Antivortex domain walls observed in permalloy rings via magnetic force microscopy

Magnetic domain walls in patterned permalloy ring elements of different widths and thicknesses have been probed by magnetic force microscopy and micromagnetic simulations. We report the experimental observation of antivortex structures in single-layer magnetic rings, previously only theoretically predicted. Furthermore, vortex-antivortex chains are observed on occasion in wider rings that prefer a circulating flux closure state. It is possible that they are pinned transient states of the relaxation path from the magnetically saturated to the circulating flux closure state. Similar tendencies are seen in micromagnetic simulations implying that vortex-antivortex pair nucleation and annihilation are fundamental parts of the said relaxation. Finally we present a phase diagram of different domain-wall configurations as a function of ring width and thickness.

Figure 1

Schematic diagrams showing (a) $V^{-}$ and (b) $V^{+}$ structure. In the center of each configuration the magnetization tilts out of plane.

Figure 2

(Color online) SEM micrograph of a $\left(w,L\right)=\left(500\text{nm},60\text{nm}\right)$ ring array with the coordinate system used in the text marked out.

Figure 3

(Color online) (a) Experimental MFM image of $2V^{+}$ walls in a $\left(w,L\right)=\left(400\text{nm},60\text{nm}\right)$ ring, $h_z=55\text{nm}$. (b) Computed 2D magnetization distribution with core polarizations marked out. (c) Computed MFM contrast of (b), $h_z=55\text{nm}$, ${\delta }_z=40\text{nm}$.

Figure 4

(Color online) (a) Experimental MFM image of a $\left(w,L\right)=\left(400\text{nm},60\text{nm}\right)$ ring with a $V^{+}{V}^{-}{V}^{+}$ configuration on the top part and a $2V^{+}$ wall on the bottom part, $h_z=35\text{nm}$. (b) Corresponding 2D magnetization distribution superimposed on the computed MFM contrast (2D) $\left(h_z=35\text{nm},{\delta }_z=40\text{nm}\right)$. (c) Blow up of the $V^{+}{V}^{-}{V}^{+}$ structure in (a). (d) Computed MFM contrast from 3D calculation ($h_z=35\text{nm}$ and ${\delta }_z=40\text{nm}$) with core polarizations marked out assigned to (c). (e)–(g) The magnetization distribution around the vortex/antivortex cores of the $V^{+}{V}^{-}{V}^{+}$ structure on the top, middle, and bottom plane, respectively, of the 3D calculation.

Figure 5

(Color online) Experimental MFM images of $V^{+}{V}^{-}$ chains in (a) $\left(w,L\right)=\left(600\text{nm},50\text{nm}\right)$. (b) $\left(w,L\right)=\left(700\text{nm},40\text{nm}\right)$. (c) $\left(w,L\right)=\left(700\text{nm},50\text{nm}\right)$. (d) Snapshot of a simulated magnetization configuration in the ring in (c) during relaxation to the CF state with its computed MFM contrast, discretization: $4\times 4\times L{\text{nm}}^3$.

Figure 6

(Color online) Observed states as a function of $\left(w,L\right)$.