. M. Albring is a member of the EPSRC supported Centre for Doctoral Training NoWNANO. We acknowledge financial support also from the FIRB Project No. RBFR12RPD1 of the Italian Ministry of Education and Research. This work has been partially supported by EC through the FET-Proactive Project “MoQuaS”, contract N.610449.

Chemical science 9(14), 3555-3562 (2018). doi:10.1039/C8SC00163D, Published by RSC, Cambridge

In the Cr7Co model-system the anisotropy of CoII 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 CoII 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 CoII 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.

Correction for ‘Anisotropy of CoII transferred to the Cr7Co polymetallic cluster via strong exchange interactions’ by Elena Garlatti et al., Chem. Sci., 2018, DOI: ; 10.1039/c8sc00163d.

Compounds of general formula [Cr7MF3(Etglu)(O2C(t)Bu)15(Phpy)] [H5Etglu = N-ethyl-d-glucamine; Phpy = 4-phenylpyridine; M = Zn (1), Mn (2), Ni (3)] have been prepared. The structures contain an irregular octagon of metal sites formed around the penta-deprotonated Etglu(5-) ligand; the chirality of N-ethyl-d-glucamine is retained in the final product. The seven Cr(III) sites have a range of coordination environments, and the divalent metal site is crystallographically identified and has a Phpy ligand attached to it. By using complementary experimental techniques, including magnetization and specific heat measurements, inelastic neutron scattering, and electron paramagnetic resonance spectroscopy, we have investigated the magnetic features of this family of {Cr7M} rings. Microscopic parameters of the spin Hamiltonian have been determined as a result of best fits of the different experimental data, allowing a direct comparison with corresponding parameters found in the parent compounds. We examine whether these parameters can be transferred between compounds and compare them with those of an earlier family of heterometallic rings.

Antiferromagnetic molecular rings are widely studied both for fundamental quantum-mechanical issues and for technological applications, particularly in the field of quantum information processing. Here we present a detailed first-principles study of two families---purple and green---of ${{\mathrm{Cr}}_{7}M}$ antiferromagnetic rings, where $M$ is a divalent transition metal ion ($M={\mathrm{Ni}}^{2+}, {\mathrm{Mn}}^{2+}$, and ${\mathrm{Zn}}^{2+}$). We employ a recently developed flexible and efficient scheme to build ab initio system-specific Hubbard models. From such many-body models we systematically derive the low-energy effective spin Hamiltonian for the rings. Our approach allows us to calculate isotropic as well as anisotropic terms of the spin Hamiltonian, without any a priori assumption on its form. For each compound we calculate magnetic exchange couplings, zero-field splitting tensors, and gyromagnetic tensors, finding good agreement with experimental results.

We investigate the magnetic properties and the phonon-induced relaxation dynamics of the first regular ${\mathrm{Cr}}_{9}$ antiferromagnetic (AF) ring, which represents a prototype frustrated AF ring. Geometrical frustration in ${\mathrm{Cr}}_{9}$ yields an energy spectrum with twofold degenerate low-lying levels and a low-spin ground state. The electronic relaxation dynamics is probed by ${}^{1}\mathrm{H}$-NMR through the temperature dependence of the spin-lattice relaxation rate $1/{T}_{1}$. We develop a microscopic model that reproduces $1/{T}_{1}(T)$ curves, taking also into account the wipeout effect. By interpreting these measurements we determine the spin-phonon coupling strength and we investigate the decay of the cluster magnetization due to the spin-phonon interaction. We find that at very low temperatures, the relaxation is characterized by a single dominating Arrhenius-type relaxation process, whereas several relevant processes emerge at higher temperatures. In addition, we calculate the temperature and magnetic field dependence of level lifetimes.

Molecular nanomagnets are among the first examples of finite-size spin systems and have been test beds for addressing several phenomena in quantum dynamics. In fact, for short-enough timescales the spin wavefunctions evolve coherently according to an appropriate spin Hamiltonian, which can be engineered to meet specific requirements. Unfortunately, so far it has been impossible to determine these spin dynamics directly. Here we show that recently developed instrumentation yields the four-dimensional inelastic-neutron scattering function in vast portions of reciprocal space and enables the spin dynamics to be determined directly. We use the Cr 8 antiferromagnetic ring as a benchmark to demonstrate the potential of this approach which allows us, for example, to examine how quantum fluctuations propagate along the ring or to test the degree of validity of the Néel-vector-tunnelling framework. © 2012 Macmillan Publishers Limited. All rights reserved.

