  The spin-one-half Falicov-Kimball model with spin-dependent on-site
interaction between localized ($f$) and itinerant ($d$) electrons is studied by
small-cluster exact-diagonalization calculations and a well-controlled
approximative method in two dimensions. The results obtained are used to
categorize the ground-state configurations according to common features (charge
and spin ordering) for all $f$ and $d$ electron concentrations ($n_f$ and
$n_d$) on finite square lattices. It is shown that only a few configuration
types form the basic structure of the charge phase diagram in the $n_f-n_d$
plane. In particular, the largest regions of stability correspond to the phase
segregated configurations, the axial striped configurations and configurations
that can be considered as mixtures of chessboard configurations and the full
(empty) lattice. Since the magnetic phase diagram is much richer than the
charge phase diagram, the magnetic superstructures are examined only at
selected values of $f$ and $d$ electron concentrations.
