  Single magnetic skyrmions are localized whirls in the magnetization with an
integer winding number. They have been observed on nano-meter scales up to room
temperature in multilayer structures. Due to their small size, topological
winding number, and their ability to be manipulated by extremely tiny forces,
they are often called interesting candidates for future memory devices. The
two-lane racetrack has to exhibit two lanes that are separated by an energy
barrier. The information is then encoded in the position of a skyrmion which is
located in one of these close-by lanes. The artificial barrier between the
lanes can be created by an additional nanostrip on top of the track. Here we
study the dependence of the potential barrier on the shape of the additional
nanostrip, calculating the potentials for a rectangular, triangular, and
parabolic cross section, as well as interpolations between the first two. We
find that a narrow barrier is always repulsive and that the height of the
potential strongly depends on the shape of the nanostrip, whereas the shape of
the potential is more universal. We finally show that the shape-dependence is
redundant for possible applications.