Correction for ‘Anisotropy of CoII transferred to the Cr7Co polymetallic cluster via strong exchange interactions’ by Elena Garlatti et al., Chem. Sci., 2018, DOI: 10.1039/c8sc00163d.

Inelastic neutron scattering, probing the temporal spin–spin correlation at the microscopic scale, is a powerful technique to study the magnetic behaviour of molecular nanomagnets. Experiments at different energy scales and different energy-transfer resolution allow precise determinations of the parameters defining the effective Hamiltonians used to model the diverse physical properties exhibited by this class of materials. The intrinsic disadvantage of the technique (low flux, requiring a sample mass in the gram scale) is over-compensated by the large amount of information that can be straightforwardly extracted. Zero-field splittings and exchange interactions can be determined with a large degree of confidence, shedding light on important issues such as magnetization tunnelling in giant-spin clusters, or the occurrence of quantum coherence phenomena and their consequences on macroscopic observables.

We present a perturbative model for crystal-field calculations in f-electron compounds, which keeps into account the mixing between states labelled by different total angular momentum J. We use this model to analyze the results of inelastic neutron scattering experiments on actinide dioxides accumulated over a number of years. By comparing our calculations with the published results of other experiments, we point out that a unified crystal-field picture for this series of compounds clearly emerges.

We present recent achievements and perspectives for the encoding of qubits with molecular spin clusters.

The anisotropy of magnetic fluctuations propagating along the high-symmetry directions in cubic systems with 3- k magnetic order is analyzed within the random-phase approximation assuming anisotropic exchange interactions. Both transverse and longitudinal structures are considered, with reference to the UO 2 and USb compounds, respectively. In the case of UO 2 , the spin-waves polarizations calculated for acoustic and optical branches are favorably compared with three-dimensional polarization analysis experiments carried out on a triple axis spectrometer. The overall spin-waves polarization behavior emerges as a consequence of the 3- k nature of the magnetic order, whatever the strength of the exchange coupling assumed.

We derive a general expression for the quasielastic part of the dynamic structure factor in the presence of a heat bath, starting from the master equation applied to the full microscopic Hamiltonian. By specializing this expression to the case of the total spin, we investigate the time autocorrelation of the molecular magnetization M for three classes of magnetic molecules (antiferromagnetic rings, grids and nanomagnets), in contact with the phonon heat bath. We find that the exponential decay of the fluctuations of M , associated with the irreversible exchange of energy with the heat bath, is characterized by a single decay time for not too high temperature and field. Such fluctuations are effectively probed by nuclear magnetic resonance (NMR), and the calculations are in very good agreement with existing experimental NMR data.

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.

Molecular magnets have been recently proposed as possible building blocks for a solid-state quantum computer. In order to substantiate and develop such a proposal, one needs to identify those molecules that are best suited for the qubit encoding and manipulation. Here, we focus on a heterometallic molecular ring, namely Cr7Ni, where the substitution of one Cr3+(S = 3/2) with Ni2+(S = 1) provides an extra spin to the otherwise compensated molecule. We show that its ground state consists in an S = 1/2 doublet, energetically well separated (Δ0/kB ∼ 13 K at zero magnetic field) from the first excited multiplet. This relatively large value of Δ0, together with the reduced mixing of the subspaces corresponding to different values of the total spin S, enables a safe encoding of the |0〉 and |1〉 states with the ground-state doublet, and allows to coherently rotate the effective S = 1/2 spin, while keeping the population loss to the excited states negligible. A further, intriguing challenge is represented by the implementation of the conditional dynamics (two-qubit gates). We present here preliminary characterization of molecular “Cr7Ni-dimers”, i.e., derivatives in which two Cr7Ni rings are linked with each other by means of delocalized aromatic amines. The resulting intercluster couplings are estimated to be ⩽1 K and are expected to be permanent, i.e., not tuneable during gating, as required by the standard approach to quantum computation. We discuss a computational scheme that allows in principle to overcome this limitation. The most relevant decoherence mechanisms for Cr7Ni and possible ways to reduce their effects are discussed as well.

