Electrical spin-wave spectroscopy in nanoscale waveguides with nonuniform magnetization

Spin wave modes in magnetic waveguides with the width down to 320 nm have been studied by electrical propagating spin-wave spectroscopy and micromagnetic simulations for both longitudinal and transverse magnetic bias fields. For longitudinal bias fields, a 1.3 GHz wide spin-wave band was observed in agreement with analytical dispersion relations for uniform magnetization. However, the transverse bias field led to several distinct bands, corresponding to different quantized width modes, with both negative and positive slopes. Micromagnetic simulations showed that, in this geometry, the magnetization was nonuniform and tilted due to the strong shape anisotropy of the waveguides. Simulations of the quantized spin-wave modes in such nonuniformly magnetized waveguides resulted in spin wave dispersion relations in good agreement with the experiments.