Ferromagnetic ground state of an orbital degenerate electronic model for transition-metal oxides: exact solution and physical mechanism

We present an exact ground state solution of a one-dimensional electronic model for transition-metal oxides in the strong coupling limit. The model contains doubly degenerated orbit for itinerant electrons and the Hund coupling between the itinerant electrons and localized spins. The ground state is proven to be a full ferromagnet for any density of electrons. Our model provides a rigorous example for metallic ferromagnetism in narrow band systems. The physical mechanism for ferromagnetism and its relevance to high-dimensional systems, like R$_{1-x}$X$_x$MnO$_3$, are discussed. Due to the orbital degeneracy of itinerant electrons, the superexchange coupling can be ferromagnetic rather than antiferromagnetic in the one-band case.