Hysteresis curves of molecular nanomagnets display a step-like behavior typical of the relaxation through quantum tunneling of the magnetization. The relaxation rate depends on the value of the so-called tunnel splitting, i.e., the gap between quasi-degenerate states in correspondence of a level anticrossing. In the case of Fe 8 , the magnitude of this gap deduced by Landau–Zener measurements seems incompatible with the value calculated by using the Hamiltonian determined by spectroscopic measurements. We show that the commonly neglected quantum fluctuations of the magnitude of the total spin of the molecule ( S mixing) hugely affect the tunnel splitting, and allow the above-mentioned discrepancy to be solved. Since the degree of S mixing is strongly influenced by the topology of the molecule, we suggest that cluster topology is one of the key ingredients in designing new nanomagnets.

Molecular nanomagnets, besides promising to open new frontiers in technology, have attracted huge interest in the scientific community because they can exhibit the phenomenon known as quantum tunnelling of the magnetization, i.e. coherent fluctuations of the direction of the total spin vector. In this paper we study a different quantum phenomenon involving fluctuations of the magnitude of the total spin vector. These fluctuations are related to the mixing between states with different spin quantum number, and imply new macroscopic effects, which we theoretically investigated in the Mn-[3x3] grid.

The experimental values of the energy levels of Er3+, Dy3+, and Nd3+ in BaY2F8 were fitted to a single-ion Hamiltonian containing free-ion and crystal-field interactions. The crystal-field parameters so evaluated were then analyzed by using Newman's Superposition Model. The agreement between the two sets of parameters is good, provided a possible distortion of the F- polyhedron around the rare-earth site is taken into account. The effects of a possible displacement of the rare-earth ion substituting for Y3+ are also evaluated.

The magnetic clusters are usually described by an effective Hamiltonian acting in a fixed S space. This single-spin description neglects the mixing between states with different total spin S produced by anisotropic interactions, such as the local crystal field and the magnetic dipole-dipole coupling. We have developed a general and simple procedure, based on a perturbational approach, where the S-mixing effects are included in some new terms to be added to the original effective Hamiltonian. These terms contain some new operators, which depend on the anisotropic interactions and on the difference ΔS between the spin of the states involved in the mixing. Interestingly, these operators are very similar (in some specific cases equal) to the well known Stevens operator equivalents. A list of them for ΔS=1 and ΔS=2 and for second-order anisotropic interactions is presented. The method has been applied to study the S-mixing in two iron nanomagnets, Fe4 and Fe8.

The energy level schemes of four rare-earth dopants (Ce 3+ , Nd 3+ , Dy 3+ , and Er 3+ ) in BaY 2 F 8 , as determined by optical absorption spectra, were fitted with a single-ion Hamiltonian and analysed within Newman's Superposition Model for the crystal field. A unified picture for the four dopants was obtained, by assuming a distortion of the F m ligand cage around the RE site; within the framework of the Superposition Model, this distortion is found to have a marked anisotropic behaviour for heavy rare earths, while it turns into an isotropic expansion of the nearest-neighbours polyhedron for light rare earths. It is also inferred that the substituting ion may occupy an off-center position with respect to the original Y 3+ site in the crystal.

We discuss the role of degrees of freedom different from the magnetic dipole in NpO 2 . Electric-quadrupole degrees of freedom appear to produce a large splitting of the main crystal-field (CEF) transition, due to the formation of mixed CEF-phonon states. A phase transition occurs at 25 K, and its phenomenology is inconsistent with a magnetic-dipole or an electric-quadrupole order parameter (OP). A magnetic-octupole of Γ 2 symmetry appears to be the best candidate OP. Such quantity can be detected in principle in a neutron diffraction experiment. The corresponding form factor is discussed.

