Fig. 1: Skyrmion creep at ultralow current densities. | Communications Materials

Fig. 1: Skyrmion creep at ultralow current densities.

From: Skyrmion lattice creep at ultra-low current densities

Fig. 1

a The dynamic response of skyrmions characterized by a competition of an external drive j (here j is an applied current density) with a pinning potential V(x) [see b] can be parametrized via its velocity v. This allows to identify three dynamic regimes that are illustrated in df and explained in the following. b Local pinning potential V(x) for different current densities. The applied current tilts the pinning potential. Above a critical current density jc, the energy barrier ΔU vanishes completely allowing the skyrmion to depin. At zero temperature T (blue line in a), this well-defined depinning threshold jc thus defines two dynamic regimes, where the skyrmion is either pinned or exhibits current-driven motion. In contrast, for finite T [red curve in a], the tilted potential promotes thermal activation of skyrmions already for \({j}_{{\mathrm{c}}}^{* }\,\,< \,\,{j}_{{\mathrm{c}}}\), resulting in a third regime defined by creep. Here \({j}_{{\mathrm{c}}}^{* }\) is the threshold when skyrmions start to depin from the local pinning center, but remain globally pinned. c A skyrmion lattice (yellow dots) pinned to a few pinning centers (blue shaded areas) is shown. The skyrmion lattice is distorted to accommodate the pinning center, with a characteristic length ξ known as the Larkin length. d For a small current density j jc a thermally activated single skyrmion follows an orbital trajectory around the pinning site because of the Magnus force. e For larger currents j < jc creep may occur. Here the skyrmion spends most of the time orbiting the pinning potential. Further, when the skyrmion escapes from one pinning center due to thermal fluctuations, it will immediately be trapped by a nearby pinning center, resulting in creep motion. f For large current densities j > jc, the skyrmion lattice flows freely through the pinning centers and the lattice order is improved as has been previously observed15.

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