Fig. 3: Schematics of skyrmion pinning in a nonflat energy landscape.

a The 3D surface schematically shows the magnetization of a skyrmion. The dashed line plot besides shows the negative energy density -w_sk of this skyrmion along a profile as shown by the purple plane. It indicates that the (exchange-)energy density is most important in the domain walls delineating the skyrmion. The bottom part shows an exemplary schematic of a non-flat energy landscape in blue exhibiting three distinct minima. The peaks in energy density of the specific skyrmion match two of the valleys which leads to a favorable state of low energy in the region shaded in green as indicated by the dashed purple line. Other states as in the case of the dotted purple line yield a higher energy and are therefore unfavorable to be pinned at this position as indicated by the red-shaded region. b shows a similar scenario for a smaller skyrmion. Here, a minimal energy is achieved at a different position where the skyrmion energy density best matches the energy landscape (dashed purple line in the favorable green region). Hence, the position which was favorable in (a) is now in the unfavorable red region.