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

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.

Figure 1

The in-medium scattering phase shift ${\varphi }_{\mathrm{m}}$ at zero center-of-mass momentum $\mathbf{P}$ for various values of the inverse gas parameters $g$ in 3D ($g=k_{\mathrm{F}}a$) and 2D [$g=-1/ln\left(k_{\mathrm{F}}{a}_2\right)$].

Figure 2

The interaction energy for the balanced case $x=0$ as a function of $-1/\left(k_{\mathrm{F}}a\right)$ in 3D (a) and of $ln\left(k_{\mathrm{F}}{a}_2\right)$ in 2D. The blue dashed lines are the results from second-order perturbation theory. The red dash-dotted line in (a) corresponds to the energy of the fully polarized state in 3D, ${\mathcal{E}}_{\mathrm{fp}}=2^{2/3}{\mathcal{E}}_0$.

Figure 3

The normalized inverse spin susceptibility ${\chi }_0/\chi$ (blue solid lines) and the pairing decay rate $\Delta$ divided by $E_{\mathrm{F}}$ (black solid lines) as functions of the gas parameters in 3D (a) and 2D (b). The green dotted lines show schematically the behavior of the decay rate when three-body processes are taken into account.