Electrical probing of field-driven cascading quantized transitions of skyrmion cluster states in MnSi nanowires.

Magnetic skyrmions are topologically stable whirlpool-like spin textures that offer great promise as information carriers for future spintronic devices. To enable such applications, particular attention has been focused on the properties of skyrmions in highly confined geometries such as one-dimensional nanowires. Hitherto, it is still experimentally unclear what happens when the width of the nanowire is comparable to that of a single skyrmion. Here, we achieve this by measuring the magnetoresistance in ultra-narrow MnSi nanowires. We observe quantized jumps in magnetoresistance versus magnetic field curves. By tracking the size dependence of the jump number, we infer that skyrmions are assembled into cluster states with a tunable number of skyrmions, in agreement with the Monte Carlo simulations. Our results enable an electric reading of the number of skyrmions in the cluster states, thus laying a solid foundation to realize skyrmion-based memory devices.