The purpose of this work is to investigate the characteristics of a volume-surface spin wave in a tangentially magnetized ferrite plate.

Methods. Without using magnetostatic and electrostatic approximations, the general problem of the propagation of a volume-surface electromagnetic wave along a tangentially magnetized bigyrotropic layer in an arbitrary direction is analytically solved, and a dispersion relation for this wave is obtained.

Results. It is shown that the amplitude distribution of high-frequency wave fields within a bi-gyrotropic layer is described by two wavenumbers, which are included in the trigonometric and exponential functions, respectively, and determine the volume and surface distribution of the wave. Using the resulting dispersion equation, the characteristics of the backward volume-surface spin wave in a ferrite plate, a special case of a bi-gyrotropic layer, are studied. For the case of wave propagation along the external magnetic field vector, the dispersion dependencies of the first modes of this wave and the wave numbers determining the surface and volume parts of the wave distribution across the ferrite thickness were calculated. The relation between the coefficients determining the contribution of the trigonometric and exponential terms to the wave distribution across the ferrite plate thickness was also calculated, allowing us to determine the extent to which the wave is a volume wave and the extent to which it is a surface wave, depending on the frequency and propagation constant. The calculated characteristics were compared with those of a backward volume magnetostatic wave. It was found that at frequencies near the plate’s ferromagnetic resonance and at low propagation constants, these characteristics differ significantly.

Conclusion. The dispersion equation presented in this paper can be used to calculate the characteristics of volume-surface spin waves and electromagnetic waves in various anisotropic layers, which are special cases of a bi-gyrotropic layer. The results obtained above should be taken into account when developing devices using spin waves.