Threshold Microwave-Field Amplitude for the Unstable Growth of Spin Waves under Oblique Pumping

Abstract

The threshold microwave‐field amplitude h_crit required for the unstable growth of spin waves has been investigated for oblique pumping with a linearly polarized microwave field applied at an arbitrary angle with respect to the static magnetic field. The experiment was performed on YIG (1% Dy) spheres at 9.2 GHz, using a rectangular TE₁₀₂ cavity and a pulsed magnetron source. Data were obtained at static external fields of 400, 600, 1100, and 1500 Oe. In general, h_crit increases with the pump angle. Theoretical expressions for the oblique pumping h_crit have been derived for ferromagnetic insulators of ellipsoidal shape and with axial symmetry about the direction of the static magnetic field sufficient to saturate the sample. The threshold field is determined by maximizing 1/h=cosψ/h_∥±sinψ/h_⊥ with respect to the angle between the internal field and the spin‐wave propagation direction. Here, h_∥ and h_⊥ are the parallel and perpendicular pump threshold fields of Schlömann and Suhl. For external fields sufficient to magnetize the spherical samples to saturation, the theoretical predictions are in good agreement with the experimental data. For small fields, the agreement is poor. However, fair agreement is obtained by assuming a transverse demagnetizing factor N_t greater than the value of ⅓, which is appropriate for saturated spherical samples. The value of N_t for the best theoretical fit depends on the way in which the sample is demagnetized. This result indicates that for samples not magnetized to saturation, the magnetic structure consists of elongated domains, and that the oblique‐pumping data can be explained from the theory for saturated systems, assuming demagnetizing factors appropriate to the domain structure.