Effective Hamiltonian in manganites: Study of the orbital and spin structures

In order to study nature of the electronic structures in manganites, the effective Hamiltonian is derived by taking the degeneracy of the e(g) orbitals and the strong electron correlation into account. The spin and orbital ordered phases in the insulating states are studied in the mean-field approximation applied to the effective Hamiltonian. It is shown that the A-type antiferromagnetic state is stabilized by the magnetic interaction, which strongly depends on the bond direction, originated from the orbital ordering and the electron-electron correlation. The spin and orbital excitations are also studied by utilizing the effective Hamiltonian. The spin excitations agree well with the recent results in the neutron-scattering experiments in LaMnO3. Although the numerical calculation is devoted to the insulating state, the effective Hamiltonian is relevant to the metallic state as well.