Compounds of general formula [Cr7MF3(Etglu)(O2C(t)Bu)15(Phpy)] [H5Etglu = N-ethyl-d-glucamine; Phpy = 4-phenylpyridine; M = Zn (1), Mn (2), Ni (3)] have been prepared. The structures contain an irregular octagon of metal sites formed around the penta-deprotonated Etglu(5-) ligand; the chirality of N-ethyl-d-glucamine is retained in the final product. The seven Cr(III) sites have a range of coordination environments, and the divalent metal site is crystallographically identified and has a Phpy ligand attached to it. By using complementary experimental techniques, including magnetization and specific heat measurements, inelastic neutron scattering, and electron paramagnetic resonance spectroscopy, we have investigated the magnetic features of this family of {Cr7M} rings. Microscopic parameters of the spin Hamiltonian have been determined as a result of best fits of the different experimental data, allowing a direct comparison with corresponding parameters found in the parent compounds. We examine whether these parameters can be transferred between compounds and compare them with those of an earlier family of heterometallic rings.

We discuss a scalable scheme for the implementation of quantum-information processing in qubits formed by superconducting resonators and spin ensembles. The scheme is based on a hybrid dual-rail encoding, which allows one to perform both single- and two-qubit gates by shifting the resonator frequency. We estimate the quantum-gate fidelity by simulating the driven dynamics through a master-equation approach. High values of the fidelity can be achieved also in the presence of the main decoherence sources, namely, cavity-photon loss, and pure dephasing of the superconductive elements that are involved in the two-qubit gates. This result allows envisioning the scalability of such elements to a quantum-computing architecture made of an array of hybrid spin-photon qubits. Analogous results are obtained for a simpler, nonscalable setup, which we propose here in order to simplify the realization of the first proof-of-principle experiments.

We study the magnetization and the spin dynamics of the Cr 7 Ni ring-shaped magnetic cluster. Measurements of the magnetization at high pulsed fields and low temperature are compared to calculations and show that the spin Hamiltonian approach provides a good description of the Cr 7 Ni magnetic molecule. In addition, the phonon-induced relaxation dynamics of molecular observables has been investigated. By assuming the spin–phonon coupling to take place through the modulation of the local crystal fields, it is possible to evaluate the decay of fluctuations of two generic molecular observables. The nuclear spin–lattice relaxation rate 1 / T 1 directly probes such fluctuations, and allows to determine the magnetoelastic coupling strength.

We report the results of inelastic neutron scattering experiments performed with triple-axis spectrometers to investigate the low-temperature collective dynamics in the ordered phase of uranium dioxide. The results are in very good agreement with the predictions of mean-field random phase approximation calculations, emphasizing the importance of multipolar superexchange interactions. By comparing neutron scattering intensities in different polarization channels and at equivalent points in different Brillouin zones, we show the mixed magnetovibrational-quadrupolar character of the observed excitations. The high-energy resolution afforded by the cold triple-axis spectrometer allowed us to study in detail the magnon-phonon interaction giving rise to avoided crossings along the $[00\ensuremath{\xi}]$ reciprocal space direction.

The phase transition occurring at 25 K in NpO2, discovered almost 50 years ago, is the most long-lasting mystery in the physics of actinide compounds. Theories based on magnetic or electric-quadrupole order lead inevitably to fundamental, qualitative inconsistencies with observations. We show that the phenomenology of NpO2 can be understood if the order parameter is assumed to be a magnetic octupole of gamma(2) ( xyz) symmetry. NpO2 is the first compound for which indications of an octupolar phase transition have been found.

We present a study performed on several LaMnO3+x/2 compositions. Detailed analysis around x=0.09 detects phase separation between a higher transition, Tc, and a lower one TN, with coexisting fluctuating and magnetically ordered clusters (the Neel point, TN, being the onset of an inhomogeneous non-collinear antiferromagnetic order detected by neutrons). The ordered clusters give rise to an extremely fast, static Kubo–Toyabe muon depolarization, while mixed static and dynamic local fields are detected inside the fluctuating clusters. Below TN precession frequency lines are resolved, despite the huge broadening introduced by localized Mn4+ ordered moments. A phase diagram is obtained and briefly discussed in the context of electronic phase separation.

