Scaling in a two-component surface-growth model

We study scaling in kinetic roughening and phase ordering during growth of binary systems. We use a 1+1-dimensional single-step solid-on-solid model with Ising-like interaction between two components. We observed that the model exhibits a crossover from an intermediate regime, with effective scaling exponents for kinetic roughening significantly larger than for the ordinary single-step growth model, to an asymptotic regime with exponents of the Kardar-Parisi-Zhang class. The crossover time and length are exponentially increasing with the strength of interaction $K.$ For a given large $K,$ scaling with enhanced exponents is valid over many decades. The effective scaling exponents are continuously increasing with $K.$ Surface ordering proceeds up to the crossover. The average size of surface domains increases during growth with the exponent close to $1/2;$ the spin-spin correlation function and the distribution of domains obey scaling with the same exponent.