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…

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.

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 …

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 …

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

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

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.