Magnetic Vortex Core Dynamics in Cylindrical Ferromagnetic Dots

We report direct imaging by means of x-ray photoemission electron microscopy of the dynamics of magnetic vortices confined in micron-sized circular permalloy dots that are 30 nm thick. The vortex core positions oscillate on a 10 ns time scale in a self-induced magnetostatic potential well after the in-plane magnetic field is turned off. The measured oscillation frequencies as a function of the aspect ratio of the dots are in agreement with theoretical calculations presented for the same geometry.

Figure 1

Schematic drawing of the time-resolved PEEM experiment. The lower right displays the waveform of the magnetic field generated by the current pulses. Rise and fall times are 8.4 ns and 240 ps, respectively.

Figure 2

(a) and (b), respectively, show the time dependence of the ratio of the $Y$ and $X$ displacements of the vortex core to the radius of $6.3\mu \mathrm{m}$ diameter dot with thickness 30 nm. Lines are guides to the eyes. At the top are XMCD images of the dot as a function of time. The corresponding data in (a) are related to the images by the letters (a)–(l). The arrows in image (a) indicate the magnetization direction. Field pulse length is 75 ns.

Figure 3

Time dependence of the ratio of the $Y$ displacement of the vortex core to the radius of 5.3 and $4.3\mu \mathrm{m}$ diameter dots of thickness 30 nm. Field pulse length is 75 ns. Lines are guides to the eyes.

Figure 4

Comparison of the XMCD experimental data (symbols) and analytical theory for the dependence of the eigenfrequency of the vortex translational mode on the dot aspect ratio $\beta =L/R$ of the cylindrical permalloy dots. The solid line is plotted according to Eq. (3). The dot thickness is $L=30\mathrm{nm}$ and the diameters are $2R=4.3$, 5.3, and $6.3\mu \mathrm{m}$.