The Double Exchange Model at Low Densities

TL;DR

This paper explores the phase diagram of the double-exchange model at low densities, highlighting the formation of a Wigner crystal of magnetic polarons due to Coulomb interactions and its stability compared to other phases.

Contribution

It introduces a detailed analysis of the low-density phase diagram of the double-exchange model, emphasizing the role of Coulomb interactions in stabilizing a Wigner crystal of magnetic polarons.

Findings

Wigner crystal of magnetic polarons forms at low densities

Coulomb interactions favor Wigner crystal over phase separation

Stability analysis of crystalline, polaronic Fermi liquid, and metallic phases

Abstract

We obtain the phase diagram of the double-exchange model at low electronic densities in the presence of electron-electron interactions. The single particle problem and its extension to low electronic densities, when a Wigner crystal of magnetic polarons is generated due to unscreened Coulomb interactions, is studied. It is argued that the Wigner crystal is the natural alternative to phase separation when the Coulomb interaction is taken into account. We discuss the thermal and quantum stability of the crystalline phase towards a polaronic Fermi liquid and a homogeneous, metallic, ferromagnetic phase. The relevance and application of our results to EuB_6 is also considered.