  A combination of small-cluster exact-diagonalization calculations and a
well-controlled approximative method is used to examine the ground-state phase
diagrams of the spin-one-half Falicov-Kimball model extended by the
spin-dependent on-site interaction ($J$) between localized spins and itinerant
($d$) electrons, as well as by external magnetic field ($h$). Both the magnetic
ordering and metamagnetic transitions are analysed as functions of $h$ and the
number of itinerant electrons ($N_d$) at selected $J$. Various magnetic
superstructures including axial and diagonal spin stripes are observed for
nonzero values of $J$ and $h$. Moreover, it is shown that increasing $h$
strongly stabilizes the fully and partially polarized states, while the non
polarized state is reduced.
