Localization-Delocalization in Bridged Mixed-Valence Metal Clusters: Vibronic PKS Model Revisited.

Here we describe a new vibronic model of mixed valence (MV) dimer inspired by the conventional Piepho, Krausz, and Schatz (PKS) approach. We attempted to partially lift the main restriction of the PKS model dealing with the vibronically independent moieties of a MV molecule. The refined version of the PKS model in which the bridging ligands are included deals with the three main interactions: electron transfer (integral t0) related to the high-symmetric ligand configuration, on-site vibronic coupling (parameter υ) arising from the modulation of the crystal field on the metal sites by the breathing displacements of their nearest ligand surroundings, and intercenter vibronic coupling (parameter ζ) describing the dependence of the electron transfer on ligand positions in the course of their breathing movement. We apply the modified model to the analysis of the adiabatic potentials and electronic density distributions in the minima of their lower sheets for the cases of one-electron MV dimer with long and short bridges and for the two-electron MV dimer exhibiting a valence disproportionation effect. The inclusion of the intercenter interaction in addition to the conventional PKS coupling is shown to produce a strong effect on the degree of localization in MV dimers and, in particular, on the assignments to the Robin and Day classes and on the conditions of stabilization of valence disproportionated states in bielectron transfer systems.

Decoherence window and electron-nuclear cross relaxation in the molecular magnet V15.

Rabi oscillations in the V(15) single molecule magnet embedded in the surfactant (CH(3))(2)[CH(3)(CH(2))(16)CH(2)](2)N(+) have been studied at different microwave powers. An intense damping peak is observed when the Rabi frequency Ω(R) falls in the vicinity of the Larmor frequency of protons ω(N). The experiments are interpreted by a model showing that the damping (or Rabi) time τ(R) is directly associated with decoherence caused by electron-nuclear cross relaxation in the rotating reference frame. This decoherence induces energy dissipation in the range ω(N) - σ(e) < Ω(R) < ω(N), where σ(e) is the mean superhyperfine field induced by protons at V(15). Weaker decoherence without dissipation takes place outside this window. Specific estimations suggest that this rapid cross relaxation in a resonant microwave field, observed for the first time in V(15), should also take place, e.g., in Fe(8) and Mn(12).

MVPACK: a package to calculate energy levels and magnetic properties of high nuclearity mixed valence clusters.

We present a FORTRAN code based on a new powerful and efficient computational approach to solve the double exchange problem for high-nuclearity MV clusters containing arbitrary number of localized spins and itinerant electrons. We also report some examples in order to show the possibilities of the program.

High-nuclearity mixed-valence clusters and mixed-valence chains: general approach to the calculation of the energy levels and bulk magnetic properties.

A general approach to the problem of electron delocalization in the high-nuclearity mixed-valence (MV) clusters containing an arbitrary number of localized spins and itinerant electrons is developed. Along with the double exchange, we consider the isotropic magnetic exchange between the localized electrons as well as the Coulomb intercenter repulsion. As distinguished from the previous approaches dealing with the MV systems in which itinerant electrons are delocalized over all constituent metal sites, here, we consider a more common case of systems exhibiting partial delocalization and containing several delocalized domains. Taking full advantage of the powerful angular momentum technique, we were able to derive closed form analytical expressions for the matrix elements of the full Hamiltonian. These expressions provide an efficient tool for treating complex mixed-valence systems, because they contain only products of 6j-symbols (that appear while treating the delocalized parts) and 9j-symbols (exchange interactions in localized parts) and do not contain high-order recoupling coefficients and 3j-symbols that essentially constrained all previous theories of mixed valency. The approach developed here is accompanied by an efficient computational procedure that allows us to calculate the bulk thermodynamic properties (magnetic susceptibility, magnetization, and magnetic specific heat) of high-nuclearity MV clusters. Finally, this approach has been used to discuss the magnetic properties of the octanuclear MV cluster [Fe(8)(mu(4)-O)(4)(4-Cl-pz)(12)Cl(4)](-) and the diphthalocyanine chains [YPc(2)].CH(2)Cl(2) and [ScPc(2)].CH(2)Cl(2) composed of MV dimers interacting through the magnetic exchange and Coulomb repulsion.

