Graph Learning and Order Parameters Reveal a Solid-to-Conformal Phase Transition in Skyrmion Lattices

Directional current driving transforms an initially hexagonal skyrmion-lattice solid through a transient quasi-liquid state into a conformally ordered lattice rather than a disordered liquid. Using in situ Lorentz transmission electron microscopy and micromagnetic simulations, we quantify this reorganization through local lattice-orientation analysis, sixfold orientational order, and a conformal order parameter. For the simulated configurations, an unsupervised workflow constructs local lattice graphs, learns node-level structural representations with an equivariant graph neural network trained by Deep Graph Infomax, and applies a two-component Gaussian mixture model to classify solid-like and conformal lattice states. This label-free framework provides a feasible route for spatially resolved phase identification in two-dimensional quasiparticle systems.

Recommended citation: W. Zhao, S. Lu, Q. Luo, G. Zhang, H. Lu, S. Fan, G. Zhao, J. Yang, Y. Hou, and L. Peng. Graph Learning and Order Parameters Reveal a Solid-to-Conformal Phase Transition in Skyrmion Lattices. Advanced Functional Materials, e78928 (2026). https://doi.org/10.1002/adfm.78928.
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