Effective Hamiltonian in manganites:mStudy 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 ${\mathrm{e}}_{\mathrm{g}}$ 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 ${\mathrm{LaMnO}}_3$. Although the numerical calculation is devoted to the insulating state, the effective Hamiltonian is relevant to the metallic state as well.