Dynamics and efficiency of magnetic vortex circulation reversal

Abstract

Dynamic switching of the vortex circulation in magnetic nanodisks by fast-rising magnetic field pulse requires annihilation of the vortex core at the disk boundary and reforming a new vortex with the opposite sense of circulation. Here we study the influence of pulse parameters on the dynamics and efficiency of the vortex core annihilation in permalloy $({\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20})$ nanodisks. We use magnetic transmission soft x-ray microscopy to experimentally determine a pulse rise time--pulse amplitude phase diagram for vortex circulation switching and investigate the time-resolved evolution of magnetization in different regions of the phase diagram. The experimental phase diagram is compared with an analytical model based on Thiele's equation describing high-amplitude vortex core motion in a parabolic potential. We find that the analytical model is in good agreement with experimental data for a wide range of disk geometries. From the analytical model and in accordance with our experimental finding we determine the geometrical condition for dynamic vortex core annihilation and pulse parameters needed for the most efficient and fastest circulation switching. The comparison of our experimental results with micromagnetic simulations shows that the micromagnetic simulations of ``ideal'' disks with diameters larger than $\ensuremath{\sim}250$ nm overestimate nonlinearities in susceptibility and eigenfrequency. This overestimation leads to the core polarity switching near the disk boundary, which then in disagreement with experimental findings prevents the core annihilation and circulation switching. We modify the micromagnetic simulations by introducing the ``boundary region'' of reduced magnetization to simulate the experimentally determined susceptibility and in these modified micromagnetic simulations we are able to reproduce the experimentally observed dynamic vortex core annihilation and circulation switching.