  The properties of surface waves in a partially ionized, compressible
magnetized plasma slab are investigated in this work. The waves are affected by
the nonideal magnetohydrodynamic effects which causes finite drift of the
magnetic field in the medium. When the magnetic field drift is ignored, the
characteristics of the wave propagation in a partially ionized plasma fluid is
similar to the fully ionized ideal MHD except now the propagation properties
depend on the fractional ionization as well as on the compressibility of the
medium. The phase velocity of the sausage and kink waves increases marginally
(by a few percent) due to the compressibility of the medium in both ideal as
well as Hall diffusion dominated regimes. However, unlike ideal regime, only
waves below certain cut off frequency can propagate in the medium in Hall
dominated regime. This cut off for a thin slab has a weak dependence on the
plasma beta whereas for thick slab no such dependence exists. More importantly,
since the cut off is introduced by the Hall diffusion, the fractional
ionization of the medium is more important than the plasma compressibility in
determining such a cut off. We discuss the relevance of these results in the
context of solar photosphere-chromosphere.
