  We investigate the zero-temperature ferromagnetic behavior of a two-component
repulsive Fermi gas in the presence of a correlated random field that
represents an optical speckle pattern. The density is tuned so that the
(noninteracting) Fermi energy is close to the mobility edge of the Anderson
localization transition. We employ quantum Monte Carlo simulations to determine
various ground-state properties, including the equation of state, the magnetic
susceptibility, and the energy of an impurity immersed in a polarized Fermi gas
(repulsive polaron). In the weakly interacting limit, the magnetic
susceptibility is found to be suppressed by disorder. However, it rapidly
increases with the interaction strength, and it diverges at a much weaker
interaction strength compared to the clean gas. Both the transition from the
paramagnetic phase to the partially ferromagnetic phase, and the one from the
partially to the fully ferromagnetic phase are strongly favored by disorder,
indicating a case of order induced by disorder.
