  In (2+1)-dimensional QED with a Chern-Simons term, we show that spontaneous
magnetization occurs in the context of finite density vacua, which are the
lowest Landau levels fully or half occupied by fermions. Charge condensation is
shown to appear so as to complement the fermion anti-fermion condensate, which
breaks the flavor U(2N) symmetry and causes fermion mass generation. The
solutions to the Schwinger-Dyson gap equation show that the fermion self-energy
contributes to the induction of a finite fermion density and/or fermion mass.
The magnetization can be supported by charge condensation for theories with the
Chern-Simons coefficient $\kappa=N e^2/2 \pi$, and $\kappa=N e^2/4 \pi$, under
the Gauss law constraint. For $\kappa=N e^2/4 \pi$, both the magnetic field and
the fermion mass are simultaneously generated in the half-filled ground state,
which breaks the U(2N) symmetry as well as the Lorentz symmetry.
