Reduced Models for Ferromagnetic Thin Films with Periodic Surface Roughness.

We investigate the influence of periodic surface roughness in thin ferromagnetic films on shape anisotropy and magnetization behavior inside the ferromagnet. Starting from the full micromagnetic energy and using methods of homogenization and [Formula: see text]-convergence, we derive a two-dimensional local reduced model. Investigation of this model provides an insight into the formation mechanism of perpendicular magnetic anisotropy and uniaxial anisotropy with an arbitrary preferred direction of magnetization.