Figure 1

(a) Topography (STM image) of a typical region of the $W$ deposited film where red dashed lines mark small linear features at the surface. The lateral size of the image is of 260 nm, with a corrugation of 5 nm. Tunneling conductance is of $3\mu \mathrm{S}$, with 2.5 mV bias voltage. In (b) we show the initial (upper panel) and final (bottom panel) images of a series composed of 33 vortex images taken, in the area with the topography shown in (a), at 100 mK when increasing the magnetic field. The final image of the series shows the trajectories of four vortices, highlighted by colored points. (c) The trajectories of 17 vortices are represented in the $x\mathrm{\text{−}}y$ plane of the topography image (a). These 17 vortices stay within the scanning window during the whole sequence. Other vortices, not highlighted, jump in and out of the scanning window during the sequence. Lines joining points in (b) and (c) are guides to the eye. See Ref. 25 for more details.Reuse & Permissions

Figure 2

(a) Histogram of the angles formed by the vector joining the initial and final vortex positions and the $x$ axis of the image (see Fig. 1). The inset shows schematically the overall vortex motion, towards an angle of around $-12°$ with respect to the $x$ axis, and the maximum overall deviations found with respect to this direction. (b) Histogram of the size of the displacements of vortices $\delta {\ell }_i$, as defined in the text. Most frequent displacements $\delta {\ell }_i$ are of a few nm.Reuse & Permissions

Figure 3

Accumulated length $\delta l=\sum _{i=1}^{i=n}\delta l_i$ (see text) vs magnetic field of four vortex trajectories. The color code is the same as in Fig. 1c. In the upper left inset, the Fourier transform of the relative displacement $\delta l_i$ as a function of the accumulated length $\delta l$ for one vortex (the one with blue points in the figure) is shown. An arrow marks the peak found at the inverse of $a_0=40\mathrm{nm}$. The lower bottom inset shows the histogram of the inverse of the position of this peak in the Fourier transforms of the accumulated lengths of many vortex trajectories. The histogram peaks at the expected intervortex distance $a\sim 43–46\mathrm{nm}$.Reuse & Permissions

Figure 4

In (a) we show the accumulated length $\delta l$ (see text and Fig. 3) of a set of vortex trajectories in a short magnetic field interval. Color code for identifying each vortex trajectory is the same as in Figs. 1, 3. Dotted lines mark the magnetic fields where we have taken the images shown in (b). There, we show vortex arrangements at 1.112 T, 1.120 T, 1.128 T and 1.132 T. Vortices in the central bundle are marked by points and have been Delaunay triangulated. Green, blue, and orange points show vortices with, respectively, five, six, and seven nearest neighbors. Red dashed lines mark the pinning centers, as in Fig. 1a.Reuse & Permissions