Magnetoelastic Wave Instability Threshold in an Axially Magnetized YIG Rod

Abstract

The instability threshold has been derived for transversely pumped magnetoelastic waves in YIG for the case where the equilibrium position of the magnetization vector is in an arbitrary direction with respect to the crystal axes. It is shown that the threshold has a finite value for magnetoelastic waves propagating parallel to the direction of the internal magnetic field and that the threshold is minimum near crossover. It is also shown that the threshold is lowest when the internal field is rotated ∼15° with respect to one of the 〈100〉 cubic axes of YIG. The recently developed geometrical ray theory analysis is used to determine the exact propagation path of the magnetoelastic waves in an axially magnetized rod and to compute the magnitude of the angle θ between the wave vector k and the direction of the internal magnetic field. Results show that the magnetoelastic waves focus about the direction of the field and that θ≅1° or less. The ray theory analysis and the nonlinear theory have been combined, and the threshold has been determined at each point along the ray. The results satisfactorily explain the experimental observations on parametric amplification of magnetoelastic waves in YIG, reported in an earlier paper.