  The phase diagram of binary mixtures of particles interacting via a pair
potential of parallel dipoles is computed at zero temperature as a function of
composition and the ratio of their magnetic susceptibilities. Using lattice
sums, a rich variety of different stable crystalline structures is identified
including $A_mB_n$ structures. [$A$ $(B)$ particles correspond to large (small)
dipolar moments.] Their elementary cells consist of triangular, square,
rectangular or rhombic lattices of the $A$ particles with a basis comprising
various structures of $A$ and $B$ particles. For small (dipolar) asymmetry
there are intermediate $AB_2$ and $A_2B$ crystals besides the pure $A$ and $B$
triangular crystals. These structures are detectable in experiments on granular
and colloidal matter.
