Anisotropic double exchange in a valence-delocalized [Fe2.5+Fe2.5+] cluster. Spin-orbit coupling in the Anderson-Hasegawa double exchange model

Anisotropic double exchange interaction is considered for the valence-delocalized [Fe2.5+Fe2.5+] cluster with strong Anderson-Hasegawa double exchange (DE) coupling. The combined effect of spin-orbit interaction and DE between the excited states of the mixed-valence Fe ions results in the inter-ion anisotropic DE coupling. The coefficients of anisotropic DE coupling are linearly proportional to the parameters B0 and Bμ of the DE interaction in the ground and excited cluster states. The anisotropic DE interaction operates between the cluster states of different localizations of the extra electron. The anisotropic DE coupling results in the zero-field splitting (ZFS) of the valence-delocalized ground state of the [Fe2.5+Fe2.5+] cluster. The ZFS of the anisotropic DE origin is specific for the delocalized mixed-valence systems and is described by the new effective ZFS Hamiltonian HZFSt. The ZFS Hamiltonian HZFSt includes the operator of the Anderson-Hasegawa DE interaction and is active between the cluster states of different localizations, whereas the standard ZFS Hamiltonian, HZFS0, acts in the localized states. The contributions of the anisotropic DE origin to the cluster ZFS parameters are linearly proportional to the DE parameters B0, Bμ and depend on the total spin S. The anisotropic DE contribution to the cluster ZFS parameter of the ground valence-delocalized state is of the same order of magnitude as the single-ion ZFS contributions.