Roughness-induced variation of magnetic anisotropy in ultrathin epitaxial films: The undulating limit

We identify an extra magnetic anisotropy contribution due to roughness in ultrathin single crystalline magnetic films grown on randomly corrugated surfaces. In this picture, the magnetization follows the roughness profile leading to a tilting of the magnetization away from the easy magnetization axis and hence to a modification of the magnetic anisotropy. This undulating magnetic state competes with the alternative possibility of uniform in-plane magnetization, which carries a cost in magnetostatic energy due to surface charges. The limits of validity of the model presented are discussed in terms of the roughness amplitude, correlation length, film thickness, and the intrinsic magnetic parameters of the film.