Alternating Ferro/Antiferromagnetic Copper(II) Chain Containing an Unprecedented Triple Formato/Hydroxido/Sulfato Bridge.

The first example of a triple formato/hydroxido/sulfato (FHS) bridge for any metal is reported in compound [Cu2(bpym)(OH)(HCO2)(SO4)(H2O)2]·3H2O (1). Its structure shows the presence of alternating triple FHS bridges and 2,2'-bipyrimidine (bpym) ones. Although in the initial synthesis the sulfate anions were introduced accidentally, here we report the rational synthesis and the magnetic properties of this compound. The magnetic properties show that 1 is an alternating ferro/antiferromagnetic (F/AF) chain compound with predominant antiferromagnetic interactions and were fit to an alternating F/AF S = (1)/2 chain with g = 2.103, JAF = -139 cm(-1), and JF = 116 cm(-1) (α = JF/|JAF| = 0.83). Th…

Magnetic Exchange between Orbitally Degenerate Metal Ions: The Problem of Magnetic Anisotropy

Abstract In this paper we show that a strong magnetic anisotropy appears in exchange mixed–valence clusters containing orbitally degenerate metal ions. Combining an effective Hamiltonian approach with the technique of the irreducible tensor operators (ITO) and pseudoangular momentum representation we have solved the problem of magnetic exchange in localized and delocalized (mixed–valence) systems with different overall symmetries ( D 2 h , D 3 h , D 4 h ). The energy pattern as well as the character of the magnetic anisotropy is closely related to the ground term of the ions, electron transfer pathways, and overall symmetry of the system being affected also by the local crystal fields, spin…

Magnetic mixed-valence d2-d1-d1 trimers with partial electron delocalization: vibronic coupling and magnetic properties

Abstract The energy levels and magnetic properties of a triangular mixed-valence cluster d1-d1-d2 with electron delocalization in a pair of sites are examined from a model that takes into account electron transfer, magnetic exchange, and vibronic coupling. We show that the electron transfer process involves besides the usual double-exchange parameter, and additional parameter referred to as exchange transfer. This last parameter accounts for the interaction between the moving electron of the mixed valence pair and the electron localized in the third side. We notice that the role of double exchange is to stabilize a ferromagnetic alignment of the spins on the mixed-valence pair. A comparison…

Classical-spin approach to a magnetic comb-like chain: application to the two-sublattice chain compound MnMn(CDTA)·7H2O

Abstract We report on the magnetic properties of the two-sublattice manganese chain MnMn(CDTA)·7H 2 O. In view of the structural features, this compound may give rise to a novel type of one-dimensional magnetic network formed by a chain of exchange coupled triangles. A classical-spin model that considers two magnetic sites coupled through two different and isotropic exchange interactions is developed and used in order to analyze the magnetic properties of this compound. The possibility of having a spinfrustration is also examined.

[MnM(egta)]· 8H2O(M= Mn, Cd): A Novel Type of Two-Dimensional Magnetic Lattice

MAGPACK1A package to calculate the energy levels, bulk magnetic properties, and inelastic neutron scattering spectra of high nuclearity spin clusters

Anisotropic double exchange in orbitally degenerate mixed valence systems

Abstract The problem of the double exchange is considered for the mixed valence dimers in which one or both transition metal ions possess orbitally degenerate ground states. In the pseudo-angular momentum representation, the general formula is deduced for the matrix elements of double exchange involving the transfer integrals and all spin and orbital quantum numbers. The pairs 3 T 1 t 2 2 – 2 T 2 t 2 1 and 3 T 1 t 2 2 – 4 A 2 t 2 3 are considered in three high-symmetric topologies: edge-shared D2h, corner-shared D4h, and face-shared D3h bioctahedra. The double exchange in orbitally degenerate systems is shown to produce strong magnetic anisotropy of an orbital nature. The character of the a…

Double Exchange in Orbitally Degenerate Mixed Valence Clusters: Magnetic Anisotropy, Vibronic Effects

In this paper we consider the vibronic problem of the double exchange in mixed-valence dimers containing transition metal ions in orbitally degenerate ground states. The vibronic model includes interaction with the breathing local modes (Piepho-Krausz-Schatz-PKS) as well as the modulation of metal-metal distances as suggested by Piepho. The double exchange in orbitally degenerate systems is shown to produce strong magnetic anisotropy of orbital nature. PKS interaction is expected to suppress the magnetic anisotropy of the system, while the intercenter vibrations tend to enhance it. The roles of spin-orbit coupling and temperature are revealed for the systems with different geometries.

