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

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 magnetic anisotropy is shown to appear in the exchange and MV clusters consisting of orbitally degenerate ions. The influence of the vibronic pseudo Jahn-Teller interaction on the degree of the magnetic anisotropy is discussed.