We study the kinetic roughening of a driven domain wall between spin-up and spin-down domains for a model with non-conserved order parameter and quenched disorder. To understand the scaling behavior of this interface we construct an equation of motion and study it theoretically.

With Monte Carlo simulations, we investigate the relaxation dynamics with a domain wall for magnetic systems at the critical temperature. The dynamic scaling behavior is carefully analyzed, and a dynamic roughening process is observed. For comparison, similar analysis is applied to the relaxation dynamics with a free or disordered surface.