Problem of the magnetic anisotropy in orbitally degenerate exchange and mixed-valence clusters

Abstract This contribution summarizes the results obtained in the problem of orbital degeneracy of the metal ions in exchange coupled and mixed-valence (MV) clusters. The theory of the double exchange is generalized and the orbitally degenerate systems are considered. The orbitally dependent double exchange parameter is deduced for the singlet–triplet and triplet–triplet transition metal pairs in three high-symmetric topologies. A new effective Hamiltonian of the magnetic exchange between the ions with unquenched orbital angular momenta is discussed. The technique of the irreducible tensor operators is applied to the problem of the kinetic exchange in these kind of metal clusters. Strong ma…

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 …

Exchange transfer in high-nuclearity mixed valence magnetic clusters: Theoretical approach and expected manifestations

Abstract We report here a general solution of the exchange transfer problem in the high-nuclearity mixed valence clusters containing arbitrary number of itinerant electrons. The concept of two kinds of exchange transfer, namely kinetic and potential, is introduced by analogy with basic Anderson's mechanisms of the magnetic exchange. The kinetic exchange transfer is treated as a second order transfer process between two centres through the excited state of a third centre. The potential exchange transfer is also considered as a three-centre interaction but in this case only the ground states of the constituent ions are involved. The actual parameters of the exchange transfer are expected to b…

Single-crystal EPR study of the bimetallic ferrimagnetic chain MnCu(EDTA)·6H2O

Abstract A single-crystal EPR study of the bimetallic chain compound MnCu(EDTA)·6H2O is reported. The angular dependence of the linewidth is discussed in relation to the magnetic dipole-dipole interaction, manganese zerofield splitting (ZFS) and copper hyperfine coupling. The calculation of the second moments indicates that ZFS is comparable to the dipolar contribution. The EPR data support the one-dimensional character of the compound.

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.

ChemInform Abstract: High Nuclearity Magnetic Clusters: Magnetic Properties of a Nine Cobalt Cluster Encapsulated in a Polyoxometalate, (Co9(OH)3(H2O)6(HPO4) 2(PW9O34)3)16-.

A rare example of nickel(ii) chains based on a heteroscorpionate-like ligand with quadruple imidazolyl interactions

The first nickel(ii) complex with the heteroscorpionate-like bridging ligand DIMMAL (2-di1H-2-imidazolylmethylmalonate), [Ni(DIMMAL)(H2O)3]n·3nH2O (1), is a one-dimensional coordination polymer whose structure shows regular Ni(ii) chains with H-bonding inter-chain interactions and a rare example of a Quadruple Imidazolyl Embrace (QIE). The Ni(ii) chain shows a weak antiferromagnetic interaction that can be modelled with a regular S = 1 chain model including a zero field splitting with g = 2.270, J = -1.5 cm(-1) and D = -2.26 cm(-1).

High-nuclearity magnetic clusters: Magnetic interactions in clusters encapsulated by molecular metal oxides

Abstract The ability of the molecular metal oxides derived from the Keggin anion [PW 12 O 40 ] 3− to accommodate magnetic ions at specific sites, giving rise to polymetallic clusters with increasing spin nuclearities is discussed. Examples of magnetic clusters with three, four and nine metal ions exhibiting ferromagnetic exchange couplings or a coexistence of ferro- and antiferromagnetic couplings are reported.

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.

