Dynamically resolved evolution and quantitative mapping of conformal skyrmion lattice

Magnetic skyrmions are nanoscale topologically protected spin textures that can be efficiently driven by electric currents, making them attractive information carriers for skyrmion-based memory and unconventional computing. Beyond single-particle behavior, skyrmions readily self-organize under confinement and external perturbations, producing collective states with rich geometry and dynamics. One particularly intriguing phenomenon is a conformal lattice: a structure with smoothly varying density and curvature while retaining local crystalline order, typically emerging through defect-mediated reorganization under spatial constraints. Conformal ordering has been studied in colloids and superconducting vortex matter, but its formation mechanism and real-space observation in magnetic skyrmion systems remain elusive. In this work, we track, in real time, how the skyrmion Hall effect drives lateral compression and reshapes a hexagonal skyrmion lattice into a conformal state. By integrating micromagnetic simulations with machine-vision trajectory analysis, we resolve the full reorganization process and quantify its key signatures: progressive curvature buildup, layer-dependent redistribution of Hall angles, and defect-mediated rearrangements that reshape global order while preserving local orientational coherence. To verify whether the resulting pattern is intrinsically conformal, we use inverse conformal mapping as a quantitative approach and demonstrate local angle preservation throughout the distorted lattice. We further realize conformal skyrmion ordering experimentally in Co9Zn9Mn2 using Lorentz transmission electron microscopy, providing direct support for the simulated mechanism. Our combined time-resolved tracking, inverse conformal mapping, and experimental observations make conformal skyrmion ordering a verifiable and engineerable collective state, with promise for geometry-tunable stochasticity in true random-number generation.

Recommended citation: W. Zhao, S. Lu, Q. Luo, X. Zhang, S. Fan, H. Lu, G. Han, T. Xin, Z. Luo, G. Zhao, J. Yang, Y. Hou, and L. Peng. Dynamically resolved evolution and quantitative mapping of conformal skyrmion lattice. Newton 2, 100443 (2026).
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