Effective Hamiltonian for an extended Kondo-lattice model and a possible origin of charge ordering in half-doped manganites

Abstract

An effective Hamiltonian is derived in the case of the strong Hund coupling and on-site Coulomb interaction by means of a projective perturbation approach. A physical mechanism for charge ordering in half-doped manganites ${(R}_{0.5}{X}_{0.5}{\mathrm{MnO}}_{3})$ is proposed. The virtual process of electron hopping results in antiferromagnetic superexchange and a repulsive interaction, which may drive electrons to form a Wigner lattice. The phase diagram of the ground state of the model is presented at half doping. In the case of formation of a Wigner lattice, we prove that spins of electrons are aligned ferromagnetically as well as that the localized spin background is antiferromagnetic. The influence of the on-site Coulomb interaction is also discussed.