  We present a strategy to design structures for which a polar lattice
distortion induces weak ferromagnetism. We identify a large class of
multiferroic oxides as potential realizations and use density-functional theory
to screen several promising candidates. By elucidating the interplay between
the polarization and the Dzyaloshinskii-Moriya vector, we show how the
direction of the magnetization can be switched between 180$^{\circ}$ symmetry
equivalent states with an applied electric field.
