Modelling the properties of magnetic clusters with complex structures: how symmetry can help us

The purpose of this article is to answer the question of how symmetry helps us to investigate and understand the properties of nanoscopic magnetic clusters with complex structures. The systems of choice will be the three types of polyoxometalates (POMs): (1) POMs containing localised spins; (2) reduced mixed-valence (MV) POMs; (3) partially delocalised POMs in which localised and delocalised subunits coexist and interact. The theoretical tools based on various kinds of symmetry are the following: (1) irreducible tensor operator (ITO) approach based on the so-called 'spin-symmetry' and MAGPACK program; (2) group-theoretical assignment of the exchange multiplets based on spin- and point symmetries; (3) group-theoretical classification of the delocalised electronic and electron-vibrational states of MV POMs; (4) general approach (based on spin symmetry) to evaluate the energy levels of large MV clusters and the corresponding MVPACK program; (5) computational approach (employing point symmetry) to solve multidimensional non-adiabatic vibronic problems in the nanoscopic systems realized as VIBPACK software. We made it our goal to avoid a conventional deductive style of presentation. On the contrary, we first consider specially selected complex POMs and then show by what methods and in what way the theoretical problems arising in the description of the properties of these molecules can be properly solved

Crossover of the magnetic levels and adiabatic magnetization of the mesoscopic cluster V 15

Abstract The magnetic three spin-1/2 model for nanometer-scale molecular cluster V 15 is analyzed with the emphasis on the origin of the mixing of different spin levels in the resonance fields that is generally important for the problem of single molecular magnets. The zero-field splitting in the ground quadruplet (two S = 1/2 levels) is shown to depend mainly on the normal component of AS exchange meanwhile the zero-field splitting in the excited S = 3/2 multiplet is a second order effect with respect to in-plane components of AS exchange. The normal component of the AS exchange is shown to lead to the exact crossing of the magnetic sublevels at the arbitrary direction of the field. The positions of two crossing/anticrossing points in the ground manifold depend mainly on the isotropic exchange and normal component of AS exchange meanwhile the gap in the avoided crossing point in parallel field is affected only by the in-plane component. We discuss the role of AS exchange in the field and temperature dependence of the adiabatic magnetization. We predict a specific field dependence of the magnetization vs. field caused by AS exchange

Vibronic Model for Intercommunication of Localized Spins via Itinerant Electron

Here we propose a vibronic pseudo Jahn-Teller (JT) model for partially delocalized mixed valence (MV) molecules aimed to the description of the magnetic coupling between the localized spins mediated by the delocalized electron. The model involves the following key interactions: electron transfer in the spin-delocalized subsystem which is mimicked by a dimeric unit, coupling of the itinerant electrons with the molecular vibrations and isotropic magnetic exchange between the localized spins and delocalized electron. The pseudo JT vibronic coupling which is considered in the framework of the Piepho, Krausz and Schatz (PKS) model adapted to the case of partially delocalized MV molecules. It is revealed (qualitatively and quantitively) how the vibronic coupling affects the connection of the localized spins via the itinerant electron

Vibronic recovering of functionality of quantum cellular automata based on bidimeric square cells with violated condition of strong Coulomb repulsion

Strong Coulomb repulsion between the two charges in a square planar mixed-valence cell in quantum cellular automata (QCA) allows us to encode the binary information in the two energetically beneficial diagonal distributions of the electronic density. In this article, we pose a question: to what extent is this condition obligatory for the design of the molecular cell? To answer this question, we examine the ability to use a square-planar cell composed of one-electron mixed valence dimers to function in QCA in a general case when the intracell Coulomb interaction U is not supposed to be extremely strong, which means that it is comparable with the characteristic electron transfer energy (violated strong U limit). Using the two-mode vibronic model treated within the semiclassical (adiabatic) and quantum-mechanical approaches, we demonstrate that strong vibronic coupling is able to create a considerable barrier between the two diagonal-type charge configurations, thus ensuring bistability and polarizability of the cells even if the Coulomb barrier is not sufficient. The cases of weak and moderate Coulomb repulsion and strong vibronic coupling are exemplified by consideration of the cation radicals of the two polycyclic derivatives of norbornadiene [C12H12]+ and [C17H16]+ with the terminal C=C chromophores playing the role of redox sites. By using the detailed ab initio data, we reveal the main characteristics of the bi-dimeric cells composed of these molecules and illustrate the pronounced effect of the vibronic recovery clearly manifesting itself in the shape of the cell-cell response function. Revealing such 'vibronic recovery' of strong localization when the strong U limit is violated suggests a way to a significant expansion of the class of molecular systems suitable as QCA cells

Magnetic relaxation in V 15 cluster: Direct spin-phonon transitions

Dedicated to Professor Achim Müller-to highlight his exceptional achievements. Keyword

Optical Lines in Europium and Terbium-Activated Yttrium Tantalate Phosphor: Combined Experimental and Group-Theoretical Analysis

