A one-dimensional analysis of magnetization ripple in uniaxial thin films with perpendicular anisotropy

Micromagnetic ripple theory is developed for uniaxial thin films with the easy axis of the magnetization perpendicular to the film plane. Assuming a one-dimensional variation of the magnetization, which is connected to variation of local anisotropy, in the direction of the film thickness, a general equation describing the out-of-plane ripple is deduced from the calculus of variation. Some features of the magnetization dispersion are discussed. The results of the theory show that the wavelength of the periodic oscillation of the magnetization is very short in comparison with the film thickness, and that the root-mean-square (rms) value of the out-of-plane ripple is dependent on the local anisotropy variation.