Electrical Control of Skyrmion Density via Skyrmion-Stripe Transformation

A comprehensive understanding of numerous electrical current-induced magnetic texture transformations is necessary to ensure the reliability of skyrmionic devices during operation. Here, we present an experimental study of unipolar current-induced skyrmion-stripe transformation in a $\mathrm{Pt}/\mathrm{Co}/\mathrm{Fe}/\mathrm{Ir}$ magnetic bilayer. High current density pulses induce a densely packed skyrmion state, as commonly reported in many other studies, and skyrmion nucleation is expected to lessen with diminishing current density. However, at a lower current density where pinning effects become significant, a regime where current-induced skyrmion annihilation and skyrmion-to-stripe transformation is observed. Kerr imaging reveals that, under a low current pulse, the rapidly expanding stripes crowd out and annihilate the skyrmions before quickly decaying and leaving behind a sparse skyrmion population. Our findings establish an additional requirement of a minimum operating current density in the design of skyrmionic devices to avoid unintended skyrmion deletion. On the other hand, this skyrmion annihilation can also be strategically employed as a technique for skyrmion density control using solely current modulation in future skyrmionic devices.

Figure 1

Hall resistance measurement of the relaxation process of current-induced magnetization transformation. (a) Measurement setup consisting of a Hall cross with widths of 20 and 10 µm. Electrical currents are injected through the wider Hall bar while Hall resistance $R_{\mathrm{Hall}}$ is measured across the narrow bar. (b) Time evolution of Hall resistance change $\mathrm{\Delta }{R}_{\mathrm{Hall}}$ after 30 current pulses of 10 ms are injected for current densities ranging from 1.11 × 10¹⁰ A/m² to 7.75 × 10¹⁰ A/m². Error bars are omitted from the graph for clarity, and the data have a standard deviation of 6 mΩ or less.

Figure 2

MOKE images of current-induced magnetic states and their relaxation process back to equilibrium. (a) Magnetization state at equilibrium. After the injection of 2.21 × 10¹⁰ A/m² current pulses, the skyrmions are transformed into a mixed state of stripes and skyrmions at (b) t = 0.4 s. Magnetization state at (c) t = 12.1 s and (d) t = 41.4 s after current injection. (e) Magnetization state at equilibrium with skyrmion density of 0.645 µm⁻². After the injection of 7.20 × 10¹⁰ A/m² current pulses, a state with a higher skyrmion density of 0.761 µm⁻² is observed at (f) t = 0.4 s. The high skyrmion density state shows a gradual reduction in density at (g) t = 12.1 s and (h) t = 41.3 s, with skyrmion density of 0.743 µm⁻², and 0.709 µm⁻², respectively. The states in (d) and (h) eventually to return to the equilibrium state.

Figure 3

Current-induced stripe formation dependence on pulse duration. (a) The plot of maximum $\mathrm{\Delta }{R}_{\mathrm{Hall}}$ during the relaxation process after low current pulse injection against pulse duration. The inset provides the plot of Hall resistance change $\mathrm{\Delta }{R}_{\mathrm{Hall}}$ over time for pulse durations ranging from 1 to 10 ms. Error bars correspond to the standard deviation. MOKE images are taken immediately after current pulse injections with a pulse duration of (b) 5 ms, (c) 10 ms, and (d) 50 ms. (e) Relative pinning potential along the wire obtained from 100 images of skyrmion-to-stripe transformation.

Figure 4

Current-induced magnetization state dependence on the out-of-plane magnetic field. MOKE images of their equilibrium and current-induced magnetization state at $H_Z$ of (a) 0.0 Oe, (b) 10.1 Oe, (c) 13.4 Oe, (d) 16.8 Oe, and (e) 20.1 Oe. (f) The plot of the initial current-induced state’s $\mathrm{\Delta }{R}_{\mathrm{Hall}}$ and its corresponding maximum $\mathrm{\Delta }{R}_{\mathrm{Hall}}$ during relaxation against $H_Z$. Error bars correspond to the standard deviation.

Figure 5

Demonstration of electrical control of skyrmion density. The plot of $\mathrm{\Delta }{R}_{\mathrm{Hall}}$ as a measure of skyrmion density over time due to alternating pulses of low (2.21 × 10¹⁰ A/m²) and high (5.51 × 10¹⁰ A/m²) current densities.