Anisotropic exchange coupling in the Keggin derivative K8[Co2(D2O)(W11O39)] · n D2O

Abstract 20 g of the fully deuterated title compound have been prepared in polycrystalline form and investigated by inelastic neutron scattering using both thermal and cold neutrons. Magnetic dimer excitations were observed and the energy-splitting pattern resulting from the exchange coupling within the Co 2+ dimer was determined. The coupling is highly anisotropic with the parameter values J =−2.24 meV and η =0.33 based on the effective coupling Hamiltonian H =−2J[S 1z S 2z +η(S 1x S 2x +S 1y S 2y )] . The anisotropy results mainly from the single-ion anisotropy of the Co 2+ ion in the distorted octahedral coordination.

High‐nuclearity mixed‐valence magnetic clusters : A general solution of the double exchange problem

We report here a general solution of the double‐exchange problem in the high‐nuclearity mixed valence systems containing arbitrary number P of the electrons delocalized over the network of N (P<N) localized spins. The developed approach is based on the successive (chainlike) spin‐coupling scheme and takes full advantage from the quantum angular momentum theory. In the framework of this approach the closed‐form analytical expressions are deduced for the matrix elements of the double exchange interaction, two‐electron transfer, and three‐center interaction that can be referred to as the potential exchange transfer. For the arbitrary nuclearity mixed‐valence systems the matrix elements of all …

A general approach for the calculation of the energy levels and the inelastic neutron scattering cross-section of highly nuclear magnetic clusters

Abstract We develop here a general approach to calculate in an efficient way the spin levels as well as the spin eigenfunctions and the INS intensities of clusters formed by large numbers of exchange-coupled magnetic metal ions. The approach is based on the successive use of the irreducible tensor operator techniques and takes into account all kinds of magnetic exchange interactions between the metal ions. The potentialities of this approach are illustrated from an example comprising nine exchange-coupled Ni (II) ions.

Mixed-valence polyoxometalate clusters. III. Vibronic problem for the 2-electron reduced heteropoly blue with the Keggin structure

Abstract A general approach to the vibronic problem of delocalized electronic pairs in mixed-valence compounds is developed and applied to understand the ways of electron delocalization in dodecanuclear polyoxometalate clusters containing two moving electrons. The interplay between electronic and vibronic interactions is examined. The electronic spectrum is shown to consist of two spin triplets 3 T 1 and 3 T 2 and three spin singlets 1 A 1 , 1 E and 1 T 2 levels determined by the double-transfer processes (parameter P ). Jahn-Teller and pseudo-Jahn-Teller problems ( 3 T 1 + 3 T 2 ) ⊗ ( e + t 2 ) and ( 1 A 1 + 1 E + 1 T 2 ) ⊗ ( e + t 2 ) have been considered in the framework of the Piepho-Kr…

Mixed-valence polyoxometalate clusters. II. Delocalization of electronic pairs in 18-site heteropoly blues with Wells-Dawson structure

Abstract The problem of delocalization of two electrons in the 18-site Wells-Dawson polyoxometalate is examined from a general approach that takes into account both single- and double-transfer processes, as well as the Coulomb interactions between the two delocalized electrons. The electronic energy levels of this mixed-valence cluster are calculated and the conditions giving rise to the stabilization of a singlet ground spin state for the electronic pair are elucidated. It is shown that the spin pairing results from the simultaneous effects of single- and double-electron transfer processes, which are operative even when the two delocalized electrons are fairly widely separated in the Wells…

Vibronic Localization of the Electronic Pair in Polynuclear Mixed-Valence Polyoxometalates*

Mixed-valence polyoxometalate clusters. I. Delocalization of electronic pairs in dodecanuclear heteropoly blues with keggin structure

Abstract The problem of delocalization of a pair of electrons over dodecanuclear polyoxometalate clusters with the Keggin structure is considered with the aim of explaining the spin pairing in these multi-nuclear mixed-valence systems. A general approach that considers the Coulomb interactions between the two delocalized electrons, as well as the single and double electron transfer processes which can be operative in delocalization of the electronic pairs is developed. The new approach is based on the site-symmetry concept which makes possible a group theoretical classification for the delocalized states of electronic pairs. This procedure proves to be very efficient in the calculation of t…

Magnetic excitations in polyoxometalate tetrameric clusters

Abstract The metal-oxide clusters with formula [M4(D2O)2(PW9O34)2]10− which contain a tetrameric magnetic cluster M4O16 provide an ideal series for the study of magnetic exchange interactions in polymetallic molecular clusters. To get a more direct information on the splitting of the spin states caused by the exchange interactions we have performed inelastic neutron scattering measurements on the Co, Mn and Ni clusters. Magnetic excitations have been observed in the range 0.5–6 meV. A tentative interpretation of these data from a Heisenberg exchange Hamiltonian and a single ion zero-field splitting is presented for Ni cluster.

Exchange Interactions II: Spin Hamiltonians

In Part I the physical mechanism of exchange interactions have been discussed. In this part we introduce the general concept of spin-hamiltonian. Isotropic exchange hamiltonian for many-electron polynuclear clusters (Heisenberg-Dirac-van Vleck-HDVV model [1-6]) will be derived. Spin-hamiltonian approach allows to separate the full exchange problem into two independent ones: 1) evaluation of the energy levels of the exchange system considering Jij as a set of semiempirical parameters, and 2) quantum mechanical calculation of exchange parameters with the aim of elucidation of the main physical mechanisms of the exchange coupling. In this part we shall focus on the problem of calculation of sp…

Magnetic Excitations in Tetrameric Clusters of Polyoxometalates Observed by Inelastic Neutron Scattering. Evidence for Anisotropic Exchange Interactions in Cobalt(II) Clusters.

Magnetic excitations in tetranuclear clusters of exchange-coupled metal ions encapsulated by polyoxotungstate ligands (1) have been observed by inelastic neutron scattering (INS) in the salts K10[M4(H2O)2(PW9O34)2]·nH2O, where M2+ = Mn, Co, and Ni. INS provides a much deeper and more detailed insight into the nature of the magnetic coupling in these clusters than bulk techniques. In particular, anisotropic exchange interactions are evidenced in the ferromagnetic Co4 cluster.