Perpendicular ferromagnetic resonance in soft cylindrical elements: Vortex and saturated states

Linear magnetic excitations in perpendicularly magnetized micrometer-sized disks have been investigated in detail both in the saturated and the vortex states using ferromagnetic resonance spectroscopy and micromagnetic simulations. Broadband ferromagnetic resonance spectra measured in disk arrays reveal a set of discrete resonance lines associated with the dipole-exchange spin-wave modes quantized by the disk edge in the saturated state and several new resonance lines (up to four) with negative slopes for the frequency-field dispersion relation omega(H-z) in the vortex state at intermediate magnetic fields. The micromagnetic simulations performed for a Py disk array (regime of negligible coupling between the disks) allow us to identify the four excitations occurring in the deformed vortex state as vortex core, disk edge, and coupled vortex core/disk edge modes, and to reproduce very satisfactorily their experimental omega(H-z) curves. In addition, the nonlinear frequency dependence of the resonance linewidth for the predominant coupled vortex core/edge mode experimentally observed is in agreement with the numerical prediction. These findings are finally confirmed by magnetic resonance force microscopy measurements conducted on an isolated NiMnSb disk. The remarkable similarity between the experimental results coming from two magnetic systems and using two different microwave probes demonstrates the robustness of the physical phenomenon.