Spin excitations in vortex-state magnetic cylindrical dots: From nanometric to micrometric size

The analytical model recently formulated to calculate spin modes frequencies in vortex-state ferromagnetic cylindrical dots based upon the tensorial Green’s function formalism is reviewed. This method has been recently used to calculate the quantized spectrum at zero applied field. In dots of radius of nanometric size, for the nonaxially symmetric modes the radial eigenvectors are Bessel functions of an order greater than one or equal to one, while the axially symmetric modes correspond to zero order Bessel functions. Instead, in dots of radius in the submicrometric and micrometric range the radial eigenvectors of the whole set of modes are Bessel functions of order one. Both the case where the dynamic magnetization is assumed uniform along the thickness and the case where a thickness-dependence is present are considered. The calculated frequencies of the most representative modes are compared to available experimental data for Permalloy disks.