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

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 D_4h dimers ^2S+1T₂-^2S+1T₂ and ^2S+1T₁-^2S+1T₁ are considered. Finally, the developed approach is applied to the calculation of the energy levels and magnetic properties of the ²T₂-²T₂ corner-shared dimer. The problem of the magnetic anisotropy arising from the orbital interactions is discussed and the influence of different relevant interactions is revealed.