Ferromagnetism of Weakly-Interacting Electrons in Disordered Systems

TL;DR

This paper demonstrates that weak electron-electron interactions in disordered two- and three-dimensional systems can induce ferromagnetism, with a finite magnetic moment forming even at minimal interaction strengths.

Contribution

It provides a direct Hartree-Fock calculation showing ferromagnetic instability in disordered systems, extending previous theoretical insights.

Findings

Ferromagnetic order occurs at arbitrarily weak interactions in 2D.

A critical interaction strength exists in 3D related to conductivity.

Finite ferromagnetic moments minimize the total energy.

Abstract

It was realized two decades ago that the two-dimensional diffusive Fermi liquid phase is unstable against arbitrarily weak electron-electron interactions. Recently, using the nonlinear sigma model developed by Finkelstein, several authors have shown that the instability leads to a ferromagnetic state. In this paper, we consider diffusing electrons interacting through a ferromagnetic exchange interaction. Using the Hartree-Fock approximation to directly calculate the electron self energy, we find that the total energy is minimized by a finite ferromagnetic moment for arbitrarily weak interactions in two dimensions and for interaction strengths exceeding a critical proportional to the conductivity in three dimensions. We discuss the relation between our results and previous ones.