  Over the last decade, substantial efforts have been devoted to understanding
the stability properties, transport phenomena, and long-term evolution of
weakly-collisional, magnetized plasmas which are stratified in temperature.
These studies have improved our understanding of the physics governing the
intra-cluster medium (ICM), but assumed that ICM is a homogeneous. This,
however, might not be a good approximation if heavy elements sediment in the
inner region of the galaxy cluster. In this paper, we analyze the stability of
a weakly-collisional, magnetized plane-parallel atmosphere which is stratified
in both temperature and composition. This allows us to discuss for the first
time the dynamics of weakly-collisional environments where heat conduction,
momentum transport, and ion-diffusion are anisotropic with respect to the
direction of the magnetic field. We show that, depending on the relative signs
and magnitudes of the gradients in the temperature and the mean molecular
weight, the plasma can be subject to a wide variety of unstable modes which
include modifications to the magnetothermal instability (MTI), the
heat-flux-driven buoyancy instability (HBI), and overstable gravity modes
previously studied in homogeneous media. We discuss the astrophysical
implications of our findings for a representative galaxy cluster where helium
has sedimented. Our findings suggest that the core insulation that results from
the magnetic field configurations that arise as a natural consequence of the
HBI, which would be MTI stable in a homogeneous medium, could be alleviated if
the mean molecular weight gradient is steep enough, i.e., $(\nabla \mu)/\mu >
(\nabla T)/T$. This study constitutes a first step toward understanding the
interaction between magnetic turbulence and the diffusion of heavy elements in
the ICM. (abridged)
