Spin Wave Mordes And Dynamics Of Three-dimensional Magnetic Nanodisks Under Perpendicular Resonant Magnetic Field

The spin excitation spectrum of ferromagnetic thin films has always been one of the important topics in modern magnetism.The stable state is related to the interaction between demagnetization energy and exchange energy for soft magnetic nanostructures with different shapes and sizes.In order to reduce the dipole energy,the nanodisks forms a magnetic vortex structure,which has an in-plane curling magnetization in the most planar area and an out-of plane magnetization in the center region.We investigate the effects of nanodisks thickness on its excitation spectrum and dynamics.Magnetic vortex in nanodisks of soft magnetic materials with different thicknesses is researched by LLG micro-magnetic simulation software.When the thickness of permalloy nanodisks is comparable to its radius,magnetic moments are nonuniform along the dot thickness,forming a football-like vortex core which middle part is larger than the ends.When a vertical excitation magnetic field is applied to three-dimensional nanodisks,we observe not only the excitation of radial spin wave modes,but also hybridization of radial modes with standing wave modes along the disk thickness.The eigenfrequencies of such hybrid modes are much larger than the low-order radial spin wave modes.When the thickness of the disk is large enough,we observe hybridization of the high-order standing wave with radial spin wave modes,but near absence of pure common radial spin wave mode.The hybrid modes can be divided into standing wave modes outside the vortex core along the disk thickness(below 35 GHz)and uniform standing wave modes along the disk thickness(above 35 GHz).In order to study dynamics of vortex in hybrid modes,we apply a uniform vertical magnetic field with a frequency matching in hybrid mode to the disk,and find that even if the external magnetic field increases greatly,the polarity of vortex cannot be switched.Then we apply a phase matched vertical external magnetic field to the disk which leads to much higher efficiency of exciting spin-wave,in comparison to the spatially uniform external magnetic field,and the amplitude ofthe magnetic moment vibration is greatly increased.The vortex polarity can be easily switched,and the time required decreases as the amplitude of the external magnetic field increases.Meanwhile,we apply a resonant external magnetic field with the same magnitude for different thickness of nanodisks.For thicker nanodisks,there is enough energy to form two Bloch points during the switching process,and the two Bloch points move toward each other along dot thickness,disappearing in the middle of nanodisk which greatly reduce the time for switching the polarity of the vortex.