We present a general approach for studying the dynamics of domain walls in biaxial ferromagnetic stripes with functionally graded Dzyaloshinskii–Moriya interaction (DMI). By engineering the spatial profile of the DMI parameter, we propose the concept of a diode, which implements the filtering of domain walls of a certain topological charge and helicity. We base our study on the phenomenological Landau–Lifshitz–Gilbert equations with additional Zhang–Li spin-transfer terms using a collective variable approach. In the effective equations of motion, the gradients of DMI play the role of a driving force, which competes with the current driving. All analytical predictions are confirmed by numerical simulations.
Here, we consider the spatial distribution of the DMI strength without the change of sign, i.e., .
The velocity of DW is calculated as , where is extracted from numerical simulations and is a time of simulation.
The principle of operation of our diode is based on the creation of a potential barrier for DWs of a certain helicity. This makes it similar to the conventional semiconductor diodes.