  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.
