Skyrmion motion induced by spin-Hall current in constrained geometries

Magnetic skyrmions are topologically protected spin textures typical of chiral magnets characterized by a special kind of exchange interaction known as Dzyaloshinkii-Moriya interaction (DMI). In the last years growing interest has been addressed to the study of these topological defects both from a fundamental point of view and for its several technological applications like for instance their usage as information carriers [1]. Great attention has been also given to skyrmion nucleation, stability and motion in confined magnetic systems under the influence of a spin-current [2,3]. Recently, the effect of confinement has been studied in the presence of spin-polarized current [2], but there are not yet studies focusing on the skyrmion motion driven by SHE in constrained geometries. Here, we solve analytically Thiele’s equation in the presence of spin-Hall effect (SHE) with no external field and by taking into account confinement. The spin-Hall current injected in the heavy metal along the x direction (see Fig.1 (a)) combined with the interfacial DMI favors the Néel skyrmion (hedgehog-like) nucleation in a thin magnetized stripe. We model confinement effects by introducing a potential V(r) which arises at the boundaries of the magnetic stripe. This potential can be thought of as a positive barrier having a repulsive nature associated to the static magnetization rotation at the stripe borders. The Nèel skyrmions is interpreted as a quasi-particle which interacts repulsively with this barrier. As a result, its trajectory is deviated