Bulk and edge modes in two-dimensional magnonic crystal slab

Magnonic crystals are novel materials that open a new field to explore in the domain of spin dynamics in nanoscale systems. They also hold great promise for technological applications. The bulk, matrix, and edge magnonic states in a slab of two-dimensional magnonic crystal in the form of a superlattice of arrays of cylindrical dots of finite thickness are considered. The presented calculations are based on the plane wave method reformulated to gain in generality and efficiency, with both the exchange and the demagnetizing fields taken into account. The analytical formulas for Fourier coefficients of position-dependent material parameters for finite arrays of rods of various cross-sectional geometry and arrangement in the unit cell have been derived and presented. The localization properties of the edge modes found result from the magnonic spectrum and not from the nonuniformity of the internal magnetic field.