Localization vs. Delocalization in Molecules and Clusters: Electronic and Vibronic Interactions in Mixed Valence Systems

The interplay between electron delocalization and magnetic interactions play a key role in areas as diverse as solid state chemistry (bulk magnetic materials, superconductors,...) [1] and biology (iron-sulfur proteins, manganese-oxo clusters ...) [2]. In molecular inorganic chemistry these two electronic processes have been traditionally studied independently. Thus, the electron dynamics has been extensively investigated in mixedvalence dimers [3] as exemplified by the Creutz-Taube complex [(NH3)5RuII(pyrazine)RuIII(NH3)5]. In this kind of molecular complexes one extra electron is delocalized over two diamagnetic metal sites. Therefore, they constitute model systems for the study of the ele…

Magnetic Polyoxometalates:  Anisotropic Antiferro- and Ferromagnetic Exchange Interactions in the Pentameric Cobalt(II) Cluster [Co3W(D2O)2(CoW9O34)2]12-. A Magnetic and Inelastic Neutron Scattering Study

The ground-state properties of the pentameric Co(II) cluster [Co(3)W(D(2)O)(2)(CoW(9)O(34))(2)](12-) were investigated by combining magnetic susceptibility and low-temperature magnetization measurements with a detailed inelastic neutron scattering (INS) study on a fully deuterated polycrystalline sample of Na(12)[Co(3)W(D(2)O)(2)(CoW(9)O(34))(2)].46D(2)O. The encapsulated magnetic Co(5) unit consists of three octahedral and two tetrahedral oxo-coordinated Co(II) ions. Thus, two different types of exchange interactions are present within this cluster: a ferromagnetic interaction between the octahedral Co(II) ions and an antiferromagnetic interaction between the octahedral and the tetrahedral…

Localisation vs. delocalisation in the dimeric mixed-valence clusters in the generalised vibronic model. Magnetic manifestations

Abstract The problem of localisation–delocalisation in the dimeric mixed-valence clusters is considered in the framework of the generalised vibronic model. The model takes into account both the local vibrations on the metal sites (Piepho–Krausz–Schatz model) and the multicenter (molecular) vibrations changing the intermetallic distances (as suggested by Piepho). In the framework of the semiclassical adiabatic approach the potential surfaces are analysed and different kinds of localised and delocalised states are found. On the basis of the calculated degrees of the localisation the conventional Robin and Day classification of mixed-valence compounds is reconsidered in view of the generalised…

Magnetic exchange interaction in a pair of orbitally degenerate ions: Magnetic anisotropy of [Ti2Cl9]−3

The theory of the kinetic exchange in a pair of orbitally degenerate ions developed by the authors [J. Phys. Chem. A 102, 200 (1998)] is applied to the case of face-shared bioctahedral dimer (overall D3h-symmetry). The effective kinetic exchange Hamiltonian is found for a 2T2–2T2 system taking into account all relevant transfer pathways and charge-transfer crystal field states. The influence of different transfer integrals involved in the kinetic exchange on the energy pattern and magnetic properties of the system is examined. The role of other related interactions (trigonal crystal field, spin–orbit coupling) is also discussed in detail. Using the pseudoangular momentum representation and …

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 u…

Magnetic Exchange between Orbitally Degenerate Ions:  A New Development for the Effective Hamiltonian

A new approach to the problem of the kinetic exchange for orbitally degenerate ions is developed. The constituent multielectron metal ions are assumed to be octahedrally coordinated, and strong crystal field scheme is employed, making it possible to take full advantage from the symmetry properties of the fermionic operators and collective electronic states. In the framework of the microscopic approach, the highly anisotropic effective Hamiltonian of the kinetic exchange is constructed in terms of spin operators and standard orbital operators (matrices of the unit cubic irreducible tensors). As distinguished from previous considerations, the effective Hamiltonian is derived for a most genera…

High nuclearity mixed-valence magnetic clusters: theoretical study of the spin coupling in the C602− fulleride ion

Abstract The problem of delocalization of a pair of electrons over the fullerene C 60 is considered, with the aim of elucidating the nature of the ground spin state, as well as the structure of the low-lying energy levels in this mixed-valence molecule C 60 2− . A model that considers the Coulomb interactions between the two extra electrons, as well as the two single-electron transfer processes involved in the electron delocalization, is developed. The influence of these electronic parameters on the spectrum of the low-lying energy levels is discussed. We find that the ground state is always a spin singlet, whatever the relative values of these parameters are.

