Magnetization reorientation due to interface roughness

We investigate the reorientation of the magnetization of a thin ferromagnet ic film subjected to a sinusoidal exchange field. We take the oscillatory e xchange as a representation of the effect of the interface roughness in the equilibrium magnetic pattern of a thin ferromagnetic film on a two-sublatt ice antiferromagnetic substrate. We find that in the limit that the wave-le ngth of the oscillatory exchange field is comparable to the domain wall wid th of the ferromagnet there is a 90 degrees reorientation of the magnetizat ion to accommodate the interface frustration, For the case of an uniaxial f erromagnetic film the reorientation only occurs if the amplitude of the osc illatory exchange field is beyond a threshold value which depends on the de gree of interface roughness and the uniaxial anisotropy energy of the ferro magnetic film, For ferromagnetic films with four-fold crystalline anisotrop y the reorientation is always possible, even if the strength of the interfa ce exchange field is rather small. In this case the reoriented uniform stat e does not cost any extra anisotropy or exchange energy and accommodates th e frustration imposed by the fluctuation in the interface exchange energy.