We studied the interplay between kinetic roughening and phase ordering
in a (1 + 1)-dimensional single-step solid-on-solid growth model with
two kinds of particles and Ising-like interaction. Evolution of both
geometrical and compositional properties was investigated by Monte Car
lo simulations for various strengths of coupling. The found that the i
nitial growth is strongly affected by the interaction between species,
scaling exponents are enhanced and ordering on the surface is observe
d. However, after a certain time, ordering along the surface stops and
the scaling exponents cross over to exponents of the Kardar-Parisi-Zh
ang universality class. For sufficiently strong coupling, ordering in
the vertical direction is present and leads to a columnar structure pe
rsisting for a long time.