First-order instability theory for magnetostatic modes in ferromagnetic spheres

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Abstract
A first-order instability theory for magnetostatic modes in ferromagnetic spheres has been developed. The analysis is based on the interaction of three modes: the uniform mode pumped at microwave frequency ωp and a pair of magnetostatic modes at lower frequencies which sum to ωp. The magnetostatic mode instability arises when the pump microwave field amplitude exceeds some threshold. The theory yields (i) selection rules for the magnetostatic mode pairs with a nonzero coupling to the uniform mode, (ii) a characteristic equation for the frequencies of these modes, and (iii) microwave field threshold amplitudes for the parametric excitation of the mode pairs. For each mode pair, one or more sharp threshold minima are found. The superposition of these sharp minima resembles the complicated structure observed in the subsidiary absorption butterfly curve for single-crystal yttrium-iron-garnet spheres.