Magnetic Excitations in Polyoxometalate Clusters Observed by Inelastic Neutron Scattering:  Evidence for Ferromagnetic Exchange Interactions and Spin Anisotropy in the Tetrameric Nickel(II) Cluster [Ni4(H2O)2(PW9O34)2]10- and Comparison with the Magnetic Properties

The ground-state properties of the tetranuclear Ni2+ cluster [Ni4(H2O)2(PW9O34)2]10- were investigated by combining magnetic susceptibility and magnetization measurements with a detailed inelastic neutron scattering (INS) study on a fully deuterated sample of K6Na4[Ni4(H2O)2(PW9O34)2]·24H2O. The temperature dependence of the magnetic susceptibility indicates a ferromagnetic coupling of the four constituent Ni2+ ions (s = 1), and a low-temperature magnetization study provides the magnitude of the S = 4 ground-multiplet splitting due to the single-ion anisotropy of the Ni2+ ions. Besides a more direct and precise determination of the anisotropic S = 4 ground-multiplet splitting, INS enabled t…

Molecular Materials from Polyoxometalates

The present article highlights recent results and provide a perspective of the interest of polyoxometalates as inorganic component of molecular materials with active physical properties. Three different aspects will be presented: i) The interest of the magnetic and mixed valence clusters provided by polyoxometalate chemistry in molecular magnetism; ii) The use of these inorganic anions as magnetic component of crystalline conducting materials based on organic donor molecules; iii) The construction of well-organized films of polyoxometalate monolayers by using the Langmuir-Blodgett technique.

Semiclassical approximation in the magnetic problem of exchange-coupled mixed valence clusters

Abstract The frameworks of the applicability of the semiclassical adiabatic approach suggested by Borras-Almenar, Coronado and Tsukerblat to the magnetic problem of mixed valence clusters are considered in a model taking into account magnetic exchange, double exchange and vibronic interaction. The results for the quantum-mechanical and semicalssical calculation of the temperature-variable magnetic moments are compared with those within the scope of the semiclassical approximation for the dimeric d 1 —d 2 clusters and trimeric d 1 —d 1 —d 2 systems with partial delocalization over a pair of ions. The semiclassical approach describes with high accuracy the temperature dependencies of the magn…

1D ferrimagnetism in homometallic chains

The magnetic properties of the cobalt zigzag chain Co(bpy)(NCS)2 (bpy=2,2′‐bipyridine) are discussed on the basis of an Ising‐chain model that takes into account alternating Landé factors. It is emphasized, for the first time, that a homometallic chain containing only one type of site can give rise to a 1D ferrimagneticlike behavior. Juan.J.Borras@uv.es , Eugenio.Coronado@uv.es

One-Dimensional Magnetism: An Overview of the Models

Magnetism and EPR spectra of the two‐sublattice manganese chain Mn2(EDTA)⋅9H2O

We report on the magnetic behavior and single‐crystal EPR spectra of the chain complex Mn2(EDTA)⋅9H2O characterized by two different alternating sites for the manganese ions. Magnetic susceptibility data are indicative of weak antiferromagnetic exchange interactions between the manganese ions, showing a maximum of about 3 K. This behavior can be accurately described on the basis of a Heisenberg chain model that assumes classical spins, giving J/k=−0.72 K and g=2.0. The EPR spectra are typically low dimensional, with an angular dependence of the linewidth of the type (3 cos2 θ−1)n (n=4/3 or 2). Nevertheless, such a behavior cannot be reproduced from a one‐dimensional model with dipolar broad…

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…

Magnetic Properties of Mixed-Valence Clusters: Theoretical Approaches and Applications

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

Magnetic exchange interaction in clusters of orbitally degenerate ions. II. Application of the irreducible tensor operator technique

