Possible orbital orderings in a model of metallic double-exchange ferromagnets

The instabilities toward orbital ordering are studied for a model of metall ic double-exchange ferromagnets. In contrast to previous studies a possibil ity 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 extensi on of Penn's work for the single-band Hubbard model to the problem of orbit al ordering. Various orbital orderings have been examined by changing the f illing in the doubly degenerate bands and considering several representativ e 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 i nteraction.