Magnetic properties of a Fermi gas in a noncommutative phase space

Motivated by the precision attained by SQUID devices in measuring magnetic fields, we study in this article the thermodynamic behaviour of a fermion gas in two and three dimen\-sional spatial space with noncommutative coordinates and momenta. An explicit expression, both for Landau's diamagnetism and Pauli's paramagnetism, is obtained for the magnetization and magnetic susceptibility of the gas in two and three spatial dimensions. These results show that an upper bound for the noncommutative parameter $\theta\lesssim (10 \,\text{Gev})^{-2}$ could be obtained.