Calculations of three-dimensional magnetic normal modes in mesoscopic permalloy prisms with vortex structure

Static flux-closure structures in three-dimensional (3D) mesoscopic ferromagnets are known to differ quite significantly from their 2D counterparts. How these differences reflect in the dynamic properties of the magnetization is, to date, an open question. Micromagnetic simulations are employed to study the normal modes of magnetic oscillations in thick (60-80 nm) rectangular Permalloy prisms with 3D Landau-type flux-closure domain structure. Various magnetic normal modes are excited by a short field pulse and extracted using methods based on Fourier analysis. In particular, well-defined modes in the range of a few GHz are identified as oscillations of vortices, domain walls, and as excitations localized in the corners. The asymmetric Bloch wall in the center of the 3D Landau structure wall is a genuinely three-dimensional feature and thus gives rise to effects which were not reported in previous studies on 2D systems. It is argued that experimental evidence of these findings can be obtained.