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.
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