Dipolar magnetic fields of spin excitations in vortex-state cylindrical ferromagnetic dots

A study of the effects of the dynamic dipolar magnetic fields on spin mode dynamics in circular cylindrical magnetic dots in vortex-state at zero applied fields is presented. The out-of-core and core dipolar magnetic fields are calculated exactly for both axially symmetric and nonaxially symmetric spin modes in terms of the nonlocal tensorial Green's-function. The exactly calculated spin mode eigenfrequencies are compared with those obtained using the local dipolar approximation for permalloy disks. The validity of the local dipolar approximation is discussed for radii ranging from the nanometric to the micrometric scale and for different thicknesses in the nanometric range. In the comparison both the case where the dynamic magnetization is assumed uniform along the thickness and the case where a thickness dependence is present are considered. In this framework, a simple formula giving the frequency splitting of the nonaxially symmetric modes (+/- vertical bar m vertical bar, n) is obtained. The calculated splitting compares well with the measured splitting at different aspect ratios. We also show that the general effect of the static exchange field arising from the curling configuration causes a downshift of the spin mode frequencies in nanometric dots. This behavior is similar to that of the demagnetizing field in the saturated state.