Interactions between atomic-scale skyrmions in 2D chiral magnets.

Skyrmions are topologically stable spin textures that hold great promise as information carriers in next-generation magnetic memories. Recently, skyrmions only a few nanometers in radius have been observed in several materials, opening a path toward ultrahigh-density integration. As a step toward improving their controllability, we numerically investigate interactions between atomic-scale skyrmions embedded in a uniformly magnetized background of two-dimensional chiral magnets, under tilted magnetic fields and magneto-crystalline anisotropy. We find that attractive potential wells, predicted for larger skyrmions from shape deformation, persist even at the atomic scale. As skyrmions shrink, the short-range repulsion is enhanced, while a tilted background magnetization increases the attraction at larger separations. Under strong magneto-crystalline anisotropy, a magnetic domain forms between skyrmions, producing a deep attractive well whose position and depth are nearly independent of skyrmion size. This shows that tightly bound skyrmion pairs with exchange-scale energies can exist even at the atomic scale. Furthermore, under the magneto-crystalline anisotropy, the atomic lattice potential increasingly affects smaller skyrmions, pinning them and suppressing motion despite attraction. These findings deepen understanding of inter-skyrmion interactions across scales and lay the groundwork for controlling atomic-scale skyrmions in future device technologies.