Robust edge states in magnetic domain-wall racetrack

TL;DR

This paper demonstrates that magnetic domain-wall racetracks can host topologically protected edge states, enabling robust DW oscillations that are insensitive to imperfections, and proposes a method to accurately measure pinning potential characteristics.

Contribution

The study maps DW dynamics to a topological model, revealing robust edge states and providing a new approach to quantify pinning potentials in racetrack devices.

Findings

Identification of topologically distinct phases in DW racetracks.

Existence of robust edge states at racetrack ends.

In-gap DW oscillation frequency depends only on geometry.

Abstract

Controllable artificial pinning is indispensable in numerous domain-wall (DW) devices, such as memory, sensor, logic gate, and neuromorphic computing hardware. The high-accuracy determination of the effective spring constant of the pinning potential, however, remains challenging, because the extrinsic pinning is often mixed up with intrinsic ones caused by materials defects and randomness. Here, we study the collective dynamics of interacting DWs in a 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. 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. We propose to accurately quantify the spring coefficient that equals the square of the robust DW frequency multiplied by its constant mass. Our findings suggest as well that the DW racetrack is an ideal platform to study the topological phase transition.