  The magnetic phases induced by the interplay between disorder acting only on
particles with a given spin projection ("spin-dependent disorder") and a local
repulsive interaction is explored. To this end the magnetic ground state phase
diagram of the Hubbard model at half-filling is computed within dynamical
mean-field theory combined with the geometric average over disorder, which is
able to describe Anderson localization. Five distinct phases are identified: a
ferromagnetically polarized metal, two types of insulators, and two types of
spin-selective localized phases. The latter four phases possess different
long-range order of the spins. The predicted phase diagram may be tested
experimentally using cold fermions in optical lattices subject to
spin-dependent random potentials.
