Magnetostatic Waves in One-Dimensional Magnonic Crystals With Magnetic and Nonmagnetic Components

This is the first report of the application of the plane wave method to the solution of the Walker equation for the magnetostatic potential in periodic magnetic composites referred to as magnonic crystals. The discussed method allows to determine the dispersion relation of magnetostatic waves in systems composed of magnetic materials as well as those comprising both magnetic and nonmagnetic materials described by the permeability tensor the elements of which are periodic functions of position. Here the method is applied to the case of one-dimensional magnonic crystals composed of alternating layers of a ferromagnet and a nonmagnetic material. The resulting band structure includes bands of backward magnetostatic waves and a band of surface magnetostatic waves, strongly dependent on the direction of propagation. The obtained results verify the applicability of the method to the considered systems, and suggest it could be used also for calculating spectra of magnetostatic and spin waves in two-dimensional magnonic crystals.