Hopfions, Torons, and Skyrmions Interacting with Nanostructure Arrays for Topological Diodes and Ratchets

Using atomistic simulations, we consider the motion of skyrmions in two-dimensional systems and Hopfions in three-dimensional systems interacting with various kinds of nanostructured arrays. For Hopfions moving through a constriction, as a function of constriction spacing and current we find a pinned state, a state in which the Hopfion slows down but can move through the constriction, and a state in which the Hopfion transitions to a toron. We also show that for certain asymmetric arrays, a Hopfion ratchet effect can be achieved under ac driving. For skyrmions, we propose a new type of channel geometry with alternating asymmetry that can generate a novel magnetic diode effect that is analogous to the current-induced diode. In this geometry, there is no diode effect for reversed currents at a fixed magnetic field, but there is a nonreciprocal response or diode effect for reversed magnetic fields at a fixed current. This magnetic diode arises due to the Magnus force causing the skyrmion to preferentially interact with one side of the channel, which reverses for reversed fields.