  Interacting two component Fermi gases are at the heart of our understanding
of macroscopic quantum phenomena like superconductivity. Changing nature of the
interaction is expected to head to novel quantum phases. Here we study the
ground state of a two component fermionic gas in a harmonic potential with
dipolar and contact interactions. Using a variational Wigner function we
present the phase diagram of the system with equal but opposite values of the
magnetic moment. We identify the second order phase transition from
paramagnetic to ferronematic phase. Moreover, we show the impact of the
experimentally relevant magnetic field on the stability and the magnetization
of the system. We also investigate a two component Fermi gas with large but
almost equal values of the magnetic moment to study how the interplay between
contact and dipolar interactions affects the stability properties of the
mixture. To be specific we discuss experimentally relevant parameters for
ultracold $^{161}$Dy.
