Angular dependence of vortex-annihilation fields in asymmetric cobalt dots

Shape asymmetries in nominally circular nanomagnets provide a potential means for vortex chirality control. However, in realistic arrays their effects are challenging to probe since asymmetric magnetization reversal processes are often averaged to include distributions over all angles. Here we investigate how shape asymmetry influences the vortex reversal in arrays of submicron edge-cut Co dots. We find that the vortices can be manipulated to annihilate at particular sites under different field orientations and cycle sequences. The vortex-annihilation field and degree of chirality control depend sensitively on the angular position of the applied field relative to the flat edge of the dots. For small angles, the major loop annihilation field is significantly larger than that found from the half loop and the vortex chirality can be well controlled. At intermediate angles the chirality control is lost and an interesting crossover in the annihilation field is found: the half loop actually extrudes outside of the major loop, exhibiting a larger vortex-annihilation field. At large angles the annihilation fields along major and half loops become degenerate.

Figure 1

(Color online) (a) SEM image of arrays of Co dots with a horizontal flat edge. The inset shows the pattern used by the e-beam writer to create each dot and the $0°$ orientation of the sample. PEEM images of a typical portion of (b) the edge-cut dots and (c) reference circular dots at zero field after saturating the dots to the right. All dots are in the single-vortex state. The chirality is controlled in (b), as shown in the inset, and random in (c).

Figure 2

(Color online) (Left) Measured major and half loops using MOKE, and (Right) simulated major and half loops with the applied field at (a, d) $0°$, (b, e) $60°$, and (c, f) $90°$ relative to the flat edge of the dots.

Figure 3

(Color online) (a) Measured FORC’s and (b–d) FORC distributions with the applied field at (b) $0°$, (a) and (c) $60°$, and (d) $90°$ relative to the flat edge of the dots. Circles in (b) highlight the three regions of FORC features. Inset in (c) shows a zoom-in view of the negative-positive-negative set of features.

Figure 4

(Color online) Angular dependence of the annihilation fields from both major (solid squares) and half loops (open circles) extracted from (a) MOKE measurements and (b) micromagnetic simulations. Error bars are included to indicate the field spacing of the measurements and the lines are guides to the eye. The locations of the simulated vortex core annihilation sites are shown in (c). Lines are used to highlight the annihilation sites for each angular position.

Figure 5

(Color online) Simulated hysteresis loops for a $5\times 5$ array (blue triangles), $3\times 3$ array (red open circles), and single dot (black squares).