Precise positioning of magnetic solitons requires controllable artificial pinning, while the accurate determination of the pinning profile remains a challenge. Here, we propose a topological solution to this problem. Taking the domain wall (DW) as a representative example, we study the collective dynamics of interacting DWs in a magnetic racetrack with pinning sites of alternate distances. By mapping the governing equations of DW motion to the Su-Schrieffer-Heeger model and evaluating the quantized Zak phase, we predict two topologically distinct phases in the racetrack. A robust edge state emerges at either one or both ends depending on the parity of the DW number and the ratio of alternating intersite lengths. We show that the in-gap DW oscillation frequency has a fixed value which depends only on the geometrical shape of the pinning notch, and is insensitive to device imperfections and inhomogeneities. The spring coefficient of the pinning potential can be quantified as the square of the robust DW frequency multiplied by its constant mass. Our findings pave the way to determining the pinning potential with high accuracy for generic magnetic solitons and suggest as well that the magnetic soliton-based racetrack is a unique playground to study topological phase transitions.

• Received 4 October 2020
• Revised 25 January 2021
• Accepted 17 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.054438