GEOMETRICAL QUANTIZATION AND SHAPE EFFECTS OF SPIN-WAVE MODES

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Abstract
The mode spectrum derived from spin-wave approximation extrapolated to the long wavelength limit is compared with the dipole-exchange solutions for a film of finite thickness with an infinite surface - the infinite film. Experimental results from a number of spin-wave experiments are compared with the mode spectrum of an infinite film with the assumption of geometrical quantization. The reasonably good agreement of such an analysis suggests that the propagation constant in the plane of the film is quantized according to the dimensions of the finite sample. Small discrepancies for the low order modes suggest departures from the simple quantization scheme. Exact solutions for the elliptical cylinder magnetized along the long axis are compared with those of the infinite plate magnetized in a direction paralle1 to the surface. It is found that under certain conditions the propagation constant is geometrically quantized in a simple manner. The effects of shape on spin-wave frequencies as a function of geometry are discussed for the elliptical cylinder, circular cylinder, sphere, disk and intermediate shapes

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