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It has long been predicted that a two-component non-localized Fermi gas willexhibit spontaneous polarization for sufficiently strong repulsiveinteractions, a phenomenon which is called itinerant ferromagnetism. Recentexperiments with ultracold atomic gases have reached the interaction strengthfor which theoretical models have predicted the occurrence of thenormal-to-itinerant-ferromagnetic phase transition, but so far this transitionhas not been observed. The instability of the repulsive branch of the Feshbachresonance prevents the formation of the itinerant ferromagnetic state, but itis not clear whether this is the only instability impeding its experimentalrealization. In this article, we use the path-integral formalism with densityfields in the Hubbard-Stratonovich transformation to study the stability of ahomogeneous two-component Fermi gas with contact interactions. Within thesaddle-point approximation we show that none of the extrema of the action areminima, meaning all extrema are unstable to small density fluctuations. Thisimplies a more general mechanical instability of the polarized (itinerantferromagnetic) and normal states of the system in the path-integral formalism.We find that it is important to consider the stability of the system whenstudying itinerant ferromagnetism. Since (mechanical) stability may beinfluenced by the details of the interaction potential, we suggest the use of amore realistic potential than the contact potential in future theoreticaldescriptions.

Contact potential instability in the path-integral description of itinerant ferromagnetism