Ferromagnetism in the Hubbard model with orbital degeneracy in infinite dimensions

TLDR

The Hubbard model in infinite dimensions includes intra‑orbital, inter‑orbital, exchange, and pair‑hopping interactions all derived from on‑site Coulomb repulsion. We study the ferromagnetism due to orbital degeneracy in the Hubbard model in infinite dimensions. The ground state of the effective one‑site problem was obtained by exact diagonalizations. At quarter filling two insulating phases appear—ferromagnetic with alternating orbital order and antiferromagnetic with uniform orbital order—and upon doping the ferromagnetic phase persists as metallic while the antiferromagnetic phase vanishes, indicating that double‑exchange stabilizes metallic ferromagnetism in infinite dimensions.

Abstract

We study the ferromagnetism due to orbital degeneracy in the Hubbard model in infinite dimensions. The model contains the intraorbital repulsion $U$, the interorbital repulsion $U^\prime$, the exchange $J$ (Hund coupling) and the pair hopping $J^\prime$, where all of them originate from the on-site Coulomb interaction. The ground state of the effective one-site problem was obtained by exact diagonalizations. At the 1/4-filling, we found two insulating phases; one is a ferromagnetic phase with alternating orbital order and the other is antiferromagnetic one with uniform orbital order. If electrons are doped into the 1/4-filling, the ferromagnetic phase still survives and becomes metallic, while the antiferromagnetic phase disappears. This result indicates that the double-exchange mechanism is relevant to stabilize metallic ferromagnetism in infinite dimensions.