Analytical modeling of the interaction between skyrmions and extended defects

The performance of skyrmion-based spintronic devices can be greatly affected by the presence of defects in the materials. Here we develop an analytic model for describing the interaction between skyrmions and defects in ultrathin films focusing on the case of extended defects. The dynamics of skyrmions under the driving of in-plane polarized current is studied, considering several types of torques. The system is modeled with Thiele's equation in the complex plane and described with a reduced number of parameters. We start by considering a Gaussian-like interaction with point defects and extend the treatment to segment, line, and grid defects. Conditions for dynamic regimes of pinning, guiding, accelerating, or arranging skyrmions by defects are established and discussed. In particular, expressions for the threshold driven current density to pin or depin skyrmions in such defects, the position of the critical points, as well as the guiding conditions along long defects are found, analytically in some cases. This enables a deeper understanding of the parameter dependence of the skyrmion dynamics under the influence of defects. Micromagnetic simulations show qualitative agreement with the analytical treatment.