Universal dimensional crossover of domain wall dynamics in ferromagnetic films

The magnetic domain wall motion driven by a magnetic field is studied in (Ga, Mn)As and (Ga, Mn)(As, P) films of different thicknesses. In the thermally activated creep regime, a kink in the velocity curves and a jump of the roughness exponent evidence a dimensional crossover in the domain wall dynamics. The measured values of the roughness exponent zeta(1d) = 0.62 +/- 0.02 and zeta(2d) = 0.45 +/- 0.04 are compatible with theoretical predictions for the motion of elastic line (d = 1) and surface (d = 2) in two- and three-dimensional media, respectively.