Abstract The irreducible tensor operator technique in R3 group is applied to the problem of kinetic exchange between transition metal ions possessing orbitally degenerate ground states in the local octahedral surrounding. Along with the effective exchange Hamiltonian, the related interactions (low-symmetry crystal field terms, Coulomb interaction between unfilled electronic shells, spin–orbit coupling and Zeeman interaction) are also taken into account within a unified computational scheme. Extension of this approach to high-nuclearity systems consisting of transition metal ions in the orbital triplet ground states is also demonstrated. As illustrative examples, the corner-shared D4h dimers…

High nuclearity magnetic clusters: Magnetic properties of a nine cobalt cluster encapsulated in a polyoxometalate, [Co9(OH)3(H2O)6(HPO4)2(PW9O34)3]16⊕

Electronic and vibronic problems of nanosized mixed valence clusters: Advances and challenges

Here we discuss the electronic and vibronic problems of mixed valency (MV) in molecular clusters which are of current interest in areas as diverse as solid-state chemistry, biochemistry, and molecular magnetism. Modern research in these areas is focused on the nanosized clusters at the border between classical and quantum scales and for this reason they are particularly difficult to study. First, we describe a general approach to the evaluation of the energy pattern of MV systems containing arbitrary number of localized spins and itinerant electrons with due account for the double exchange and other relevant interactions, like interelectronic Coulomb repulsion in instantly localized configu…

[MnM(egta)]. 8H2 = (M = Mn, Cd): Verbindungen mit einem neuartigen zweidimensionalen magnetischen Gitter

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…

Crystal Structures and Magnetic Properties of Novel [LnIIICuII4] (Ln = Gd, Dy, Ho) Pentanuclear Complexes. Topology and Ferromagnetic Interaction in the LnIII−CuII Pair

The first pentanuclear complexes of formula {Dy[Cu(apox)](2)[Cu(apox)(H(2)O)](2)}[ClO(4)](3).7H(2)O (1), {Ho[Cu(apox)][Cu(apox)(H(2)O)](3)}[PF(6)](3).4.5H(2)O (2), {Gd[Cu(apox)](2)[Cu(apox)(H(2)O)](2)}[ClO(4)](3).7H(2)O (3) and {Gd[Cu(apox)][Cu(apox) (H(2)O)](3)}[PF(6)](3).4.5H(2)O (4) (H(2)apox = N,N'-bis(3-aminopropyl)oxamide) have been synthesized. The crystal structures of complexes 1 and 2 have been determined by X-ray diffraction methods. Complexes 3 and 4 are isostructural with 1 and 2, respectively. Crystallographic data are as follows: 1 and 3, monoclinic, space group C2/c and Z = 4, with a = 14.646(6) Å, b = 29.496(7) Å, c = 16.002(7) Å, and beta = 111.76(2) degrees for 1 and a = …

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.

Modeling the properties of lanthanoid single-ion magnets using an effective point-charge approach

Herein, we present two geometrical models based on an effective point-charge approach to provide a full description of the lowest sublevels in lanthanoid single ion magnets (SIMs). The first one, named as the Radial Effective Charge (REC) model, evaluates the crystal field effect of spherical ligands, e.g. F(-), Cl(-) or Br(-), by placing the effective charge along the Ln-ligand axes. In this case the REC parameters are obtained fitting high-resolution spectroscopic data for lanthanoid halides. The second model, named as the Lone Pair Effective Charge (LPEC) model, has been developed in order to provide a realistic description of systems in which the lone pairs are not pointing directly tow…

Alternating antiferromagnetic and ferromagnetic exchange interactions in the S = 1 Heisenberg chain. Theory and magnetic properties

Abstract We focus on the magnetic properties of the S = 1 Heisenberg chain with alternating antiferromagnetic and ferromagnetic exchange interactions J 1 and J 2 . The magnetic behavior of this system is calculated as a function of the alternation parameter α = J 2 /| J 1 |, from a general numerical procedure based on closed spin chains of increasing length. These theoretical results are fitted to rational unified expressions, which are subsequently used to describe the magnetic behavior of a nickel (II) complex, [Ni(bipy)(N 3 ) 2 ] n , exhibiting an alternating chain structure with a dominant ferromagnetic exchange.

