Competition between paramagnetism and diamagnetism in charged Fermi gases

TL;DR

This paper investigates the magnetic behavior of charged Fermi gases, identifying a critical g-factor that determines whether the gas is diamagnetic or paramagnetic, and compares these properties across different quantum statistics.

Contribution

It calculates the critical g-factor separating diamagnetic and paramagnetic phases in charged Fermi gases and compares it with Bose and Boltzmann gases.

Findings

Critical g-factor g_c = 1/√12 at high and low temperatures in weak magnetic fields.

g_c increases with temperature in finite magnetic fields.

g_c for Bose gases is larger, and for Boltzmann gases is smaller, than for Fermi gases.

Abstract

The charged Fermi gas with a small Lande-factor $g$ is expected to be diamagnetic, while that with a larger $g$ could be paramagnetic. We calculate the critical value of the $g$-factor which separates the dia- and para-magnetic regions. In the weak-field limit, $g_{c}$ has the same value both at high and low temperatures, $g_{c}=1/\sqrt{12}$. Nevertheless, $g_{c}$ increases with the temperature reducing in finite magnetic fields. We also compare the $g_{c}$ value of Fermi gases with those of Boltzmann and Bose gases, supposing the particle has three Zeeman levels $\sigma=\pm1, 0$, and find that $g_{c}$ of Bose and Fermi gases is larger and smaller than that of Boltzmann gases, respectively.