Microwave spectrum of square Permalloy dots: Quasisaturated state

Abstract

We report on an experimental and theoretical study of the spin-wave spectrum $(1--20\phantom{\rule{0.3em}{0ex}}\mathrm{GHz})$ in square Permalloy dots ($30\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick, $3\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ wide) subjected to a saturating in-plane field $(10--150\phantom{\rule{0.3em}{0ex}}\mathrm{mT})$. By changing the pumping geometry, we could favor the excitation of modes with different spatial profiles. Spin-wave frequencies and mode profiles were estimated using both numerical calculations (a micromagnetic simulation and a diagonalization of the dynamical matrix) and approximate methods (use of a quantization condition and of a simplified micromagnetic edge potential). Comparison between the measurements and those calculations allows us to identify unambiguously up to 13 modes. Among those modes, we distinguish magnetostatic waves quantized both parallel (i) and perpendicular (ii) to the magnetization, spin-wave wells (iii), and a mode condensation feature (iv) resulting from a large density of states close to a minimum in the spin-wave dispersion.