The rare-earth ions in crystals such as terbium (YTaO4:Tb3+) and europium (YTaO4:Eu3+)-activated yttrium tantalate phosphors have a number of attractive features that predetermine their crucial role in practical application in contemporary optoelectronic devices. In this article, we employ the group-theoretical arguments aimed to reveal the group-theoretical classification of the crystal field levels and selection rules for the allowed optical transition between the crystal field components of Tb3+ and Eu3+ of the low symmetry crystal field in the activated yttrium tantalate phosphors. We also establish possible polarization rules for the lines corresponding to the allowed transitions. We deduce the symmetry-assisted results for the selection rules in the optical transitions accompanied by the absorption/emission of the vibrational quanta. The selection rules for the vibronic satellites of the zero-phonon lines are expected to be useful for the identification of the lines in the spectra of rare-earth ions with a weak vibronic coupling. The results of the low-temperature measurements of photoluminescence under the 325 nm excitation are in compliance with the group-theoretical analysis. The aim of the paper is to establish symmetry-assisted results that are the background of the quantitative crystal field theory based on the quantum-mechanical consideration

Crossover of the magnetic sublevels in spin frustrated clusters: The role of static and dynamic deformations

Tarantul A, Tsukerblat B, Müller A. Crossover of the magnetic sublevels in spin frustrated clusters: The role of static and dynamic deformations. SOLID STATE SCIENCES. 2008;10(12):1814-1819.We model the magnetic behavior of spin frustrated trinuclear clusters in the region of field induced crossover of the levels. The emphasis is made on a competitive role of the antisymmetric (AS) exchange and static structural distortions as well as on the consequences of the dynamic pseudo-Jahn-Teller (JT) instability. We employ the three-spin model for the cluster anion present in K-6[(V15As6O42)-As-IV(H2O)]center dot 8H(2)O (V-15 cluster) and analyze the role of different components of AS in the half step magnetization. Both types of deformations (static and dynamic) are shown to be competitive with the AS exchange and tend to reduce the magnetic anisotropy caused by AS. (C) 2008 Elsevier Masson SAS. All rights reserved

Static magnetization of V-15 cluster at ultra-low temperatures: Precise estimation of antisymmetric exchange

Tarantul A, Tsukerblat B, Müller A. Static magnetization of V-15 cluster at ultra-low temperatures: Precise estimation of antisymmetric exchange. INORGANIC CHEMISTRY. 2007;46(1):161-169.In this article, the low-temperature static (adiabatic) magnetization data of the nanoscopic V-15 cluster present in K-6[(V15As6O42)-As-IV(H2O)]center dot 8H(2)O is analyzed. The cluster anion, which attracted much attention in the past, contains a triangular V-3(IV) array causing frustration as a function of applied field and temperature. In the analysis, a three-spin (S = 1/2) model of V-15 was employed that includes isotropic antiferromagnetic exchange interaction and antisymmetric (AS) exchange in the most general form compatible with the trigonal symmetry of the system. It was shown that, along with the absolute value of AS exchange, the orientation of the AS vector plays a significant physical role in spin-frustrated systems. In this context, the role of the different components of the AS in the low-temperature magnetic behavior of V-15 was analyzed, and we were able to reach a perfect fit to the experimental data on the staircaselike dependence of magnetization versus field in the whole temperature range including extremely low temperature. Furthermore, it was possible for the first time to precisely estimate the two components of the AS vector coupling constant in a triangular unit, namely, the effective in-plane component, D, and the perpendicular part, D-n

Field induced crossover in antiferromagnetic spin-frustrated clusters: Influence of static and dynamic structural deformations

Tarantul A, Tsukerblat B, Müller A. Field induced crossover in antiferromagnetic spin-frustrated clusters: Influence of static and dynamic structural deformations. JOURNAL OF MOLECULAR STRUCTURE. 2008;890(1-3):170-177.We propose a theoretical study of the magnetic behavior of spin frustrated trinuclear clusters in the region of the field induced crossover of the levels which are crucial for the description of the static magnetization and dynamic behavior in a sweeping field. The emphasis is made on a competitive role of the antisymmetric (AS) exchange and static structural distortions of the metal center network as well as on the consequences of the dynamic pseudo Jahn-Teller (JT) instability that is closely related to spin frustration. The structural conformations are shown to be controlled by the magnetic field in the anticrossing region (magnetoelastic coupling). We employ the three-spin model for the cluster anion present in K-6[(V15As6O42)-As-IV(H2O)] center dot 8H(2)O (V-15 cluster) and analyze the role of different components of AS exchange in the shape of the magnetic susceptibility vs field. Both types of deformations (static and dynamic) are shown to be competitive to the AS exchange and tend to reduce the magnetic anisotropy caused by the AS exchange. (c) 2008 Elsevier B.V. All rights reserved