Standing spin waves in ferromagnetic thin films

A theory of spin wave resonance in ferromagnetic thin films is discussed in a manner that permits a computation of the real and imaginary parts of the circularly polarized RF fields as well as the power absorption spectrum. The case of the dc field intensity applied normal to the surface of the film is considered, and the saturation magnetization is taken as constant throughout the body of the film. Variations in dc fields near the surfaces are treated in the boundary conditions for the RF magnetization by considering the unsymmetrical nature of the exchange interaction at the surfaces. The boundary conditions are characterized by a constant for each surface that controls the degree of surface pinning in the RF magnetization. Damping is included in the formulation by means of a phenomenological constant in the spin wave equation and by simulaneous solution of this equation with Maxwell's equations for a conductor. The results of a computer program are presented showing the roles of the various parameters in determining the power absorption spectrum and RF fields. A comparison with experimental spectra is made, and an anomalous resonance at field intensities higher than that for the principal resonance is predicted.