Steady motion of 80-nm-size skyrmions in a 100-nm-wide track

Magnetic skyrmions are nanoscale, topologically protected spin textures (topological charge Q = ∫(∇×n)·n dxdy) attractive for racetrack-like spintronic devices due to their small size (3–150 nm), stability, and low current thresholds for motion via spin transfer torques. Practical implementation requires stable, controllable motion along nanotracks, but two key challenges persist: (1) realizing controlled motion of nanometer-sized skyrmions in ultrathin (sub-100 nm) nanostripes compatible with high-density microelectronics, and (2) eliminating the skyrmion Hall effect (SHA) to avoid edge annihilation from the Magnus force. Prior work provided numerical insights into confined geometries, but experimentally only larger (>hundreds of nm) skyrmions or small skyrmions moving at an angle had been demonstrated in nanostripes. This study engineers a 100 nm-wide FeGe nanostripe and uses in situ electrical contacting with Lorentz TEM to observe and control the motion of individual 80 nm skyrmions driven by sub-10 ns current pulses, achieving straight, steady, one-dimensional motion with effectively vanishing SHA.

Past studies established skyrmion formation and dynamics in chiral magnets and thin films, including low-current motion of skyrmion lattices and room-temperature stabilization in multilayers. Numerical works predicted current-driven dynamics and confinement effects in sub-100 nm tracks, including conditions for isolated skyrmion stability (w/Λ ~1.2). Experimentally, nanotrack demonstrations have largely involved skyrmions a few hundred nanometers in size or small skyrmions exhibiting nonzero SHA. Considerable effort has targeted SHA suppression using synthetic antiferromagnetic skyrmions, ferrimagnetic systems near compensation, antiferromagnetic skyrmions, and skyrmionium states, but complete elimination of SHA had not been realized experimentally. The present work builds on these foundations by implementing ultrathin FeGe nanostripes with direct in situ observation and control, aiming to demonstrate SHA-free, steady motion of ultrasmall skyrmions.

Experimental: FeGe nanostripe devices (~10 μm length, ~100 nm width, ~150 nm thickness along the TEM beam direction) were fabricated via FIB on a customized electrical chip with four Au electrodes. Carbon protection layers were deposited to preserve sharp edges and minimize damage; amorphous side layers were <3 nm (confirmed by HRTEM/EELS). Pt contacts connected the nanostripe to Au electrodes; overall device resistance ~1000 Ω dominated by contact resistance. In situ Lorentz TEM (Thermo Fisher Talos F200X, 200 kV, objective off) at 95 K used a Gatan cryotransfer holder enabling electrical pulses and calibrated out-of-plane magnetic fields. Current pulses (frequency 1 Hz) were applied along the stripe; skyrmions were nucleated via Joule heating under moderate magnetic field. Imaging used Lorentz contrast to track skyrmion positions. Displacements and velocities were extracted from trajectories using a Python GUI, typically using 15–30 pulses per measurement over total displacements of 3–6 μm; velocities from displacement–time fits with error bars from slope fits. COMSOL simulations estimated local heating vs current density and pulse duration to ensure operation below Curie temperature for j–v measurements. Magnetic fields were optimized (often 234 mT) to widen the stable current window for motion; temperature fixed at 95 K for stability of the holder. Micromagnetic simulations: Using MicroMagnetic.jl on GPU for a 100 nm-wide, 150 nm-thick track with periodic boundary in x, cell size 2×2×2 nm^3. Energy terms included exchange (A=3.25×10^−12 J/m), bulk DMI (D=5.83×10^−4 J/m^2), Zeeman (H=150 mT), and anisotropy (Ku for disorder). Material parameters: Ms=3.84×10^5 A/m, α=0.0167, β=0.1336, spin polarization P=0.7 for effective spin velocity vs. Disorder/pinning modeled as spatially distributed uniaxial anisotropy sites (K=2×10^5–2×10^6 A/m^3) generated via Poisson disc sampling. Current pulses (e.g., τ=5 ns) were applied to compute trajectories, j–v curves, transient motion, energy vs time, and annihilation thresholds. The vertical confinement potential from edge twists was extracted from total energy to approximate a harmonic potential U(Y)=kY^2, enabling analysis of inertia and stability barriers.

