Interaction energy and itinerant ferromagnetism in a strongly interacting Fermi gas in the absence of molecule formation

TL;DR

This paper studies the interaction energy and the potential for itinerant ferromagnetism in a strongly interacting Fermi gas without molecule formation, revealing a maximum in interaction energy and its implications for ferromagnetic phases in 2D and 3D.

Contribution

It introduces a perturbative approach to calculate interaction energy and explains the absence or presence of ferromagnetism in different dimensions without molecule formation.

Findings

Interaction energy shows a maximum before resonance in 3D and 2D.

Reentrant ferromagnetic transition in 3D near the energy maximum.

No itinerant ferromagnetism in 2D according to the theoretical model.

Abstract

We investigate the interaction energy and the possibility of itinerant ferromagnetism in a strongly interacting Fermi gas at zero temperature in the absence of molecule formation. The interaction energy is obtained by summing the perturbative contributions of Galitskii-Feynman type to all orders in the gas parameter. It can be expressed by a simple phase space integral of an in-medium scattering phase shift. In both three and two dimensions (3D and 2D), the interaction energy shows a maximum before reaching the resonance from the Bose-Einstein condensate side, which provides a possible explanation of the experimental measurements of the interaction energy. This phenomenon can be theoretically explained by the qualitative change of the nature of the binary interaction in the medium. The appearance of an energy maximum has significant effects on the itinerant ferromagnetism. In 3D, the ferromagnetic transition is reentrant and itinerant ferromagnetism exists in a narrow window around the energy maximum. In 2D, the present theoretical approach suggests that itinerant ferromagnetism does not exist, which reflects the fact that the energy maximum becomes much lower than the energy of the fully polarized state.