Magnetostatic Modes of a Ferromagnetic Slab

The characteristic modes of a thin slab magnetized in its plane are obtained in the magnetostatic limit, and the mode spectrum and configuration are discussed. The wavelength dependence of magnetostatic mode density is determined and utilized to establish a connection to the modes obtained in the spin-wave approximation. In this geometry the modes lying above the spin-wave band are surface waves, decaying toward the interior of the slab, while volume modes occur in the same frequency range as the long-wavelength limit of the spin-wave band of an infinite medium. The mode density exhibits poles at the upper and lower frequency limits of the surface mode spectrum. The surface modes become statistically less important at shorter wavelengths because the ratio of surface mode density to volume mode density varies approximately as $\text{1/|k|}$ .