Excitation of propagating dipole-exchange spin waves in ferromagnetic double-film

The aim of this work is to present a theory of excitation of propagating spin waves (SW) in perpendicularly magnetized double-film structure by microstrip transducer. The theory is based on the dipole-exchange SW spectrum. To solve the boundary problem, we write the equation for the magnetization M (r, t) within each ferromagnetic film (numbers I = 1, 2). The effective field H (r, t), being part of the equation of motion, corresponding to each film, is considered to be equal to the sum of the constant internal magnetic field H, the variable dipole field, the "driving" microwave magnetic field, and exchange field. To find the joint solution of the equations of motion and Maxwell's equations (in magnetostatic limit) we apply earlier elaborated technique: Green's tensor function defining the dipole field and spin wave normal mode expansion technique. As a result we obtain the dispersion equation defining dipole-exchange spin wave spectrum of perpendicularly magnetized double-film structure and the solution for the excited magnetization.