Ferromagnetism of electron gas

TL;DR

This paper investigates the magnetic properties of an electron gas using relativistic formalism, revealing conditions under which ferromagnetism can or cannot occur at various densities and temperatures.

Contribution

It introduces a relativistic approach to analyze the ferromagnetic phase transition in an electron gas, considering density and temperature dependencies.

Findings

Ferromagnetism appears at specific critical densities and temperatures.

At zero temperature, exact polarization and susceptibility are obtained.

Ferromagnetic phase does not exist at very low or very high densities at nonzero temperatures.

Abstract

In current work, we investigate the density and temperature dependence of polarization parameter; using the relativistic formalism for the electron-electron interaction within the Fermi liquid model. we calculate the spin dependent scattering matrix elements in relativistic region, and then obtain the non-relativistic behavior to study the magnetic properties of an electron gas. By varying the polarization parameter, we minimized the free energy and then obtain the polarization of the system as a function of density and temperature. At zero temperature the exact results for polarization and magnetic susceptibility have obtained. It has been shown that for a given temperature (density) there is critical density (temperature) that the ferromagnetic phase can appears in electron gas. Our results show that at nonzero temperatures and in very low and very high densities the ferromagnetism phase can not be exist.