Figure 1

Scanning electronic microscope (SEM) images of vortex patterns obtained after field cooling to 1.8 K in (a) macroscopic film ($H=30\mathrm{Oe}$), (b) part of an array containing $\sim 2\mu \mathrm{m}$ dots ($H=40\mathrm{Oe}$), (c) vortex configurations in disks with $d=2.3$, 3.4, and $5.0\mu \mathrm{m}$ obtained in the same experiment at $H=40\mathrm{Oe}$. Scale bars in all images correspond to $5\mu \mathrm{m}$.Reuse & Permissions

Figure 2

Vorticity $L$ vs normalized flux through disk area, $\Phi /{\Phi }_0$. Data points show measurements for individual disks rather than a statistical average. Different symbols correspond to different experiments. The inset shows normalized excess flux $\delta \Phi /{\Phi }_0=(\Phi -{\Phi }_{0}L)/{\Phi }_{0}L$ (see text). The dashed line shows a fit to the function $\delta \Phi /{\Phi }_0=(a+bL)/(1+cL)$ (see 3). The corresponding fit for $\Phi /{\Phi }_0$ vs $L$ is shown by the dashed line in the main panel.Reuse & Permissions

Figure 3

(a) Histogram of different vortex states observed in the same experiment ($H=60\mathrm{Oe}$) on disks with $d=3\mu \mathrm{m}$. SEM images of the corresponding states are shown as insets. (b) Evolution of vortex states with increasing $\Phi$ (arrows are guides to the eye). Different symbols correspond to different shell configurations: ◆, states $(L)$; ○, states $(1,L-1)$; ●, states $(2,L-2)$; ◇, states $(3,L-3)$. SEM images of some of the states are shown as insets: left to right states (3), (4), $(1,5)$, (6), $(1,6)$, and (3,8).Reuse & Permissions

Figure 4

Number of vortices populating different shells as a function of $L$. Two or more different states were found for some vorticities (see text), e.g., $(1,7,14)$ and $(2,7,13)$ for $L=22$, $(1,5,12,17)$, $(1,5,11,18)$, $(1,6,11,17)$, and $(1,6,12,16)$ for $L=35$, etc. Open circles show numbers of vortices in a shell corresponding to the configurations that we could clearly identify as metastable. Arrows indicate magic numbers, i.e., $L$ corresponding to closed shell configurations, just before the appearance of the 2nd, 3rd, and 4th shell. The first magic number, $L=5$, corresponds to the stable state (5) rather than the metastable state $(1,4)$. Insets: SEM images of vortex states with different numbers of shells: 1-shell state (5) $[L=5]$; 2-shell state $(1,7)$ $[L=8]$; 3-shell state $(1,5,11)$ $[L=17]$; 4-shell state $(1,5,11,18)$ $[L=35]$.Reuse & Permissions