Magnetic Moment of a Magnetized Fermi Gas

In this paper we have calculated the exact expression for the magnetic moment of a Fermi gas in a magnetic field (magnetized Fermi gas). The susceptibility obtained from our result becomes the classical Curie-Langevin law in the weak-field limit for a nondegenerate and nonrelativistic gas. The induced magnetic moment $\mathfrak{M}$ was found to be proportional to the square of the electron density, but at higher densities $\mathfrak{M}$ passes through a maximum and eventually becomes negative; hence a magnetized gas is first paramagnetic but later becomes diamagnetic. We have also shown that spontaneous magnetization cannot take place in a noninteracting electron gas.