Inelastic neutron scattering with polarization analysis has been used to study the evolution of the magnetic response across the antiferromagnetic to paramagnetic transition in a single crystal of uranium dioxide ${(T}_{N}=30.8 \mathrm{K})$. The spin-wave dispersion curves have been determined at 16 K by measuring the spin-flip channel of the neutron cross section along the principal crystallographic directions. Evidence of magnon-phonon interactions along the $(0,0,\ensuremath{\xi})$ direction is given by the splitting of the lowest spin-wave branch, and by the Q dependence of the energy-integrated dynamic susceptibility. Above ${T}_{N},$ a magnetic inelastic response consisting of two dispersive peaks was observed between 3 and 10 meV. This signal was easily measurable even at 200 K, more than six times the N\'eel temperature, where spatial correlations between the uranium spins are essentially zero. We assume this result as evidence that in the time scale of our experiment the uranium triplet ground state is split into three singlets, due to a dynamical Jahn-Teller (JT) distortion of the oxygen cage which reduces the point symmetry at the uranium site. Since the position of the peaks and their dispersion are compatible to a $1\ensuremath{-}\mathbf{k}$ distortion along the $〈100〉$ direction, a picture emerges in which local, uncorrelated $1\ensuremath{-}\mathbf{k}$ dynamical JT distortions occur above ${T}_{N}$ along the three directions of the $〈100〉$ star; as ${T}_{N}$ is approached, a correlation builds up between the phases of the corresponding vibrations until, eventually, a static $3\ensuremath{-}\mathbf{k}$ structure is obtained below ${T}_{N}.$

Various magnetic measurements on , x = 0, 1, 1.5, 2, indicate that increasing Kondo interaction due to Cu/Al substitution causes a substantial decrease of the magnetic moment in the crystal-field ground state. A theoretical description on the basis of the non-crossing approximation, taking into account the primary interaction mechanisms, yields excellent agreement with the data and shows that the moment is reduced even at high values of applied magnetic field.

The low-temperature inelastic neutron scattering spectrum measured for the p-tert-butylcalix[4]arene(2:1)p-xylene complex has been interpreted in the framework of a quantum dynamical model assuming a rotational motion of the p-xylene groups correlated to the translational motion of their centre of mass. By comparing the experimental data with calculated energies and intensities, the effective anharmonic and anisotropic molecular potential experienced by the methyl groups has been derived. The wavefunctions deduced from the spectroscopy results are used to calculate the proton density distribution in the plane of the motion.

Neutron powder diffraction has been used to investigate the magnetic order in a series of RMn4Al8 (space group I4/mmm) compounds with R = (Nd, Dy, Ho and Er). For compounds with Mn, no magnetic order was detected down to 1.6 K, whilst for the compound ErCr4Al8, two very weak magnetic reflections were observed at 1.6 K. The observed magnetic peaks cannot be indexed on the tetragonal unit cell, indicating a possible incommensurate magnetic structure. For ErCu4Al8, a type 1 antiferromagnetic structure is observed. The magnitude and temperature dependence of the Er3+ magnetic moment can be adequately modelled by a combined isotropic exchange and tetragonal crystal field Hamiltonian within the Mean Field Approximation.

Susceptibility and magnetisation measurements on the dense Kondo compound CeCu 5 are interpreted on the basis of selfconsistent calculations using the non-crossing approximation. Crystal-field effects and molecular fields are taken into account in both paramagnetic and antiferromagnetically ordered phases. The results give clear evidence for the presence of a Kondo effect on the paramagnetic susceptibility at temperatures much larger than the Kondo temperature, as well as for a reduction of the induced magnetic moment under high external fields.

We report the results of Raman, infrared, and inelastic neutron scattering investigations of the vibrational spectrum of the complex p-tert-butylcalix[8]arene(1:1)fullerene, a system with almost isolated ${\mathrm{C}}_{60}$ molecules confined inside neutral cages. All the internal optical-active modes of the ${\mathrm{C}}_{60}$ guest have been identified, and further modes which can be attributed to ${\mathrm{C}}_{60}$ intramolecular vibrations appear in the neutron scattering function. A comparison with the vibrational spectrum of empty p-tert-butylcalix[8]arene indicates that the host-guest interaction is very weak. As solid-state effects are also practically suppressed, the investigated complex gives the unique opportunity to study almost free fullerene balls confined in the solid state.

