Inconsistencies of the magnetostatic approximation in the description of a bi-component magnonic slab

•We show a strict analysis of the mathematical formulation for spin wave propagation.•Our results include waves traveling in all possible directions.•Magnetostatic approximation for bi-component magnonic crystals shows inconsistencies.•The application of the Walker’s equation in bi-component structures is not valid. A complete theoretical analysis of inconsistencies of the magnetostatic model when applied to describe the propagation of spin waves through a bi-component system is presented. The standard magnetostatic theory, widely used to study propagation in a single homogenous magnetic media, has been used incorrectly in some recent papers to describe the spin wave propagation in bi-component systems. Our results demonstrate, in fact, that the application of the standard magnetostatic theory applied to this kind of system leads exclusively to a trivial solution. We discuss the boundary conditions to be fulfilled when two ferromagnetic media with different magnetic properties are coupled, as occurs at each interface of a bi-component magnonic crystal.