Kinetic exchange Hamiltonian for orbitally degenerate ions

Abstract A new approach to the problem of the kinetic exchange for orbitally degenerate ions is developed. The highly anisotropic effective Hamiltonian is expressed in terms of unit irreducible tensor operators and spin operators. All parameters of the exchange Hamiltonian are expressed through relevant transfer integrals, crystal field and Racah parameters for the metal ions. As an example the edge-shared ( D 2 h ) bioctahedral cluster is discussed and some comments on the considerations of Anderson, Goodenough and Kanamori and McConnell are given.

Exchange-transfer in mixed-valence clusters with one migrating hole

Abstract A new mechanism for exchange-transfer specific to hole-type mixed-valence clusters is proposed. The intermediate state in the second-order exchange-transfer process is achieved by the jump of the electron from the spin-core of the dn+1 ion into the empty orbital of the dn ion. As distinguished from the mixed-valence clusters with one delocalized electron this intermediate state is the high-spin one giving rise to a ferromagnetic contribution to the ground manifold. On the basis of angular momentum theory a general solution of the exchange-transfer problem is given for arbitrary nuclearity mixed-valence hole-type clusters with many-electron paramagnetic spin-cores. The interplay bet…

Magnetic excitations in an exchange-coupled tetramer cluster of cobalt (II): a study by inelastic neutron scattering

Abstract The polyoxometalate K 10 [Co 4 (H 2 O) 2 (PW 9 O 34 ) 2 ].20H 2 O contains a ferromagnetically exchange-coupled tetramer of Co 11 encapsulated in between two diamagnetic molecules (PW 9 O 34 -9 . At 2.5K several inelastic peaks are observed in the energy range 1.5–7 meV, which are assigned to magnetic excitations in the cluster. A tentative interpretation of these data from an anisotropic exchange model yields a cobalt-cobalt interaction of 3meV (24cm -1 ) and an amount of anisotropy J xy / J z ≌0.6. These values are consistent with the magnetic susceptibility measurements.

Magnetic exchange interaction in clusters of orbitally degenerate ions. I. Effective Hamiltonian

Abstract A new effective Hamiltonian is reported for the kinetic exchange between two arbitrary terms 2S A +1 Λ A and 2S B +1 Λ B that can be ground or excited in octahedrally coordinated transition metal ions. This Hamiltonian is applicable to both homo- and heterometallic clusters. For the homonuclear cluster the resonance part of the effective Hamiltonian is also presented for the case when one of the ions is excited. The operator part of the exchange Hamiltonian contains symmetry adapted products of the cubic irreducible tensors acting in orbital spaces ΛA and ΛB and scalar product of site spin operators. The parameters of the Hamiltonian are defined by the relevant intercenter transfer…

Electric Field Generation and Control of Bipartite Quantum Entanglement between Electronic Spins in Mixed Valence Polyoxovanadate [GeV14O40]8–

As part of the search for systems in which control of quantum entanglement can be achieved, here we consider the paramagnetic mixed valence polyoxometalate K2Na6[GeV14O40]·10H2O in which two electrons are delocalized over the 14 vanadium ions. Applying a homogeneous electric field can induce an antiferromagnetic coupling between the two delocalized electronic spins that behave independently in the absence of the field. On the basis of the proposed theoretical model, we show that the external field can be used to generate controllable quantum entanglement between the two electronic spins traveling over a vanadium network of mixed valence polyoxoanion [GeV14O40]8–. Within a simplified two-lev…

Orbitally dependent kinetic exchange in cobalt(II) pairs: origin of the magnetic anisotropy

Abstract A comprehensive theoretical study of the magnetic exchange between Co 2+ ions is reported. Using the microscopic background we deduce the general Hamiltonian for a corner-shared bioctahedral system involving kinetic exchange, spin–orbit coupling and low-symmetry local crystal field. This Hamiltonian acting within orbitally degenerate ground manifold 4 ( T 1g ) A ⊗ 4 ( T 1g ) B of the cobalt pair is expressed in terms of orbital and spin operators. We elucidate the major electronic factors controlling the exchange anisotropy in the Co(II) pairs. The degree of the magnetic anisotropy is shown to depend on the strength of the cubic crystal field and on the relative efficiency of two k…

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.