Dynamic Vortex-Antivortex Interaction in a Single Cross-Tie Wall

A fascinating property of micromagnetism comes from the possibility to control the domain and vortex configuration through the sample shape and size. For instance, in a rectangular platelet a configuration containing a stable combination of vortices and an antivortex can be created. Such a single cross-tie wall can be understood as being a coupled micromagnetic system with three static solitons. Here we report on its magnetization dynamics including the vortex-antivortex interactions. The spectrum of eigenmodes is investigated as well as the effect of different vortex core orientations. We show that the vortex dynamics can be used to identify the core configuration, which is not directly accessible to x-ray microscopy because of its limited spatial resolution.

Figure 1

(a) Micromagnetic simulation showing $M_y(\overrightarrow{r})$ for a rectangular platelet ($5\mu \mathrm{m}\times 3\mu \mathrm{m}\times 20\mathrm{nm}$) containing a single cross-tie wall. (b) Sketch depicting the 90° Néel walls (solid lines, blue) and the 45° pseudo Néel walls (dashed lines, red). The vortex cores have an out of plane magnetization with positive ($u$ or ⊙) or negative ($d$ or $\otimes$) $z$ direction. Here we find $[udu]$.

Figure 2

Magnetization $M_y(\overrightarrow{r},\Delta t$) at characteristic delay times. Experimental results (top row) and difference images (third row) are compared to the corresponding simulation (second and fourth row).

Figure 3

Spatial distribution of the Fourier components of the magnetization $M_y(\overrightarrow{r})$ at characteristic frequencies showing amplitude (top) and phase (bottom: $\mathrm{\text{dark gray, blue online}}=0$, $\mathrm{\text{light gray, red online}}=\pi$).

Figure 4

(a) Trajectories of the two vortex (left and right, blue and green online) and the antivortex (center, red online) core displacements as extracted from micromagnetic simulations [18] ($\Delta t=0-16\mathrm{ns}$) (see text). The arrows indicate the sense of rotation for the core motion. (b) Horizontal core displacement from experiment (▪) and the three possible configurations [configuration (I) (dashed line), configuration (II) (solid line), and configuration (III) (dotted line)].