Parametric excitation of spherical modes in ferromagnetic spheres by perpendicular and parallel pumping

The fine structures of the threshold of subsidiary absorption and parallel pumping, observed on highly polished YIG spheres in 1975 by W. Jantz et al., are discussed with a model which uses instead of plane spin-waves the true modes regarding the shape of the sphere. These spherical modes are magnetostatic modes taking additionally the exchange interaction into account. At the closely spaced resonances of the fine structure of parallel pumping single spherical modes with angular-momentum quantum numberm=0 are excited, whereas at the resonances of subsidiary absorption pairs of spherical modes with big angular-momentum quantum numbers (|m|1000) satisfying the selection rulem+m=1 are excited. The analysis of the fine structure of subsidiary absorption shows that in regimes where the plane wave approximation predicts the excitation of spin-waves with formalk0, modes withk1.5·10⁵ cm^–1 have the lowest threshold. This discrepancy is discussed with the effect of surface pit scattering, which increases the threshold of modes withk < 2/_pit, where _pit is a typical size of the surface pits. Consequently modes withk22/_pit instead ofk0 have the lowest threshold.