Resonantly exited precession motion of three-dimensional vortex core in magnetic nanospheres

We found resonantly excited precession motions of a three-dimensional vortex core in soft magnetic nanospheres and controllable precession frequency with the sphere diameter 2R, as studied by micromagnetic numerical and analytical calculations. The precession angular frequency for an applied static field $H_{DC}$ is given as $\omega_{MV}= \gamma_{eff} H_{DC}$, where $\gamma_{eff} = \gamma <m_{\Gamma}>$ is the effective gyromagnetic ratio in collective vortex dynamics, with the gyromagnetic ratio $\gamma$ and the average magnetization component $<m_{\Gamma}>$ of the ground-state vortex in the core direction. Fitting to the micromagnetic simulation data for $<m_{\Gamma}>$ yields a simple explicit form of $<m_{\Gamma}> = (73.6 \pm 3.4)(l_{ex}/2R)^{2.20 \pm 0.14}$, where $l_{ex}$ is the exchange length of a given material. This dynamic behavior might serve as a foundation for potential bio-applications of size-specific resonant excitation of magnetic vortex-state nanoparticles, for example, magnetic particle resonance imaging.