Itinerant Ferromagnetism in a polarized two-component Fermi gas

We analyze when a repulsively interacting two-component Fermi gas becomes thermodynamically unstable against phase separation. We focus on the strongly polarised limit where the free energy of the homogeneous mixture can be calculated accurately in terms of well-defined quasiparticles, the repulsive polarons. Phase diagrams as a function of polarisation, temperature, mass imbalance, and repulsive polaron energy, as well as scattering length and range parameter are provided. We show that the lifetime of the repulsive polaron increases significantly with the interaction range and the mass of the minority atoms, raising the prospects of detecting the transition to the elusive itinerant ferromagnetic state with ultracold atoms.