Derivation and generalization of the Suhl spin-wave instability relations

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Abstract
The Suhl spin-wave instability relations are shown to be derivable using linear-stability theory and the method of averaging. This makes rigorous Suhl’s early work on formulas for the critical radio frequency field for spin-wave instabilities as well as reformulating the problem in more mathematical terms. It also makes possible several generalizations and extensions including formulas for spin waves with frequencies near the usual detuned frequency, and a direct application of second-order averaging theory to show that the first-order results here and in Suhl’s original work are very accurate within the infinite time-averaging approximations used. Appendixes on the full equations of motion, including the Landau-Lifshitz damping, and the complete expressions for the Jacobian from the variational equations are also given.