The spin-polarized ferromagnetic state of a cold Fermi gas

Abstract

The spin-polarized ferromagnetic state of a cold Fermi gas is investigated for interacting and non-interacting charge-neutral and $β$-equilibrated gases. The standard minimal couplings between the magnetic field and the fermions' charges and magnetic dipole moments define the fermions' interaction with the magnetic field. Assuming a variable coupling strength between the magnetic field and the fermion (baryon) dipole moments, it is shown that a ferromagnetized state can be achieved that corresponds to a lower energy spin-polarized state with a magnetic field entirely due to the gas's magnetic response. We find that, depending on the density, a very large increase in the baryon dipole moments is needed to achieve this ferromagnetized state. While the required increase seems unlikely, the induced magnetic field is of the order $\sim10^{17}$ gauss. Furthermore, while externally magnetized Fermi gases have an anisotropic pressure, the pressure of the ferromagnetized gas is completely isotropic and the thermodynamically preferred magnetized state.