Ferromagnetic resonance in epitaxial garnet thin films

The chemical vapor deposition process for growing epitaxial yttrium iron garnet (YIG) has matured to the point where films of varying geometry and thickness from 1/2 to as great as 40 μ can be readily grown on several orientations of gadolinium gallium garnet, yttrium aluminum garnet, and YIG, itself. As a measure of the quality of the films, line widths (at 9.4 GHz and room temperature) as small as 0.6 and 1.4 Oe were obtained in samples with substrates removed and intact, respectively, without a major effort toward improvement. Magnetostatic modes, exchange modes, and ferromagnetic normal modes having comparable exchange and demagnetization energies were observed in these films and in thin bulk disks and were explained in detail by a new theory which applies not only to films, but also to samples of arbitrary shape and size, and includes the effects of exchange and demagnetization energies. The frequencies of the general normal modes were calculated by casting the linearized equation of motion of the magnetization into the form of an eigenvalue equation and solving this equation by a variational method. In addition to explaining the experiments in detail, the theory affords a new method of studying pinning from the observation of magnetostatic modes, has implications concerning the main-resonance position in finite films, and, together with the experiments, further verifies Portis' mode-spacing theory. The behavior of the magnetostatic modes in the epitaxial films and thin bulk samples, when interpreted according to the present theory, gives direct information about the pinning conditions which the magnetization obeys at the edges and surfaces of these ferrite samples. For a single-crystal bulk sample 0.005 in. thick and for a single-crystal film 12.5 μ thick, the magnetization was pinned at the small edges of the film and was unpinned at the large faces, indicating that the surface-anisotropy pinning mechanism is not effective in these samples. It is well known, that the frequency of the main resonance in a finite film is shifted slightly from the frequency of the uniform precession mode (k=0) in an infinite film. The present theory indicates that this shift is a consequence of the volume microwave demagnetization field [arising from ∇·≠0 in the volume, as opposed to the edges, of the sample]. The shift is not based on a spatial average of the static internal field H_i as previously thought. The average 〈H_i〉 should be a weighted average, and the weighting factor m_x²+m_y² is small at the small edges of the film where H_i differs from its infinite-film value.