Interplay between phase ordering and roughening on growing films

We study the interplay between surface roughening and phase separation during the growth of binary films. Renormalization group calculations are performed on a pair of equations coupling the interface height and order parameter fluctuations. We find a larger roughness exponent at the critical point of the order parameter compared to the disordered phase, and an increase in the upper critical dimension for the surface roughening transition from two to four. Numerical simulations performed on a solid-on-solid model with two types of deposited particles corroborate some of these findings. However, for a range of parameters not accessible to perturbative analysis, we find non-universal behavior with a continuously varying dynamic exponent.