Magnetization reorientation due to interface roughness

We investigate the reorientation of the magnetization of a thin ferromagnetic film subjected to a sinusoidal exchange field. We take the oscillatory exchange as a representation of the effect of the interface roughness in the equilibrium magnetic pattern of a thin ferromagnetic film on a two-sublattice antiferromagnetic substrate. We find that in the limit that the wavelength of the oscillatory exchange field is comparable to the domain wall width of the ferromagnet there is a 90 degrees reorientation of the magnetization to accommodate the interface frustration. For the case of an uniaxial ferromagnetic film the reorientation only occurs if the amplitude of the oscillatory exchange field is beyond a threshold value which depends on the degree of interface roughness and the uniaxial anisotropy energy of the ferromagnetic film. For ferromagnetic films with four-fold crystalline anisotropy the reorientation is always possible, even if the strength of the interface exchange field is rather small. In this case the reoriented uniform state does not cost any extra anisotropy or exchange energy and accommodates the frustration imposed by the fluctuation in the interface exchange energy.