Magnetostatic modes of a ferromagnet slab

The characteristic modes of a thin slab magnetized in its plane are obtained in the magnetostatic limit. It is found that the magnetostatic mode spectrum is bounded by the same frequency limits as for the spheroid. In the slab, however, the mode configuration clearly changes from a volume distribution to a surface wave as the frequency is increased above the extrapolated spin-wave region. In general, the characteristic functions are travelling waves which propagate along the slab transversely to the applied d.c. magnetic field. The mode distribution in wave-vector space is obtained for both the volume and surface modes, and the dependence of mode density on wavelength is discussed. The mode density variation shows that the volume modes connect smoothly to the spin-wave spectrum of a medium of infinite extent. The surface modes also exist even at very short wavelengths, but become statistically less important as the wavelength decreases.