Electromagnetic waves in a tangentially magnetized bi-gyrotropic layer (with an example of analysis of spin wave characteristics in a ferrite plate)

We discuss difficulties arising from the description of spin waves in the magnetostatic approximation, in which neither the microwave electric field nor the Poynting vector is associated with the wave. To overcome these difficulties, we present for the first time a correct solution to the problem of electromagnetic wave propagation in an arbitrary direction along a tangentially magnetized bi-gyrotropic layer (a special case of this problem is the propagation of spin waves in a ferrite plate). It is shown that the wave distribution over the layer thickness is described by two different wave numbers $k_{x21}$ and $k_{x22}$, which can take real or imaginary values; in particular, three types of spin wave distributions can occur inside the ferrite plate — surface-surface (when $k_{x21}$ and $k_{x22}$ are real numbers), volume-surface ($k_{x21}$ is imaginary and $k_{x22}$ is real), and volume-volume ($k_{x21}$ and $k_{x22}$ are imaginary numbers), which fundamentally distinguishes the obtained description of spin waves from their description in the magnetostatic approximation.