Dual pumping of magnetostatic and spin-wave modes in yttrium–iron–garnet spheres

Abstract

In ferrimagnetic materials subjected to a static magnetic field H, a parallel rf magnetic field h gives rise to nonlinear absorption due to the unstable growth of certain spin waves when exceeding a parametric instability threshold (PIT), h=hc. The excited spin waves have half the pumping frequency and a wave number k that depends on H, such that the curve hc vs H resembles the Greek symbol ν and is thus called a “butterfly curve.” Recent experiments in a yttrium–iron–garnet sphere have shown that the PIT is resonantly reduced in the presence of a simultaneous perpendicular rf field at half the parallel-pumping frequency only on the right wing of the butterfly curve, where “volume” magnetostatic modes (k∼0) are primarily excited. Here, dual pumping experiments are reported at lower frequencies (8.882 and 4.441 GHz), allowing the presence of “surface” magnetostatic modes on the left wing and corresponding resonant PIT reduction in that region, where spin waves with k∼105 cm−1 are primarily excited by the parallel-pumping field. The results qualitatively agree with a model that put no restriction on the pumping frequency, thus extending earlier calculations by White and Schlömann [R. M. White and Schlömann, J. Appl. Phys. 33, 2437 (1962)].