Spin-wave resonance spectra of inhomogeneous bubble garnet films

Abstract

Spin‐wave resonance at 10 GHz has been observed in thin (? 5 μm) garnet films of approximate composition Y_2.85La_0.15Fe_3.75Ga_1.25O₁₂. The films were grown by LPE on [111]‐oriented gadolinium gallium garnet substrates, both from a nonstirred melt (vertical mode of dipping) and a stirred melt (horizontal dipping, applying axial substrate rotation). The spectra exhibit large numbers of strongly excited modes with large deviations from quadratic spacing, which are interpreted in terms of a volume inhomogeneity of the uniaxial anisotropy constant K_u. Two models are used to explain the experimental spectra. In one model the film is considered as being built up of exchange coupled layers having different uniaxial anisotropy constants K_u. In the second model it is assumed that K_u varies linearly with the distance from the substrate, but with different slopes in different regions. No pinning is assumed at the surfaces. A simple graphical method is presented for determining the normal modes of films with these types of variations. It is shown that the normal modes can be separated into two types. The low‐order modes are localized modes, which are wavelike in only part of the film. These are strongly excited and their spacing is nonquadratic. High‐order modes are volume modes, which are sinusoidal throughout the films, though with varying wave vector. These are weakly excited. The low‐order modes bear information on the variations of K_u within the thickness. The nature of these variations is determined experimentally by examining the changes of these modes when the films are thinned down by chemical etching. Examples are given of films which are homogeneous except for a narrow (? 1 μm) region next to the substrate and of films whose anisotropy varies linearly throughout the major part of the thickness. The high‐order modes are only slightly affected by the variations. From their positions, using the universal numbering scheme n = 0,1,2,... for all the modes, the exchange stiffness constants have been determined.