Electronic Hamiltonian for transition-metal oxide compounds

TLDR

The authors present an effective electronic Hamiltonian for transition‑metal oxide compounds and compare it with the standard double‑exchange model. The model is built from a Kondo‑lattice Hamiltonian with mobile \(e_g\) electrons and localized \(t_{2g}\) spins in the large Hund’s coupling limit, yielding spin‑2 moments and spin‑3/2 holes for Mn oxides, with bond‑hopping amplitudes that change sign with bond spin and acquire a complex Berry phase in the large‑spin limit. The model predicts ferromagnetic ground states at finite hole density and low temperatures, with critical temperatures potentially lower than the standard double‑exchange model because of Berry‑phase‑induced frustration, and shows that aligned electrons acquire a complex hopping amplitude and Berry phase in loops.

Abstract

An effective electronic Hamiltonian for transition-metal oxide compounds is presented. For Mn oxides, the Hamiltonian contains spin-2 "spins" and spin-$\frac{3}{2}$ "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 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.