  We study linear theory of the magnetized Rayleigh-Taylor instability in a
system consisting of ions and neutrals. Both components are affected by a
uniform vertical gravitational field. We consider ions and neutrals as two
separate fluid systems where they can exchange momentum through collisions.
However, ions have direct interaction with the magnetic field lines but
neutrals are not affected by the field directly. The equations of our two-fluid
model are linearized and by applying a set of proper boundary conditions, a
general dispersion relation is derived for our two superposed fluids separated
by a horizontal boundary. We found two unstable modes for a range of the
wavenumbers. It seems that one of the unstable modes corresponds to the ions
and the other one is for the neutrals. Both modes are reduced with increasing
the collision rate of the particles and the ionization fraction. We show that
if the two-fluid nature is considered, RT instability would not be suppressed
and also show that the growth time of the perturbations increases. As an
example, we apply our analysis to the Local clouds which seems to have arisen
because of the RT instability. Assuming that the clouds are partially ionized,
we find that the growth rate of these clouds increases in comparison to a fully
ionized case.