The phenomena of Kondo screening and moment reduction in almost localized Kondo systems are studied on the basis of a molecular-field approach. An interpretation of moment reduction as observed by elastic neutron scattering is given; it is shown how to describe the perturbative conduction electron polarization, and that the long-ranged Kondo screening cloud cannot be measured by neutron scattering. The interplay between Kondo reduction of magnetic moment and the effect of crystal fields is investigated. The model is applied to several cubic Ce systems, where the amount of Kondo reduction is found to be substantial.

Resonant X-ray scattering (RXS) experiments on NpO 2 provide indications for a low-temperature phase where magnetic octupole order is established in absence of magnetic dipole order. The interpretation of the RXS findings has led to a controversy about the symmetry of the primary order parameter, which has been identified either with Γ 2 or with Γ 5 octupoles. A consequence of long-range octupole order is that the degeneracy of the Γ 8 crystal field ground state is removed. Γ 8 would be split into two doublets if Γ 2 octupoles order, and into two singlets and one doublet if the order parameter has Γ 5 symmetry. Here we present specific heat measurements between 0.7 K and 300 K supporting a singlet ground state in the ordered phase below 25.5 K.

The magnetic properties of the triangular molecular nanomagnet [UO2L]3 (L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate) have been investigated through electron paramagnetic resonance spectroscopy, high-field magnetization and susceptibility measurements. The experimental findings are well reproduced by a microscopic model including exchange interactions and local crystal fields. These results show that [UO2L]3 is characterized by a non-magnetic ground doublet corresponding to two oppositely twisted chiral arrangements of the uranium moments. The non-axial character of single-ion crystal fields leads to quantum tunneling of the noncollinear magnetization in the presence of a magnetic field applied perpendicularly to the triangle plane.

We investigate the phonon-induced relaxation dynamics in the Fe-7 magnetic molecule, which is made of two Fe3+ triangles bridged together by a central Fe3+ ion. The competition between different antiferromagnetic exchange interactions leads to a low-spin ground state multiplet with a complex pattern of low-lying excited levels. We theoretically investigate the decay of the time correlation function of molecular observables, such as the cluster magnetization, due to the spin-phonon interaction. We find that more than one time contributes to the decay of the molecular magnetization. The relaxation dynamics is probed by measurements of the nuclear spin-lattice relaxation rate 1/T-1. The interpretation of these measurements allows the determination of the magnetoelastic coupling strength and to set the scale factor of the relaxation dynamics time scales. In our theoretical interpretation of 1/T-1 data we also take into account the wipeout effect at low temperatures.

The magnetic form factor in Kondo systems, as measured by polarized neutron elastic scattering, is uniformly reduced (with respect to the atomic form factor in the crystal field) due to the Kondo effect, and moreover it shows deviations at small scattering vector due to a spin polarization of conduction electrons: the sign of the deviations in Ce compounds is positive, which is opposite to what is observed in normal rare earths of the first half of the series, and expected from the s-f exchange Hamiltonian. In the present work the above two anomalies are interpreted within a theory for the magnetic form factor in Kondo systems. The uniform reduction of the form factor follows from a variational calculation for the one-impurity Anderson model in an effective magnetic field: Kondo reduction of the localized moment is distinguished here from the presence of a screening cloud, which cannot be observed by neutron scattering. The conduction electron polarization is first studied for the Coqblin-Schrieffer Hamiltonian, which we find to lead again to negative deviations of the form factor. Within the Anderson impurity model, the conduction electron contribution to the form factor is found to be the sum of two terms: a negative RKKY-like polarization, and a positive superexchange term, which is nonzero even for a filled (or empty) band. Dominance of the superexchange polarization could explain the observed sign of the deviations in Ce compounds. A variational basis which describes both Kondo reduction and conduction electron polarization effects is studied: the two effects are clearly separated, since they appear in different orders of the calculations. The conduction electron polarization is shown to be reduced due to the Kondo effect by the same spin-fluctuation factor which reduces the localized moment.