• Demonstration of steady, straight, current-driven motion of individual ~80 nm skyrmions in a 100 nm-wide FeGe nanostripe with effectively vanishing skyrmion Hall angle (SHA), confirmed by Lorentz TEM.
• Motion achieved with ultrashort pulses down to τ=2 ns; at τ=2 ns, maximum velocity v≈90 m/s. For τ=5 ns, flow regime linear up to j≈8.69×10^10 A/m^2 with v≈50 m/s; above this, Joule heating can cause instability or annihilation.
• Critical current density for depinning at τ=5 ns: jc≈4.24×10^10 A/m^2; jc decreases exponentially with increasing τ: jc≈7.89×10^10 A/m^2 at 2 ns and ≈3.67×10^10 A/m^2 at 8 ns. Shorter pulses below 2 ns increase pinning likelihood.
• Linear j–v relation in flow with slope Δvx/Δj ≈ 8.0×10^−10 m^3/As, implying high efficiency; interpreted via Thiele equation as bβ/α≈8.0×10^−10 m^3/As (with b=gL μB Ms^−1 P), larger than some theoretical expectations, enabling high speed at low current in 1D confinement.
• Magnetic field dependence: jc first decreases then increases with field due to crossover from edge-dominated pinning (weakened with field) to disorder-dominated pinning as skyrmion size shrinks at higher fields.
• Micromagnetic simulations reproduce straight trajectories without apparent SHA, j–v depinning and flow regimes, and transient dynamics: during a 5 ns pulse at j=5.7×10^10 A/m^2, horizontal displacement ~40 nm with slight vertical (~5 nm), followed by inertia-driven forward motion after pulse-off adding ~85 nm before saturation.
• Edge twist induces a vertical confining potential approximated as harmonic U(Y)=kY^2, creating an energy barrier ΔE that stabilizes skyrmions and yields inertia. Annihilation at the edge requires sufficiently long pulses; at j=1.4×10^11 A/m^2, critical τ≈21 ns. Experimental operation was within a safe pink region (current–pulse window) where thermal limits, not vertical displacement, set the upper current bound.
• Skyrmion ensembles: two isolated skyrmions, pairs, and chains (e.g., 7 skyrmions) move steadily and collinearly with similar j–v characteristics; velocities nearly independent of skyrmion number. Inter-skyrmion interactions can cause non-synchronous motion at small spacing; adequate spacing or chain formation yields coherent, translational motion.
• COMSOL estimates: at τ=5 ns, j=13×10^10 A/m^2 raises local T to ~260 K (near TC=278 K). j–v measurements were made below j=10×10^10 A/m^2 giving Tmax 180 K; at j=7×10^10 A/m^2, ΔT40 K, indicating modest Joule heating in the linear regime.

Confining ~80 nm skyrmions within a 100 nm-wide FeGe nanostripe enforces one-dimensional motion along the track. The magnetic edge twists create a vertical confining potential that counters the Magnus force, effectively nullifying the skyrmion Hall effect and preventing edge-driven annihilation during short pulses. This confinement, together with optimized pulse durations, yields efficient, linear current–velocity behavior at relatively low current densities. The depinning-to-flow transition and jc’s exponential dependence on pulse duration highlight the role of disorder-induced pinning and its interplay with pulse width; shorter pulses require larger j to overcome pinning centers with characteristic spatial extent. Field tuning modifies edge versus disorder pinning, explaining the nonmonotonic jc(B). Simulations corroborate the experimental j–v trends and reveal inertia arising from relaxation in the edge-induced potential after pulse termination, providing a mechanistic explanation for additional forward displacement. Device-wise, the large j–v slope (bβ/α) implies low energy cost per shift event, and the observed stable motion of skyrmion chains with number-independent velocities suggests scalability toward racetrack-like memories with high linear density. Thermal effects, rather than vertical-displacement-induced annihilation, set the upper operating current bound, guiding safe operational windows.

This work demonstrates controlled, steady, straight motion of ~80 nm skyrmions in an ultrathin 100 nm-wide FeGe nanostripe using nanosecond electrical pulses, with an effectively vanishing skyrmion Hall angle. Linear current–velocity relations in the flow regime, high velocities at low currents (up to ~90 m/s at 2 ns), and robust operation across single skyrmions, pairs, and chains validate feasibility for skyrmion-based racetrack devices. Micromagnetic simulations attribute the stability and inertia to a vertical edge-induced harmonic potential and quantify safe operating windows relative to annihilation thresholds. These results address long-standing challenges of SHA and geometric confinement, offering a practical pathway toward device implementation. Future efforts could target room-temperature operation, multilayer architectures, further reduction of pinning through materials engineering, and circuit-level demonstrations of reliable, high-density, low-energy skyrmion shift registers.

Experiments were performed at 95 K; room-temperature operation was not demonstrated. Joule heating imposes an upper limit on current density in practice, constraining the operational window despite high theoretical vertical-displacement thresholds. The stable j–v relation was limited to certain magnetic fields; at other fields, the usable current range was narrower and a stable j–v curve was not established. Pinning from material disorder influences jc, pulse-width dependence, and can induce non-synchronous motion for closely spaced skyrmions, indicating sensitivity to sample quality. The nanostripe thickness (~150 nm) was chosen for fabrication robustness rather than fully optimized for dynamics, and ultra-thinner membranes risk deformation during preparation.