Band ferromagnetism versus collective Kondo state in lattice fermion models

TL;DR

This paper reviews the limitations of the one-band Hubbard model in explaining itinerant ferromagnetism and explores how two-band Hubbard models and Anderson lattices can exhibit ferromagnetism alongside a collective Kondo state.

Contribution

It introduces the connection between two-band Hubbard models and Anderson lattices, highlighting the competition between ferromagnetism and the Kondo state.

Findings

One-band Hubbard model does not explain itinerant ferromagnetism.

Two-band Hubbard models can exhibit ferromagnetism.

Ferromagnetic phase competes with a collective Kondo state.

Abstract

It is becoming widely recognized that, contrary to earlier expectations, the usual one-band Hubbard model does not give an explanation for itinerant ferromagnetism. After reviewing the status of magnetic ordering in the one-band model, we discuss the possibility of ferromagnetism in some recently introduced two-band Hubbard models, and in generalized Anderson lattices. It is argued that these two classes of models are closely related and that it is their common feature that the ferromagnetic phase has to compete with a collective Kondo state.