Collective Transport Properties of Driven Skyrmions with Random Disorder

We use particle-based simulations to examine the static and driven collective phases of Skyrmions interacting with random quenched disorder. We show that nondissipative effects due to the Magnus term reduce the depinning threshold and strongly affect the Skyrmion motion and the nature of the dynamic phases. The quenched disorder causes the Hall angle to become drive dependent in the moving Skyrmion phase, while different flow regimes produce distinct signatures in the transport curves. For weak disorder, the Skyrmions form a pinned crystal and depin elastically, while for strong disorder the system forms a pinned amorphous state that depins plastically. At high drives the Skyrmions can dynamically reorder into a moving crystal, with the onset of reordering determined by the strength of the Magnus term.

Figure 1

Real-space image of Skyrmions (dark red dots) driven through randomly arranged pinning sites (light blue dots) for a plastic flow phase at $F_p=0.03$ and $F_D=0.0125$. The trajectory of a single Skyrmion is highlighted, showing spiraling motions inside the pinning sites.

Figure 2

(a) Average Skyrmion velocity in the drive direction, $⟨V_{\text{drive}}⟩$ (open squares), and perpendicular to the drive, $⟨V_{\perp }⟩$ (filled circles), vs $F_D$ for a system with $F_p=0.03$. Inset: Hall angle $\theta$ vs $F_D$; dotted line is the result for the clean system. (b) Corresponding $⟨V_{\text{drive}}⟩$ (open squares) and the fraction of sixfold coordinated particles $P_6$ (filled triangles) vs $F_D$; the dashed line shows $⟨V_{\text{drive}}⟩$ for the clean system. A dynamical ordering transition into a moving crystal state occurs at $F_D\approx 0.03$.

Figure 3

Dynamical phase diagram for $F_D$ vs $F_p$ highlighting the different Skyrmion phases. PC: pinned crystal; PG: pinned amorphous glass; ML: moving liquid; MC: moving crystal. Circles: elastic depinning from PC to MC; squares: plastic depinning from PG to ML; triangles: dynamical ordering transition from ML to MC. Upper inset: structure factor $S(\mathbf{k})$ of Skyrmion positions in the MC state. Lower inset: $S(\mathbf{k})$ in the ML state.

Figure 4

(a) $⟨V_{\text{drive}}⟩$, $⟨V_{\perp }⟩$, and $\theta$ vs $F_p$ at $F_D=0.0075$. (b) Critical depinning force $F_c$ vs ${\alpha }_m/{\alpha }_d$ for $F_p=0.15$, 0.12, 0.09, 0.06, and 0.03 (top to bottom). (c) Phase diagram for $F_D$ vs ${\rho }_s$ at $F_p=0.03$, highlighting the transitions from PG to ML (circles), ML to MC (squares), and PC to MC (triangles). Inset: Depinning threshold (PG-ML transition line) for Magnus-dominated (circles) and damping-dominated (triangles) systems. (d) Phase diagram of $F_D$ vs ${\alpha }_m/{\alpha }_d$ for $F_p=0.03$, showing transitions from PG to ML (circles) and ML to MC (squares). Overdamped particles with ${\alpha }_m/{\alpha }_d=0$ form a moving smectic state (heavy line).