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Skyrmion is a topologically protected spin texture excited in magnetic thinfilms. The radii of skyrmions are typically 10-100 nm. Because of the size, theskyrmion is expected to be a candidate for memory and novel-device usages. Torealize the futuristic devices that will be using the skyrmion circuit, thetracks which guide the motion of skyrmions are needed. The tracks patternedwith differences in the magnetic-anisotropy energy are well-paved without apotential pocket, whereas the tracks carved out of magnetic films have thepotential pockets at corners due to the demagnetizing field. Therefore, thetracks patterned with the magnetic anisotropy plays a key role in making theskyrmion circuits. The experiment along this idea has been conducted for thehub and bent tracks. However, we have little known the motion of skyrmions inthese tracks. This work aims to identify the forces acting between skyrmionsand walls of the tracks. The static force on a skyrmion can be expressed asminus the gradient of the potential energy caused by the magnetic-anisotropyundulation. The potential can be estimated numerically, modeling the shape ofskyrmions with their radii and domain wall widths. We find that the forcesdepend not only on the distance from the wall but also on the shape ofskyrmions. We have also performed micromagnetic simulations where the Magnusforce and the acceleration by the magnetic-anisotropy gradient are taken intoaccount as well as the force by the walls. The simulation results show goodagreement with those calculated from the modeled skyrmions.

Skyrmion confinement and dynamics in tracks patterned with magnetic anisotropy: theory and simulations