Current-driven domain wall ratchet in a nanomagnet with functionally graded Dzyaloshinskii-Moriya interaction

We develop a concept of functionally graded Dzyaloshinskii-Moriya interaction, which provides novel ways of efficient control of the magnetization dynamics. Using this approach we realize the ratchet motion of the domain wall in a magnetic nanowire driven by spin polarized current with potential applications in magnetic devices such as race-track memory and magnetic logical devices. By engineering the spatial profile of Dzyaloshinskii-Moriya parameters we provide a unidirectional motion of the domain wall along the wire. We base our study on phenomenological Landau-Lifshitz-Gilbert equations using a collective variable approach [1]. In effective equations of motion the functionally graded Dzyaloshinskii-Moriya interaction appears as a driving force, which can either suppress the action of the pumping by the current or can reinforce it. All analytical predictions are well confirmed by numerical simulations. \\ [1] K. V. Yershov et al., Phys. Rev. B {\bf 93}, 094418 (2016).