Possible Orbital Orderings in a Model
of Metallic Double-Exchange Ferromagnets

Abstract

The instabilities toward orbital ordering are studied for a model of metallic double-exchange ferromagnets. In contrast to previous studies a possibility of octupole ordering is also considered in addition to ordinary orbital ordering (corresponding to quadrupole ordering). The present theory, which is based on the simplest RPA and mean-field approach, is a natural extension of Penn's work for the single-band Hubbard model to the problem of orbital ordering. Various orbital orderings have been examined by changing the filling in the doubly degenerate bands and considering several representative ordering wave-vectors and order parameters. Thereby the phase diagram has been constructed. It has turned out that a staggered octupole ordering is possible in the intermediate range of electron density and strong Coulomb interaction.