Dipole-exchange theory of hybrid electromagnetic-spin waves in layered film structures

A theory has been developed for normal mode electromagnetic-spin waves propagating in metal–dielectric-ferromagnetic-dielectric-metal film structures. Dipole and exchange interactions are taken into account. An arbitrary direction of the internal bias magnetic field is assumed. A dispersion equation for hybrid waves is derived. Effects of varying the dielectric constants of the dielectric layers and the geometry of the layered structure are analyzed for the dispersion characteristics of hybrid waves. The obtained results are applied to layered structures containing ferromagnetic and ferroelectric layers that could be used as waveguiding structures for dual electrically or/and magnetically tunable microwave devices.