Ferromagnetism in Two-component Fermi gases: Variational and Green's Function Monte Carlo Studies

We study the possibility of a ferromagnetic instability in both repulsive and attractive two-component Fermi gases using lowest-order constrained variational (LOCV), variational Monte Carlo (VMC), and fixed-node Green's function Monte Carlo (GFMC) methods. For repulsive interactions, where the range $r_0$ is of order the scattering length $a >0 $, we find clear evidence for a ferromagnetic Stoner instability at $k_F a \sim {\cal O}(1)$. The occurrence of ferromagnetism is robust though the precise value of $k_F a$ at the instability is not universal and depends upon the shape of the potential. To model the recent experiments [1], where the underlying interactions are attractive with $|a| \gg r_0$, one must be on the repulsive excited branch on the $a>0$ side of the Feshbach resonance. We write the many-body wavefunction as a suitable Jastrow factor times a fermionic determinant, with a nodal structure that ensures the system is on the excited branch. We will report on the possible ferromagnetic instability in this Fermi-liquid state and its implications for experiments. \bigskip [1] G-B. Jo {\it et al.}, Science {\bf 325}, 1521 (2009).