Deep Generative Learning of Magnetic Frustration in Artificial Spin Ice from Magnetic Force Microscopy Images

Increasingly large datasets of microscopic images with atomic resolution facilitate the development of machine learning methods to identify and analyze subtle physical phenomena embedded within the images. In this work, microscopic images of honeycomb lattice spin-ice samples serve as datasets from which we automate the calculation of net magnetic moments and directional orientations of spin-ice configurations. In the first stage of our workflow, machine learning models are trained to accurately predict magnetic moments and directions within spin-ice structures. Variational Autoencoders (VAEs), an emergent unsupervised deep learning technique, are employed to generate high-quality synthetic magnetic force microscopy (MFM) images and extract latent feature representations, thereby reducing experimental and segmentation errors. The second stage of proposed methodology enables precise identification and prediction of frustrated vertices and nanomagnetic segments, effectively correlating structural and functional aspects of microscopic images. This facilitates the design of optimized spin-ice configurations with controlled frustration patterns, enabling potential on-demand synthesis.