Electronic Hamiltonian for Transition Metal Oxide Compounds

An effective electronic Hamiltonian for transition metal oxide compounds is presented. For Mn-oxides, the Hamiltonian contains spin-2 ``spins'' and spin-3/2 ``holes'' as degrees of freedom. The model is constructed from the Kondo-lattice Hamiltonian for mobile $e_g$ electrons and localized $t_{2g}$ spins, in the limit of a large Hund's coupling. The effective electron bond hopping amplitude fluctuates in sign as the total spin of the bond changes. In the large spin limit, the hopping amplitude for electrons aligned with the core ions is complex and a Berry phase is accumulated when these electrons move in loops. The new model is compared with the standard double exchange Hamiltonian. Both have ferromagnetic ground states at finite hole density and low temperatures, but their critical temperatures could be substantially different due to the frustration effects induced by the Berry phase.