Magnetostatic theory of collective excitations in ferromagnetic and antiferromagnetic superlattices with magnetization perpendicular to the surface

The dispersion relations for both bulk and surface waves on magnetic superlattices is obtained in the case where the magnetization is perpendicular to the surfaces of the layers. Using magnetostatic theory, we find an infinite set of bulk bands where the widths of the bands are very sensitive to the separation between magnetic layers. There are no superlattice surface modes in the perfect semi-infinite structure; however, if the parameters of the outermost unit cell of the superlattice are slightly changed, an infinite set of surface modes are found. We present numerical examples for the ferromagnets EuS and Fe and for the antiferromagnet ${\mathrm{MnF}}_2$. Our results for the ferromagnets show that the bulk and surface modes should be easily observable by light scattering.