Spin-wave spectra in thin magnetic films

Spin-wave spectra have been studied in Permalloy films of varying thickness. In many of the films, the low-lying spin peaks exhibit the uniform spacing and slowly decreasing intensities associated with a parabolic variation in magnetization through the film, whereas the higher modes show the quadratic spacing and rapidly decreasing intensities associated with an abrupt change in magnetization or spin-pinning near the surface. The transition between these two regions depends upon the amplitude of the variation in magnetization and the film thickness, or in other words, the depth and width of the parabolic "well." When the angle of the applied field is changed with respect to the film, the lowest modes are virtually unchanged, but the linear-quadratic transition moves to a lower mode number. This is probably because the parabolic well appears shallower as the field approaches the "critical" angle at which the resonance frequency is independent of the magnetization. One series of films shows line spacings which are virtually independent of the film thickness.