Magnetic vortex dynamics in the presence of pinning

Abstract

We have measured the frequency ${f}_{G}$ of the gyrotropic mode of a magnetic vortex formed in individual soft ferromagnetic disks with diameters from 600 nm to $2\text{ }\ensuremath{\mu}\text{m}$. For low excitation amplitudes, we observe fluctuations in ${f}_{G}$ as a function of applied magnetic field. The relationship between the applied field and the spatial displacement of the vortex core from the center of the disk indicates that the fluctuations are due to a distribution of nanoscale defects that pin the vortex core, which has a diameter of $\ensuremath{\sim}10\text{ }\text{nm}$. In the limit of high excitation amplitude, the gyrotropic frequency is independent of field, indicating that the core is depinned. In this limit ${f}_{G}={f}_{ideal}$ where ${f}_{ideal}$ is the frequency predicted by analytical models and micromagnetic simulations of ideal vortex behavior. We also find both experimentally and in simulations that the average frequency shift $⟨\ensuremath{\Delta}f⟩=⟨{f}_{\text{max}}\ensuremath{-}{f}_{ideal}⟩$ is independent of disk diameter. From this observation we argue that $\ensuremath{\Delta}f$ for a particular fluctuation is proportional to the interaction energy ${W}_{P}$ of the vortex core with a single nanoscale defect and estimate the average energy to be ${W}_{P}/e\ensuremath{\approx}2\text{ }\text{eV}$ for the defects in these sputtered permalloy films.