Ferronematic Ground State of the Dilute Dipolar Fermi Gas

It is shown that a homogeneous two-component Fermi gas with (long-range) dipolar and short-range isotropic interactions has a ferronematic phase for suitable values of the dipolar and short-range coupling constants. The ferronematic phase is characterized by having a nonzero magnetization and long-range orientational uniaxial order. The Fermi surface of the spin-up (-down) component is elongated (compressed) along the direction of the magnetization.

Figure 1

Schematic phase diagram as a function of ${\lambda }_s=gn/{ϵ}_F$ and ${\lambda }_d=n{\mu }^2/{ϵ}_F$. It has a paramagnetic phase ($M=0$), and a ferronematic phase with partial ($0<M<1$) and full polarization ($M=1$). Dashed (full) curve: first (second) order phase transitions; $A$: tricritical point.

Figure 2

Magnetization $M$ and Fermi surface distortion parameters ${\alpha }_1$ and ${\alpha }_2$ vs the dimensionless dipolar coupling ${\lambda }_d$ for an $s$-wave coupling ${\lambda }_s=1.34$.

Figure 3

(a)–(d): Spin up and down FS, labeled by $n_1$ and $n_2$, for several values of ${\lambda }_s$ and ${\lambda }_d$ and fixed particle density $n$. $a_d=m{\mu }^2/{\hslash }^2$ is the dipole-dipole interaction length scale. Dashed lines: Free fermion FS.

Figure 4

Pressure (broken), bulk compressibility (full) and chemical potential (dashed) (normalized to their values at the noninteracting Fermi gas) vs the dimensionless dipolar coupling ${\lambda }_d$, for ${\lambda }_s=0.8$. At ${\lambda }_d\sim 0.3$ there is a 1st order paramagnetic-ferronematic transition. The gas becomes unstable at ${\lambda }_d\simeq 0.52$.