Characterizing Skyrmion Flow Phases with Principal Component Analysis

TL;DR

This work addresses the challenge of characterizing nonequilibrium flow phases of magnetic skyrmions moving over quenched disorder. It introduces a position–velocity based PCA (PVB PCA) that uses an asymmetric feature vector derived from distances to neighbors and their speeds, enabling identification of multiple dynamical phases as a function of drive and Magnus-to-damping strength. The analysis recovers known phases (pinned, channel flow, moving fluids, moving crystals) and reveals new disordered states, moving liquid and cluster liquid, with PCA order parameters correlating to transport curves, defect density, and skyrmion Hall angle. The approach provides a general framework for detecting disordered dynamical phases in driven nonequilibrium systems and can be extended to other time-dependent contexts.

Abstract

Principal component analysis (PCA) is a powerful method that can identify patterns in large, complex data sets by constructing low-dimensional order parameters from higher-dimensional feature vectors. There are increasing efforts to use space-and-time-dependent PCA to detect transitions in nonequilibrium systems that are difficult to characterize with equilibrium methods. Here, we demonstrate that feature vectors incorporating the position and velocity information of driven skyrmions moving through random disorder permit PCA to resolve different types of disordered skyrmion motion as a function of driving force and the ratio of the Magnus force to the dissipation. Since the Magnus force creates gyroscopic motion and a finite Hall angle, skyrmions can exhibit a greater range of flow phases than what is observed in overdamped driven systems with quenched disorder. We show that in addition to identifying previously known skyrmion flow phases, PCA detects several additional phases, including different types of channel flow, moving fluids, and partially ordered states. Guided by the PCA analysis, we further characterize the disordered flow phases to elucidate the different microscopic dynamics and show that the changes in the PCA-derived order parameters can be connected to features in bulk transport measures, including the transverse and longitudinal velocity-force curves, differential conductivity, topological defect density, and changes in the skyrmion Hall angle as a function of drive. We discuss how asymmetric feature vectors can be used to improve the resolution of the PCA analysis, and how this technique can be extended to find disordered phases in other nonequilibrium systems with time-dependent dynamics.

Figures (18)

• Figure 1: Particle positions (dots), pinning sites (open circles), and trajectories (lines) for a system with $\alpha_m/\alpha_{d} = 0.0$ (the superconducting vortex limit) at different drives. The trajectories here and throughout this work are imaged over a time equal to that required for an individual particle moving through a pin-free sample to travel a distance of $50\lambda$ when subjected to the driving force $F_D$. Phase I, the pinned state, is not shown. (a) Phase II, the non-ergodic isolated static channel flow phase, at $F_D = 0.165$. (b) Phase III, the lightly braided channel flow phase, at $F_D = 0.31$. (c) Phase IV, the heavily braided channel flow phase, at $F_D = 0.48$. (d) Phase V,the inhomogeneous ergodic plastic flow phase, at $F_D = 0.61$. (e) Phase VI, the emerging ordered flow phase, at $F_D = 0.85$: (f) DR, the dynamically reordered phase, at $F_D=2.0$. Here the vortices dynamically reorder into a moving smectic state.
• Figure 2: (a) The longitudinal velocity $\langle V_x\rangle$ vs $F_D$ for systems with $\alpha_m/\alpha_d = 0.0$ (black), 0.5 (purple), 2.0 (blue), 4.0 (green), 6.0 (yellow), and 8.5 (red). (b) The corresponding transverse velocity $\langle V_y\rangle$ vs $F_D$. (c) The corresponding fraction of particles with six neighbors $\langle p_6\rangle$ vs $F_D$.
• Figure 3: (a) $d\langle V_x\rangle/dF_D$ vs $F_D$ for the samples from Fig. \ref{['fig:2']} with $\alpha_m/\alpha_d = 0.0$ (black), 0.5 (purple), 2.0 (blue), 4.0 (green), 6.0 (yellow), and 8.5 (red). (b) The corresponding $d\langle V_y\rangle/dF_D$ vs $F_D$. (c) The corresponding average skyrmion Hall angle $\langle \theta_{sk}\rangle$ vs $F_D$.
• Figure 4: Particle positions (dots), pinning sites (open circles), and trajectories for a system with $\alpha_m/\alpha_d = 0.5$. (a) Phase II, isolated channel flow, at $F_D = 0.15$. Here the Hall angle is zero. (b) Phase III, lightly braided channel flow, at $F_D = 0.31$. There is now some evidence of tilt in the trajectories due to the emergence of a finite Hall angle. (c) Phase IV, heavily braided channel flow, at $F_D = 0.48$. The Hall angle has increased, and there are still some pinned particles present. (d) Phase V, inhomogeneous ergodic plastic flow, at $F_D = 0.63$. The system is in a moving fluid state, but some particles can be temporarily pinned. (e) Phase VI, emerging ordered flow, at $F_D = 0.97$, where all particles are flowing at all times but with varying speeds. (f) The DR phase at $F_D = 2.0$, where the system forms a triangular lattice moving at a finite Hall angle.
• Figure 5: Particle positions (dots), pinning site locations (open circles), and trajectories (lines) for a system with $\alpha_m/\alpha_d = 2.0$. (a) Phase II at $F_D=0.13$. (b) Phase III at $F_D=0.36$. (c) Phase IV at $F_D=0.6$. (d) DR or moving crystal phase at $F_D=1.11$.