Phonon parallel-pump instability in the (110) plane of a ferromagnetic crystal

The critical phonon amplitude for the excitation of spinwave pairs in a saturated ferromagnet is calculated by the canonical formulation. The phonon propagates in the direction of the applied biasing field, which is directed at an arbitrary angle in a (110) plane. The analysis is applied to the degenerate case, but the critical phonon amplitude for the applied field along a [100] direction is also calculated for the nondegenerate case. The latter result agrees with an earlier calculation by Matthews and Morgenthaler.