Spin waves in a magnonic crystal with sine-like interfaces

The spectrum of exchange spin waves in a magnonic crystal (periodic magnetic multilayer) with diffuse interfaces is derived for a model with a cosine-like profile of the uniaxial anisotropy value at the interfaces. The dependence of the band gap size upon the interface thickness and the depth of modulation of the anisotropy value is analyzed. In particular, it is shown that diffuse interfaces may lead to a magnonic spectrum in which band gaps have size equal to or even larger than those in the model with sharp (infinitely thin) interfaces (Kronnig-Penney model).