Several dense Kondo compounds have a low-temperature ordered phase in which the magnetic moments are reduced with respect to the values expected for the crystal-field (CEF) ground state. In the present work the phenomenon of moment reduction is studied within a molecular-field theory combined with a variational solution of the one-impurity Anderson model with CEF effects. The calculated zero-temperature magnetization and susceptibility agree well with available exact results; the present method is easily applied to systems of any symmetry. We first study the f1 configuration in cubic symmetry, for small values of the ratio TK/Δ between Kondo temperature and CEF splitting. With a Γ∞ ground state and a field along a 〈100〉 direction, an inflection point occurs in the magnetization curve, which gives rise to a first order transition in the zero-temperature phase diagram. This feature is not found for a field along 〈110〉 or 〈111〉, for which the transition is second order. For a Γ7 ground state and small values of TK/Δ, the magnetic-nonmagnetic transition is second order for all field directions. On increasing TK/Δ an inflection point in the magnetization curve appears first for a field along 〈111〉. The theory is applied to a study of cubic CeAg, CeAl2, CePb3, CeIn3, CeTe, and hexagonal CePd2Ga3. The bare value of the moment is found to be strongly increased by exchange coupling to excited CEF states, and the amount of Kondo reduction is found to be substantial, confirming the importance of the Kondo effect in these compounds.

Macroscopic quantum phenomena arising from S-mixing in molecular nanomagnets are studied. While in the lack of an external magnetic field such effects are usually negligible, when a field of suitable intensity and direction is applied total-spin fluctuations can be amplified to the point that they dominate the macroscopic behavior at low temperature. In particular, the behavior of torque and heat capacity as a function of the field strength is dominated by S-mixing, and the former is characterized by peculiar peak-like structures. Our calculations show that the Mn-[3×3] grid is particularly suited to observe these effects.

By substituting one Cr3+(s=3/2) with Cd2+(s=0) in molecular octanuclear rings, a diluted ensemble of identical nanomagnets with a S=3/2 ground state, weakly split in zero field, is obtained. The lattice contribution and the essential parameters of the spin Hamiltonian of these uncompensated antiferromagnetic cyclic spin systems are determined by fitting specific heat data between 0.4 and 20 K in magnetic fields up to 7 T. Different entropy contributions are evaluated and results suggest a possible way of engineering molecular magnets to exploit low temperature magnetocaloric effect.

A generalization of the linear theory for J-mixing compounds has recently been reported; this allows to describe the system as an effective isolated multiplet, keeping J-mixing effects into account as second-order perturbative corrections. Within this framework, analytical expressions for the free energy can be obtained. In the present paper the effect of fourth-order J-mixing corrections on the anisotropy is discussed for Sm-based intermetallic alloys, and it is found to be important for magnetic compounds with strong exchange interaction.

Inelastic neutron scattering experiments and specific heat measurements have been performed on polycrystalline samples of PrFe2X2 (X=Si, Ge), a tetragonal intermetallic system showing a low-temperature antiferromagnetic ordering of the Pr sublattice, with no local magnetic moment on the iron site. The temperature variation of the specific heat, and the values of the magnetic entropy, indicate for both compounds a crystal-field energy level scheme characterized by two closely spaced singlets, split by about 1 meV for X=Ge and by about 2.5 meV for X=Si, with the other levels positioned above 7 meV. These conclusions are confirmed by the observation of only one excitation peak in the magnetic neutron scattering response in this energy range. In the paramagnetic phase, the inelastic peak is centred at 2.4(1) meV for X=Si and at 0.8(1) meV for X=Ge. Below TN, the peak position shifts to 2.8(1) meV for X=Si, and to 2.7(1) meV for X=Ge. The experimental findings are explained by a crystal- and molecular-field model with two low-lying singlets, coupled by exchange in the ordered phase. The different size of the molecular field in the two compounds, with respect to the crystal-field splitting of the low-lying singlets, causes the large difference in the ordered moments of the Pr3+ ions (1.41 mu B for Si and 2.75 mu B for Ge). The asymmetric shape of the peaks in the neutron scattering function has been attributed to the presence of two branches of magnetic excitons in these crystal-field systems showing manifestly Van Vleck-induced antiferromagnetism of singlet-singlet type.