Magnetic properties of spin-1/2 Fermi gases with ferromagnetic interaction

TL;DR

This paper studies the magnetic behavior of spin-1/2 Fermi gases with ferromagnetic interactions, revealing how magnetization and susceptibility depend on temperature, magnetic field, and ferromagnetic coupling through mean-field theory.

Contribution

It provides a theoretical analysis of magnetic properties in ferromagnetically coupled Fermi gases, highlighting the interplay of paramagnetism, diamagnetism, and ferromagnetism, and deriving the Curie-Weiss law for susceptibility.

Findings

Spontaneous magnetization occurs with increasing ferromagnetic coupling.

Magnetization density shows a domed temperature dependence.

Susceptibility follows the Curie-Weiss law and is proportional to the Landé factor.

Abstract

We investigate the magnetic properties of spin-$1/2$ charged Fermi gases with ferromagnetic coupling via mean-field theory, and find the interplay among the paramagnetism, diamagnetism and ferromagnetism. Paramagnetism and diamagnetism compete with each other. When increasing the ferromagnetic coupling the spontaneous magnetization occurs in a weak magnetic field. The critical ferromagnetic coupling constant of the paramagnetic phase to ferromagnetic phase transition increases linearly with the temperature. Both the paramagnetism and diamagnetism increase when the magnetic field increases. It reveals the magnetization density $\bar M$ increases firstly as the temperature increases, and then reaches a maximum. Finally the magnetization density $\bar M$ decreases smoothly in the high temperature region. The domed shape of the magnetization density $\bar M$ variation is different from the behavior of Bose gas with ferromagnetic coupling. We also find the curve of susceptibility follows the Curie-Weiss law, and for a given temperature the susceptibility is directly proportional to the Land\'{e} factor.