Capturing of a magnetic skyrmion with a hole

Magnetic whirls in chiral magnets, so-called skyrmions, can be manipulated by ultrasmall current densities. Here we study both analytically and numerically the interactions of a single skyrmion in two dimensions with a small hole in the magnetic layer. Results from micromagnetic simulations are in good agreement with effective equations of motion obtained from a generalization of the Thiele approach. Skyrmion-defect interactions are described by an effective potential with both repulsive and attractive components. For small current densities a previously pinned skyrmion stays pinned whereas an unpinned skyrmion moves around the impurities and never gets captured. For higher current densities, j(c1) < j < j(c2), however, single holes are able to capture moving skyrmions. The maximal cross section is proportional to the skyrmion radius and to root alpha, where a is the Gilbert damping. For j > j(c2) all skyrmions are depinned. Small changes of the magnetic field strongly change the pinning properties; one can even reach a regime without pinning, j (c2) = 0. We also show that a small density of holes can effectively accelerate the motion of the skyrmion and introduce a Hall effect for the skyrmion.