Quantum oscillations in a molecular magnet.

The term 'molecular magnet' generally refers to a molecular entity containing several magnetic ions whose coupled spins generate a collective spin, S (ref. 1). Such complex multi-spin systems provide attractive targets for the study of quantum effects at the mesoscopic scale. In these molecules, the large energy barriers between collective spin states can be crossed by thermal activation or quantum tunnelling, depending on the temperature or an applied magnetic field. There is the hope that these mesoscopic spin states can be harnessed for the realization of quantum bits--'qubits', the basic building blocks of a quantum computer--based on molecular magnets. But strong decoherence must be overcome if the envisaged applications are to become practical. Here we report the observation and analysis of Rabi oscillations (quantum oscillations resulting from the coherent absorption and emission of photons driven by an electromagnetic wave) of a molecular magnet in a hybrid system, in which discrete and well-separated magnetic clusters are embedded in a self-organized non-magnetic environment. Each cluster contains 15 antiferromagnetically coupled S = 1/2 spins, leading to an S = 1/2 collective ground state. When this system is placed into a resonant cavity, the microwave field induces oscillatory transitions between the ground and excited collective spin states, indicative of long-lived quantum coherence. The present observation of quantum oscillations suggests that low-dimension self-organized qubit networks having coherence times of the order of 100 micros (at liquid helium temperatures) are a realistic prospect.

High-Nuclearity Magnetic Clusters: Generalized Spin Hamiltonian and Its Use for the Calculation of the Energy Levels, Bulk Magnetic Properties, and Inelastic Neutron Scattering Spectra.

A general solution of the exchange problem in the high-nuclearity spin clusters (HNSC) containing arbitrary number of exchange-coupled centers and topology is developed. All constituent magnetic centers are supposed to possess well-isolated orbitally non-degenerate ground states so that the isotropic Heisenberg-Dirac-Van Vleck (HDVV) term is the leading part of the exchange spin Hamiltonian. Along with the HDVV term, we consider higher-order isotropic exchange terms (biquadratic exchange), as well as the anisotropic terms (anisotropic and antisymmetric exchange interactions and local single-ion anisotropies). All these terms are expressed as irreducible tensor operators (ITO). This allows us to take full advantage of the spin symmetry of the system. At the same time, we have also benefitted by taking into account the point group symmetry of the cluster, which allows us to work with symmetrized spin functions. This results in an additional reduction of the matrices to diagonalize. The approach developed here is accompanied by an efficient computational procedure that allows us to calculate the bulk magnetic properties (magnetic susceptibility, magnetization, and magnetic specific heat) as well as the spectroscopic properties of HNSC. Special attention is paid to calculate the magnetic excitations observed by inelastic neutron scattering (INS), their intensities, and their Q and temperature dependencies. This spectroscopic technique provides direct access to the energies and wave functions of the different spin states of the cluster; thus, it can be applied to spin clusters in order to obtain deep and detailed information on the nature of the magnetic exchange phenomenon. The general expression for the INS cross-section of spin clusters interacting by all kinds of exchange interactions, including also the single-ion zero-field splitting term, is derived for the first time. A closed-form expression is also derived for the particular case in which only the isotropic exchange interactions are involved. Finally this approach has been used to model the magnetic properties as well as the INS spectra of the polyoxometalate anion [Ni(9)(OH)(3)(H(2)O)(6)(HPO(4))(2)(PW(9)O(34))(3)](16)(-), which contains a central magnetic cluster formed by nine exchange-coupled Ni(II) ions surrounded by diamagnetic phosphotungstate ligands (PW(9)O(34))(9)(-).