Bandgaps and Demagnetizing Effects in a Py/Co Magnonic Crystal

The magnonic mode dispersion in a bi-component ferromagnetic system composed by a periodic arrangement of cobalt cylindrical nanodots of diameter 310 nm totally etched into a permalloy film 16 nm thick is theoretically investigated. The array lattice constant of the 2-D magnonic crystal is 600 nm and the in-plane magnetic field is applied along the y-direction and perpendicularly to the in-plane Bloch wave vector. The simulations are based on a finite-difference micromagnetic approach, the so-called dynamical matrix method (DMM). The calculated frequency bandgaps for the most relevant magnonic modes according to the DMM are discussed and compared with the ones obtained by means of an analytical approach based on the plane wave method. An analytical expression of the effective static demagnetizing field experienced by localized collective modes whose spatial profiles are mainly concentrated in the horizontal rows containing cobalt cylindrical nanodots is derived and its dependence on the modulus of the Bloch wave vector of the magnonic modes is studied.